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Math 141: Precalculus I
Common Course Number
Prior to Summer 2009, this course was known as Math 131; only the course number has changed.
Course Description
Math 141 is the first course in a two-quarter precalculus sequence that also includes Math 142. Math 141 focuses on the general nature of functions. Topics include: linear, quadratic, exponential, and logarithmic functions; and applications.
Who should take this course?
Generally, students seeking to take the 151–152–153 calculus sequence take the 141–142 precalculus sequence first. Some students in programs like business take this course (in place of Math 140) and then take Math 148 instead of Math 142. You should consult the planning sheet for your program and consult an advisor to determine if this sequence is appropriate for you.
Who is eligible to take this course?
The prerequisite for this course is Math 90 with a grade of 2.0 or higher. Students new to EdCC with an appropriately high Accuplacer score may also consider taking Math 141 used 142.
What else is required for this course?
Students are required to have a graphing calculator; the TI-83 Plus or TI-84 Plus is recommended. |
Difference and Differential Equations in Mathematical Modelling demonstrates the universality of mathematical techniques through a wide variety of applications. Learn how the same mathematical idea governs loan repayments, drug accumulation in tissues or growth of a population, or how the same argument can be used to find the trajectory of a dog pursuing a hare, the trajectory of a self-guided missile or the shape of a satellite dish. The author places equal importance on difference and differential equations, showing how they complement and intertwine in describing natural phenomena.
...
A First Course in Computational Algebraic Geometry is designed for young students with some background in algebra who wish to perform their first experiments in computational geometry. Originating from a course taught at the African Institute for Mathematical Sciences, the book gives a compact presentation of the basic theory, with particular emphasis on explicit computational examples using the freely available computer algebra system, Singular. Readers will quickly gain the confidence to begin performing their own experiments.
way and using an easy to follow format, it will help boost your understanding and develop your analytical skills. Focusing on the core areas of numeracy, it will help you learn to answer questions without using of a calculator and...
This book makes quantitative finance (almost) easy! Its new
visual approach makes quantitative finance accessible to a broad
audience, including those without strong backgrounds in math or
finance. Michael Lovelady introduces a simplified but powerful
technique for calculating profit probabilities and graphically
representing the outcomes. Lovelady's "pictures" highlight key
characteristics of structured securities such as the increased
likelihood of profits, the level of virtual dividends being
generated, and market risk exposures. After explaining his visual
approach, he applies it to one...
Based on the award winning Wiley Encyclopedia of Chemical Biology, this book provides a general overview of the unique features of the small molecules referred to as "natural products", explores how this traditionally organic chemistry-based field was transformed by insights from genetics and biochemistry, and highlights some promising future directions. The book begins by introducing natural products from different origins, moves on to presenting and discussing biosynthesis of various classes of natural products, and then looks at natural products as models and the possibilities of using...
Quantitative Techniques: Theory and Problems adopts a fresh and novel approach to the study of quantitative techniques, and provides a comprehensive coverage of the subject. Essentially designed for extensive practice and self-study, this book will serve as a tutor at home. Chapters contain theory in brief, numerous solved examples and exercises with exhibits and tables.
...
The book is meant for an introductory course on Heat and Thermodynamics. Emphasis has been given to the fundamentals of thermodynamics. The book uses variety of diagrams, charts and learning aids to enable easy understanding of the subject. Solved numerical problems interspersed within the chapters will help the students to understand the physical significance of the mathematical derivations.
...
Applied Mathematical Methods covers the material vital for research in today's world and can be covered in a regular semester course. It is the consolidation of the efforts of teaching the compulsory first semester post-graduate applied mathematics course at the Department of Mechanical Engineering at IIT Kanpur for two successive years.
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Economics, far from being the "dismal science," offers us valuable lessons that can be applied to our everyday experiences. At its heart, economics is the science of choice and a study of economic principles that allows us to achieve a more informed understanding of how we make our choices, whether these choices occur in our everyday life, in our work environment, or at the national or international level. This book represents a common sense approach to basic macroeconomics, and begins by explaining key economic principles and defining important terms used in macroeconomic discussion. It uses...The UK Clinical Aptitude Test (UKCAT) is used by the majority of UK medical and dentistry schools to identify the brightest candidates most suitable for training at their institutions.
With over 600 questions, the best-selling How to Master the UKCAT, 4th edition contains more practice than any other book. Questions are designed to build up speed and accuracy across the four sections of the test, and answers include detailed explanations to ensure that you maximize your learning.
Now including a brand new mock test to help you get in some serious score improving practice, How to Master the...
As advancements in technology continue to influence all facets of society, its aspects have been utilized in order to find solutions to emerging ecological issues. Creating a Sustainable Ecology Using Technology-Driven Solutions highlights matters that relate to technology driven solutions towards the combination of social ecology and sustainable development. This publication addresses the issues of development in advancing and transitioning economies through creating new ideas and solutions; making it useful for researchers, practitioners, and policy makers in the socioeconomic sectors....Mathematical problems such as graph theory problems are of increasing importance for the analysis of modelling data in biomedical research such as in systems biology, neuronal network modelling etc. This book follows a new approach of including graph theory from a mathematical perspective with specific applications of graph theory in biomedical and computational sciences. The book is written by renowned experts in the field and offers valuable background information for a wide audience.
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Praise for the Third Edition
"This book provides in-depth coverage of modelling techniques used throughout many branches of actuarial science. . . . The exceptional high standard of this book has made it a pleasure to read." —Annals of Actuarial Science
Newly organized to focus exclusively on material tested in the Society of Actuaries' Exam C and the Casualty Actuarial Society's Exam 4, Loss Models: From Data to Decisions, Fourth Edition continues to supply actuaries with a practical approach to the key concepts and techniques needed on the job. With updated material and extensive... |
Math Class Offerings
Monday, 03 January 2011 10:58 | Posted by Admin IT | |
Mathematics courses at Springfield High School address the Vermont Grade Level Expectations and the Vital Results, along with preparing students for the New England Common Assessment Program, college entrance, and S.A.T. Exams. The Mathematics Department offers a wide range of upper level courses, such as; Statistics, Algebra III, Pre-Calculus, and College Board Certified A.P. Statistics and A.P. Calculus.
375 Math Lab
This course provides support for beginning high school students. Participants will be required to stay organized. In addition to supplementary help in High School Mathematics, participants will work on areas of deficit, identified by their NECAP scores and their primary math teacher. Participants will develop skill sets and gain confidence as they experience sustained success with math.
344 Algebra I (CP)
1 credit
Open to: grades 9-12
Prerequisite: none
This course provides the student with a strong foundation for High School mathematics. Problem solving and mastery are emphasized through whole class, small group, and individual explorations. In addition to algebra and functions, statistics and probability, Geometry and discrete mathematics concepts are developed. A scientific calculator is suggested.
354 Geometry (CP)
1 credit
Open to: grades 9-12
Prerequisite : credit of Algebra I
Scheduled: all year
Plane355 Geometry CATS (CP)
1 credit
Open to: grades 9-12
Prerequisite : credit of Algebra I
Scheduled: all year
In coordination with the Arts academy, plane362A Algebra II A (CP)
A brief review of Algebra I naturally extend to the following topics: equations in three variables, quadratic equations and functions, irrational numbers and polynomials. Students are expected to have a scientific calculator.
362B Algebra II B (CP)
1/2 credit
Open to: grades 10 - 12
Prerequisite: credit in 362A
Topics studied this term will include: complex numbers, triangle trigonometry, an introduction to circular functions and quadratic relations. Students are expected to have a scientific calculator.
333 Applied Algebra II
This course employs an interactive, applied approach to teaching advanced topics in high school mathematics. Students build upon their algebra and geometry foundations as they learn abstract concepts through concrete experience. This course is ideal for the technical center student who has completed Algebra I and Geometry or two years of an integrated high school level math program. Students are expected to have a scientific calculator.
361A Advanced Algebra II A (AC)
This challenging option is specifically designed for the Advanced Placement intending student. A review of the real number system leads to the study of first and second degree equations in both one and two variables. Exponential and logarithmic functions will be introduced. Students are expected to have a scientific calculator.
361B Advanced Algebra II B (AC)
1/2 credit
0pen to: grades 10-12
Prerequisite: credit in 361A
The study of relations and functions will continue with the exploration of the properties of conic sections, polynomial and rational functions, and an introduction to the trigonometric functions. Students are expected to have a scientific calculator.
calculator.
325 Integrated Math II (CP)
1 credit
Open to: grades 10-12
Prerequisite: credit of Integrated I
Scheduled: all Year
This second course in the Integrated series continues the study of Algebra and Geometry, probability, statistics, and discrete math. The underpinnings of trigonometry are established. Students who successfully complete both Integrated Math I & II will have the foundation of Algebra I and Geometry needed for Algebra II or Integrated Math III. A TI-83, or TI-84 calculator is suggested.
326 Integrated Math III (CP)
Students will continue collaborating to explore and solve problems with algebra and geometry. They will use multiple-variable, symbolic, and discrete models along with patterns and families of functions as preparation for college math. A TI-82, TI-83, or TI-83+ calculator are suggested.
334 Finance I
1/2 credit
Open to: grade 12
Prerequisite: none
Students will develop a long-range view of budgeting, exploring investment options and debt management strategies with an eye toward financial independence. Areas of study include stocks, mutual funds, credit, insurance and retirement. A scientific calculator is required.
335 Finance II
1/2 credit
Open to: grade 12
Prerequisite: none
Students will develop a long range view of budgeting, exploring investment options and debt management strategies with an eye toward financial independence. Areas of study include stocks, mutual funds, credit, insurance and retirement. A scientific calculator is required.
371A Algebra III A (CP)
This course will focus on refining skills with functions, including linear, quadratic, polynomials, rational, exponential, logarithmic, and the trigonometric functions. Students are expected to have a scientific calculator.
371B Algebra III B (CP)
1/2 credit
Open to: grades 11 and 12
Prerequisite: credit in 371A
This course will include an introduction to counting theory, probability and statistics as well as matrix algebra and mathematical vector and analysis. Students are expected to have a scientific calculator.
379A Statistics A (CP)
This course is a non-AP level introduction to statistics. The course covers statistical methods and reasoning as they apply to such fields as medicine, environmental science, sports, politics and entertainment. Students will produce and organize data and will then analyze their findings using measures of central tendency and statistical tests.
379B Statistics B (CP)
1/2 credit
Open to: grade 11-12
Prerequisite: credit in 379A
This course is a continuation of 379A. The focus is on developing and evaluating inferences and predictions that are based on data. Students will understand and apply basic concepts of chance and probability
381A Pre-Calculus RF (CP)
This is a college preparatory course designed for the student with above average interest and ability in mathematics. Topics include polynomial functions, rational functions, and exponential functions. Students are encouraged to have a TI-83+ or TI-84 graphing calculator.
381B Pre-Calculus TD (CP)
1/2 credit
Open to: grades 11 and 12
Prerequisite: credit in 381A
This college preparatory course includes a thorough study of elementary trigonometry. Other topics introduced include combinations, probability as well as sequences and series. Students are encouraged to have a TI-83+ or TI-84 graphing calculator.
380 Statistics AP
This is a college level introduction to probability and statistical analysis. The material covered in this course will be sufficient to prepare students to take the Statistics Advanced Placement Examination. A TI-83+ or TI-84 graphing calculator is required for this course.
390 Calculus AP
This is a college level introduction to differential and integral calculus. The material covered in this course will be sufficient to prepare students to take the AB Calculus Advanced Placement Examination. A TI-83+ or TI-84 graphing calculator is required for this course. |
By Wenersamy Ramos de Alcântara ([email protected]) - Published on Amazon.com
Format:Hardcover
If you want to learn analysis with this book, forget it, but if you have a good text book, this is one of the best tools you'll need to master problem solving in calculus. Well explained and well organized problem solving tips and technics, step by step from the very beginning until more advanced topics, together with a large numbers of exercises, everyone with the proper result in the end of the book, make it a must have in the library of anyone who seriously needs calculus problem solving skills.
4 of 4 people found the following review helpful
5.0 out of 5 starsGreat problem book on mathematical analysis12 Sep 2002
By Alen Lovrencic - Published on Amazon.com
Format:Hardcover
When I was on my graduate study of mathematics this book was very important when I was learning for the exams in mathematical analysis. The book contains thousands of problems in all fealds of elementary mathematical analysis, and I solve all of them.
The only drawback of the book is that the problems in it are rather simple and easy to solve. So, I had to use some other problem books with harder problems. But, if you are not on the study of math, but engeneering study, this will be surely very usefull book to you.
4 of 4 people found the following review helpful
5.0 out of 5 starsThey used to call him "Demoniovich" when I was in college...26 Aug 2002
By Manny Hernandez - Published on Amazon.com
Format:Hardcover
This book used to be referred to as the one by "Demoniovich" and not casually, when I was in college taking Calculus, some 15 years ago. It's plain and simply a classic to master Calculus. Not an introductory book by any means, but definitely a book to go into once you've had your first take on other more basic books. If you can work out the problems in this book, any Calculus test you encounter will feel like a breeze: I am serious about this. |
Innovative Textbooks
Publishers of the Modules in Mathematics
A New Idea in Mathematics Education. You Design the Textbook!
A series of independent modules designed for the general college level
student.
Prerequisites are kept to a minimum. The modules provide an opportunity to
introduce your liberal arts students to some modern (and traditional) topics in
mathematics, and you will have more fun too!
Choose four to six modules as a complete course, or choose one or two
modules to supplement another text.
Modules are moderately priced and your students save money because they buy
exactly what they need.
For more information, please call Innovative Textbooks at
949-854-5667 (9AM-5PM Pacific Time).
Return to the Home Page
There are currently 13 Modules in Mathematics, all authored by
Steven Roman. The titles are listed below, followed by a brief description of
each, with tables of contents. Click on a title to see the description, or
simply use the navigation keys to browse the entire list.
Third Edition, 93 pages, ISBN 1-878015-20-6
An elementary discussion of how mathematics may be used in the social
sciences. Requires only basic arithmetic skills. Chapter 1 contains a discussion
of how to form a group ranking of products, based on a set of individual
rankings. The chapter concludes with a brief discussion of the famous Arrow
Impossibility Theorem. Chapter 2 is devoted to measuring an individual's power,
or influence, in a group setting. For instance, how much more power does a
permanent member of the U.N. security council have than a temporary member?
Chapter 3 contains a discussion of various methods for apportioning seats in the
U.S. House of Representatives—a very important contemporary political
problem. The final section gives a fascinating historical perspective on this
200 year old problem.
Third Edition, 68 pages, ISBN 1-878015-21-4
A survey of the contemporary topic of codes and coding. Prerequisites are
minimal, since all of the necessary mathematics is developed in the module.
Chapter 1 contains a discussion of the ubiquitous check digit codes that are
used for error detection, and can be found in a wide variety of common
circumstances, such as Universal Product Codes (Bar Codes), credit card numbers,
bank check numbers, driver's licence numbers and ISBN's. We compare various
commonly used methods and show which ones work best for detecting errors.
Chapter 2 contains a discussion of the most famous code of all — the
Hamming code for error correction. The final chapter discusses the Huffman
coding scheme, which is used to encode data for space saving purposes (rather
than for error detection or correction).
Third Edition, 54 pages, ISBN 1-878015-19-2
This module requires no special mathematical background. Its aim is to
acquaint the student with the basics of symbolic logic, such as how to correctly
use DeMorgan's Laws, what the difference is between a conditional statement and
its converse and how to recognize when an argument is logically valid. The
module concludes with a brief discussion of how logic can be used to design
circuits.
Second Edition, 66 pages, ISBN 1-878015-23-0
Prerequisites are intermediate algebra. The goals of this module are to
introduce the basic terminology related to interest, loans, leases and bonds;
to show how various quantities, such as the monthly payments on a loan, can be
computed using mathematical formulas; and to show how business calculators are
designed to make these computations easier. Examples are done using a
scientific calculator, the TI BA II Plus and the HP 10B. This module would make
a nice supplement to a course in business calculus.
Third Edition, 42 pages, ISBN 1-878015-16-8
An introduction to the fascinating field of secret messages, requiring no
formal mathematical prerequisites for the first chapter, and an acquaintance
with exponents for the second chapter. Chapter 1 describes some traditional, pre
World War 2 methods for encoding messages. In Chapter 2, the author discusses
one of the most used contemporary methods for encoding — the RSA method. At
present, this method is believed to be secure, but may prove otherwise if
efficient methods for factoring large numbers are ever discovered!
Fourth Edition, 49 pages, ISBN 1-878015-22-2
This module shows how exponents and logarithms play a role in the processes
of growth and decay. Prerequisites are intermediate algebra. After a short
review of logarithms, there follows a discussion of compound interest. The next
section is devoted to the time value of money, including how to compute the
payments on an auto loan or home mortgage. Then comes a discussion of famous
logarithmic scales, such as the Richter scale. The final section concerns the
exponential growth of organisms and the decay of radioactive substances.
Second Edition, 52 pages, ISBN 1-878015-26-5
Each chapter of this module is independent of the others, and contains a
different topic in mathematics. The only prerequisite is intermediate algebra.
This module would make a nice supplement to a precalculus course.
126 pages, ISBN 1-878015-10-9
The first two chapters of a standard college algebra book, this module is
designed for self-study and as a supplement to a calculus course for those
students who need a little review or reference in algebra. |
The "Ready... Set... Calculus" book has been designed to help guide incoming Science and Engineering majors in assessing and practicing their "initial" mathematical skills. The problems involve arithmetic, algebra, inequalities, trigonometry, logarithms, exponentials and graph recognition and do not require the use of a calculator. The book has problems, examples and links to web pages with further help and can be used online. |
Contents of the Mathematics Placement Test
Since 1978, UW system faculty and Wisconsin high school teachers have been collaborating to develop a test for placing incoming students into college Mathematics courses. The current test includes four components: elementary algebra, intermediate algebra, college algebra, and trigonometry. These components are available for each UW System campus to use according to its individual needs and resources. Each campus determines the appropriate scores for entry into specific courses. The purpose of this brochure is to introduce you to the test, describe the rationale behind its creation, and outline future plans for its continued development.
Background and Purpose of the Test
In 1978, following the publication of the UW System Basic Skills Task Force Report, members of Mathematics Department Faculties from UW System institutions met in Madison to discuss common entry-level curriculum problems. One problem most departments shared was how to effectively place incoming freshmen into an appropriate mathematics course. Placement procedures and tests varied from campus to campus and it seemed that some consistency was desirable. The decision was made to develop a System-wide test for placement into an introductory mathematics curriculum.
The committee that would begin this task would consist of representatives from any UW System Mathematics Department that chose to participate. The departments would select their representatives and participation would be strictly voluntary.
The first step in the project was to carefully analyze each of the individual curricula in the System and write a detailed set of prerequisite objectives for all courses prior to calculus. After this list was approved by all campuses, the committee began developing test items on the skills identified in their test objectives. Through a series of pilot administrations at area high schools and UW campuses, the committee obtained valuable information about how the individual items performed, and gained important insights into item writing strategies and techniques. Many items were refined or corrected, as necessary, and repiloted in an effort to improve their ability to distinguish between students with different levels of mathematical preparedness. After a sufficient number of high quality items had been developed, they were assembled into a complete test. The first operational form of the Mathematics Placement Test was administered in 1984.
Placement into college courses is the sole purpose of this test. The experienced teacher will quickly realize that many skills which are taught in the high school mathematics courses are not included in the test. This was by design, as the test is a tool to assist advisors in placing students into the best course in the university-level mathematics sequence. The questions on the test were specifically selected with this single purpose in mind. This means the test is not a measure of everything that is learned in high school Mathematics courses. The test was not designed to measure program success or to compare students from one high school with students from another. It should be viewed only as a tool to be used for placing students at the university level.
As a placement instrument, the test has to be easy enough to identify those students needing remedial help, yet it also has to be complex enough to identify those students who are ready for calculus. Scores have to be precise enough to allow placement into many different levels of university coursework. In addition, the test has to be efficient to score, since thousands of students each year need to have their results promptly reported. In order to meet these criteria, the test development committee selected a multiple-choice format. The items measure four different areas of mathematical competence: elementary algebra, intermediate algebra, college algebra, and trigonometry. Each skill area has a different set of detailed objectives, carefully developed to best match university mathematics curricula across the University of Wisconsin System.
Every year, a new form of the Mathematics Placement Test is published, along with some new pilot items for each component of the test, and administered to all incoming Freshmen in the UW System. All items are subjected to a statistical review to identify which items effectively distinguish the students with the strongest mathematics skills or the weakest mathematics skills from the general population of students. Only the items which are most useful for differentiating among students are ever considered for use on a future form of the test.
Although faculty cannot be considered disinterested observers, those who are familiar with the placement test feel that its quality is extremely high. The feeling among faculty at the participating UW institutions is that the test has helped enormously in placing students into appropriate courses. One of the strengths of the Mathematics Placement Test is that it is developed by faculty from throughout the University of Wisconsin System. Therefore, this test represents a UW System perspective with respect to the underlying skills that are necessary for success in our courses. One of the challenges, in this regard, is that the UW System campuses do not have a single Mathematics curriculum. Instead, each campus has its own curriculum and its own courses, which may or may not correspond well with courses on other UW campuses. To ensure that the placement test works well on each UW campus, each UW institution determines its own cutscores so as to optimize placement into its own Mathematics course sequence. Consequently, cutscores will vary from campus to campus as a result of curricular differences and student population differences. Also, on many campuses, the placement test is but one of several variables used for placing students, often also including ACT/SAT score, units of high school mathematics, and grades in high school mathematics courses.
The ability of this test to appropriately place students into courses rests in the quality of the match between test content and the institutional curricula at each UW campus. To ensure that the test mirrors the curriculum in introductory mathematics courses throughout UW System, the Mathematics Placement Test Development Committee has expanded to include one representative from most of the 14 UW institutions, as well as one Wisconsin high school mathematics teacher. This committee generally convenes twice each year to write and revise test items and discuss issues pertaining to test content and university curricula.
Recent Developments
Over the past few years, the Mathematics Placement Test has changed in several very important ways. Prior to the fall of 2000, the different campuses were combining items in different ways to form placement scores and make placement decisions. The particular set of items used by any one campus was selected to best match that campus' introductory curriculum. However, because campuses combined the test items in different ways, students who transferred from one UW institution to another often found themselves without valid placement scores and needing to retake the test. In 2000, the Mathematics Placement Test Development Committee agreed upon a common method for combining test objectives to create a uniform set of scores for reporting performance on the placement test. The three agreed-upon scores, one corresponding to each new objective, are labeled mathematics basics, algebra, and trigonometry. These three scores are now used by all System institutions.
Historically, the Mathematics Placement Test has always been organized in three different sections, labeled A, B, and C. Students were instructed to take either sections A and B (which contained elementary and intermediate algebra) or sections B and C (which contained intermediate and college algebra and trigonometry), depending upon their mathematics background and desired college placement. However, our experience was that many students found it difficult to accurately assess their level of preparedness and would often take the wrong two sections. On most campuses, students who scored too high on the AB test or too low on the BC test could not be placed accurately and were required to retest with the appropriate two sections of the test. This was very inconvenient, both for the students and for the university's testing office. Beginning in the fall of 2002, the three different sections were shortened and combined, and all students were asked to complete the entire test. This has helped eliminate the confusion over which two sections to take and has reduced the number of students needing to retest.
General Characteristics of the Test
1. All items are to be completed by all students. The items are roughly ordered from elementary to advanced. The expectation is that less prepared students will answer fewer questions correctly than more prepared students.
2. The test consists entirely of multiple choice questions, each with five choices.
4. The Mathematics Placement Test is designed as a test of skill and not speed. Ample time is allowed for most students to answer all questions. Ninety (90) minutes are allowed to complete the test.
5. The mathematics basics component has a reliability of .85. The algebra component has a reliability of .90. The trigonometry component has a reliability of .85. For all three sections, items are selected of appropriate difficulty to provide useful information within the range of scores used for placement throughout the System campuses.
Test Description
The Mathematics Test Development Committee decided on three broad categories of items: mathematics basics, algebra, and trigonometry. The entire Mathematics Placement Test is designed to be completed in 90 minutes, sufficient time for most students to complete the test.
Items for each of the three components are selected to conform to a carefully created set of detailed objectives. The percentage of items selected from each component are shown in Table 1 below.
Sample Items from the Trigonometry Component
Sample Trigonometry Items
Sample Geometry Items
Additional Statements About High School Preparation for College Mathematics Study
CALCULUS
The number of high schools offering some version of calculus has increased markedly since the UW System Math Test Committee's first statement of objectives and philosophy, and experience with these courses has shown the validity of the Committee's original position. This position was that a high school calculus program may work either to the advantage or to the disadvantage of students depending on the nature of the students and the program. Today, it seems necessary to mention the negative possibilities first.
A high school calculus program not designed to generate college calculus credit is likely to mathematically disadvantage students who go on to college. This is true for all such students whose college program entails use of mathematics skills, and particularly true of students whose college program involves calculus. High school programs of this type tend to be associated with curtailed or superficial preparation at the precalculus level and their students tend to have algebra deficiencies which hamper them not only in mathematics courses but in other courses in which mathematics is used.
The positive side is that a well-conceived high school calculus course which generates college calculus credit for its successful students will provide a mathematical advantage to students who go on to college. A study by the Mathematical Association of America identified the following features of successful high school calculus programs:
1. they are open only to interested students who have completed the standard four year college preparatory sequence. A choice of mathematics options is available to students who have completed this sequence at the start of their senior year.
2. they are full year courses taught at the college level in terms of text, syllabus, depth and rigor.
3. their instructors have had good mathematical preparation (e.g. at least one semester of junior/senior level real analysis) and are provided with additional preparation time.
4. instructors expect that their successful graduates will not repeat the course in college, but will get college credit for it.
A variety of special arrangements exist whereby successful graduates of a high school calculus course may obtain credit at one or another college. A generally accepted method is for the students to take the Advanced Placement Examinations of the College Board. Success rates of students on this exam can be a good tool for evaluation of the success of a high school calculus course.
GEOMETRY
The range of objectives in this document represents a small portion of the objectives of the traditional high school geometry course. The algebra objectives represent a substantial portion of the objectives of traditional high school algebra courses. The imbalance of test objectives can be explained in part by the nature of the entry level mathematics courses available at most colleges. The first college mathematics course generally will be either calculus or some level of algebra. A choice is usually based on three factors: (1) high school background; (2) placement test results; (3) curricular objectives. One reason for the emphasis on algebra in this document and on the test is that virtually all college placement decisions involve placement into a course which is more algebraic than geometric in character.
Still, there are reasons for maintaining a geometry course as an essential component in a college preparatory program. Since there are no entry level courses in geometry at the college level, it is essential that students master geometry objectives while in high school. High school geometry contributes to a level of mathematical maturity which is important for success in college.
LOGIC
Students should have the ability to use logic within a mathematical context, rather than the ability to do symbolic logic. The elements of logic which are particularly important include:
1. Use of the connectives "and' and "or" plus the "negation" of resultant statements, and recognition of the attendant relationship with the set operations "intersection," "union," and "complementation."
2. Interpretation of conditional statements of the form "if P then Q," including the recognition of converse and contrapositive.
3. Recognition that a general statement cannot be established by checking specific instances (unless the domain is finite), but that a general statement can be disproved by finding a single counter example. This should not discourage students from trying specific instances of a general statement to conjecture about its truth value.
Moreover, logical thinking or logical reasoning as a method should permeate the entire curriculum. In this sense, logic cannot be restricted to a single topic or emphasized only in proof-based courses. Logical reasoning should be explicitly taught and practiced in the context of all topics. From this, students should learn that forgotten formulas can be recovered by reasoning from basic principles, and that unfamiliar or complex problems can be solved in a similar way.
Although only two of the objectives explicitly refer to logic, the importance of logical thinking as a curriculum goal is not diminished. This goal, as well as other broad-based goals, is to be pursued despite the fact that it is not readily measured on placement tests.
PROBLEM SOLVING
Problem solving involves the definition and analysis of a problem together with the selecting and combining of mathematical ideas leading to a solution. Ideally, a complete set of problem solving skills would appear in the list of objectives. The fact that only a few problem solving objectives appear in the list does not diminish the importance of problem solving in the high school curriculum. The limitations of the multiple choice format preclude the testing of higher level problem solving skills.
MATHEMATICS ACROSS THE CURRICULUM
Mathematics is a basic skill of equal importance with reading, writing, and speaking. If basic skills are to be considered important and mastered by students, they must be encouraged and reinforced throughout the curriculum. Support for mathematics in other subject areas should include:
– a positive attitude toward mathematics
– attention to correct reasoning and the principles of logic
– use of quantitative skills
– application of mathematics curriculum.
COMPUTERS IN THE CURRICULUM
The impact of the computer on daily life is apparent, and consequently many high schools have instituted courses dealing with computer skills. While the learning of computer skills is important, computer courses should not be construed as replacements for mathematics courses.
CALCULATORS
There are occasions in college math courses when calculators are useful or even necessary (for example, to find values of trig functions), so students should be able to use calculators at a level consistent with the level at which they are studying mathematics (four-function calculators initially, scientific calculators in pre-calculus). A more compelling reason for being able to use calculators is that they will be needed in other courses involving applications of mathematics. The ability to use a calculator is very definitely a part of college preparation.
On the other hand, students need to be able to rapidly supply from their heads – whether by calculation or from memory – basic arithmetic, in order to be able to follow mathematical explanations. They should also know the conventional priority of arithmetic operations and be able to deal with grouping symbols in their heads. For example, students should know that (-3)2 s is 9, that -32 is -9, and that (-3)3 is -27 without needing to push buttons on their calculators. Moreover, students should be able to do enough mental estimation to check whether the results obtained via calculator are approximately correct.
Beginning in the spring of 1991, the use of scientific calculators has been allowed on the UW Mathematics Placement Test. The test was redesigned to accommodate the use of scientific calculators, so as to minimize the effects on placement due to the use or nonuse of calculators. Exact numbers such as π, continue to appear in both questions and answers where appropriate.
Use of scientific, non-graphing calculators is optional. Each student is advised to use or not use a calculator in a manner consistent with his or her prior classroom experience. Calculators will not be supplied at the test sites.
Mathematics curricula and faculty throughout UW are divided on whether or not to permit graphing calculators in classrooms. There remain many college-level courses for which graphing calculators are not allowed. Therefore, the placement test has not been revised to accommodate the use of graphing calculators. Students may not use graphing calculators for the Mathematics Placement Test.
PROBABILITY AND STATISTICS
Although university curricula are somewhat in a state of flux, with many basic issues and philosophies being examined, the normal entry level courses in mathematics remain the traditional algebra and calculus courses. Therefore, the placement tests must reflect those skills which are necessary for success in these courses. This is not intended to imply that courses stressing topics other than algebra and geometry are not vital to the high school mathematics curriculum, but rather that those topics do not assist in placing students in the traditional university entry level courses.
Probability and statistics are topics of value in the mathematical training of young people today that are not reflected on the placement test. It is the Committee's feeling that these topics are important to the elementary and secondary curriculum. They are gaining significance on university campuses, both within mathematics departments and within those departments not normally thought of as being quantitative in nature. The social sciences are seeking mathematical models to apply, and in general these models tend to be probabilistic or statistical. As a result, the curriculum in these areas is becoming heavily permeated with probability and statistics.
Mathematics departments are finding many of their graduates going into jobs utilizing computer science or statistics. Consequently, their curricula are beginning to reflect these trends. The Committee urges the educational community to develop and maintain meaningful instruction in probability and statistics.
How Teachers Can Help Students Prepare for the Test
The best way to prepare students for the placement tests is to offer a solid mathematics curriculum and to encourage students to take four years of college preparatory mathematics. We do not advise any special test preparation, as we have found that students who are prepared specifically for this test, either by practice sessions or the use of supplementary materials, score artificially high. Often such students are placed into a higher level course than their background dictates, resulting in these students either failing or being forced to drop the course. Due to enrollment difficulties on many campuses, students are unable to transfer into a more appropriate course after the semester has begun.
Significant factors in the placement level of a student are the high school courses taken as well as whether or not mathematics was taken in the senior year. Data indicate that four years of college preparatory mathematics in high school not only raises the entry level mathematics course, but predicts success in other areas as well, including the ability to graduate from college in four years.
Teachers should certainly feel free to encourage students to be well-rested and try to remain as relaxed as possible during the test. We intend that the experience be an enjoyable, yet challenging one. Remember that the test is designed to measure students at many different levels of mathematical preparedness; all students are not expected to answer all items correctly. There is no penalty for guessing, and intelligent guessing will most likely help students achieve a higher score.
Use of the Tests
When the UW System Mathematics Placement Tests were developed, they were written to be used strictly as a tool to aid in the most appropriate placement of students. They were not designed to compare students, to evaluate high schools or to dictate curriculum. The way an institution chooses to use the test to place students is a decision made by each institution. The Center for Placement Testing can and does help institutions with these decisions.
Each campus will continue to analyze and modify its curriculum and hence will continue to modify the way in which it uses the placement tests to place students. Cutoff scores might need to be changed over time to reflect the prerequisites for a campus' curriculum. It is also important for follow-up studies to be made to determine the effectiveness of the placement procedures. Contact must be maintained with the high schools so that modifications in the curriculum in both the high schools and in the UW System can be discussed. |
[
Calculus Essentials For Dummies
Publisher: For Dummies ,Wiley Publishing, Inc.
Mark Ryan
English
2010
196 Pages
ISBN: 0470618353
PDF
22.1 MB
Just the key concepts you need to score high in calculus
From limits and differentiation to related rates and integration, this practical, friendly guide provides clear explanations of the core concepts you need to take your calculus skills to the next level. It's perfect for cramming, homework help, or review.
Test the limits (and continuity) — get the low-down on limits and continuity as they relate to critical concepts in calculus
Ride the slippery slope — understand how differ-entiation works, from finding the slope of a curve to making the rate-slope connection
Integrate yourself — discover how integration and area approximation are used to solve a bevy of calculus problems
[/color][/quote][/b] |
Humble CalculusBioStatistics is extremely similar to other statistics courses. The calculations are the same. The statistical and probability interpretations are the sameWe are now able to solve a variety analytical geometry problems which we could not solve with trigonometry and algebra alone. Prealgebra covers factoring and how to solve for the unknown variable for basic equations. It also makes sure that the student has a thorough understanding of fractions. |
M145 Math Grade 9 - Algebra I
$40.00
Algebra I is built logically,
moving smoothly from one concept to another. Letters are used to
represent numbers in expressions and equations. Expressions are
simplified and equations are solved. As they work with the axioms,
rules and principles of algebra, students are encouraged to use their
reasoning ability. Revised 2007. |
Precalculus, College Prep (5 periods, 5 credits) - Elective
Prerequisite: Algebra II
This course is designed for students who study college level mathematics and for students who simply want further enrichment of their mathematical backgrounds. The course will cover analytic geometry. trigonometric sequences, series, probability, and functions (trigonometric, exponential, logarithmic and polynomial). Throughout the course, emphasis will be given to sketching graphs and finding the zeros of the venous functions. The course will also include appropriate use of calculators to solve problems. |
It's great and easy to understand. It's broken into many different lessons that are really easy to comprehend.
Reviewed by a reader
The book is broken down very nicely into sections. The topics are introduced clearly and briefly in understandable terms. Following the introductions are some examples that apply the concepts and/or equations. Each example has the step by
Structure & Method: Algebra & Trigonometry, Book 2
Reviewed by a reader
The author does a very nice job dividing the contents of the book into small sections. Each section builds on the previous section and allows the user to gain a better understanding little by little. Every section opens with examples that
Basic Algebra
Reviewed by "taylorls", (Michigan)
?" I totally agree. Why can't we?
Reviewed by a reader
I was having a lot of problems with algebra while going for my GED and bought every book on the subject, my teacher had me try this one and I love it and bought myself a copy. It is extremely easy to follow and takes you step by step. The
Intermediate Algebra
Reviewed by a reader
If you haven't been able to ever understand Algebra you will if you read Siever's book. His explanations are clear and his sample problems are representative of problems you will have to work out in tests and other books. I use his book a
Cdn Algebra and Geometry
Reviewed by a reader
There are too many wrong answers in the back of the book. An updated list of answers would be really helpful to the students who are still using this text book. The lessons and examples are also confusing, as they jump from step to step w
Algebra 1
Reviewed by Deedy Davis, (Merced, CA United States)
m by moving slowly through the text. My students do well in College Algebra with little or no problem. I would love to see a Geometry text written as well.
Reviewed by "tigerlily302", (Kalamazoo, MI, USA)
Well, this book conside
Algebra 2 and Trigonometry
Reviewed by a reader
's!
Reviewed by "michaellross", (Forest Grove, Or United States)
spects of the exercises were done for C rather than Basic or Pascal, but that's easily fixed by anyone that knows C.
Reviewed by Jon Steelman, (Alpharetta, GA United States)
do agree that this is not spoon feeding material, but for teachers who really want to convey the subject matter and for children who have the prerequisite math skills and any interest in math, I think this book is right on target.
Reviewed by Jerome Dancis, (Greenbelt MD, USA)
Generator of math phobiasThis book deserves MINUS 5 stars.I assume that this is the same book Algebra 2 and Trig by Dolciani, Graham, Swanson and Sharron inflicted on my child a decage or so ago. If not it is a later edition, the changes |
Calculus is widely recognized as a difficult course that requires extra study and practice. The Calculus Workbook for Dummies will continue the light-hearted, practical approach taken in the original book, while providing practice opportunities and detailed solutions to hundreds of problems that will help students master the maths that is critical for future success in engineering, scince, and other complex disciplines.
Authentic Books are proud to stock the fantastic The Calculus Affair Adventures Of Tintin. With so many available today, it is wise to have a brand you can trust. The The Calculus Affair Adventures Of Tintin is certainly that and will be a great acquisition. For this reduced price, the The Calculus Affair Adventures Of Tintin comes widely respected and is always a regular choice amongst most people. Egmont Books Ltd have provided some great touches and this results in great value for money.
Tintin was created in 1929 by the Belgian cartoonist Hergé, then aged just 21, for a weekly children's newspaper supplement. Tintin is a young reporter, aided in his adventures by his faithful fox terrier dog Snowy (Milou in French). In Tintin, Hergé created a hero who embodied human qualities and virtues, without any faults.
Product Description Master pre-calculus from the comfort of homeWritten by bestselling author and creator of the immensely popular Demystified series, Pre-Calculus Know-it-ALL offers anyone struggling with this essential mathematics topic an intensive tutorial. The book provides all the instruction you need to master the subject, providing the perfect resource to bridge the massive and key topics of algebra and calculus.If you tackle this book seriously, you will finish with improved ability to...
Product Description This practical treatment explains the applications complex calculus without requiring the rigor of a real analysis background. The author explores algebraic and geometric aspects of complex numbers, differentiation, contour integration, finite and infinite real integrals, summation of series, and the fundamental theorem of algebra. The Residue Theorem for evaluating complex integrals is presented in a straightforward way, laying the groundwork for further study. A working knowledge...
Written by a professional physicist, Calculus in Focus teaches you everything you need to know about first semester calculus. Topics covered include computation of limits and derivatives, continuity, one-sided limits, finding maxima and minima, related rates problems, implicit differentiation, integration and more. Each chapter is packed with sample problems that guide the reader through the procedures used to solve calculus problems. End of chapter exercises, based on the solved problems in the...
First published by Silvanus P. Thompson in 1910, this text aims to make the topic of calculus accessible to students of mathematics. In the first major revision of the text since 1946, Martin Gardner has thoroughly updated the text to reflect developments in method and terminology, written an extensive preface and three new chapters, and added more than 20 recreational problems for practice and enjoyment.
The aim of this book is to give a through and systematic account of calculus of variations which deals with the problems of finding extrema or stationary values of functionals. It begins with the fundamentals and develops the subject to the level of research frontiers.
This ADVANTAGE SERIES Edition of Swokowski's text is a truly valuable selection. Groundbreaking in every way when first published, this Book is a simple, straightforward, direct calculus text. Its popularity is directly due to its broad use of applications, the easy-to-understand Writing style, and the Wealth of examples and exercises, which reinforce conceptualization of the subject matter. The author wrote this text with three objectives in mind. The first was to make the book more student-oriented...
Based on a series of lectures given by the author this text is designed for undergraduate students with an understanding of vector calculus, solution techniques of ordinary and partial differential equations and elementary knowledge of integral transforms. It will also be an invaluable reference to scientists and engineers who need to know the basic mathematical development of the theory of complex variables in order to solve field problems. The theorems given are well illustrated with examples.
Tintin was created in 1929 by the Belgian cartoonist Herge, then aged just 21, for a weekly children's newspaper supplement. Tintin is a young reporter, aided in his adventures by his faithful fox ter...
This book will prove to be a good introduction, both for the physicist who wishes to make applications and for the mathematician who prefers to have a short survey before taking up one of the more voluminous textbooks on differential geometry.'--MathSciNet (Mathematical Reviews on the Web), American Mathematical Society A compact exposition of the fundamental results in the theory of tensors, this text also illustrates the power of the tensor technique by its applications to differential geometry...
How does cooperation emerge among selfish individuals? When do people share resources, punish those they consider unfair, and engage in joint enterprises? These questions fascinate philosophers, biologists, and economists alike, for the "invisible hand" that should turn selfish efforts into public benefit is not always at work. The Calculus of Selfishness looks at social dilemmas where cooperative motivations are subverted and self-interest becomes self-defeating. Karl Sigmund, a pioneer in evolutionary...
Facing Tough Test Questions? Missed Lectures? Not Enough Time? Fortunately for you, there's Schaum's. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Solved Problem book helps you cut study time, hone problem-solving skills, and achieve your personal best on exams! You get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaum......
Ideal for self-instruction as well as for classroom use, this text helps students improve their understanding and problem-solving skills in analysis, analytic geometry, and higher algebra. More than 1,200 problems appear in the text, with concise explanations of the basic notions and theorems to be used in their solution. Many are followed by complete answers; solutions for the others appear at the end of the book. Topics include sequences, functions of a single variable, limit of a function, differential...
Full of relevant, diverse, and current real-world applications, Stefan Waner and Steven Costenoble's FINITE MATHEMATICS AND APPLIED CALCULUS, 6E, International Edition helps you relate to mathematics. A large number of the applications are based on real, referenced data from business, economics, the life sciences, and the social sciences. Thorough, clearly delineated spreadsheet and TI Graphing Calculator instruction appears throughout the book. Acclaimed for its readability and supported by the...
An innovative text that emphasizes the graphical, numerical and analytical aspects of calculus throughout and often asks students to explain ideas using words. This problem driven text introduces topics with a real-world problem and derives the general results from it. It can be used with any technology that can graph and find definite integrals numerically. The derivative, the integral, differentiation, and differential equations are among the topics covered.
This lucid and balanced introduction for first year engineers and applied mathematicians conveys the clear understanding of the fundamentals and applications of calculus, as a prelude to studying more advanced functions. Short and fundamental diagnostic exercises at the end of each chapter test comprehension before moving to new material. |
A Mathematical Dictionary for Schools contains contains over 500 definitions of technical terms found within GCSE syllabuses. Key words and phrases are explained in clear, si [more]
A Mathematical Dictionary for Schools contains contains over 500 definitions of technical terms found within GCSE syllabuses. Key words and phrases are explained in clear, simple language with illustrations to aid understanding of more difficult terms.[less] |
1. Course
Description. This yearlong course provides continuation to the mathematics
concepts and processes introduced in Integrated Mathematics I. The intend of
this course is to provide additional algebraic concepts and processes to the
student and demonstrate how they are utilized in the workplace. Topics include
quadratics, linear systems, probability, statistics, and higher level
measurements.
2.Grading. Grades will be
collected from tests, quizzes, and daily work. Daily work will include study
guides, lab activities, and problems. Grades will be determined by the
following plan:
Tests: 50%
Quizzes: 25%
Daily Assignments: 25%
Late assignments
will be accepted but will only receive 50% for what is correct upon the
assignment. The handbook, pg.7 explains the grading scale. Your book number is
your identification number for the posted grades. If you do not want people to
know your grade do not tell them your number.
3.Retest Policy. If a
student scores less than 80% upon a test, he/she has the option to retake the
test. A retestís maximum score will be 80% and must be retaken before the next
unitís test. |
Welcome to the website that is designed to help anyone who is studying Secondary School Mathematics at Level 2, Level 3, Standard Grades or Higher Still Levels Intermediate 1 or 2 and Higher.
Created by Mr. Lafferty
First Class Bsc Hons in MathSci (Open) GIMA,
Teacher of Mathematics in East Dunbartonshire.
The site does not let you print off materials or solutions to past papers as it is not meant to be a simple way of getting the correct answers to questions but rather an aid to understanding and developing your Mathematical knowledge. Most topics are presented in PDF format with some topics covered in PowerPoint Presentation format. If you find the site useful please inform other students of its existence. Finally if you have any constructive feedback please email below. |
Interpreting Distance – Time Graphs A6 pictures of situations rather than abstract representations. In addition, they also find it difficult to interpret the significance of the
gradients of these graphs. In this session, students begin by discussing a question that is
designed to reveal common misconceptions about distance–time graphs. They then work in pairs and threes to match descriptions, graphs and tables. As they do this, they will interpret their meaning and begin to link the representations together. (GCSE grades A - D |
After obtaining a referral from the Math Advising Office, students withdisabilitiesshould contact the Ohio State Office for Disability Services, (614)
292-3307, to make alternate arrangements for taking any math exam.
Students in Math 1050 and 1075 may use any non-graphing calculator.
Students in Math 1130 and higher courses may use any graphing calculator no higher than the TI-84 (Texas Instrument).
Most math courses do not require a computer. Choose one for yourself that suits you best.
Math Tutoring
MSLC Resource Center - This room includes current textbooks and their
supporting materials, such as student solution manuals, which you may
use in the Resource Center or the tutor rooms. There are also alternate
textbooks which you can take home, and computer aids and instructional
videos which you may watch. We also have calculators which can be
borrowed on a short-term basis.
SELF STUDY- The Schaum's Outlines for mathematics are an excellent resource for self study. It is possible to begin a review with basic arithmetic and carry it through calculus. These outlines are reasonably priced and are available in the campus area bookstores. |
Personal tools
Mathematics
The Mathematics Department at ASFM has developed a spiral and coherent curriculum using standards and benchmarks.
The main source for developing the Mathematics Department standards and benchmarks document is Content Knowledge: A Compendium of Standards and Benchmarks for K-12 Education from Mid-continental Research for Education and Learning (McREL) and Association for Supervision and Curriculum Development (ASCD).
The Mathematics Department document is a dynamic document, which is under constant review to be sure it is meeting the needs of the educational community. The purpose of a Mathematics Department standards and benchmarks document is to clarify what students are expected to understand and accomplish at each course and grade level, and provide a common set of expectations for the entire educational community.
Additional courses offered by the Mathematics Department include Honors courses in grades nine through twelve, a Mathcounts extra-curricular opportunity in grades six through eight and Advanced Placement Calculus in grade twelve. For more information about AP, go to our Advanced Placement page. |
The following computer-generated description may contain errors and does not represent the quality of the book: Decimal separatrixes 49 Present trends in arithmetic 51 Multiplication and division of decimals.59 Arithmetic in the Renaissance 66 Napiers rods and other mechanical aids to calculation. 6 gAxioms in elementary algebra 73 Do the axioms apply to equations?76 Giecking; the solution of an equation 81 Algebraic fallacies 83 Two highest common factors.89 Positive and negative numbers go Visual representation of complex numbers.92 Illustration of the law of signs in algebraic multiplication.97 A geometric illustration. 97 From a definition of multiplication.98 A more general form of the law of signs.99 Multiplication as a proportion lOO Gradual generalization of multiplication.100 Exponents loi An exponential equation 102 Two negative conclusions reached in the 19 th century 103 The three parallel postulates illustrated.105 Geometric puzzles 109 Paradromic rings 117 Division of plane into regular polygons.118 A homemade leveling device 120 Rope stretchers.121 The three famous problems of antiquity.122 The circle squarers paradox 126 The instruments that are postulated 130 The triangle and its circles 133 Linkages and straight-line motion 136 The four-colors theorem. |
The Mathematics Department is committed to expanding students' understanding and appreciation of mathematics through a comprehensive, content-based plan that acknowledges and addresses differences in motivation, goals, ability, and learning styles. All students must complete three years of mathematics and pass a Regents examination.
All mathematics courses are year-long courses.
Course Offerings
Integrated Algebra - This is the first mathematics course in high school. The completion of this course -- 1 to 2 years -- depends on the entry level of the student. Algebra provides tools and develops ways of thinking that are necessary for solving problems in a wide variety of disciplines such as science, business, and fine arts. Linear equations, quadratic functions, absolute value, and exponential functions are studied. Coordinate geometry is integrated into this course as well as data analysis, including measures of central tendency and lines of best fit. Elementary probability, right triangle trigonometry, and set theory complete the course. Students will take the Integrated Algebra Regents examination at the conclusion of this course.
Geometry - This is the second course in mathematics for high school students. In this course, students will have the opportunity to make conjectures about geometric situations and prove in a variety of ways that their conclusion follows logically from their hypothesis. Congruence and similarity of triangles will be established using appropriate theorems. Transformations including rotations, reflections, translations, and dilations will be taught. Properties of triangles, quadrilaterals and circles will be examined. Geometry is meant to lead students to an understanding that reasoning and proof are fundamental aspects of mathematics. Students will take the Geometry Regents examination at the conclusion of this course.
Algebra 2 and Trigonometry - This is the third of the three courses in high school mathematics. In this course, the number system will be extended to include imaginary and complex numbers. Students will learn about polynomial, absolute value, radical, trigonometric, exponential, and logarithmic functions. Problem situations involving direct and indirect variation will be solved. Data analysis will be extended to include measures of dispersion and the analysis of regression models. Arithmetic and geometric sequences will be evaluated. Binomial expressions will provide the basis for the study of probability theory, and the normal probability distribution will be analyzed. Right triangle trigonometry will be expanded to include the investigation of circular functions. The course will conclude with problems requiring the use of trigonometric equations and identities. Students will take the Algebra 2 and Trigonometry Regents examination at the conclusion of this course.
Calculus - This course includes an overview of analytic geometry and trigonometry as it applies to the study of functions, graph limits, derivatives and their applications.
Calculus AB, Advanced Placement - This is a full-year course in college-level calculus that culminates in the Advanced Placement (AB) examination. Included is the study of functions, graphs, and limits, derivatives, applications of derivatives, integrals, applications of integrals, the fundamental theorem of calculus, anti-differentiation, applications of the anti-derivative, and slope fields.
Calculus BC, Advanced Placement - This is a full-year course in college-level calculus that culminates in the Advanced Placement (BC) examination. Included is the study of: additional techniques for integration, calculus with parametric equations and polar equations, infinite series, and Taylor and Maclaurin series. |
Table of Contents, MEAP Chapters & Resources
Table of Contents
Resources
PART 1: BASICS AND ALGEBRA ON THE TI-83 PLUS/TI-84 PLUS 1What can your calculator do? - FREE 2 Get started with your calculator - AVAILABLE 3 Basic graphing - AVAILABLE 4 Variables, matrices, and lists - AVAILABLE
DESCRIPTION
With so many features and functions, the TI-83 Plus/TI-84 Plus graphing calculator can be a little intimidating. This easy-to-follow book turns the tables and puts you in control! In it you'll find terrific tutorials that guide you through the most important techniques, dozens of examples and exercises that let you learn by doing, and well-designed reference materials so you can find the answers to your questions fast.
Using the TI-83 Plus/TI-84 Plus starts by giving you a hands-on orientation to the calculator so you'll be comfortable with its screens, buttons, and the special vocabulary it uses. Then, you'll start exploring key features while you tackle problems just like the ones you'll see in your math and sciences classes. TI-83 Plus/TI-84 Plus calculators are permitted on most standardized tests, so the book provides specific guidance for SAT and ACT math. Along the way, easy-to-find reference sidebars give you skills in a nutshell for those times when you just need a quick reminder.
WHAT'S INSIDE
Get up and running with your calculator fast!
Engaging and approachable examples
Learn by doing
Special sections on the brand new TI-84 Plus C Silver Edition
Covers the new MathPrint OS for the TI-84 Plus, which makes calculations look more like what you see in your textbook
This book is written for anyone who wants to use the TI 83+/84+ series of graphing calculators and requires no prior experience. It assumes no advanced knowledge of math and science. It's a perfect companion to Programming the TI-83 Plus/TI-84 Plus, where you discover how your calculator can accelerate algebra, pre-calculus, probability, statistics, physics, and much more.
Why learn the TI 83 Plus/84 Plus? The TI-83 Plus and TI-84 Plus series is the de facto standard for graphing calculators used by students in grades 6 through college. These calculators can do everything from basic arithmetic through graphing, pre-calculus, calculus, statistics, and probability, and are even great tools for learning programming. With the Spring 2013 introduction of the TI-84 Plus C Silver Edition, a color screen calculator, the TI-83 Plus/TI-84 Plus line promises to be relevant for decades to come.
About the Author
Christopher Mitchell is a teacher, student, and recognized leader in the TI-83+/TI-84+ enthusiast community. You'll find Christopher (aka Kerm Martian) and his community of calculator experts answering questions and sharing advice on his website cemetech.net.
About the Early Access Version
This Early Access version of Using the TI-83 Plus/TI-84 Plus |
Course: mathematics I
Solving of exercises related to the corresponding subjects of Mathematics.
Objectives:
Basic knowledge of mathematical methods in the natural and technical sciences. Ability to solve exercises related to the corresponding subjects of Mathematics.
Course contents:
Numbers, vectors and matrices. Linear algebra, vector algebra.
Systems of linear equations. Complex numbers.
Rows and sums, real functions of one variable.
Introduction in the differential and integral calculus. Analysis of functions of one variable. Basic knowledge in power series. |
Specification
Aims
The course unit will deepen and extend students' knowledge and understanding of commutative algebra. By the end of the course unit the student will have learned more about familiar mathematical objects such as polynomials and algebraic numbers, will have acquired various computational and algebraic skills and will have seen how the introduction of structural ideas leads to the solution of mathematical problems.
Brief Description of the unit
The central theme of this course is factorisation (theory and practice) in commutative rings; rings of polynomials are our main examples but there are others, such as rings of algebraic integers.
Polynomials are familiar objects which play a part in virtually every branch of mathematics. Historically, the study of solutions of polynomial equations (algebraic geometry and number theory) and the study of symmetries of polynomials (invariant theory) were a major source of inspiration for the vast expansion of algebra in the 19th and 20th centuries.
In this course the algebra of polynomials in n variables over a field of coefficients is the basic object of study. The course covers fairly recent advances which have important applications to computer algebra and computational algebraic geometry (Gröbner bases - an extension of the Euclidean division algorithm to polynomials in 2 or more variables), together with a selection of more classical material.
Learning Outcomes
On successful completion of this course unit students will be able to demonstrate
facility in dealing with polynomials (in one and more variables);
understanding of some basic ideal structure of polynomial rings;
appreciation of the subtleties of factorisation into prime and irreducible elements;
ability to compute generating sets and Gröbner bases for ideals in polynomial rings;
ability to relate polynomials to other algebraic structures (algebraic varieties and groups of symmetries);
ability to solve problems relating to the factorisation of polynomials,
irreducible polynomials and extension fields.
Future topics requiring this course unit
None, though the material connects usefully with algebraic geometry and Galois theory.
Textbooks
The first two books are useful general references on algebra though neither covers Gröbner bases (which is a relatively new topic). For Gröbner bases see the book by Cox, Little and O'Shea. The last book is a new textbook which combines Gröbner bases with more traditional material.
Teaching and learning methods
Two lectures and one examples class each week. In addition students should expect to spend at least four hours each
week on private study for this course unit.
Course notes will be provided, as well as examples sheets and solutions. The notes will be
concise and will need to be supplemented by your own notes taken in lectures, particularly
of worked examples. |
...a free program useful for solving equations, plotting graphs and obtaining an in-depth analysis of a function....especially for students and engineers, the freeware combines graph plotting with advanced numerical calculus, in a very...intuitive approach. Most equations are supported, including algebraic equations, trigonometric equations, exponential...equations, parametric equations.
...are combined the intuitive interface and professional functions.
FlatGraph allows:
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...3D Grapher is a feature-rich yet easy-to-use graph plotting and data visualization software suitable for students,...to work with 2D and 3D graphs. 3D Grapher is small, fast, flexible, and reliable. It offers...of the functionality of heavyweight data analysis and graphing software packages for a small fraction of their...it works, but can just play with 3D Grapher for several minutes and start working.
3D Grapher...
...curve fitting.
Fit thousands of data into your equations in seconds:
Curvefitter gives scientists, researchers and engineers...model for even the most complex data, including equations that might never have been considered. You can...data fitting includes the following capabilities:
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...MadCalc is a full featured graphing calculator application for your PC running Windows. With...MadCalc you can graph rectangular, parametric, and polar equations. Plot multiple equations...at once. Change the colors of graphs and the background. Use the immediate window feature...allows you to zoom in and out on graphs or set the scale in terms of x...explicitly or scroll just by clicking on the graph and dragging it.
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Graphs can be printed, saved as BMP picture files...or copied and pasted in other applications. This graphing program is as easy-to-use as typing an equation...
...* x) + c
Quickly Find the Best Equations that Describe Your Data:
DataFitting gives students, teachers,...complex data, by putting a large number of equations at their fingertips. It has built-in library that...of linear and nonlinear models from simple linear equations to high order polynomials.
Graphically Review Curve Fit...fit, DataFitting automatically sorts and plots the fitted equations by the statistical criteria of Standard Error. You...
...:
> >Can store up to three algeriac equations internally
>Programmable
>It can do the operations of...subtract, multiply, and divide of any two algebraic equations algebraically and produce an algebraic result, it can...easy exciting and fast to use
3. Plot graph :
>Can plot up to three graphs simultaneously.... |
Math Anxiety
Throughout grade school and maybe even in high school, many students felt there was no reason to take math.
These students hated math and felt they were never going to use it. There is still the tendency to think that only those who go into technical fields need math. Math teaches us to think. Math helps us to organize or thoughts, analyze information, and better understand the world around us.
There are myths about math that we have accepted as true and these tend to hold us back when it comes to learning math.
Some popular myths are:
Females aren't any good at math
The majority can't do well in math because only a few people really have mathematical minds. (We are happy to get a "C" in math whereas we won't accept a "C" in English or any other subject that we like. We expect to do poorly in math).
Some hints for studying math:
Read your text first, before you try any problems.
Write down the theorems and definitions, read them out loud, and then rewrite them into your own words.
Do a lot of problems and practice tests.
Don't cram for tests. Frequent practice and review is the key to learning math. If you cram, you will be unsure of yourself. Formulas will become confused and problems will look differently.
Don't keep looking in the back of your debt at the answers a. You may have the right answer but may not have done the problem correctly. b. If you have the wrong answer, it could affect your confidence and concentration.
When you aren't sure of a problem, ask for help, but never erase your work. Even if the problem is wrong, find to where you were wrong and where you were right. You can learn just as much from your mistakes as from what you've done correctly.
Set aside a certain time everyday to study math.
Get extra help when you need it. Come to the PLC for tutoring; ask your teacher or a classmate for help. Remember, you need to understand math; that does not mean memorizing it.
Begin at the right place. If you feel that you need a review, be sure to start with a math class that begins at your level.
A common story instructors hear from math students is that the students can do the work or homework and in class but when it comes down to the test, the students freeze.
The number one problem of math test anxiety is negative self-talk. Negative self-talk is when you talk yourself deeper into anxiety. You think "what if" or "I can't". You worry about finishing the test on time. You tend to concentrate on how you are feeling, on how the anxiety is affecting you instead of on the test itself.
Some hints to counteract math test anxiety:
Confront your anxiety by admitting that you are worried about this test. Anxiety and fear react in the body in the same way, and admitting that you re anxious relieves some of the anxiety.
Use positive self-talk. Keep telling yourself that you can do this math, that you know this stuff, and that you are prepared.
Control your physical self. Take a brisk walk around the classroom buildings using positive self-talk while walking. Keep your heart rate and respiration steady by doing slow, five count deep breathing exercises. Loosen tight muscles on your neck by doing shoulder rolls forward and backward. Relax legs and arms by shake outs before you walk into the classroom.
Focus your attention away from yourself and towards the problem.
When taking practice tests or working on homework, keep a diary of the kinds of thoughts you are having while working out the problems. Relate these concerns to your tutor or teacher.
While the above suggestions will be helpful for the physical and emotional self, the following suggestions may be beneficial for the academic self.
Some hints to better test taking:
Write down formulas and other memorized information directly onto the test. This eliminates the risk of forgetting or altering the information incorrectly as you work the problems.
Preview the test. Find a problem you are comfortable with and start there. It is not necessary to work in numerical order. Try instead to choose an order that helps you stay positive.
Start with the easier problems. Also keep in mind the total point of the test and plan a strategy to get the most amount of points possible in the shortest amount of time.
Pass over difficult problems. Give yourself a certain time limit to solve it; if more time is needed, circle the number and come back to it later. Use the strategy you've planned and remain positive. If you find yourself becoming anxious, try some relaxation techniques to calm down physically and then focus back on the test.
Review the problems you've skipped. Maybe other problems you have solved can give you a better insight to the work needed for this problem.
Show some work for each problem, even if it's a guess. Partial credit is still good.
Allow for some time to look back over your work. Make sure you have read the directions correctly and look for careless errors.
Use all of the test time. Anxiety can induce a need to escape. Try to control the anxiety before this feeling takes over. Leaving a test early may mean a loss of points on your test as well as other negative feedback. Remember, always try to remain positive.
Remember, the key to conquering math anxiety is practice, practice, practice. The more confident you become in your ability, the better you will do. |
A selective study of mathematical concepts for liberal arts students. Concepts include: number sense and numeration, geometry and measurement, patterns and functions, and data analysis. Topics covered include: sets, logic, graphs of quadratic and exponential functions, systems of linear equations and inequalities and symmetry. Emphasis is on the use of algebra in applications for the liberal arts and sciences. Skills prerequisites: ENG 020 and MAT 029C or MAT 029. |
GOOD COURSES
CONTENTS
I. Undergraduate mathematics
A discussion of what a good undergrad programme in
mathematics should be about can be found here.
The book concerns mathematics in the American system, where applied
mathematics was
rarely taught in maths departments (at the time of writing). It also
discusses the content often presented in four-year American liberal arts
colleges, and two-year community colleges, and criticises the specialist
nature of the topics
chosen. The courses offered to students of science and engineering by
departments of mathematics are also panned, one point being that the
professor doing this job knows no science or engineering at all.
The author, Morris Kline, talks of the research professor, who hates
teaching undergraduates of any sort, and also mentions the wide use made
of graduate student tutors, who have neither training nor
experience. Scarce mention is made of full, associate and assistant
professors, who form (in my experience) the bulk of the academic staff in
most departments of mathematics in American universities, and who do a
very professional job in their teaching, as well as research and admin.
Some of the criticism of present methodology is way off centre. For
example, Kline objects to the teaching of applied mathematics by using
over-simplified models. He argues that there is no point teaching the laws
of falling bodies as if there were no air friction: tell that to a
parachutist, he quips. In this he fails to capture the essence of
science: we must study models, and compare with experiment, so that we may
shoot them down, and revise them. More, we can usually find a range of
applicability of
the simple model, outside of which it is no longer a good one. But
worse: he seems to be saying that only a fully developed, correct model
should be taught. This goes against the teaching of Picasso: a teacher
should mix a little bit of what we do not know with a lot of what we do
know. I taught physics at Virginia Tech., a course in which the technician
had prepared the "Galileo Bench". This was an inclined plane on an air
cushion, in which Galileo's laws of falling bodies, s = s(0) + vt + 1/2 at2,
was true, to within the experimental error. Some of the students
found these laws hard to understand, even without friction. When they had achieved
that, we went on to the refinements coming from friction. To start with
the full theory, would place them in a similar position to Galileo... who
had to cope with Aristotle's dictum that a force was needed to keep a
body moving; when Galileo had abandoned this, he broke the 2000 year stalemate
in science.
Most of the points made about the limited syllabus of a maths degree do
not apply to the UK, where applied
mathematics traditionally forms half of the degree in
mathematics. However, with the possible replacement of A-levels with a
bacc., our school programme might become more like the American one. We
should then think about whether the university course might also move in
that direction. Should we have four-year degree courses in mathematics, with
the first year devoted to maths, physics, chemistry and computing? These
could cover the four subjects to replace the omitted parts of A-level. The
mathematics course
could cover analytic geometry with calculus, trig, probability and
statistics,
complex numbers, and vectors, with a little theory of matrices.
Physics could include Newton's laws, with examples from one
dimension, such as motion under constant gravity, friction,
simple damped oscillator, sinusoidal wave
motion, interference of waves, the laws of thermodynamics, Eulerian fluid equations,
and electricity and magnetism (before Maxwell). Chemistry might contain
the Bohr atom, the Mendeleev table, the inorganic chemistry of
acids and bases, salts and metals. Some physical chemistry such as the law
of mass-action, and some organic chemistry, should be
included. Lab work in physics and chemistry should be at the
level now done in schools in the UK. Computing might introduce a useful
language such as Java, Maple or Mathematica, and should give a general
competence in Windows.
Kline suggests that scholarship in mathematics would serve a purpose,
to reduce the number of pointless and empty papers, by critical reviews.
This used to be the job of Mathematical Reviews, until it changed its
policy, and now bans controversy in the reviews. Kline suggests that a new
degree of high status, Doctor in Arts, should be awarded, which would not
require
original theorems, but would be readable and deep. We have something
similar, in
the M. Phil., which however has not got the status of the Ph. D.
III.Abstract Algebra
IV. Graph theory
V. The Kentucky Archives on
Mathematics
The site of the University
of Kentucky hosts a list of free material on mathematics, of which
III. above is just one. I found the course on partial
differential equations very useful. The course
on Hilbert Space Methods for Partial Differential Equations, by
R. E. Showalter, is very pleasant indeed. It is slightly informal in its
definition
of distributions, but this is all that is needed for partial
differential equations at this level.
VI.Wikipedia
Wikipedia is a free internet
encyclopaedia, written by its viewers. There
is quite a large set of mathematics pages, as well as pages on physics and
other sciences, and all other subjects. Some pages are sketchy, and others
are literally empty,
awaiting the first volunteer. I found a mistake in Wightman's
biography: it said he was British. I was able to edit that page and
correct it. The statement of the Navier-Stokes equations could not be
right, as the terms do not all have the same physical dimension.
The site is worth a browse, and might become more reliable as time
passes. |
Short Description for Mathematics Levels 5-8 This workbook provides practice material for all the key topics. It contains warm-up questions, followed by short-answer questions, building to more demanding questions, to help students improve and progress. Full description
Full description for Mathematics Levels 5-8
This workbook provides practice material for all the key topics. It contains warm-up questions, followed by short-answer questions, building to more demanding questions, to help students improve and progress. |
SciPy (pronounced "Sigh Pie") is open-source software for mathematics, science, and engineering. It is also the name of a very popular conference on scientific programming with Python. The SciPy library depends ...
... a better understanding of fundamental concepts in pre-algebra, algebra, trigonometry, physics, chemistry, and calculus. Microsoft Mathematics includes a full-featured graphing calculator that's designed to work just like a handheld ...
Scilab is free and open source software for numerical computation providing a powerful computing environment for engineering and scientific applications. Scilab is available under GNU/Linux, Mac OS X and ...
... The libraries include numerical and analytical calculations, linear algebra operations, equation solving algorithms. Many libraries are based on the JAIDA classes for data manipulation, construction of histograms and functions. jHepWork ...
... The libraries include numerical and analytical calculations, linear algebra operations, equation solving algorithms. Many libraries are based on the JAIDA classes for data manipulation, construction of histograms and functions. SCaVis ...
... in ...
... by step solutions to most problems in arithmetic, algebra, trigonometry and introductory/intermediate calculus for middle- to high-school students and first year university students. All solutions are accompanied by step by ...
Logic Minimizer is an innovative, versatile application for simplifying Karnaugh maps and logical expressions step by step. It is geared for those involved in engineering fields, more precisely digital and formal ...
It is a calculator for algebra.The inputs and outputs are in algebraic format.It can do the operations of add, subtract, ... factorized. It records the history of operations on algebraic functions.You can copy one function to another which ... |
Pre-Algebra
Pre-Algebra. Nice choice! During our long and celebrated (OK, so maybe we're exaggerating a little)
years in various math classes, we've found that a solid foundation is extremely important. So we're glad
you came here, and we hope it helps you out!
In this section of the site, we'll try to clear up some common problems encountered in pre-algebra. We'll
cover everything from the basics of equations and graphing to everyone's favorite -- fractions.
After each section, there is an optional (though highly recommended) quiz that you can take to see if
you've fully mastered the concepts. Also, don't forget to visit the
message board and the
formula database.
Follow any of the links below to go to the section you need help with. |
Prerequisite: completion of a general education required core course in mathematics. Number systems, primes, and divisibility; fractions; decimals; real numbers; algebraic sentences. Successful completion of a basic skills exam in mathematics is required for credit in this course.Designed for preservice teachers P-9. |
The story of geometry is the story of mathematics itself: Euclidean geometry was the first branch of mathematics to be systematically studied and placed on a firm logical foundation, and it is the prototype for the axiomatic method that lies at the foundation of modern mathematics. It has been taught to students for more than two millennia as a model of logical thought.
This book tells the story of how the axiomatic method has progressed from Euclid's time to ours, as a way of understanding what mathematics is, how we read and evaluate mathematical arguments, and why mathematics has achieved the level of certainty it has. It is designed primarily for advanced undergraduates who plan to teach secondary school geometry, but it should also provide something of interest to anyone who wishes to understand geometry and the axiomatic method better. It introduces a modern, rigorous, axiomatic treatment of Euclidean and (to a lesser extent) non-Euclidean geometries, offering students ample opportunities to practice reading and writing proofs while at the same time developing most of the concrete geometric relationships that secondary teachers will need to know in the classroom.
Readership
Undergraduate students interested in geometry and secondary mathematics teaching.
Reviews
"Lee's "Axiomatic Geometry" gives a detailed, rigorous development of plane Euclidean geometry using a set of axioms based on the real numbers. It is suitable for an undergraduate college geometry course, and since it covers most of the topics normally taught in American high school geometry, it would be excellent preparation for future high school teachers. There is a brief treatment of the non-Euclidean hyperbolic plane at the end."
-- Robin Hartshorne, University of California, Berkeley
"The goal of Lee's well-written book is to explain the axiomatic method and its role in modern mathematics, and especially in geometry. Beginning with a discussion (and a critique) of Euclid's elements, the author gradually introduces and explains a set of axioms sufficient to provide a rigorous foundation for Euclidean plane geometry.
"Because they assume properties of the real numbers, Lee's axioms are fairly intuitive, and this results in a presentation that should be accessible to upper level undergraduate mathematics students. Although the pace is leisurely at first, this book contains a surprising amount of material, some of which can be found among the many exercises. Included are discussions of basic trigonometry, hyperbolic geometry and an extensive treatment of compass and straightedge constructions."
-- I. Martin Isaacs, University of Wisconsin-Madison
"Jack Lee's book will be extremely valuable for future high school math teachers. It is perfectly designed for students just learning to write proofs; complete beginners can use the appendices to get started, while more experienced students can jump right in. The axioms, definitions, and theorems are developed meticulously, and the book culminates in several chapters on hyperbolic geometry--a lot of fun, and a nice capstone to a two-quarter course on axiomatic geometry." |
Many of the problems students experience with A-Level Physics are associated with the mathematics involved. This title deals with this problem offering support for mathematics in physics. 'Maths boxes' present the mathematics needed to grasp a concept. It includes: objectives stated; color illustrations; and graduated questions and practice. |
Calculators Are for Calculating, Mathematica Is for Calculus
Mathematica is the perfect tool to help calculus professors and instructors overcome limitations with traditional approaches to teaching calculus. Students can experience a more enriching calculus rather than the algorithm-driven method they are used to seeing. We'll look at different ways Mathematica can be used to enhance your calculus class, such as using interactive models to engage students and connecting calculus to the real world with built-in datasets. Topics include the squeeze theorem, derivative tests, revolving solids about axes, and more. |
partial differential equations that govern scalar and vector fields are the very language used to model a variety of phenomena in solid mechanics, fluid flow, acoustics, heat transfer, electromagnetism and many others. A knowledge of the main equations and of the methods for analyzing them is therefore essential to every working physical scientist and engineer. Andrea Prosperetti draws on many years' research experience to produce a guide to a wide variety of methods, ranging from classical Fourier-type series through to the theory of distributions and basic functional analysis. Theorems are stated precisely and their meaning explained, though proofs are mostly only sketched, with comments and examples being given more prominence. The book structure does not require sequential reading: each chapter is self-contained and users can fashion their own path through the material. Topics are first introduced in the context of applications, and later complemented by a more thorough presentation. less |
Find a Revere, MA Algebra 2 TutorSystems of linear equations occur when using Kirchhoff's laws in Physics to solve for currents/resistances in electric circuits.
2. Matrix transformations are used extensively by computer graphics systems. For example OpenGL makes extensive use of vectors and matrices to render objects in 2D/3D.
3. |
eBook Ordering Options
DescriptionExamining how information technology has changed mathematical requirements, the idea of Techno-mathematical Literacies (TmL) is introduced to describe the emerging need to be fluent in the language of mathematical inputs and outputs to technologies and to interpret and communicate with these, rather than merely to be procedurally competent with calculations. The authors argue for careful analyses of workplace activities, looking beyond the conventional thinking about numeracy, which still dominates policy arguments about workplace mathematics. Throughout their study, the authors answer the following fundamental questions:
What mathematical knowledge and skills matter for the world of work today?
How does information technology change the necessary knowledge and the ways in which it is encountered?
How can we develop these essential new skills in the workforce?
With evidence of successful opportunities to learn with TmL that were co-designed and evaluated with employers and employees, this book provides suggestions for the development of TmL through the use of authentic learning activities, and interactive software design. Essential reading for trainers and managers in industry, teachers, researchers and lecturers of mathematics education, and stakeholders implementing evidence-based policy, this book maps the fundamental changes taking place in workplace mathematics.
Contents
Acknowledgements
1. Introduction
1.1 New Demands on Commerce and Industry
1.2 Information Technology and the Changing Nature of Work
1.3 Background to the Research
1.4 A Description of Key Ideas
1.5 Aims and Methods
2. Manufacturing 1: Modelling and Improving the Work Process in Manufacturing Industry
2.1 Process Improvement in Manufacturing
2.2 Workplace Observations of Process Improvement
2.3 Learning Opportunities for Process Improvement
2.4 Outcomes for Learning and Practice
2.5 Conclusions
3. Manufacturing 2: Using Statistics to Improve the Production Process
3.1 Process Control and Improvement Using Statistics
3.2 Workplace Observations of Statistical Process Control
3.3 Learning Opportunities for Statistical Process Control
3.4 Outcomes for Learning and Practice
3.5 Conclusions
4. Financial Services 1: Pensions and Investments
4.1 The Techno-Mathematics of Pensions and the Work of Customer Services
Related Subjects
Name: Improving Mathematics at Work: The Need for Techno-Mathematical Literacies (Paperback) – Routledge
Description: By Celia Hoyles, Richard Noss, Phillip Kent, Arthur Bakker. Improving Mathematics at Work questions the mathematical knowledge and skills that matter in the twenty-first century world of work, and studies how the use of mathematics in the workplace is evolving in the rapidly-changing context of new technologies...
Categories: Adult Education and Lifelong Learning, Educational Research, Post-Compulsory Education, Teaching & Learning, Education Policy, Work-based Learning, Operational Research / Management Science |
Discovering Geometry Intro
Discovering Geometry began in my classroom over 35 years ago. During my first ten years of teaching I did not use a textbook, but created my own daily lesson plans and classroom management system. I believe students learn with greater depth of understanding when they are actively engaged in the process of discovering concepts and we should delay the introduction of proof in geometry until students are ready. Until Discovering Geometry, no textbook followed that philosophy.
I was also involved in a Research In Industry grant where I repeatedly heard that the skills valued in all working environments were the ability to express ideas verbally and in writing, and the ability to work as part of a team. I wanted my students to be engaged daily in doing mathematics and exchanging ideas in small cooperative groups.
The fourth edition of Discovering Geometry includes new hands-on techniques, curriculum research, and technologies that enhance my vision of the ideal geometry class. I send my heartfelt appreciation to the many teachers who contributed their feedback during classroom use. Their students and future students will help continue the evolution of Discovering Geometry. |
Course Descriptions
Following certain course descriptions are the designations: F (Fall), Sp (Spring), Su (Summer) . These
designations indicate the semester(s) in which the course is normally offered and are intended as an aid to students planning their programs of study.
601 Using the Graphing Calculator in the School Curriculum-1 hour. In this 24-hour workshop participants will develop a better understanding of graphing technology while considering the following topics: domain, range, linear and quadratic functions, common solutions, inequalities, extreme values, slope, translations, rational and trigonometric functions, asymptotes, statistical menus and data, exponential and logarithmic functions. Problem solving and programming will be included throughout.
602 Concepts and Practices in General Mathematics-3 hours. A practical approach to the development of programs, methods of motivation, and mathematical concepts for the teacher of general mathematics. Prerequisite: 15 hours of math including calculus.
603 Fundamental Concepts of Algebra-3 hours. The conceptual framework of algebra, recent developments in algebraic theory and advanced topics in algebra for teachers and curriculum supervisors. Prerequisite: 24 hours of math including calculus.
604 Fundamental Concepts of Geometry-3 hours. The conceptual framework of many different geometries, recent developments in geometric theory, and advanced topics in geometry for teachers and curriculum supervisors. Prerequisite: 24 hours of math including calculus.
605 Problem Solving in Mathematics-3 hours. Theory and practice in mathematical problem-solving; exploration of a variety of techniques; and finding solutions to problems in arithmetic, algebra, geometry, and other mathematics for teachers of mathematics and curriculum supervisors. Prerequisite: 24 hours of math including calculus.
606 Data Analysis and Probability for Teachers
of Middle-Level Mathematics-3 hours. This course is designed to
deepen middle-level teachers of mathematics' understanding of data
analysis and probability. Topics to be studied in this course are:
selecting and using appropriate statistical methods to analyze data,
developing and evaluating inferences and predictions that are based on
data, and understanding and applying the basic concepts of probability.
Pedagogical approaches to students' learning of data analysis and
probability will be incorporated into the study of these topics.
611 Introduction to Analysis for Secondary Teachers-3 hours. A study of continuity, differentiability and integrability of a function of a real variable particularly as these properties appear in the secondary school mathematics curriculum. Prerequisite: at least an undergraduate minor in mathematics.
613 Algebra and Functions for Middle School
Teachers-3 hours. This course is designed to deepen
middle-school mathematics teachers' understanding of algebra through the
study of patterns, symbolic language, problem solving, functions,
proportional reasoning, generalized arithmetic, and modeling of physical
situations. Pedagogical approaches to students' learning of algebra
will be incorporated into the study of these topics.
614 Basic Topics in Mathematics for the Elementary Teacher-3 hours. For the elementary teacher who needs to have a better understanding of mathematical content. Sets, numeration systems and algorithms for computation are studied in conjunction with a logical but non-rigorous development of the real numbers.
621 Using Technology in the School Curriculum-3 hours. This course was designed to facilitate the teacher of mathematics in the use of technology. Graphing utilities and calculator based laboratories through the study of the following topics: domain, range, linear and quadratic functions, common solutions, inequalities, extrema, slope, translations, rational and trigonometric functions, asymptotes, statistical menus, regression equations, data collection and analysis, parametric equations, exponential and logarithmic functions, problem solving and programming.
624 Intermediate Topics in Mathematics for the Elementary Teacher-3 hours. Topics included are an intuitive study of geometric figures, measurement, basic algebra and functions, and the rudiments of statistics and probability. Designed for the elementary teacher who needs a better understanding of mathematical content.
636 Geometry and Measurement for Teachers of
Middle-Level Mathematics-3 hours. This course is designed to deepen
middle-level teachers of mathematics' understanding of geometry as a
study of size, shape, properties of space; a tool for problem solving;
and one way of modeling physical situations. This course will also
address connections between geometry to other mathematical concepts;
historical topics relevant to geometry in the middle grades; and
pedagogical approaches to students' learning of geometry.
638 Fundamental Models in Statistical Inference-3 hours. This class emphasizes the study of probability models that form the basis of standard statistical techniques. Statistical techniques considered include inferences involving measures of central tendency and measures of variability, linear regression model estimation and goodness of fit hypothesis testing. Prerequisite: at least an undergraduate minor in mathematics. |
Trigonometry Workshops
Trigonometry
This semester, Math Services is offering a free, informal seven-week series of workshops to build students' intuition and skill in trigonometry.
These workshops afford students the opportunity to work collaboratively with one another to uncover the definitions, practices, and uses of trigonometry through a progression of small-group activities. On the seventh week, students will have the option of completing a certification test to affirm their successful completion of the workshop's objectives.
The workshops are offered at no cost, and students from any BSU course are invited to attend. The schedule, activities, and practice problems are given below.
Workshop materials and schedule
All workshops meet on Tuesday from 4:00—6:00 p.m. in the Academic Achievement Center Classroom on the dates listed below. |
Mathscribe
We offer free on-line Algebra I Lessons, Exercises, and Tests.
The lessons use dynamic graphing and guided discovery to strengthen and connect both
symbolic and visual reasoning. They give the student a hands-on visual introduction to all
important Algebra I topics, reinforced by standards based adaptive exercises and randomly
generated tests. All homework and tests are checked and graded automatically. |
Chapter 3: Graphs, Linear Equations, and Functions 3.1 The Rectangular Coordinate System 3.2 The Slope of a Line 3.3 Linear Equations in Two Variables Summary Exercises on Slopes and Equations of Lines 3.4 Linear Inequalities in Two Variables 3.5 Introduction to Functions
This is a very good copy with slight wear. The dust jacket is included if the book originally was published with one and could have very slight tears and rubbing.
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Math e-Books for $0
[29 Aug 2011]
Most of the following free (or low cost) math e-books are PDF versions of ordinary math books.
You probably won't find your assigned text book here, but you'll find something that is pretty close. And for the millions of keen students who cannot afford the high price of math text books, this will be a valuable list.
Copyright information: It's not clear if copyright permission has been granted in some of these collections. In some cases, the business model involves advertising throughout the book (but the quality tends to be higher). In Google Books' case, for many of the books, they've been given permission to show selected pages only.
Google Books
Google wanted to digitize every book in the world, but not surprisingly, they ran up against copyright issues. Many of these books are not complete, but can still be very useful for that nugget of information you're looking for. |
Mora covers the classical theory of finding roots of a univariate polynomial, emphasising computational aspects. He shows that solving a polynomial equation really means finding algorithms that help one manipulate roots rather than simply computing them; to that end he also surveys algorithms for factorizing univariate polynomials. more... |
Consumer Math develops consumer skills in a biblical framework. It was written with the hope and prayer that students would know Christ as Savior, grow in their knowledge of Him, and understand the value of mathematics for their Christian growth and service. Bible verses and applications are included throughout, and each chapter has an in-depth Bible study on stewardship. These features include a mathematics-related theme verse, which you may want your students to memorize. The text is designed to be flexible. It is intended to meet needs of various teachers and teaching goals. Since each class is unique and students have varying abilities, the teacher should adapt the materials to his students. Determine which sections will demand extra time and which sections will be skipped. Select resources and ideas from this Teacher's Edition that are appropriate for the students. |
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Reading Math
My Algebra II kids don't like to read the textbook. Heck, neither do my calculus students. This isn't surprising. It's extra work and it's hard. My class also makes it hard for them, because I do not use the textbook as a skeletal structure for the course. I teach mainly out of my own materials, and use the book more as a supplement.
But that doesn't mean that I don't want them reading math. Kids are never taught to "read" a math textbook. If they ever do approach a math textbook, they approach it like a history book. The read it linearly. They also read it passively. Their eyes glaze over. They read words, but they don't try to connect the words to the equations or pictures. They don't read with a pencil in their hands. They hope for some Divine Knowledge to descend upon them simply by having the book open and their eyes on it.
That doesn't work. We all know this. Reading math is an active thing.
And so recently I've started talking with my class about it. To start this process/discussion, one that I hope continues, I gave my students a worksheet to fill out (see above). I love the honesty with which they responded.
For question A, some representative responses:
"I read what was assigned to me but did not read anything extra."
"I find that textbook reading is pretty boring, so I don't do it unless I have to."
"I did not because I had assumed I wouldn't learn things I needed. All I would do was look at examples."
"No, I find it difficult to understand math when reading it in paragraphs; it makes more sense to me with a teacher."
"I did not generally read my math textbooks. I did, however, always look over the example problems."
Some responses for Question B:
1. The writing can be confusing, wordy, and not thorough
2. The book is BORING
3. Small print
4. Too many words for math
5. Outdated examples
Some responses for Question C
1. Everything is all in one place
2. Have a glossary
3. Can read at own pace; refer pack to the text when I get stuck
4. Sidenotes! Diagrams! Pictures
5. Real life examples
6. Definitions clear
7. Key terms are highlighted
8. Wide range of example problems with step by step instructions
9. Colors!
I hope to do more as we go along. I might have them learn on their own, using the textbook (and the online video help) a whole section or two. There's no reason they can't learn to use the book to be independent learners. I will give them class time and photocopies of the section they need to learn, and they will have to figure things out by the end of the class for a 3 question quiz.
I also hope that by the end of the year, we can use their critique of math textbooks for them to write their own textbook. Okay, okay, not quite. That's way too ambitious for me. Two years ago I had my Algebra II kids write really comprehensive Study Guides for the final exam. This year I might ask my kids to pick some of the hardest material and create their own "textbook" for it. They'll get to write it in pairs, and then they can share their finished product with the rest of the class. That will probably happen in the 3rd for 4th quarter.
Anyway, I thought I'd share. Since I like to emphasize the importance of mathematical communication to my kids (though I don't do it nearly enough), I thought I'd talk about this one additional component in addition to getting students to talk and write math… READING MATH!
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3 thoughts on "Reading Math"
I found that reading "How to read a book" by Mortimer J Adler really helped me learn how to read a book I intended (or needed to) learn from. Most people (according to the book, and I agree) never learn to read beyond an elementary level, and this book teaches you how to read at a higher level. Works really well when you start using the techniques and such while reading the book. I'd encourage you to check it out.
My son has learned most of his math from reading books—he finds classroom instruction excruciatingly slow and has a hard time staying alert. He does sometimes need an explanation different from the one in the book, which (so far) I've been able to provide for him. Unlike your students, he finds the colors, sidebars, and gratuitous pictures distracting rather than helpful. So far, the best books for him have been from the Art of Problem Solving series, which have very clear but concise explanations.
I think that reading speed makes a big difference: kids who read slower than talking speed have a harder time gathering information from books than from oral presentation.
I still remember that linear algebra class I took at the local college. The prof taught the value of sloooooow reading. (it ruined his ability to read a novel at a fast pace) I turned this into a lesson. |
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Learning algebra can be tricky. Just when you finally feel like you have mastered the art of numbers, they decide to throw all these letters into the mix just to confuse you. Don't worry, we have just the tools to help you understand what these X's and Y's are all about.
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On MindBites, there are a wide range of Algebra I topics to choose from include multiplying integers, graphing lines and equations, finding common factors, simplifying radicals, multiplying polynomials, and much more. All the lessons include Algebra I problems so you can practice along. Yourteacher.com has 40 Algebra I lessons available which can be purchased individually or as a series.
The MindBites family would wish you luck, but we don't think you need any! We are positive that once you are done with these series, you will be an Algebra I Whiz. Need help with more advanced algebra material? We have that too. Check out the Algebra subcategory on the MindBites site to find all your algebra tutorial needs. |
This is a course in the algebra of matrices and Euclidean spaces that emphasizes the concrete and geometric. Topics to be developed include: solving systems of linear equations; matrix addition, scalar multiplication,
and
multiplication, properties of invertible matrices; determinants; elements of the theory of abstract finite dimensional real vector spaces; dimension of vector spaces; and the rank of a matrix. These ideas are used to
develop
basic ideas of Euclidean geometry and to illustrate the behavior of linear systems. We conclude with a discussion of eigenvalues and the diagonalization of matrices. For a more conceptual treatment of linear algebra,
students
should enroll in MATH223.
MAJOR READINGS
To be announced.
EXAMINATIONS AND ASSIGNMENTS
Two midterm exams, homework assignments, final exam for most sections, various problem sets and occasional quizzes for some sections. Students will take midterm exams at 7:30 p.m. on Monday, October 10 and Wednesday,
Novmber 16.
ADDITIONAL REQUIREMENTS and/or COMMENTS
MATH121, 122 or the high school equivalent is strongly recommended as background, but not required. |
MichMATYC 2002 Presenters
Haitham Al
Khateeb, University of
Indianapolis
Title: Undergraduate
studentsí understanding of division of fractions
Strands: Teacher
Preparation† 1-hour session
Abstract:† This
research study was designed to assess undergraduate students' understanding of
division of fractions. A paper and pencil instrument was administered as
a pre- and posttest to 59 undergraduate students who major in elementary
education. Analysis by independent t test of written responses provided
by students on the pre- and posttests showed lack of understanding, even
post-instruction.
John
Dersch, Grand Rapids CC
Title: Ahhh, the good old days:
The First 250 Years of Mathematics in America.†† 1-hour session
Strands: History of Mathematics†
Abstract:† What was mathematics like in America in 1700? In 1800? What
topics were taught at the college level? In the lower grades? What
were the textbooks like? What was the instruction like? What kind
of research was being done? How thorough was teacher training? Come
and find out! †Representative examples
of 18th and 19th century textbooks will be available for your perusal.
Jim
Ham, Delta College †Title: An Emerging Assessment Program†† 1-hour session
Strands: Assessment
Abstract: Delta College has been working on its assessment program for ten
years. This emerging model includes assessment at the classroom, course
and program levels. The mathematics faculty are involved in assessment
projects at all three levels. The presenter will provide updates of these
projects. In addition, the presenter will share successes, failures, and
some positive unintended consequences that resulted from the department's
engagement in assessment activities. Come share your own college's assessment
successes and challenges.
Barbara Jur, Macomb CC
Title:† "The Lens of the Udjat
Eye"†††† 1-hour session
Strands: History of Mathematics, applications/enrichment, and
developmental mathematics.
Abstract: Egypt has produced some important and useful mathematics, both
practical and instructive. From the use of unit fractions which the Greeks used
to practical geometry to study texts, the mathematics of the Nile region is
still of interest today. New discoveries and speculations are still being made
about what the ancients knew about mathematics.
Doug Mace, Kirtland CC
Title: Introduction to the MathWorks Project†††
1-hour session
Strands:† Application/Enrichment
Abstract:† Mathworks is an
interdisciplinary collection of open-ended laboratories designed by community
college mathematics faculty. Results of the usage of these laboratories
at Kirtland Community College will be discussed along with an introduction to
selected laboratories.
Jeff Morford, Henry Ford Community College
Title: Conclusions of Henry Ford Community College's Developmental Education
Task Force
Strands: Developmental Mathematics
Abstract: HFCC spent the last year reviewing its developmental program
campus wide. Come find out some of the conclusions we reached and some
changes we are planning. Find out what resources- colleges, articles and
books- that we used in crafting our report. Finally share what is new in
developmental math on your campus.
Kathy Mowers, Owensboro CC, Owensboro, KY
Title: Online Elementary Algebra: Can it work? †† 1-hour session
Strands: Developmental Mathematics, Distance Learning
Abstract: This presentation will focus on the presenter's experiences
teaching elementary algebra online including successes, challenges, and format.
It will also include her thoughts on ways to web-enhance other mathematics
courses, students' comments and her impressions and experiences.
Chuck Nicewonder, Owens CC, Toledo, Ohio
Title: Humor in the Mathematics Classroom?*.But Seriously†† 1-hour session
Strands: Articulation Abstract: This presentation will explore humor as a
necessary and fun component of any math class. Math-related jokes and other
bits of humor relating to various levels of mathematics, as well as their use
in the classroom and their effect on student performance, will be presented and
discussed. There will be time for input and discussion by all those in
attendance.
Jeffrey A. Oaks, University of Indianapolis
Title: Algebra and Inheritance in 9th Century Baghdad† 1-hour session
Strands: History of Mathematics
Abstract: To properly assess a medieval mathematical text we need to consider
both its relationship to previous works in the same field, and to the social
setting in which the work was produced. I will be examining the _Algebra_
of al-Khwarizmi from these perspectives. This will allow us to see not
only what is innovative and what is not in his work, but why he took his
particular approach to the subject.
Ann Savonen, Monroe County Community College
Title: Less Lecture = More Fun
Strands: Teacher
Preparation† 1-hour session Abstract: Do your math students love listening to long
lectures with lots of abstract concepts, theory, and definitions? Do long
reading assignments with the same information get them even more excited? If
so, do not come to this session. This session will present the idea of a
curriculum which minimizes lecture and the reading of long boring
textbooks. Instead, it encourages discovery, interaction, discussion,
hands-on experience, and fun. And yes, they will learn too!
Randy Schwartz, Schoolcraft College
Title:† Making Historical Arab
Mathematics Come Alive††† 1-hour session
Strands: History of Mathematics, Multicultural Mathematics
Abstract: Our curricula have scarcely acknowledged the scientific contributions
of non-European people.† My slideshow
illustrates why the medieval Arab world soared in mathematics.† Iíll also share activities whereby students
in Finite Math, Statistics, Linear Algebra and Business Calculus can use these
techniques to solve problems in combinatorics, linear modeling, and
optimization.
Abstract: Learn how
to use and incorporate new and exciting TI-83 + applications into your current
Algebra classes.† You will learn how to
use Algebra I, Inequalities, Transformations, Finance, and Polynomial Root
Finder Applications to motivate students and teach algebra more effectively.
Gwen Terwilliger, University of Toledo
Title:† Trials and Tribulations of
Teaching Math via Distance Learning†††
2-hour workshop
Strands: Distance Learning
Abstract:† Distance Learning encompasses
a wide variety of methods from videos to interactive multi-media Internet
presentation.† What works for one course
and/or instructor does not necessarily mean it will work for the next course
and/or instructor Ė or even for that same course and instructor for the next
group of students.† Also, distance
learning as a means for students to be able to complete their college education
is an excellent tool.† But, that does
not mean that all students will be able to succeed in this type of learning
environment any more than all students have†
one learning style.†† A successful
distance learning course takes at least or more time than teaching in a
traditional classroom.† This means that
any instructor planning or currently teaching a distance-learning course needs
1. careful planning of course, 2. ongoing assessment of the course, the
presentation, the students, etc., 3. immediate evaluation after the course is
completed for needed changes, and 4. constant learning about distance
learning† from what is available, what
works (and does not work) for others, about the students taking the course,
etc. This presentation will discuss a variety of resources and ideas for
teaching math via the Internet. Participants will be able to access some of the
Internet sites.
Mario F. Triola, Dutchess CC
Title:† Issues in Teaching
Statistics†† †††1-hour session
Strands:† Probability/Statistics
Abstract:† Why divide by n-1 for
standard deviation?† Why not use mean
absolute deviation?† What features make
a statistics course effective?† Which
technology should be used?† Are projects
important?† Which topics can be
omitted?† These and other important
issues facing statistics teachers will be discussed.
Deborah Zopf and Anna Cox, Henry Ford CC, Kellogg
CC
Title:† Letís Talk: Conversations about
Math for Elementary Teachers Courses††
1-hour session
Strands:† Teacher Preparation;
Collaboration Learning/ Learning Communities
Abstract:† This session will be an
informal conversation focused on Mathematics for Elementary Teachers
courses.† Participants will be
encouraged to bring ideas that they have employed while teaching these courses.
Highlights from the AMATYC Summer Session on Teacher Preparation will be given. |
Other Materials
Description
Algebra 1 will weave together a variety of concepts, procedures, and processes in mathematics including basic algebra, geometry, statistics and probability. Students will develop the ability to explore and solve mathematical problems, think critically, work cooperatively with others, and communicate their ideas clearly as they work through these mathematical concepts |
Syllabus Structure and Content
3.1 INTRODUCTION
The way in which the mathematical content in the syllabuses is organised and presented in the syllabus document is described in sections 3.2 and 3.3. Section 3.3 also discusses the main alterations, both in content and in emphasis, with respect to the preceding versions. The forthcoming changes in the primary curriculum, which will have "knock-on" effects at second level, are outlined in Section 3.4. Finally, in Section 3.5, the content is related to the aims of the syllabuses.
3.2 STRUCTURE
For the Higher and Ordinary level syllabuses, the mathematical material forming the content is divided into eight sections, as follows:
Sets
Number systems
Applied arithmetic and measure
Algebra
Statistics
Geometry
Trigonometry
Functions and graphs
The corresponding material for the Foundation level syllabus is divided into seven sections; there are minor differences in the sequence and headings, resulting in the following list:
Sets
Number systems
Applied arithmetic and measure
Statistics and data handling
Algebra
Relations, functions and graphs
Geometry
The listing by content area is intended to give mathematical coherence to the syllabuses, and to help teachers locate specific topics (or check that topics are not listed). The content areas are reasonably distinct, indicating topics with different historical roots and different main areas of application. However, they are inter-related and interdependent, and it is not intended that topics would be dealt with in total isolation from each other. Also, while the seven or eight areas, and the contents within each area, are presented in a logical sequence combining, as far as possible, a sensible mathematical order with a developmental one for learners it is envisaged that many content areas listed later in the syllabus would be introduced before or alongside those listed earlier. (For example, geometry appears near the end of the list, but the course committee specifically recommends that introductory geometrical work is started in First Year, allowing plenty of time for the ideas to be developed in a concrete way, and thoroughly understood, before the more abstract elements are introduced.) However, the different order of listing for the Foundation level syllabus does reflect a suggestion that the introduction of some topics (notably formal algebra) might be delayed. Some of these points are taken up in Section 4.
Appropriate pacing of the syllabus content over the three years of the junior cycle is a challenge. Decisions have to be made at class or school level. Some of the factors affecting the decisions are addressed in these Guidelines in Section 4, under the heading of planning and organisation.
3.3 SYLLABUS CONTENT
The contents of the Higher, Ordinary and Foundation level syllabuses are set out in the corresponding sections of the syllabus document. In each case, the content is presented in the two-column format used for the Leaving Certificate syllabuses introduced in the 1990s, with the lefthand column listing the topics and the right-hand column adding notes (for instance, providing illustrative examples, or highlighting specific aspects of the topics which are included or excluded). Further illustration of the depth of treatment of topics is given in Section 5 (in dealing with assessment) and in the proposed sample assessmentmaterials (available separately).
CHANGES IN CONTENT
As indicated in Section 1, the revisions deal only with specific problems in the previous syllabuses, and do not reflect a root-and-branch review of the mathematics education appropriate for students in the junior cycle. The main changes in content, addressing the problems identified in Section 1, are described below. A summary ofall the changes is provided in Appendix 1.
Calculators and calculator-related techniques
As pointed out in the introduction to each syllabus, calculators are assumed to be readily available for appropriate use, both as teaching/learning tools and as computational aids; they will also be allowed in examinations.
The concept of "appropriate" use is crucial here. Calculators are part of the modern world, and students need to be able to use them efficiently where and when required. Equally, students need to retain and develop their feel for number, while the execution of mental calculations, for instance to make estimates, becomes even more important than it was heretofore. Estimation, which was not mentioned in the 1987 syllabus (though it was covered in part by the phrase "the practice of approximating before evaluating"), now appears explicitly and will be tested in examinations.
The importance of the changes in this area is reflected in two developments. First, a set of guidelines on calculators is being produced. It addresses issues such as the purchase of suitable machines as well as the rationale for their use. Secondly, in 1999 the Department of Education and Science commissioned a research project to monitor numeracy-related skills (with and without calculators) over the period of introduction of the revised syllabuses. If basic numeracy and mental arithmetic skills are found to disimprove, remedial action may have to be taken. It is worth noting that research has not so far isolated any consistent association between calculator use in an education system and performance by students from that system in international tests of achievement.
Mathematical tables are not mentioned in the content sections of the syllabus, except for a brief reference indicating that they are assumed to be available, likewise for appropriate use. Teachers and students can still avail of them as learning tools and for reference if they so wish. Tables will continue to be available in examinations, but questions will not specifically require students to use them.
Geometry
The approach to synthetic geometry was one of the major areas which had to be confronted in revising the syllabuses. Evidence from examination scripts suggested that in many cases the presentation in the 1987 syllabus was not being followed in the classroom. In particular, in the Higher level syllabus, the sequence of proofs and intended proof methods were being adapted. Teachers were responding to students' difficulties in coping with the approach that attempted to integrate transformational concepts with those more traditionally associated with synthetic geometry, as described in Section 1.1 of these Guidelines.
For years, and all over the world, there have been difficulties in deciding how indeed, whether to present synthetic geometry and concepts of logical proof to students of junior cycle standing. Their historical importance, and their role as guardians of one of the defining aspects of mathematics as a discipline, have led to a wish to retain them in the Irish mathematics syllabuses; but the demands made on students who have not yet reached the Piagetian stage of formal operations are immense. "Too much, too soon" not only contravenes the principle of learnability (section 2.5), but leads to rote learning and hence failure to attain the objectives which the geometry sections of the syllabuses are meant to address. The constraints of a minor revision precluded the question of "whether" from being asked on this occasion. The question of "how" raises issues to do with the principles of soundness versus learnability. The resulting formulation set out in the syllabus does not claim to be a full description of a geometrical system. Rather, it is intended to provide a defensible teaching sequence that will allow students to learn geometry meaningfully and to come to realise the power of proof. Some of the issues that this raises are discussed in Appendix 2.
The revised version can be summarised as follows.
The approach omits the transformational elements, returning to a more traditional approach based on congruency.
In the interests of consistency and transfer between levels, the underlying ideas are basically the same across all three syllabuses, though naturally they are developed to very different levels in the different syllabuses.
The system has been carefully formulated to display the power of logical argument at a level which hopefully students can follow and appreciate. It is therefore strongly recommended that, in the classroom, material is introduced in the sequence in which it is listed in the syllabus document. For theHigher level syllabus, the concepts of logicalargument and rigorous proof are particularlyimportant. Thus, in examinations, attempted proofsthat presuppose "later" material in order to establish"earlier" results will be penalised. Moreover, proofsusing transformations will not be accepted.
To shorten the Higher level syllabus, only some of the theorems have been designated as ones for which students may be asked to supply proofs in the examinations. The other theorems should still beproved as part of the learning process;students should be able to follow the logical development, and see models of far more proofs than they are expected to reproduce at speed under examination conditions. The required saving of time is expected to occur because students do not have to put in the extra effort needed to develop fluency in writing out particular proofs.
Students taking the Ordinary and (a fortiori)Foundation level syllabuses are not required to prove theorems, but in accordance with the level-specific aims (Section 2.4) should experience the logical reasoning involved in ways in which they can understand it. The general thrust of the synthetic geometry section of the syllabuses for these students is not changed from the 1987 versions.
It may be noted that the formulation of the Foundation level syllabus in 1987 emphasised the learning process rather than the product or outcomes. In the current version, the teaching/learning suggestions are presented in theseGuidelines (chiefly in Section 4), not in the syllabus document. It is important to emphasise that the changed formulation in the syllabus is not meant to point to a more formal presentation than previously suggested for Foundation level students.
Section 4.9 of this document contains a variety of suggestions as to how the teaching of synthetic geometry to junior cycle students might be addressed.
Transformation geometry still figures in the syllabuses, but is treated separately from the formal development of synthetic geometry. The approach is intended to be intuitive, helping students to develop their visual and spatial ability. There are opportunities here to build on the work on symmetry in the primary curriculum and to develop aesthetic appreciation of mathematical patterns.
Other changes to the Higher level syllabus
Logarithms are removed. Their practical role as aids to calculation is outdated; the theory of logarithms is sufficiently abstract to belong more comfortably to the senior cycle.
Many topics are "pruned" in order to shorten the syllabus.
Other changes to the Ordinary level syllabus
The more conceptually difficult areas of algebra and coordinate geometry are simplified.
A number of other topics are "pruned".
Other changes to the Foundation level syllabus
There is less emphasis on fractions but rather more on decimals. (The change was introduced partly because of the availability of calculators though, increasingly, calculators have buttons and routines which allow fractions to be handled in a comparatively easy way.)
The coverage of statistics and data handling is increased. These topics can easily be related to students' everyday lives, and so can help students to recognise the relevance of mathematics. They lend themselves also to active learning methods (such as those presented in Section 4) and the use of spatial as well as computational abilities. Altogether, therefore, the topics provide great scope for enhancing students' enjoyment and appreciation of mathematics. They also give opportunities for developing suitably concrete approaches to some of the more abstract material, notably algebra and functions (see Section 4.8).
The algebra section is slightly expanded. The formal algebraic content of the 1987 syllabus was so slight that students may not have had scope to develop their understanding; alternatively, teachers may have chosen to omit the topic. The rationale for the present adjustment might be described as "use it or lose it". The hope is that the students will be able to use it, and that suitably addressed it can help them in making some small steps towards the more abstract mathematics which they may need to encounter later in the course of their education.
Overall, therefore, it is hoped that the balance between the syllabuses is improved. In particular, the Ordinary level syllabus may be better positioned between a more accessible Higher level and a slightly expanded Foundation level.
CHANGES IN EMPHASIS
The brief for revision of the syllabuses, as described in Section 1.2, precluded a root-and-branch reconsideration of their style and content. However, it did allow for some changes in emphasis: or rather, in certain cases, for some of the intended emphases to be made more explicit and more clearly related to rationale, content, assessment, and via the Guidelines methodology. The changes in, or clarification of, emphasis refer in particular to the following areas.
Understanding
General objectives B and C of the syllabus refer respectively to instrumental understanding (knowing "what" to do or "how" to do it, and hence being able to execute procedures) and relational understanding (knowing "why", understanding the concepts of mathematics and the way in which they connect with each other to form so-called "conceptual structures"). When people talk of teaching mathematics for or learning it with understanding, they usually mean relational understanding. The language used in the Irish syllabuses to categorise understanding is that of Skemp; the objectives could equally well have been formulated in terms of "procedures" and "concepts".
Research points to the importance of both kinds of understanding, together with knowledge of facts (general objective A), as components of mathematical proficiency, with relational understanding being crucial for retaining and applying knowledge. The Third International Mathematics and Science Study, TIMSS, indicated that Irish teachers regard knowledge of facts and procedures as particularly important unusually so in international terms; but it would appear that less heed is paid to conceptual/relational understanding. This is therefore given special emphasis in the revised syllabuses. Such understanding can be fostered by active learning, as described and illustrated in Section 4. Ways in which relational understanding can be assessed are considered in Section 5.
Communication
General objective H of the syllabus indicates that students should be able to communicate mathematics, both verbally and in written form, by describing and explaining the mathematical procedures they undertake and by explaining their findings and justifying their conclusions. This highlights the importance of students expressing mathematics in their own words. It is one way of promoting understanding; it may also help students to take ownership of the findings they defend, and so to be more interested in their mathematics and more motivated to learn.
The importance of discussion as a tool for ongoing assessment of students' understanding is highlighted in Section 5.2. In the context of examinations, the ability to show different stages in a procedure, explain results, give reasons for conclusions, and so forth, can be tested; some examples are given in Section 5.6.
Appreciation and enjoyment
General objective I of the syllabus refers to appreciating mathematics. As pointed out earlier, appreciation may develop for a number of reasons, from being able to do the work successfully to responding to the abstract beauty of the subject. It is more likely to develop, however, when the mathematics lessons themselves are pleasant occasions.
In drawing up the revised syllabus and preparing the Guidelines, care has been taken to include opportunities for making the teaching and learning of mathematics more enjoyable. Enjoyment is good in its own right; also, it can develop students' motivation and hence enhance learning. For many students in the junior cycle, enjoyment (as well as understanding) can be promoted by the active learning referred to above and by placing the work in appropriate meaningful contexts. Section 4 contains many examples of enjoyable classroom activities which promote both learning and appreciation of mathematics. Teachers are likely to have their own battery of such activities which work for them and their classes. It is hoped that these can be shared amongst their colleagues and perhaps submitted for inclusion in the final version of the Guidelines.
Of course, different people enjoy different kinds of mathematical activity. Appreciation and enjoyment do not come solely from "games"; more traditional classrooms also can be lively places in which teachers and students collaborate in the teaching and learning of mathematics and develop their appreciation of the subject. Teachers will choose approaches with whichthey themselves feel comfortable and which meet thelearning needs of the students whom they teach.
The changed or clarified emphasis in the syllabuses will be supported, where possible, by corresponding adjustments to the formulation and marking of Junior Certificate examination questions. While the wording ofquestions may be the same, the expected solutions may bedifferent. Examples are given in Section 5.
3.4 CHANGES IN THE PRIMARY CURRICULUM
The changes in content and emphasis within the revised Junior Certificate mathematics syllabuses are intended, inter alia, to follow on from and build on the changes in the primary curriculum. The forthcoming alterations (scheduled to be introduced in 2002, but perhaps starting earlier in some classrooms, as teachers may anticipate the formal introduction of the changes) will affect the knowledge and attitudes that students bring to their second level education. Second level teachers need to be prepared for this. A summary of the chief alterations is given below; teachers are referred to the revised Primary School Curriculum for further details.
CHANGES IN EMPHASIS
In the revised curriculum, the main changes of emphasis are as follows.
There is more emphasis on
setting the work in real-life contexts
learning through hands-on activities (using concrete materials/manipulatives, and so forth)
understanding (in particular, gaining appropriaterelational understanding as well as instrumentalunderstanding)
appropriate use of mathematical language
recording
problem-solving.
There is less emphasis on
learning routine procedures with no context provided
doing complicated calculations.
CHANGES IN CONTENT
The changes in emphasis are reflected in changes to the content, the main ones being as follows.
New areas include
introduction of the calculator from Fourth Class (augmenting, not replacing, paper-and-pencil techniques)
(hence) extended treatment of estimation;
increased coverage of data handling
introduction of basic probability ("chance").
New terminology includes
the use of the "positive" and "negative" signs for denoting a number (as in +3 [positive three], -6 [negative six] as well as the "addition" and "subtraction" signs for denoting an operation (as in 7 + 3, 24 9)
explicit use of the multiplication sign in formulae (as in 2 ×r , l ×w).
The treatment of subtraction emphasises the "renaming" or "decomposition" method (as opposed to the "equal additions" method the one which uses the terminology "paying back") even more strongly than does the 1971 curriculum. Use of the word "borrowing" is discouraged.
The following topics are among those excluded from the revised curriculum:
unrestricted calculations (thus, division is restricted to at most four-digit numbers being divided by at most two-digit numbers, and for fractions to division of whole numbers by unit fractions)
(Some of these topics were not formally included in the 1971 curriculum, but appeared in textbooks and were taught in many classrooms.)
NOTE
The reductions in content have removed some areas of overlap between the 1971 Primary School Curriculum and the Junior Certificate syllabuses. Some overlap remains, however. This is natural; students entering second level schooling need to revise the concepts and techniques that they have learnt at primary level, and also need to situate these in the context of their work in the junior cycle.
3.5 LINKING CONTENT AREAS WITH AIMS
Finally, in this section, the content of the syllabuses is related to the aims and objectives. In fact most aims and objectives can be addressed in most areas of the syllabuses. However, some topics are more suited to the attainment of certain goals or the development of certain skills than are others. The discussion below highlights some of the main possibilities, and points to the goals that might appropriately be emphasised when various topics are taught and learnt. Phrases italicised are quoted or paraphrased from the aims as set out in the syllabus document. Section 5 of these Guidelines indicates a variety of ways in which achievement of the relevant objectives might be encouraged, tested or demonstrated.
SETS
Sets provide a conceptual foundation for mathematics and a language by means of which mathematical ideas can be discussed. While this is perhaps the main reason for which set theory was introduced into school mathematics, its importance at junior cycle level can be described rather differently.
Set problems, obviously, call for skills of problem-solving; in particular, they provide occasions for logical argument. By using data gathered from the class, they even offer opportunities for simple introduction to mathematical modelling in contexts to which the students can relate.
Moreover, set theory emphasises aspects of mathematics that are not purely computational. Sets are about classification, hence about tidiness and organisation. This can lead toappreciation of mathematics on aesthetic grounds and can help to provide a basis forfurther education in the subject.
An additional point is that this topic is not part of the Primary School Curriculum, and so represents a new start, untainted by previous failure. For some students, therefore, there are particularly important opportunities for personal development.
NUMBER SYSTEMS
While mathematics is not entirely quantitative, numeracy is one of its most important aspects. Students have been building up their concepts of numbers from a very early stage in their lives. However, moving from familiarity with natural numbers (and simple operations on them) to genuine understanding of the various forms in which numbers are presented and of the uses to which they are put in the world is a considerable challenge.
Weakness in this area destroys students' confidence andcompetence by depriving them of theknowledge, skillsand understanding needed for continuing theireducation and for life and work. It therefore handicaps their personal fulfilment and hencepersonaldevelopment.
The aspect of "understanding" is particularly important or, perhaps, has had its importance highlighted with advances in technology.
Students need to become familiar with the intelligent and appropriate use of calculators, while avoiding dependence on the calculators for simple calculations.
Complementing this, they need to develop skills in estimation and approximation, so that numbers can be used meaningfully.
APPLIED ARITHMETIC AND MEASURE
This topic is perhaps one of the easiest to justify in terms of providing mathematics needed for life, workand leisure.
Students are likely to use the skills developed here in "everyday" applications, for example in looking after their personal finances and in structuring the immediate environment in which they will live. For many, therefore, this may be a key section in enabling studentsto develop a positive attitude towards mathematics as avaluable subject of study.
There are many opportunities for problem-solving, hopefully in contexts that the students recognise as relevant.
The availability of calculators may remove some of the drudgery that can be associated with realistic problems, helping the students to focus on the concepts and applications that bring the topics to life.
ALGEBRA
Algebra was developed because it was needed because arguments in natural language were too clumsy or imprecise. It has become one of the most fundamental tools for mathematics.
As with number, therefore, confidence andcompetence are very important. Lack of these underminethepersonal development of the students by depriving them of the knowledge, skills and understanding needed forcontinuing their education and for life and work.
Without skills in algebra, students lack the technical preparation for study of other subjects in school, and in particular their foundation for appropriate studies lateron including further education in mathematics itself.
It is thus particularly important that students develop appropriate understanding of the basics of algebra so that algebraic techniques are carried out meaningfully and not just as an exercise in symbol-pushing.
Especially for weaker students, this can be very challenging because algebra involves abstractions andgeneralisations.
However, these characteristics are among the strengths and beauties of the topic. Appropriately used, algebra can enhance the students' powers of communication, facilitate simplemodelling and problem-solving, and hence illustrate the power of mathematics as a valuablesubject of study.
STATISTICS
One of the ways in which the world is interpreted for us mathematically is by the use of statistics. Their prevalence, in particular on television and in the newspapers, makes them part of the environment in which children grow up, and provides students with opportunities for recognition and enjoyment of mathematics in the worldaround them.
Many of the examples refer to the students' typical areas of interest; examples include sporting averages and trends in purchases of (say) CDs.
Students can provide data for further examples from their own backgrounds and experiences.
Presenting these data graphically can extend students'powers of communication and their ability to shareideas with other people, and may also provide anaesthetic element.
The fact that statistics can help to develop a positiveattitude towards mathematics as an interesting andvaluable subject of study even for weaker students who find it hard to appreciate the more abstract aspects of the subject explains the extra prominence given to aspects of data handling in the Foundation level syllabus, as mentioned earlier. They may be particularly important in promotingconfidence and competence in both numerical and spatial domains.
GEOMETRY
The study of geometry builds on the primary school study of shape and space, and hence relates to mathematics in the world around us. In the junior cycle, different approaches to geometry address different educational goals.
More able students address one of the greatest of mathematical concepts, that of proof, and hopefully come to appreciate theabstractions andgeneralisations involved.
Other students may not consider formal proof, but should be able to draw appropriate conclusions from given geometrical data.
MATHEMATICS
Explaining and defending their findings, in either case, should help students to further their powersof communication.
Tackling "cuts" and other exercises based on the geometrical system presented in the syllabus allows students to develop their problem-solving skills.
Moreover, in studying synthetic geometry, students are encountering one of the great monuments to intellectual endeavour: a very special part of Western culture.
Transformation geometry builds on the study of symmetry at primary level. As the approach to transformation geometry in the revised Junior Certificate syllabus is intuitive, it is included in particular for its aesthetic value.
With the possibility of using transformations in artistic designs, it allows students to encounter creative aspectsof mathematics and to develop or exercise their own creative skills.
It can also develop their spatial ability, hopefully promotingconfidence and competence in this area.
Instances of various types of symmetry in the natural and constructed environment give scope for students' recognition and enjoyment of mathematics in the worldaround them.
Coordinate geometry links geometrical and algebraic ideas. On the one hand, algebraic techniques can be used to establish geometric results; on the other, algebraic entities are given pictorial representations.
Its connections with functions and trigonometry, as well as algebra and geometry, make it a powerful tool for the integration of mathematics into a unified structure.
It illustrates the power of mathematics, and so helps to establish it with students as a valuable subject of study.
It provides an important foundation for appropriatestudies later on.
The graphical aspect can add a visually aestheticdimension to algebra.
TRIGONOMETRY
Trigonometry is a subject that has its roots in antiquity but is still of great practical use to-day. While its basic concepts are abstract, they can be addressed through practical activities.
Situations to which it can be applied for example, house construction, navigation, and various ball games include many that are relevant to the students' life, work and leisure.
It can therefore promote the students' recognition andenjoyment of mathematics in the world around them.
With the availability of calculators, students may more easily develop competence and confidence through their work in this area.
FUNCTIONS AND GRAPHS
The concept of a function is crucial in mathematics, and students need a good grasp of it in order to prepare a firm foundation for appropriate studies lateron and in particular, a basis for further education inmathematics itself.
The representation of functions by graphs adds a pictorial element that students may find aesthetic as well as enhancing their understanding and their abilityto handle generalisations.
This topic pulls together much of the groundwork done elsewhere, using the tools introduced and skills developed in earlier sections and providing opportunities forproblem-solving and simple modelling.
For Foundation students alone, simple work on the set-theoretic treatment of relations has been retained. In contexts that can be addressed by those whose numerical skills are poor, it provides exercises in simple logical thinking.
NOTE
The foregoing argument presents just one vision of the rationale for including the various topics in the syllabus and for the ways in which the aims of the mathematics syllabus can be achieved. All teachers will have their own ideas about what can inspire and inform different topic areas. Their own personal visions of mathematics, and their particular areas of interest and expertise, may lead them to implement the aims very differently from the way that is suggested here. Visions can profitably be debated at teachers' meetings, with new insights being given and received as a result.
The tentative answers given here with regard to whycertain topics are included in the syllabus are, of course, offered to teachers rather than junior cycle students. In some cases, students also may find the arguments relevant. In other cases, however, the formulation is too abstract or the benefit too distant to be of interest. This, naturally, can cause problems. Clearly it would not be appropriate to reduce the syllabus to material that has immediately obvious applications in the students' everyday lives. This would leave them unprepared for further study, and would deprive them of sharing parts of our culture; in any case, not all students are motivated by supposedly everyday topics.
Teachers are therefore faced with a challenging task in helping students find interest and meaning in all parts of the work. Many suggestions with proven track records in Irish schools are offered in Section 4. As indicated earlier, it is hoped that teachers will offer more ideas for an updated version of the Guidelines. |
A Level Maths Core 2 Collins Student Support Materials for Edexcel AS Maths Core 2 covers all the content and skills your students will need for their Core 2 examination, including: * Algebra and functions * Coordinate geometry in the (x, y) plane * Sequences and series * Trigonometry * Exponentials and logarithms * Differentiation * Integration * EXAM PRACTICE * Answers |
Pre-Algebra
"Glencoe Pre-Algebra" is focused, organized, and easy to follow. The program shows your students how to read, write, and understand the unique ...Show synopsis"Glencoe Pre-Algebra" is focused, organized, and easy to follow. The program shows your students how to read, write, and understand the unique language of mathematics, so that they are prepared for every type of problem-solving and assessment situation |
Computer algebra system
A computer algebra system (CAS) is a software program that facilitates symbolic mathematics. The core functionality of a CAS is manipulation of mathematical expressions in symbolic form.
The expressions typically include polynomials in multiple variables; standard functions of expressions (sin, exponential, etc.); arbitrary functions of expressions; integrals, sums, and products of expressions; truncated series with expressions as coefficients, matrices of expressions, and so on. (This is a recursive definition.)
The symbolic manipulations supported typically include
simplification
substitution of symbolic or numeric values for expressions
change of form of expressions: expanding products and powers, rewriting as partial fractions, etc.
Many also include a high level programming language, allowing users to implement their own algorithms.
The study of algorithms useful for computer algebra systems is known as computer algebra.
The run-time of numerical programs implemented in computer algebra systems is normally longer than that of equivalent programs implemented in systems such as MATLAB, GNU Octave, or directly in C, since they are programmed for full symbolic generality and thus cannot use machine numerical operations directly.
History
Computer algebra systems began to appear in the early 1970s, and evolved out of research into artificial intelligence, though the fields are now regarded as largely separate. The first popular systems were Reduce, Derive, and Macsyma which are still commercially available; a copyleft version of Macsyma called Maxima is actively being maintained. The current market leaders are Maple and Mathematica; both are commonly used by research mathematicians, scientists, and engineers. MuPAD is a commercial system, also available in a free version with slightly restricted user interface for non-commercial research and educational use. Some computer algebra systems focus on a specific area of application; these are typically developed in academia and |
,
Title Description:
The Trachtenberg Speed System of Basic Mathematics
Author : Jakow Trachtenberg adapted by Ann Cutler and Rudolph Mcshane
Bibliography : None
PaperBack : ISBN : 0285629166
Price: 24.95
Price: US $ 24.95
Details
The Trachtenberg Speed System of Basic Mathematics
Price: US $ 24.95
Book Background
Jakow Trachtenberg created the Trachtenberg system of mathematics, whilst a political prisoner in Hilter's concentration camps during the Second World War To keep himself sane whilst living in an extremely brutal and harsh environment, Trachtenberg immersed his mind in a world of mathematics and calculations. As concentration camps do not provide books, paper, pen or pencils nearly all of his calculations had to be performed mentally. This forced Trachtenberg to develop methods and shortcuts for performing calculations mentally. Trachtenberg developed his discoveries into a complete system of mathematics.
After the Second World War, Trachtenberg started teaching his system of mathematics. He started teaching the more backward children to prove that anyone could learn his system. In 1950 he founded the Mathematical Institute in Zurich, where both children and adults were taught the system.
The system has been thoroughly tested in Switzerland and is found to produce an increase in self confidence and general aptitude to study, as the students prove to themselves what they are capable of, by their accomplishments in calculating results to computations.
The Trachtenberg system is based on a series of keys which must be memorized. There is no need for multiplication tables or division as the system only relies on the ability to count. The system also places an emphasis on getting the right answer and provides a number of methods for checking the answers achieved by the system.
Research on the system, indicates that the system shortens time for mathematical computations by twenty percent and produces correct results, ninety nine percent of the time, due to the checking method used as part of the system. |
Normal 0 false false false The Sullivan/Struve/Mazzarella Algebra Series was written to motivate students to "do the math" outside of the classroom through a design and organization that models what you do inside the classroom. The left-to-right annotations in the examples provide a t... |
A formal framework to convey ideas about the components of a host-parasite interaction. Construction requires three major types of information: (a) a clear understanding of the interaction within the individual host between the infectious agent and the host, (b) the mode and rate of transmission between individuals, and (c) host population characteristics such as demography and behaviour. Mathematical models can aid exploration of the behaviour of the system under various conditions from which to determine the dominant factors generating observed patterns and phenomena. They also aid data collection and interpretation and parameter estimation, and provide tools for identifying possible approaches to control and for assessing the potential impact of different intervention measures.
Related Topics: [ model] A set of mathematical equations which attempts to predict the behavior of a physical system(s). For example, the Rational Formula, Q = Cia, is a mathematical model for peak runoff rate prediction with a single dependent variable, Q, and three independent parameter s: C, i and A. Often the term "simulation model" is used in lieu of mathematical model, because the relationships are intended to simulate actions of physical systems.
An abstraction of a real-world problem into a mathematical problem. Creating a mathematical model can involve making assumptions and simplifications; creating geometric figures, graphs, and tables; or finding equations that approximate the behavior of a real event. The mathematical problem can then be solved. When the solution is interpreted it may provide a solution to the real-world problem (Lesson 1.6). |
Algebraic Videogame Programming
Bootstrap is a FREE curriculum for students ages 12-16, which teaches them to program their own videogames using purely algebraic and geometric concepts.
Our mission is to use students' excitement and confidence around gaming to directly apply algebra to create something cool.
We work with schools, districts and tech-educational programs across the country, reaching hundreds of students each semester. Bootstrap has been integrated into math and technology classrooms across the country, reaching thousands of students since 2006.
Programming. Not just writing code.
Knowing how to write code is good, but it doesn't make you a programmer.
Sure, Bootstrap teaches students a programming language. But most
importantly, it teaches solid program design skills, such as
stating input and types, writing test cases, and explaining code to others.
Bootstrap builds these elements into the curriculum in a gentle way
that helps students move from a word problem to finished code.
After Bootstrap, these skills can be put to use in other programming environments, letting students take what they've learned into other programming classes.
Watch the video to hear students, engineers, teachers, and the Bootstrap team describe what excites them about Bootstrap!
Real, Standards-Based Math
Unlike most programming classes, Bootstrap uses algebra as the vehicle for creating images and animations. That means that concepts students encounter in Bootstrap behave the exact same way that they do in math class. This lets students experiment with algebraic concepts by writing functions that make a rocket fly (linear equations), respond to keypresses (piecewise functions) or make it explode when it hits a meteor (distance formula). In fact, many word problems from standard math textbooks can be used as as programming assignments!
The entire curriculum is designed from the ground up to be aligned with Common Core standards for algebra. Bootstrap lessons cover mathematical topics that range from simple arithmetic expressions to the Pythagorean Theorem, Discrete Logic, Function Composition and the Distance Formula. The program is based on cognitive science research and best practices for improving critical thinking and problem solving.
""
—
Our team
Bootstrap is the creation of Emmanuel Schanzer, M.Ed. (in the hat). After earning a bachelors of Computer Science (Cornell University), he worked in the private sector for a number of years as a programmer (Microsoft, Vermonster, and others) until he switched careers and became a math teacher, starting out in Boston Public Schools. He is now a doctoral student at the Harvard Graduate School of Education.
Our Supporters
We would like to thank the following, for their volunteer and financial support over the years: Apple, Cisco, the Entertainment Software Association (ESA), Facebook, Google, as well as the Google Inc. Charitable Giving Fund of Tides Foundation, IBM, Jane Street Capital, LinkedIn, Microsoft, The National Science Foundation, NVIDIA, Thomson/Reuters, and the generous individuals who have given us private donations.
If you would like to support Bootstrap with a donation, send a check made out to Brown University to our PI, Shriram Krishnamurthi,
at his mailing address. Be sure to include this letter, indicating that you wish for the funds to be put towards Bootstrap. Once your check is received, we'll send you a reciept for your tax records. |
Quizzes and tests will contain two sections: one with the use of a calculator and one without the use of a calculator. Calculators may not be used on multiple choice questions. This is to parallel the NYS Mathematics Exam.
Partial credit may be obtained for correct procedures, even though your final answer may be incorrect due to a computational error. Please be sure to show all work!!
WHAT SUPPLIES DO I NEED TO BRING EACH DAY?
§Sharpened PENCILS with erasers §3-ring binder with loose-leaf paper
§Current Unit Packet
§Agenda
§Composition notebook (kept in our classroom)
§Textbook should be kept in class!
§Scientific calculator's will be supplied in class - It is recommended that you have a scientific calculator at home for homework (calculator with a square root keyÖ )
WHAT DO I DO IF I AM ABSENT?
Please SEE ME when you return! It is YOUR responsibility to find out what was completed in class.
When you return to school, please check the absent folder for any work that you missed.
If we took notes that day, please be sure to get the notes from someone on our team. If you cannot get the notes from someone, please see me.
HOW WILL I BE GRADED?
§Quarter grades will be based on a total point system that includes bellwork, classwork, homework quizzes and tests. |
What to learn in pure math for applied math?
What to learn in pure math for applied math?
So I finished my undergrad last year in applied math and physics. I'm currently applying to applied math phD programs (but they are separate depts from the pure math depts). I don't exactly what I want to focus on, but I was thinking something in mathematical physics, PDEs, functional analysis, and operator theory. Perhaps the program I go to will let me work with a pure math prof doing stuff in string theory
The applied math courses I've taken include proof-based fourier analysis, linear algebra, and analysis. Also, courses in prob/stats, complex analysis, ODEs, PDEs, dynamical systems, and numerical analysis. So what should I self-study in the meantime? I was thinking topology or the second half of real analysis (integration, metric spaces. Lebesgue, etc).
I've been told by three advisor-type people in my department that analysis is absolutely necessary for any math program (and as such, all math majors are required to take one semester). Since most of the math grad programs I've looked at start with a year of analysis study, I'd recommend doing as much of that as possible. Topology is probably a good idea too.
It really depends on the area of applied mathematics that you want to work on and taking certain courses will be completely useless in other areas, for example if you want to study string theory then a course such as algebraic topology or non commutative geometry seems good but that has almost no applicability in most other areas. However, there are courses that let you keep your options open. I would recommend any of the following courses, if you have not decided on your specialty yet.
definitely study complex analysis if you have not taken a course in it already.
a second course in partial differential equations
a course in applied nonlinear equations
As many courses as you can in numerical analysis( a good choice is computational methods for PDE's or high-performance scientific computation)
a course in linear programming
a course in combinatorics
maybe a course in control theory
If you are more into mathematical physics then you can take the following courses that don't require serious knowledge of physics.
Differential Geometry
mathematics of Fluid Mechanics
mathematics of Quantum Mechanics
mathematics of Quantum Field Theory
mathematics of General Relativity
If you are interested in theoretical computer science(which is a branch of applied math) you can study,
As many courses in real analysis as possible
As many courses in statistics, probability.
a second course in numerical analysis.
a course in nonlinear optimization
a course in mathematical theory of finance.
BTW, take topology only if you are going into mathematical physics, or you want to do serious
coursework in real analysis, other than that topology has little applicability in other areas.
I don't exactly what I want to focus on, but I was thinking something in mathematical physics, PDEs, functional analysis, and operator theory.
If I wanted to do the math of QFT and relativity, I sure hope those don't require much knowledge of physics. I hate studying relativity
First of all, I don't think you should go for mathematical physics if you hate studying relativity. After all, all those courses do involve physics.
But I am pretty sure that the courses I listed under mathematical physics don't require any serious knowledge of physics, I myself took General Relativity and did well. The only physics courses I had taken were general physics I and II. The only course requirement for that was introductory differential geometry. Mathematics of QM and QFT require some knowledge of PDE's operator theory and functional analysis and basic probability and again no physics beyond freshman year. Topology is also very helpful in QFT and latter on if you want to study a specialized course in string theory. So I think overall topology is a good idea if you wanna go for mathematical physics. |
MATH 103 College Algebra 4 cr. (GE5) This course explores fundamental college algebra topics, either as preparation for further study in mathematics or to meet the general education requirement. Topics of study include the following: relations, functions, and graphing; equations and inequalities; complex numbers; radical, polynomial, rational, exponential, and logarithmic functions; systems of equations; matrices; sequences and series; and the binomial theorem. Prerequisite(s): MATH 102 with a C or better, qualifying math placement test score, or ACT math subtest score of 22 or higher.
MATH 104 Finite Mathematics 4 cr. (GE5) This course is for students whose majors do not require MATH 103 College Algebra, MATH 107 Precalculus, or courses in calculus. This course emphasizes the understanding and application of mathematics as they are used in everyday life. Topics of study include systems of linear equations and inequalities, matrices, linear programming, logic, mathematics of finance, elementary probability, and descriptive statistics. This course does not serve as the prerequisite for any other math course. Prerequisite(s): MATH 102 with a C or better, qualifying math placement test score, or have an ACT math subtest score of 22 or higher.
MATH 105 Trigonometry 2 cr. A study of angles, trigonometric function and their inverses, solving triangles, trigonometric identities and equations, polar coordinates and applications. Prerequisite: MATH 103 with a C or better or ACT of 25 or higher.
MATH 240 Applied Statistics 4 cr. (GE5) An examination of introductory statistics concepts, including sampling, descriptive statistics, probability, correlation, regression, binomial and normal distributions, confidence intervals and hypothesis testing of one and two populations, ANOVA, and Chi-square tests. Technology will be used to enhance learning and mirror statistical applications and practices in the larger world. Prerequisite(s): MATH 102 with a C or better, qualifying math placement test score, or and ACT math subtest score of 22 or higher.
MATH 277 Mathematics for Elementary Teachers I 3 cr. A course for elementary education majors. Topics include problem solving, number systems (natural numbers through the reals), number theory, and proportional reasoning. Technology and manipulatives are used throughout the course.Prerequisite(s) MATH 103 or MATH 104 or equivalent.
MATH 294 Intro to Research in Math 1-2 cr. Students explore topics, expand their mathematical knowledge, and begin to conduct introductory research under the direction of a faculty mentor. The number of credits is proportional to the time committed to the research (1 SH = 3 hours of student work per week on average.) Prerequisite: MATH 165 with a B or better; instructor permission required. Repeatable for up to 4 credits total.
MATH 315 Intro To Mathematical Modeling 3 cr. An introduction to mathematical modeling is the translation of a real world problem into a well formulated mathematical model. Students will develop the basic skills and techniques of formulation, simulation, analysis, and testing of mathematical models for describing and predicting a variety of phenomena. Understanding the fundamental principles in model formulation in physics, chemistry, biology, business, economics, medicine, and social and environmental sciences will be emphasized. Prerequisite(s): MATH 165.
MATH 371 Early Practicum 1 cr. This course will require a minimum of 45 clock hours in a practicum experience. The experience can be any one of or combination of the following: secondary classroom, teaching assistant on campus, tutor on or off campus, tutor in the MSU Math Clinic, tutor at Job Corps, or some other experience approved by the Mathematics Department. Repeatable for credit. Prerequisite(s): Math 165.
MATH 377 Mathematics for Elementary Teachers II 2 cr. A course for elementary education majors. Topics include probability, statistics, and geometry. Calculators, computer software, and manipulatives are used throughout the course. Prerequisite(s): MATH 103 or MATH 104 or equivalent.
MATH 380 History of Mathematics 3 cr. Development of mathematics from its early beginning through the present axiomatic approach. Problems from each era are included. Prerequisite(s): MATH 107 or advanced placement.
MATH 381 Secondary Math Practicum 1 cr. This course will require a minimum of 45 clock hours in a practicum experience. The experience will take place in a grades 7-12 setting. Prerequisite(s): Admission to Teacher Education, MATH 371; Prereq/Co-req: MATH 391.
MATH 393 Math Education Seminar 2 cr. This is a support course for BSE math majors that provides students with opportunities to discuss curriculum and pedagogical issues that arise in their student teaching placements. Other topics addressed include preparation for job searching, reflections on INTASC standards and each student's level of competence. Prerequisite(s): Admission to Teacher Education. Co-requisite(s): ED 493.
MATH 494 Directed Research in Math 1-4 cr. Students conduct research under the direction of a faculty mentor. The general topic and specific goals and activites are agreed upon by the student and the mentor. while publication or presentation is not a requirement, all projects have a goal of producing publishable/presentable results. The number of credits is proportional to the time committed to the research (1 SH = 3 hours of student work per week on average.) Prerequisite: MATH 294 (2 SH); instructor permission required. Repeatable for up to 8 credits total.
MUSC 099 Recitals/Concerts 0 cr. This is a non-credit course which will appear on each music major's semester program. It is designed to accumulate information as to the student's required attendance at predesignated recitals, concerts, and seminars. Grading Basis: S/U. Repeatable.
MUSC 100 Music Appreciation 3 cr. (GE3) Designed for the non-music major and may be used as partial fulfillment of Humanities requirement. Representative works from many cultures will be studied.
MUSC 101 Fundamentals of Music 2 cr. Introduction to fundamental elements of music and functional musicianship for non-music majors.
MUSC 110 Audio/Video Technology 1 cr. This course is designed to provide basic knowledge and gain experience with recording live perfromances. Employing both on campus and online resources, the students will study basic practices for recording and production as they apply that knowledge to recording projects with the Division of Music.
MUSC 121 Intro to Music Theory 2 cr. Foundations of music notation and basic music literacy. Course provides a background for MUSC 122 Music Theory and a foundation for successful pursuit of the Music Major. Co-requisite: MUSC 123.
MUSC 122 Music Theory I 3 cr. Study of music notation and basic structure of music, including key signatures, scales, chords, four-part writing and instrumental notation. Provides students with practical applications of music theory concepts.
MUSC 150 Orchestra 1 cr. (GE4) Rehearses Thursday evening. The Minot Symphony Orchestra is a university-community organization. Open to qualified students upon approval of director. Repeatable for credit.
MUSC 153 Accompanying 3 cr. Open to music majors with declared piano or organ performing medium. This course helps the student develop skill at accompanying soloists, being a partner in a chamber music ensemble, and as a community music leader. Repeatable for credit.
MUSC 155 Wind Ensemble 1 cr. (GE4) Open to qualified students subject to approval of director. Repeatable for credit.
MUSC 160 Concert Band 1 cr. (GE4) Open to qualified students subject to approval of director. Repeatable for credit.
MUSC 163 Beaver Athletic Band 1 cr. Brass & Percussion Ensemble which performs at athletic events, in concert and in recital, community events and tours regularly. Members are selected by audition. Repeatable for credit.
MUSC 165 Jazz Ensemble 1 cr. Open to qualified students subject to approval of director. Repeatable for credit.
MUSC 167 Jazz Combo 1 cr. Open to qualified students subject to approval of director. Repeatable for credit.
MUSC 177 Functional Piano 1 cr. A piano class designed for students who are beginners on the instrument, first year theory students, and elementary education majors. Course restricted to majors. (Class meets twice weekly.) Repeatable for credit.
MUSC 201 World Music 3 cr. (GE3-Diversity) Designed to introduce the world's major music's in order to encourage and enhance cultural diversity.
MUSC 205 History of the United States Through its Music 3 cr. (GE3-Diversity) Designed for the non-music major. American music which accompanied significant historical eras and development will be studied.
MUSC 206 Intro to Music History 3 cr. Survey of the history and traditions of western civilization through its music. Students will focus on the musical content and trace developmental trends through the common periods of music history.
MUSC 207 History of Pop and Rock Music 3 cr. (GE3-Diversity) Pop Music and American liberal capitalism helped to create a planetary culture. Twentieth Century events that brought the world to this pass were not so much a movement as a force of creativity and capitalism yoked by the first global communications network. This class brings liberal arts students into contact with tools and information on this subject.
MUSC 222 Music Theory III 3 cr. A continuing study of the underlying theoretical background of tonal music, begun in Theory I and II. Topics include a thorough study of chromatic harmony and the deterioration of functional harmony in the late 19th century to the demise of tonality in the 20th. Analytical techniques are stressed. Prerequisite(s): MUSC 123, 124 or 125.
MUSC 250 Basic Conducting 2 cr. A Foundation of knowledge and manual proficiency that allows the conductor to communicate with an ensemble. The focus of the course is on the conductor's individual skill.
MUSC 301 Music Methods for the Elementary Teacher 2 cr. Methods and materials for the classroom teacher in guiding young children in musical experiences K-6. Prerequisite(s): MUSC 101 or 122 and Admission to Teacher Education.
MUSC 306 Music History & Literature I 3 cr. This course will develop the students' knowledge of Western Civilization through its musical history and literature dating from ancient Greece to 1750. Students will focus on analytical and listening skills to further their understanding of musical styles.
MUSC 307 Music History & Literature II 3 cr. This course will develop the students' knowledge of Western Civilization through its musical history and literature dating from 1750 to the present. Students will focus on analytical and listening skills to further their understanding of musical styles.
MUSC 325 Vocal Pedagogy 3 cr. Techniques and materials for the voice teacher. Diction practices in English, Italian, German and French prepare the student to not only perform in those languages, but also to teach those song literatures. This course benefits BA and BSE majors equally.
MUSC 341 String Methods 1 cr. A practical class involving the playing and techniques of teaching the bowed, orchestral string instruments (violin, viola, cello, and string bass) at an elementary level. Teaching materials and string pedagogy are also considered.
MUSC 342 Woodwind Methods 1 cr. The purpose of this course is to give the student an introduction to the techniques of playing and teaching woodwinds. Teaching methods, proper playing position, embouchure, common problems and errors made by students, equipment, maintenance and repair of the instruments, and both pedagogical and performance literature will be presented.
MUSC 343 Brass Methods 1 cr. Teaching techniques and performance proficiency on each of the brass family instruments.
MUSC 345 Wind Band Literature 2 cr. Services the needs of large ensemble literature for the wind and symphonic band musician. Secondary education relies heavily on this body of literature for both quality performance and teaching material. Many contemporary composers and arrangers make this genre one that provides and prolific source of new works. Knowledge of this genre benefits the educator and performing musician, as well as opening the door for the developing composer.
MUSC 346 Symphonic Literature 2 cr. Services the need of large ensemble literature for the string and wind orchestral musician. It further represents one of the largest and most performed bodies of musical composition in all of classical literature. Knowledge of this genre benefits the educator and performing musician alike.
MUSC 347 Chamber Music Literature 2 cr. Services the needs of small ensemble literature for the string, wind and piano student. It further represents one of the largest bodies of musical composition and employs numerous combination of instrumentation.
MUSC 350 Adv. Conducting and Arranging 3 cr. Objectives of this course are to develop and refine gestures which convey musical meaning, to successfully arrange simple scores for a variety of ensembles using standard notational software, to refine interpretive skills, and to develop an ability to critique and improve one's own conducting.
MUSC 366 Instrumental Jazz Improvisation I 2 cr. Study of the utilization and translation of basic musical elements such as scales, mixolydian modes, dominant seventh chords, rhythm, form, and melody into an individually creative jazz performance. Open to all instruments including strings.
MUSC 367 Instrumental Jazz Improvisation II 2 cr. Continuation of MUSC 36666 by studying the dorian modes, minor seventh chords, and integration rhythm and melody with actual playing to further the students progress. Prerequisite(s): MUSC 36666.
MUSC 384 Orchestra Methods in Secondary Education 3 cr. Provides the parallel alternative for Band and Choral Methods classes. The string educator is often hired to teach only strings for a school system. This course includes methods and materials relative to a successful string program. Prerequisite: MUSC 124 and admission to teacher education.
MUSC 390 Band Methods in Secondary Education3 cr. Instrumental conducting, score reading and performance preparation, including examination of methods and materials used in the secondary band program. Prerequisite(s): MUSC 124 and admission to teacher education.
MUSC 397 Elementary Music Field Experience 1 cr. Provides the opportunity for the music education students to achieve 25-30 of the required practicum hours for observation and visitation in the public school classroom. This "hands on" time in the classroom is invaluable in forming the expectations and realities of life in the teaching field. Prerequisite(s): MUSC 124 and Admission to Teacher Education.
MUSC 441 Piano Tuning 2 cr. Study of piano tuning, piano construction and repair in addition to organ tuning. Prerequisite(s): The ability to play all major chords and any two note interval. Repeatable for credit.
NURS 363 Nursing Theory and Research 3 cr. Surveys contribution of theory and research to the development of the discipline of nursing. Focuses on nursing theories, conceptualizations, and research utilization for decision making within professional nursing. Prerequisite(s): Admission to nursing. CS = 45*
NURS 383 Professional Nursing I 3 cr. Introduces the student to the nature of baccalaureate nursing, including the Department of Nursing philosophy and curricular concepts. Students explore various nursing roles and theories in a variety of traditional and nontraditional settings. Prerequisite(s): Acceptance into RN to BSN program. CS = 45*
NURS 456 Public Health Nursing 6 cr. Demonstrates population-focused community-oriented nursing through the synthesis of nursing theory and public health theory applied to promoting, preserving and maintaining the health of popuations and grounded in social justice. Provides experience in a variety of urban, rural, and frontier community settings. Prerequisite(s): Admission to nursing and NURS 344,354,361, and 364. CS = 45; C/L = 135*
NURS 457 Public Health for the Professional Nurse I 3 cr. Focuses on theory of population-focused community- orientated nursing through the synthesis of nursing theory and public health theory applied to promoting, preserving and maintaining the health of populations and grounded in social justice. Prerequisites: Admission ot RN to BSN program, NURS 363 and 383.
NURS 483 Professional Nursing II 3 cr. Provides the student with an opportunity to examine professional nursing in a changing health care delivery system, including the current and future focus of nursing care. Prerequisite(s): acceptance into RN to BSN program. CS = 45*
NURS 493 Professional Nursing III 3 cr. This integrative capstone provides the student opportunity to design and implement a project in collaboration with faculty by integrating leadership and management concepts into nursing practice in a health care system. Prerequisite: acceptance into RN to BSN program.CS = 45*
NURS 496 Study Abroad 1-6 cr. Provides opportunities for MSU faculty-led study trips to appropriate locations. Focuses on becoming more culturally knowledgeable about global health care by immersion in a nursing culture of a different country. Will include additional requirements beyond travel itself. May be repeated for up to 24 credits for different countries. Prerequisite(s): Sophomore status, minimum cumulative GPA of 2.5 and prior approval by the Office of International Programs.
PHYS 110 Astronomy 4 cr. (GE6) A study of the universe that begins with the earth as a planet, the planets and the satellites of our solar system, and moves out through stellar astronomy to galaxies and into the very fabric of the universe. It includes an evaluation of the methods and techniques of astronomy. Offered fall semester. Both day and night laboratories. Lecture, 3 hours; laboratory, 2 hours.
POLS 115 American Government 3 cr. (GE7) Principles of American government, political behavior, institutions.
POLS 116 State and Local Government 3 cr. Structures, politics, and behavior in state and local governments.
POLS 220 International Politics 3 cr. Students learn about how the different governments of the world interact through this introductory course. By the end of the semester, students are expected to know the different theories and models that relate to international conflict and consensus. In addition, students learn about the different world organizations and how they are involved in politics on a global scale.
POLS 275 Contemporary Community Issues 3 cr. This course is designed to develop your understanding of the different communities you are a member of and the issues facing them in the 21st century. Drawing on theories and concepts from various disciplines, we will expand on how communities and the issues associated with them are defined, constructed and addressed at multiple levels of society. Specifically, we will examine various political and social issues facing our communities including but not limited to: crime, ecology, inequalities, health care and the family. We will also set those issues in their larger state, national and global context, address the impact of that context and the proposed possible outcomes for the future.
POLS 299 Special Topics 1-6 cr. Topics will cover, but are not limited to, recent issues and in-depth investigation into areas of interest to students. Repeatable for credit as topics change.
POLS 375 Contemporary Political Issues 3 cr. This course is designed to develop your understanding of the larger political world and the issues facing it in the 21st century. Drawing on theories and concepts from various disciplines, we will expand on how political issues are defined, constructed and addressed at multiple levels of society. Specifically, we will look at various political issues and policies facing the United States, including but not limited to: crime, ecology, inequalities, health care and the family. We will also set those issues in their larger global context, address the impact of that context and the proposed possible outcomes for the future.
POLS 451 Political Sociology 3 cr. Political sociology broadly conceived is the study of power and domination in social relationships to include the relationship between state and society. The course draws upon comparative history to analyze socio-political trends and thereby includes the analysis of the family, the mass media, universities, trade unions, etc. a typical research question might, for example, be: what factors explain why so few American citizens choose to vote.
POLS 499 Special Topics 1-6 cr. Topics will cover, but are not limited to, recent issues and in-depth investigation into areas of interest to students. Repeatable for credit as topics change.
PSY 111 Introduction to Psychology 3 cr. (GE7) A survey of the scientific study of behavior and mental processes. Topics studied include development of normal and abnormal behavior, learning, biopsychology, development, memory, personality, cognition, therapy, and social psychology. This course is a Prerequisite(s) to most other psychology courses.
PSY 112 Foundations of Psychology 3 cr. Designed for psychology and addiction studies majors, this course will emphasize the tools necessary to advance in these fields. Prerequisite(s): PSY 111.
PSY 201 Dynamics of Adjustive Behavior and Mental Health 3 cr. Presents the principles of behavior adjustment. It is concerned with how socially relevant behavior is learned, what the motivating functions are, and how they operate in life. Prerequisite(s): PSY 111.
PSY 242 Research Methods in Psychology 4 cr. A study of the scientific method as it is used in the investigation of problems in psychology. A variety of types of research methodologies, as well as the advantages and disadvantages of their use. Ethical implications of the use of various methodologies will also be discussed. Prerequisite(s): PSY 241 or department approval.
PSY 252 Child Psychology 3 cr. Overview of theories of human development from conception through childhood including physical, cognitive, language, social, and self-help skills in family, school, and community settings. Prerequisite(s): PSY 111.
PSY 255 Child and Adolescent Psychology 3 cr. Overview of theories of human development from conception through adolescence including the physical, cognitive, language, social, and educational aspects of the individual development. Special emphasis will be given to the individuals learning capabilities. This course cannot be applied towards the Psychology or Addiction Studies majors, minors or concentrations. Prerequisite(s): PSY 111.
PSY 313 Industrial Organizational Psychology 3 cr. This course will examine human behavior in industrial and organizational settings. Psychological principles are applied to selection, placement, and training. The effectiveness of individuals and groups within organizations, including leadership and control, conflict and cooperation, motivation, and organizational structure and design, is examined. Prerequisite(s): PSY 111.
PSY 338 Professional Relations and Ethics 3 cr. Study of Federal Confidentiality Laws and ND Commitment Law and process in order to protect the rights of the client. Prerequisite(s): PSY 111.
PSY 365 Evolutionary Psychology 3 cr. Examines the important aspects of human behavior as it is explained as a result of natural selection. The course will focus on a number of topics including sex differences, mate selection, selfishness and altruism, homicide and violence. Prerequisite(s): PSY 111.
PSY 375 History and Systems of Psychology 3 cr. Examines the historical development of the science of psychology. Special emphasis is placed upon cultural context and its influences on the developing systems of psychology. Prerequisite(s): PSY 111.
PSY 376 Social Psychology 3 cr. An interdisciplinary approach to the study of behavior of individuals in relation to social stimulus situation. Prerequisite(s): PSY 111 and SOC 110.
PSY 379 Psychology of Adult and Aging 3 cr. Overview of theories of human development from young adulthood through old age focusing on demands of personal adjustment, family, work, retirement, and community life. Prerequisite(s): PSY 111; recommended: PSY 252 or 352.
PSY 394 Independent Study 1-4 cr. Election of a topic and a course of study. Must be approved by a psychology staff member and the psychology chair. Student must be a psychology major and have 12 semester credits.
PSY 410 Cognitive Psychology 3 cr. Examines the research dealing with the processing of sensory information, attention, short term and long term memory, decision making and problem solving, as well as related topics. Prerequisite(s): PSY 111.
PSY 411 Introduction to Personality Theories 3 cr. Examines the basic concepts of personality development as viewed by the psychoanalytic, learning, humanistic, and trait-type theorists. Special emphasis is placed on the comparison of various perspectives. Prerequisite(s): PSY 111.
PSY 413 Theories and Practice of Psychotherapy 3 cr. Aimed at the development of a balanced view of the major concepts of various therapies and an awareness of practical applications and implementation of techniques used by the various therapists. Prerequisite(s): PSY 111.
PSY 423 Introduction to Counseling 3 cr. Study of the theories of counseling and application of these principles for dealing with behavioral problems in agencies, schools, or hospitals. Prerequisite(s): PSY 111.
PSY 424 Advanced Counseling 3 cr. Further study of counseling theory with students being required to develop a workable methodology of their own. Prerequisite(s): PSY 111, and 423
PSY 435 Theories of Learning 3 cr. Examines the basic concepts of learning theory as viewed by the more prominent theorists in the area. Emphasis is placed on the comparison of the various perspectives within historical contexts. Prerequisite(s): PSY 111.
PSY 460 Sensation and Perception 3 cr. Focus on the principles of our sensory systems and the laws which govern the sensory processes. The course includes research and theories on the visual system, auditory system, chemical senses, and the skin senses. Prerequisite(s): PSY 111.
PSY 473 Behavior Modification 3 cr. Description of behavioral principles and procedures for assessment and treatment that can be used by helping professionals to enhance behavioral development. Class projects are required. Prerequisite(s): PSY 111.
PSY 476 Group Dynamics 3 cr. Actual group experience in a lecture/lab format. Readings and written assignments focus on organizing groups and skills required of group facilitators. A problem solving/personal growth group meets each week. Prerequisite(s): PSY 111.
PSY 485 Practicum 15 cr. Participation in one of the North Dakota consortia to provide experience in the addiction field. This is a 4.5 month, full time experience, where the student actively participates as an addiction counselor in training. Course restricted to psychology or addiction studies majors. Grading Basis: S/U.
PSY 486 Practicum 15 cr. Participation in one of the North Dakota consortia to provide experience in the addiction field. This is the second part of the nine month practicum experience required for licensure as an addiction counselor. The course involves a 4.5 month, full time experience, where the student actively participates as an addiction counselor in training. Course restricted to psychology or addiction studies majors.Grading Basis: S/U.
PSY 494 Directed Behavioral Research 1-4 cr. This course provides students with the practical applications of research designs. Although a resulting publication is not required for the course, it is a desired outcome. Students will need to work with a faculty sponsor on a specific research project. Prerequisite(s): PSY 241 and PSY 242 or consent of instructor.
PSY 495 Service Learning 3 cr. This course provides students with the ability to work in meaningful community service coupled with instruction about the service and reflection on their service.
PSY 496 Senior Research Paper 3 cr. Students will formulate an original research topic and write a paper ON that topic. Restricted to psychology majors and senior status. |
Standards Driven MathT addresses the California Content Standards individually through this Student Standards HandbookT. Students can focus more directly on content standards for improved math success. In addition to standards being covered one-at-a-time, explanations of the meaning of each content standard are provided and appropriate problem sets are included. There is also a subject index by standard. Standards driven means that the standard is the driving force behind the content. No matter what textbook students are using, all will benefit from the direct standards approach of Standards Driven MathT. Every student should practice directly from a Student Standards HandbookT. Developed directly from one of the nation's most rigorous sets of state standards-California, this book is useful for spring standards test prep. No classroom should be without one for every student. Nathaniel Max Rock, an engineer by training, has taught math in middle school and high school including math classes: 7th Grade Math, Algebra I, Geometry I, Algebra II, Math Analysis and Calculus. Max has been documenting his math curricula since 2002 in various forms, some of which can be found on MathForEveryone.com, StandardsDrivenMath.com and MathIsEasySoEasy.com. Max is also an AVID elective teacher and the lead teacher for the Academy of Engineering at his high school.
Our resource meets the measurement concepts addressed by the NCTM standards and encourages the students to learn and review the concepts in unique ways. We provide students the opportunity to learn, ...
This book contains 40 quizzes covering the entire Texas math grade 3 curriculum. It includes one quiz for every skill that grade 3 students need to have and covers every skill that is tested on the ... |
MAT 162 — Functions and Algebra
Mathematics
3 Credits
This course is designed for students who plan to teach. It involves a study of Number & Operations and Functions & Algebra with the depth required for successful mathematics instruction. Topics include, but are not limited to, proportional reasoning; number systems, signed numbers, and the real number line; variables, algebraic expressions and functions; solving equations; exploring graphs of equations; and connecting algebra and geometry. |
This course aims to introduce the basic concepts and techniques of linear algebra and single variable calculus which are necessary for undertaking subsequent courses in the Mechanical Design and Electronic themes. It is aimed at students without A Level Pure Mathematics (or its equivalent). The course will help students develop skills in logic thinking.
Course Intended Learning Outcomes (CILOs) Upon successful completion of this course, students should be able to:
No.
CILOs
Weighting (if applicable)
1.
explain concepts from basic linear algebra and single variable calculus.
develop simple mathematical models through linear systems of equations, derivatives and integrals, and apply mathematical and computational methods to a range of problems in scientific and engineering applications involving basic linear algebra and single variable calculus.
2
5.
the combination of CILOs 1-4
3
Teaching and Learning Activities (TLAs)
(Indicative of likely activities and tasks designed to facilitate students' achievement32 hours in total
Learning through tutorials is primarily based on interactive problem solving allowing instant feedback.
2
2 hours
3
2 hours
1
1 hour
4, 5
2 hours
Learning through take-home assignments helps students understand basic mathematical concepts and techniques of linear algebra and single variable calculus, and apply mathematical methods to some problems in scientific and engineering applications.
1--5
after-class
Learning through online examples for applications helps students apply mathematical and computational methods to some problems in scientific and engineering applications.
4
after-class
Learning activities in Math Help Centre provides students extra help.
2
70, 2
15-30%
Questions are designed for the part of linear algebra to see how well the students have learned basic concepts and techniques of linear algebra.
Hand-in assignments
1-4
0-15%
These are skills based assessment to see whether the students are familiar with basic concepts and techniques of linear algebra and single variable calculus and some applications in science and engineering.
Examination
5
70%
Examination questions are designed to see how far students have achieved their intended learning outcomes. Questions will primarily be skills and understanding based to assess the student's versatility in linear algebra and single variable calculus.
Formative take-home assignments
1--4
0%
The assignments provide students chances to demonstrate their achievements on linear algebra and single variable calculus learned in this course.
Grading of Student Achievement: Refer to Grading of Courses in the Academic Regulations
Part III
Keyword Syllabus
Vectors and coordinate geometry in space. Matrices and determinants. Complex numbers. Sequences and series. Differential calculus and integral calculus. System of linear equations. |
MA Mathematics Domains of Study
Areas of Study Within the
M.A. in Mathematics Education Degree
The WGU Master of Arts in Mathematics Education (K-6, 5-9 or 5-12) program content is based on research on effective instruction as well as national and state standards. It provides the knowledge and skills that enable teachers to teach effectively in diverse classrooms. The M.A. in Mathematics Education program content and training processes are consistent with the accountability intent of the No Child Left Behind Act of 2001. The degree program is focused on the preparation of highly qualified teachers. As described in the federal legislation, a highly qualified teacher is one who not only possesses full state certification, but also has solid content knowledge of the subject(s) he or she teaches.
The following section includes the larger domains of knowledge, which are then followed by the subject-specific subdomains of knowledge.
Elementary Mathematics Education Domain (for the K-6 program)
This domain focuses on the following mathematics content, as well as central issues related to the teaching of these topics in grades K–6:
Mathematics (K-6) Content
This subdomain focuses on the following mathematics content with integrated mathematics pedagogy: Introduction to Number Sense; Patterns and Functions; Integers and Order of Operations; Fractions, Decimals, and Percentages; Coordinate Pairs and Graphing; Ratios and Proportional Reasoning; Equations and Inequalities; Geometry and Measurement; and Statistics, Data Analysis, and Probability.
Finite Mathematics
This subdomain focuses on the real number system, symbolic logic, number theory, set theory, graph theory and their applications.
Middle School Mathematics Content Domain (for the 5-9 program)
This domain focuses on the following areas of mathematics: Finite Mathematics, College Algebra, Pre-calculus, Probability and Statistics I, College Geometry and Calculus I.
Finite Mathematics
This sub-domain focuses on the real number system, symbolic logic, number theory, set theory, graph theory and their applications.
College Algebra
This sub-domain focuses on equations, inequalities, polynomials, conic sections, and functional analysis including logarithmic, exponential, and inverse functions in problem solvingComprehensive Exam
The CYV1 is a comprehensive exam assessing the student's knowledge of the subdomains listed above.
High School Mathematics Content Domain (for the 5-12 program)
This domain focuses on the following areas of mathematics: This domain focuses on the following areas of mathematics: Pre-Calculus, Probability and Statistics, College Geometry, Calculus and Analysis, Linear Algebra, Abstract Algebra, and Mathematical Modeling and ConnectionsCalculus II
This sub-domain focuses on integration techniques and applications, the solution of differential equations, and the analysis of sequences.
Research Fundamentals Domain (for the K-6 and 5-9 programs)Capstone Project (for the K-6 program)
The Capstone Project is the culmination of the student's WGU degree program. It requires the demonstration of competencies through a deliverable of significant scope that includes both a written capstone project and an oral defense.
Students will be able to choose from two areas of emphasis, depending on personal and professional interests. These two areas include instructional design and research. If carefully planned in advance, the individual domain projects may serve as components of the capstone. For capstones with the instructional design emphasis, students will design, manage, and develop an instructional product for which there is an identified need. The product can be delivered via the medium of choice (e.g., print-based, computer-based, video-based, web-based, or a combination of these), but you must provide a rationale for the medium selected. The instructional product you develop for your capstone should be an exportable form of instruction designed to bring your target audience to a mastery of predetermined knowledge and skills.
For capstones with the research emphasis, students will design and conduct a data-based investigation of a conclusion-oriented question (decision-oriented investigations are most generally considered to be evaluation projects). The project report should be of publishable quality and may be submitted to an appropriate professional journal at the completion of the project. At the minimum you should plan to share your results with your school or organization questions covering the mathematics content domain. The purpose of the exam is a checkpoint to ensure that you have acquired the critically required skills and knowledge specified in the program competencies.
Teacher Work Sample Written Project (for the 5-9 and 5-12 programs)
The Teacher Work Sample Written Project is the culmination of the student's WGU degree program. It requires the demonstration of competencies through a deliverable of significant scope that includes both a written project and an oral defense.
The Teacher Work Sample is a written project containing a comprehensive, original, research based curriculum unit designed to meet an identified educational need. It provides direct evidence of the candidate's ability to design and implement a multi-week, standards-based unit of instruction, assess student learning, and then reflect on the learning process. The WGU Teacher Work Sample requires students to plan and teach a multi-week standards-based instructional unit consisting of seven components: 1) Contextual factors, 2) learning goals, 3) assessment, 4) design for instruction, 5) instructional decision making, 6) analysis of student learning, and 7) self-evaluation and reflection a presentation (typically PowerPoint) and defense of the Teacher Work Sample (TWS). Candidates will be asked to reflect upon the TWS, note its strengths and weaknesses, discuss its impact on student learning, and suggest future improvements. The purpose of the exam is a checkpoint to ensure that you have acquired the critically required skills and knowledge specified in the program competencies.
NBC News Reports on WGU
"The dreams of 19 governors have become [WGU Grad Angie Gonzalez's] dream fulfilled." |
Hi Math Gurus, I have been trying to work out a couple of questions based on cramer's rule. They are a part of our homework in Pre Algebra and are to be submitted in 4 days. Could you please aid us in winding it. We are actually searching for a software that can guide us in getting this done.
You might want to check out Algebra Buster. I bought it some time back to help me with my Algebra 2 course and I can say that it was really a wise decision. There are so many demos given which you can go through. You can also try out the questions related to converting decimals and adding numerators by just typing them in. Algebra Buster provides complete description to the problems which helps to make difficult concepts very clear. I would say that this program is absolutely the best that money can buy.
It is good to know that you wish to improve your math and are taking efforts to do so. I think you should try Algebra Buster. This is not exactly a tutoring software but it offers solutions to math problems in a very descriptive manner. And the best thing about this software product is that it is very user friendly. There are a lot of examples given under various topics which are quite useful to learn the subject. Try it and wish you good luck with math.
I remember having often faced difficulties with function definition, simplifying fractions and cramer's rule. A truly great piece of math program is Algebra Buster software. By simply typing in a problem from workbook a step by step solution would appear by a click on Solve. I have used it through many algebra classes – Basic Math, Intermediate algebra and Pre Algebra. I greatly |
Saxon Math programs are designed and structured for immediate, measurable and long-lasting results. By employing a proven method of incremental development and continual review strategies, each piece of supplementary curriculum provides time to practice, process and learn beyond mastery.
This Math Intermediate 3 Written Practice Workbook contains exercises designed to refresh students' memories, deepen understanding of concepts, shift gears between different types of problems, and see how different math topics are related. (Workbook reprints exercises from the text with space for the student to show their work).
Product:
Saxon Math Intermediate 3: Written Practice Workbook
Author:
Hake
Prepared by:
Saxon Publishers
Edition Description:
Student
Binding Type:
Paperback
Media Type:
Book
Minimum Age:
8
Maximum Age:
8
Minimum Grade:
3rd Grade
Maximum Grade:
3rd Grade
Number of Pages:
240
Weight:
0.89 pounds
Length:
10.9 inches
Width:
8.3 inches
Height:
0.41 inches
Publisher:
Saxon Publishers
Publication Date:
March 2007
Subject:
Math
Curriculum Name:
Saxon
Learning Style:
Auditory, Kinesthetic, Visual
Teaching Method:
Charlotte Mason, Classical, Traditional, Unit Study, Unschooling
There are currently no reviews for Saxon Math Intermediate 3: Written Practice Workbook.
I have found Saxon Math to be very thorough. I have used Saxon 1, 2, 3 and 5/4 now. Thus far, we have been very pleased with the curriculum. It allows me, the teacher to move a quickly or as slowly as the student needs. I am able to use the tests and assessments included in the student workbook to determine where to place the child and to even skip ahead if needed so that valuable time is not spent on things already mastered. The Teachers Manual is able to be reused with other students, but we always purchase a new workbook for each new student. The price of the workbooks are very reasonable.
We used four other math curricula in the course of 15 years of homeschooling. I looked at Saxon Math when our oldest was in the 5th grade and didn't think I could do it. I was wrong. After years of struggling with other math programs I made the switch for our two smallest in 1st grade. We have used the Saxon Math for three years now and it has made a big difference in how we look at Math. I would highly recommend this curriculum. There is no DVD from Saxon for k-3, but starting in 4/5 you can purchase one. There is a company called Destination Math that has an online program that runs right with the Saxon Math. Just for the record, Math was not my best subject when I was in school. So those first years of teaching were a struggle for me to try to teach something I had a hard time understanding. Saxon Math has helped me while I have been teaching. It's very easy to follow and one of the few subjects that I actually follow very closely by the teacher's book.
We just switched to Saxon month a few months ago. I have a daughter who really doesn't like math. I took her to Mardel's and let her choose a math program (I got final approval rights. ;) ) She surprised me and picked Saxon. It is extremely black and white and not like the colorful books we have used before. She loves it so far and seems to be grasping the concepts. We didn't buy the manipulatives as I had a lot of them at home already (from other math programs we've used.) I can't really give this an excellent review as we are still new into it.
This curriculum was perfect for my sons needs at the moment. He did go through the years worth of work very quickly, but he has a real thirst for math. My son wanted a few math games added to suppliment his text work. It is a good curriculum. |
Middle School Math 2 continues to build on the concepts introduced in seventh grade. Students will continue to deepen their understanding of mathematics in preparation for high school mathematics. Students will continue to explore and solve mathematical problems, think critically, work cooperatively with others, and communicate their ideas clearly as they work through mathematical concepts. A summary of the major concepts and procedures learned in this course follows. Students will work with lines and angles, especially as they solve problems involving triangles, using square roots and the Pythagorean Theorem. In eighth grade, students will solve a variety of linear equations and inequalities. They will represent and determine the slope and y-intercept of linear functions with verbal descriptions, tables, graphs and symbolic expressions. Students will work with lines and angles, especially as they solve problems involving triangles, using square roots and the Pythagorean Theorem. Students will build on their extensive experience organizing and interpreting data, by using mean, median, and mode to analyze, summarize, and describe information. Additionally, students will be introduced to scientific notation, the laws of exponents, and irrational numbers |
Graphing Calculator Manual For Stats - 3rd edition
Summary: Organized to follow the sequence of topics in the text, this manual is an easy-to-follow, step-by-step guide on how to use the TI-83/84 Plus and TI-89 graphing calculators. It provides worked-out examples to help students fully understand and use their graphing calculator.
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MATH 213: Foundations for Higher Mathematics
This course will serve as a bridge between introductory and advanced mathematics. The context of set theory and logic will be used to develop the skills of constructing and interpreting mathematical proofs. Topics include principles of logical argument, congruence modulo, induction, sets, functions, relations, equivalence relations, countability and uncountability of sets. Fall. Prerequisite: MATH 104 or MATH 110, or permission of instructor.... more »
Credits:3
Overall Rating:0 Stars
N/A
Thanks, enjoy the course! Come back and let us know how you like it by writing a review. |
Role in Curriculum
First developmental-level math course for students who were not exempted from CUNY proficiency and failed both parts I and II of the COMPASS placement exam used to assess CUNY proficiency. MTH 020 with similar learning goals, is for students who have passed at least one part of the COMPASS placement exam. Students successfully passing both the COMPASS and the course content have similar options as those passing MTH 020.
Learning Goals and Assessment Plans
Learning Goal
Assessment
The student will understand lines, including solving linear equations, the concept of slope, the point-slope formula, and graphing of linesThe student will be familiar with applications involving percents, ratios and proportions.
Students will establish CUNY proficiency
The percentage of students passing each part of the COMPASS exam will be tracked |
Purpose
of the course
This course discusses both theoretical and
practical aspects of
numerical interpolation and approximation. Such techniques form the
core of Numerical Analysis and are the basis for solution of many
important problems. We review the relevant mathematical theory and show
how it can be used to construct practical algorithms. These
algorithms are implemented and tested in matlab.
Our focus is on applications to numerical differentiation and
integration of functions. However, we also review certain related
special topics such as Galerkin and wavelet approximation theory. |
principal aim of this book is to introduce university level
mathematics — both algebra and calculus. The text is suitable for
first and second year students. It treats the material in depth, and
thus can also be of interest to beginning graduate students.
New concepts are motivated before being introduced through rigorous
definitions. All theorems are proved and great care is taken over the
logical structure of the material presented. To facilitate
understanding, a large number of diagrams are included. Most of the
material is presented in the traditional way, but an innovative
approach is taken with emphasis on the use of Maple and in presenting
a modern theory of integration. To help readers with their own use of
this software, a list of Maple commands employed in the book is
provided. The book advocates the use of computers in mathematics in
general, and in pure mathematics in particular. It makes the point
that results need not be correct just because they come from the
computer. A careful and critical approach to using computer algebra
systems persists throughout the text. |
Graphs: An Introductory Approach - A First Course in Discrete Mathematics
An introduction to discrete mathematics, this new text on graph theory develops a mathematical framework to interrelate and solve different problems. ...Show synopsisAn introduction to discrete mathematics, this new text on graph theory develops a mathematical framework to interrelate and solve different problems. It introduces the concepts of logic, proof and mathematical problem-solving and places an emphasis on algorithms in every chapter Every heavytail order includes with a sweet! We carefully...Good 9780471513407 Book is in good to acceptable condition with minor...Fair. Book is in good to acceptable condition with minor blemishes on the cover. Pages have highlighting and minor writing. Ships next business day.
Description:Fine. Book The book looks like new, unread and clean. Edges are...Fine. Book The book looks like new, unread and clean. Edges are sharp and fine. No tears or creases. Minor highlights |
Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op
Objective: On completion of the lesson the student will be able to convert ordered pairs to elements of a matrix, multiply matrices together, where possible, and interpret the answer matrix on a number plane.
Objective: On completion of the lesson the student will be able to place ordered pairs into a matrix, then perform translation by addition using a transformation matrix, then extract ordered pairs from an answer matrix.
Objective: On completion of the lesson the student will be able to state whether matrix by matrix multiplication is possible, predict the order of the answer matrix, and then perform matrix by matrix multiplication. able to use the degree of polynomials and polynomial division to assist in graphing rational functions on the coordinate number plane showing vertical, horizontal and slant asymptotes |
Tograduate,allstudentsMUSTcompleteaGrade10Mathematicscourseaswellasanothermathcourseatthe Grade11or12level. YoumightneedmorethanonemathcourseifyouplantocontinueschoolbeyondGrade 12. Depending on the schoolyou attend,there could be many Mathematics options available to you.
Students,parentsandeducatorsareencouragedtoresearchtheadmissionrequirementsforpost-secondary programs of study as they vary byinstitution and by year.
Thispathway isdesignedforentry into post-secondaryprograms suchas Arts orHumanitiesthatdonot require thestudyoftheoreticalcalculus.Topicsincludefinancialmathematics,statistics,logic andreasoning,and research into the history of mathematics. (Coursesat grade 11 and 12)
Whilethereisno"rule"aboutwhichMathcourseisrightforeachstudent,thedecisioncanbemadeeasierbythinkingaboutyourchild'sabilityandinterestinMath,andfutureeducationandcareerplans. Thenewcourses havebeen designed to facilitate studentsuccess after high school.
For example:
If your child has struggled in Math 8 or 9, enjoys working on projects or hands-on activities, or intends to pursuea trade or technical job after high school, then the Apprenticeship and Workplace pathway is the best choice.
If your child enjoys working on projects or hands-on activities, or is planning further studying in the Social Sciences like Economics or Arts or Humanities at post-secondary, then the Foundations pathway will be the best choice
If your child has been very successful in Math 9, enjoys the challenges of Math, and is thinking about futureeducation or a career that involves Sciences or Engineering at a university, then starting the Pre-Calculus pathway will be the best choice.
Whathappens if we change our mind aboutthecourse decision that we have made?
Becausethethreepathwaysweredesignedtogivestudentsdifferentskills,attitudesandknowledgefordifferent careerandpost-secondarypaths,theywerenotdesignedspecificallytoallowfor lateralmovementbetween pathways. Asaresult,schoolswillnotbesuggestingstudentsmovefromonepathwaytoanotheroncea choice has been made and a student is working is one pathway's courses. |
Basic Business Statistics
Berenson's fresh, conversational writing style and streamlined design helps students with their comprehension of the concepts and creates a thoroughly readable learning experience. Basic Business Statistics emphasises the use of statistics to analyse and interpret data and assumes that computer software is an integral part of this analysis.
Berenson's 'real world' business focus takes students beyond the pure theory by relating statistical concepts to functional areas of business with real people working in real business environments, using statistics to tackle real business challenges. Read More
Business Statistics
Berenson's fresh, conversational writing style and streamlined design helps students with their comprehension of the concepts and creates a thoroughly readable learning experience. Business Statistics emphasises the use of statistics to analyse and interpret data and assumes that computer software is an integral part of this analysis.
Business Statistics covers the key content in first year business statistics courses as well as further coverage of topics such as decision making, statistical applications, Chi-square tests and nonparametric tests. Read More
Numeracy in Nursing and Healthcare: Calculations and Practice
Australian Edition
Do your students find maths and medications challenging?
Would you like to be able to give your students more personalised support and feedback?
Would you like to provide more support for students with varying mathematical ability?
Numeracy in Nursing and Healthcare Australian Edition with MyMathLab is the perfect package to help your students prepare for their nursing program. Read More
MyMathLab Global, Australia/New Zealand Edition
MyMathLab Global is a powerful online homework, revision and assessment tool to help students and instructors.MyMathLab Global engages students in active learning—it's modular, self-paced, accessible anywhere with internet access and adaptable to each student's learning style.
Independent of any textbook, it has been designed so instructors can easily customise MyMathLab Global to better meet their students' needs. |
Other Courses
Home Schooling A level Maths and Mechanics – The Course
The Maths A Level course is split into two major components – AS and A2. The AS level may be sat as a separate qualification in its own right.
Each lesson begins with a set of clearly stated objectives and an explanation of its place in the overall programme of study. Effective learning is encouraged through frequent activities and self-assessment questions. The AS Level has thirteen tutor-marked assignments (known as TMAs). The A2 has a further eleven TMAs.
Key Topics Covered
AS Level
MPC1: algebra, trigonometry, integration, etc
MPC2: exponentials, logarithms, etc
MM1B: Mechanics: vectors, forces, projectiles, etc
A2 Level
MPC3: algebraic functions, coordinate geometry etc
MPC4: sequences, series and vectors, etc
MM2B: Moments, Work and Energy, etc
The Syllabus
This course prepares candidates for the AQA Mathematics AS level syllabus 5361, for examination in 2013 and later years. Most candidates will then study the A2 syllabus 6361. The full Advanced Level qualification comprises AS and A2. We have chosen this syllabus as the most suited for Home Schooling.
Assessment is by three written papers for the AS Level and three written papers for the A2 Level. |
Secondary Schools/Adult
About this title.
Great student and teacher reference handbook! 'Maths Terms and Tables' is an essential maths aid specifically written for teachers, parents, and students aged 9-15. 120 pages of simple descriptions of terms, and clear tables, charts and diagrams, it is easy to understand and beneficial.
Features:
comprehensive listing of common mathematical terms, tables and concepts
brief yet accurate definitions
written in unambiguous, easily understood language
explanatory diagrams and examples used whenever appropriate or necessary
topic-based overview of key ideas in the latter half of the book
a highly accessible resource for users at all levels–students, teachers and parents |
Algebra With Trigonometry For College Students - With Cd - 5th edition
ISBN13:978-0534432959 ISBN10: 0534432956 This edition has also been released as: ISBN13: 978-0030344466 ISBN10: 0030344468
Summary: This text, written by best-selling developmental mathematics author Pat McKeague, features a more streamlined review of elementary algebra, allowing for earlier coverage of intermediate topics. An early introduction to graphing presents the foundation for a wide variety of graphing problems throughout the text. Early coverage of functions helps students feel comfortable with the many examples and graphs of functions that occur in later chapters. The first ten chapter...show mores of this book cove the topics usually found in a college-level algebra course. The last three chapters cover the essential topics from trigonometry. Optional technology sections and integrated throughout text as a way for students to better understand the material being discussed. ...show less
Paired Data and the Rectangular Coordinate System. The Slope of a Line. The Equation of a Line. Linear Inequalities in Two Variables. Introduction to Functions. Function Notation. Algebra with Functions. Variation. Summary. Review. Test. Cumulative Review. Projects.
053443295698 |
Introduction To Precalculus
posted on: 20 Jun, 2012 | updated on: 21 Jun, 2012
In mathematical world, we study different topic, here we will see the pre Calculus introduction. Pre calculus is a topic which comes from the study of motion. It deals with different ideas, areas and volumes, rates of change, the orbits of planets, and infinite sequences.
Pre calculus consists of those subjects, skills, and insights which are necessary to recognize calculus. It involves arithmetic, algebra, coordinate Geometry, trigonometry, and, functions. In Pre calculus we study many different type of topics which includes, sets, real numbers, complex numbers, composite and polynomial Functions, trigonometry, limits, vectors, metrics, binomial theorem, and many other topics. Let's understand few basic topic of pre calculus.
Set: - We know that Set is a collection of different type of objects which are defined in proper manner. Different types of operation are present in the set that are Union, intersection, complements and Cardinality product. Sets are of different type like Empty set, Universal set, etc.
If no element is available in the set then it is known as empty set, and the Sets are present in the universe of conversation are universal set.
Empty set is denoted by the symbol '∅' and universal set is denoted by 'U'
Real number: - In the Real Numbers all the Rational and Irrational Numbers and whole numbers are present.
For example: Whole numbers are (1, 4, 6, 8, 10). Sometime the number 0 is also involved in Whole Number.
Rational number – The Rational Numbers are 3/5, 0.16, 0.33…2.2 etc.
Irrational number – Irrational numbers are (⊼, √ 3) etc.
If we have √ -3, this number is not considered in the category of real number because it contains imaginary value and '∞' and it is not a real number.
This is a brief introduction to Precalculus in which we come across few Basic Terms of pre calculus. |
Choose a format:
Paperback
Overview
Book Details
McGraw-Hills GED Mathematics Workbook
English
ISBN:
0071407073
EAN:
9780071407076
Category:
Study Aids / Ged (General Educational Development Tests)
Publisher:
McGraw-Hill Companies, The
Release Date:
09/24/2002
Synopsis:
Problem-solving and computational skills, with special focus on the use of the Casio FX-260 calculator, understanding grids, and strategies for handling word problems.Announcing the companion workbook series to the GED test seriesPractice makes perfect with McGraw-Hills updated GED Workbook series, which reflects the 2002 test guidelines. These workbooks provide invaluable hands-on experience for students as they tackle hundreds of GED format questions and check results against an answer key. Simulated test-taking situations boost not only content retention but also confidence for the big day. Ideal study guides for a student weak in a particular subject area or sitting for one GED test at a time, these activity books function as a companion to McGraw-Hills GED Test titles and McGraw-Hills GED. |
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Quantitative Reasoning
Quantitative Reasoning courses are intended for first-year and sophomore students. Approved substitute courses are available for other students still needing to satisfy the Quantitative Reasoning component of the MAP.
FALL 2010 V55.0101 Quantitative Reasoning: Math Patterns in Nature Prof. Hanhart (Mathematics) Examines the role of mathematics as the language of science through case studies selected from the natural sciences and economics. Topics include the scale of things in the natural world; the art of making estimates; cross-cultural views of knowledge about the natural world; growth laws, including the growth of money and the concept of "constant dollars"; radioactivity and its role in unraveling the history of the earth and solar system; the notion of randomness and basic ideas from statistics; scaling laws and why things are the size they are; the cosmic distance ladder; and the meaning of "infinity." This calculator-based course is designed to help you use mathematics with some confidence in applications.
FALL 2010 V55.0105 Quantitative Reasoning: Elementary Statistics
Prof. Hanhart (Mathematics)FALL 2010 V55.0107 Quantitative Reasoning: Probability, Statistics & Decision-Making Prof. Hanhart (Mathematics) This course examines the role in mathematics in making ``correct'' probability, game theory, division strategies, and optimization.
FALL 2010 V55.0109 Quantitative Reasoning: Math & Computations Using Python Prof. Marateck (Computer Science) This course teaches key mathematical concepts using the new Python programming language. The first part of the course teaches students how to use the basic features of Python: operations with numbers and strings, variables, Boolean probability. Students use Python to explore the mathematical concepts in labs and homework assignments. No prior knowledge of programming is required.
SPRING 2011 V55.0101 Quantitative Reasoning: Math Patterns in Nature Prof. Hanhart (Mathematics) syllabus Examines the role of mathematics as the language of science through case studies selected from the natural and social sciences. Topics include growth laws, including the growth of money and the concept of "constant dollars"; radioactivity and its role in unraveling the history of the earth and solar system; the notion of randomness and basic ideas from probability and statistics; scaling principles and trigonometry and its role in determining measurements from antiquity to today. This calculator-based course is designed to help you use mathematics with some confidence in applications.
SPRING 2011 V55.0105 Quantitative Reasoning: Elementary Statistics Prof. Kalaycioglu (Mathematics) syllabusSPRING 2011 V55.0107 Quantitative Reasoning: Probability, Statistics & Decision-Making Prof. Hanhart (Mathematics) syllabus This course examines the role in mathematics in making ``correct'' decisions. Special attention is devoted to quantifying the notions of "correct,'' "fair,'' and "best'' and using these ideas to establish optimal decisions and algorithms to problems of incomplete information and uncertain outcomes. The mathematical tools used include a selection of topics in statistics, probability, optimization, and geometric growth.
Spring 2011 V55.0109 Quantitative Reasoning: Math & Computations Using Python Prof. Marateck (Computer Science) syllabus This
course teaches key mathematical concepts using the new Python
programming language. The first part of the course teaches students how
to use the basic features of Python: operations with numbers and
strings, variables, Boolean logic, control structures, loops and
functions. The second part of the course focuses on the phenomena of
growth and decay: geometric progressions, compound interest,
exponentials and logarithms. The third part of the course introduces
three key mathematical concepts: trigonometry, counting problems and
probability. Students use Python to explore the mathematical concepts in
labs and homework assignments. No prior knowledge of programming is
required.
Natural Science I
The prerequisite for all Natural Science I courses is completion of or exemption from Quantitative Reasoning, or completion of an approved substitute course.
FALL 2010 V55.0203 Natural Science I: Energy and the Environment Prof. Jordan (MAPFALL 2010 evaluate environmental issues and make informed decisions about them.
FALL 2010 V55.0205 Natural Science I: Exploration of Light and Color Prof. Stroke (Physics) syllabus Color science is an interdisciplinary endeavor that incorporates both the physics and the perception of light and color. It provides an understanding of visual effects that dramatically enhances our appreciation of what we see. The study of color, light, and optics has applications to photography, art, natural phenomena, and technology. We also study the eye as both an optical and an image processing instrument. Topics include how color is classified and measured (colorimetry), how light is produced, how atoms and molecules affect light, how the human retina detects light, and how lenses are used in cameras.
FALL 2010 V55.0209 Natural Science I: Quarks to Cosmos Prof. Gabadadze (Physics) syllabus Modern science has provided us with some understanding of age-old fundamental questions, while at the same time opening up many new areas of investigation. How old is the Universe? How did galaxies, stars, and planets form? What are the fundamental constituents of matter and how do they combine to form the contents of the Universe? The course will cover measurements and chains of scientific reasoning that have allowed us to reconstruct the Big Bang by measuring little wisps of light reaching the Earth, to learn about sub-atomic particles by use of many-mile long machines, and to combine the two to understand the Universe as a whole from the sub-atomic particles of which it is composed.
FALL 2010 V55.0214 Natural Science I: How Things Work Prof. SteinFALL 2010 V55.0214 Natural Science I: How Things Work Prof. AdlerSPRING 2011 V55.0203 Natural Science I: Energy and the Environment Prof. Jerschow (Chemistry) syllabus Explores the scientific foundations of current environmental issues and the impact of this knowledge on public policy. One goal is to examine several topics of pressing importance and lively debate in our society—e Relevant topics include the structure of atoms and molecules, the interaction of light with matter, energy relationships in chemical reactions, and the properties of acids and bases. Throughout, we also examine how scientific studies of the environment are connected to political, economic, and policy concerns.
SPRING 2011 V55.0204 Natural Science I: Einstein's Universe Prof. Schucking (Physics) syllabus Addresses the science and life of Einstein in the context of 20th-century physics, beginning with 19th-century ideas about light, space, and time in order to understand why Einstein's work was so innovative. Einstein's most influential ideas are contained in his theories of special relativity, which reformulated conceptions of space and time, and general relativity, which extended these ideas to gravitation. Both these theories are explored quantitatively, together with wide-ranging applications of these ideas, from the nuclear energy which powers the sun to black holes and the big bang theory of the birth of the universe.
SPRING 2011 V55.0214 Natural Science I: How Things Work Prof. Stroke We explore for0214 Natural Science I: How Things Work Prof. GrierNatural Science II
The prerequisite for all Natural Science II courses is completion of or exemption from Quantitative Reasoning, or completion of an approved substitute course. The completion of Natural Science I is recommended prior to taking Natural Science II.
FALL 2010 V55.0303 Natural Science II: Human Genetics Prof. Rockman (Biology) syllabus We are currently witnessing a revolution in human genetics, where the ability to scrutinize and manipulate DNA has allowed scientists to gain unprecedented insights into the role of heredity. Beginning with an overview of the principles of inheritance such as cell division and Mendelian genetics, we explore the foundations and frontiers of modern human genetics, with an emphasis on understanding and evaluating new discoveries. Descending to the molecular level, we investigate how genetic information is encoded in DNA and how mutations affect gene function. These molecular foundations are used to explore the science and social impact of genetic technology, including topics such as genetic testing, genetically modified foods, DNA fingerprinting, and the Human Genome Project. Laboratory projects emphasize the diverse methods that scientists employ to study heredity.
FALL 2010 V55.0306 Natural Science II: Brain and Behavior Prof. SuzukiFALL 2010 V55.0309 Natural Science II: The Body - How It Works Prof. Goldberg (Chemistry) syllabus The human body is a complex system of mutually interdependent molecules, cells, tissues, organs and organ systems. We examine the human body with the goal of understanding how physiological systems operate at these varying levels. Examples include the circulation of blood, the function of our muscles, the utilization of oxygen in respiration, and how our immune system detects and fights foreign invaders. Disturbing the delicate balance of these systems can produce various human diseases, which will also be examined throughout the course. Laboratory work provides firsthand experience with studying molecular processes, cell structures, and physiological systems.
FALL 2010FALL 2010 V55.0313 Natural Science II: The Brain: A User's Guide Prof. Azmitia (Biology) syllabus The Human Brain is the most complex organ. Despite the central position it has in nearly every aspect of our daily lives, it remains to many a mystery. How does it work? How can we care for it? How long will it function? This MAP course is designed to provide answers to these questions, and many more at an academic level accessible to the non-scientist student, and of interest to the scientist with little exposure to neuroscience. The aims of the course are to provide the student with a firm foundation in what the brain looks like and what each of the parts do. To accomplish this, we will learn about the functions of the cortex in higher learning and memory, as well as discuss the basic work of the brainstem in regulating the internal environment of the body. The importance of nutrition on neurotransmitter synthesis, the function of sleep on memory and why we need so much of it, and the effects of alcohol and drugs on brain harmony and the meaning of addiction will be some of the points covered in this course. We will look at brain development and the special needs of children, as well as brain aging and illness and the difficulty of helping. The laboratories are designed to provide hands-on experience in exploring the structure of the brain as well as learning how to measure brain functioning. We will provide specially prepared slides so the student can recognize a neuron and differentiate a dendrite from an axon. The molecular shape of neurotransmitter will be covered, as well as learning how to measure alcohol and determining its levels in your body. It is expected that by the end of the course, the student will be familiar with the biological basis of brain structure and function, and not only be able to detect how a normal brain works, but also how to help keep it healthy.
SPRING 2011 V55.0305 Natural Science II: Human Origins Prof. Bailey (Anthropology) syllabus An introduction to the approaches and methods scientists use to investigate the origins and evolutionary history of our own species. This interdisciplinary study synthesizes research from a number of different areas of science. Topics include reconstructing evolutionary relationships using molecular and morphological data, the mitochondrial Eve hypothesis, ancient DNA, human variation and natural selection, the use of stable isotopes to reconstruct dietary behavior in prehistoric humans, the Neandertal enigma, the importance of studies of chimpanzees for understanding human behavior, and the 6-million-year-old fossil evidence for human evolution.
SPRING 2011 V55.0306 Natural Science II: Brain and Behavior Prof. HawkenSPRING 2011SPRING 2011 V55.0311 Natural Science II: Lessons from the Biosphere Prof. Volk (Biology) syllabus Provides a foundation of knowledge about how Earth's biosphere works. This includes the biggest ideas and findings about biology on the global scale-the scale in which we live. Such knowledge is especially crucial today because we humans are perturbing so many systems within the biosphere. We explore four main topics: (1) Evolution of Life: How did life come to be what it is today? (2) Life's Diversity: What is life today on the global scale? (3) Cycles of Matter: How do life and the non-living environment interact? (4) The Human Guild: How are humans changing the biosphere and how might we consider our future within the biosphere? Laboratory experiments are complemented by an exploration at the American Museum of Natural History.
SPRING 2011 V55.0314 Natural Science II: Genomes and Diversity Prof. Siegal (Biology) syllabus Millions of species of animals, plants and microbes inhabit our planet. Genomics, the study of all the genes in an organism, is providing new insights into this amazing diversity of life on Earth. We begin with the fundamentals of DNA, genes and genomes. We then explore microbial diversity, with an emphasis on how genomics can reveal many aspects of organisms, from their ancient history to their physiological and ecological habits. We follow with examinations of animal and plant diversity, focusing on domesticated species, such as dogs and tomatoes, as examples of how genomic methods can be used to identify genes that underlie new or otherwise interesting traits. Genomics has also transformed the study of human diversity and human disease. We examine the use of DNA to trace human ancestry, as well as the use of genomics as a diagnostic tool in medicine. With the powerful new technologies to study genomes has come an increased power to manipulate them. We conclude by considering the societal implications of this ability to alter the genomes of crop plants, livestock and potentially humans.
Texts and Ideas
Note: Previously listed as Conversations of the West
Fall 2010 V55.0400 Texts and Ideas: Topics - Animal Humans Prof. Lezra (Comparative Literature) syllabus "One might go so far as to define man as a creature that has failed in its effort to keep its animalness…" So writes the German philosopher Peter Sloterdijk. What sort of animal were we? Where, how, and by whom has the line between the human and the animal been drawn? With what consequences for our "human" understanding of the world? Of concepts like the "soul," "society," politics, the family? Is the line between the human and the animal drawn differently in different genres--in literary works, theological treatises, natural histories, paintings, films? We come at these questions from different angles, following them from antiquity to early modern responses to these questions, and in essays by contemporary philosophers and advocates. Readings: Genesis, Numbers, Euripides' Bacchae, Plato's Phaedrus, Ovid's Metamorphoses, Apuleius' Golden Ass, Marie de France' Bisclavret, Shakespeare's Midsummer Night's Dream, Montaigne's "Apology in Defense of Raymond Sebond, Machiavelli's Prince, H. G. Wells's Island of Dr. Moreau and Island of Lost Souls, Derrida's "The Animal that therefore I am," selections from Boccaccio, Peter Singer, Giorgio Agamben, Donna Haraway.
Fall 2010 V55.0400 Texts and Ideas: Topics - Spectatorship—Ethics, Politics, Aesthetics Prof. Harries (English) syllabus Are you responsible for what you see? Sometimes? Never? Always? How do you decide? Why do works of art so often represent suffering? Does art allow us to witness suffering without having to take responsibility for that suffering? What happens when we witness real suffering as though it were art? We consider crucial texts on spectatorship from Plato to the present, how various thinkers and artists have approached these and other questions, and how looking from a distance has informed thinking about aesthetics, ethics, and politics. Throughout our discussions of these readings, we ask what it means that thinkers insist that looking has power: power to produce various emotions from desire to sympathy, or power to produce social and even political bonds. These thinkers will, in turn, challenge us to think about the function of images in the present. Readings and films: Plato's Republic, Ovid's Metamorphoses, Shakespeare's King Lear, Smith's Theory of Moral Sentiments, Rousseau's Letter to M. d'Alembert on the Theatre, Nietzsche's Birth of Tragedy, selections from Freud, Beckett's Endgame, Buster Keaton's Sherlock Jr., Hitchcock's Rear Window.
FALL 2010 V55.0400 Texts and Ideas: Topics-- The Deliberating Citizen Prof. Connolly (Classics) syllabus What do we need to function as citizens of a democracy--capacities of reason, imagination, or eloquence? Skills in analyzing public discourse or habits of historical memory? Is belief in God required, or particular emotional tendencies or sympathies? What kind of humanistic values, if any, can and should a democracy promote? We examine these questions on the assumption that intensive close reading (and listening, in Mozart's case) promotes the habits of engaged, articulate talking and writing that are the bedrock of civic education. Music of Mozart and readings from Plato, Thucydides, Vergil, Shakespeare, Rousseau, Kant, Adam Smith, John Dewey, Hannah Arendt.
FALL 2010 V55.0402 Texts and Ideas: Antiquity and the Renaissance Prof. Bolduc (French) syllabus Explores how books give shape, meaning, and purpose to the world and human experience. As it reinterprets the Greek and Roman legacy, the Renaissance faces crucial epistemological shifts triggered by new discoveries that call to mind our own struggles: making sense of a world in constant flux where truths are not only put into question but also lead to bloodshed. Grouped under four main themes--epic and the human experience, tales of beginnings and ends, battles for truth, writings of the self--we consider the purpose of this conversation between writers of different epochs and its relevance for understanding our own culture. Reading: Vergil's Aeneid, Cervantes' Don Quixote, Hesiod's Theogony, selections from Hebrew and Christian Scriptures, Machiavelli's Prince, Navarre's Heptameron, Sophocles' Antigone, Shakespeare's Hamlet, Plato's Symposium, Augustine's Confessions, selections from Montaigne's Essays.
FALL 2010FALL 2010 V55.0403 Texts and Ideas: Antiquity and the Enlightenment Prof. Garrett (Philosophy) syllabus All animals live, but only human beings consider how to live; and only reflective human beings deliberate among different ways to decide how to live. Should one look for guidance to tradition, to religion, to the state, to nature, to feeling, to reason? Versions of this question were raised and addressed repeatedly and with urgency in both Antiquity and the Enlightenment. We examine some of the most important and influential attempts to answer it and some of the dialogue that such attempts have had with one another. Readings include Hebrew and Christian scriptures, Greek tragedy and philosophy, Spinoza, Locke, Rousseau, Hume, Kant, Wollstonecraft.
FALL 2010 V55.0404 Texts and Ideas: Antiquity and the 19th Century Prof. Ulfers (German) syllabus A conversation between two paradigms informing Western culture: the dominant, optimistic one, revolving around notions of historical progress toward absolute knowledge and utopian visions of the world and society; and the subterranean, pessimistic one, which looks on the former as a human construct or fiction that must come to naught. Readings: works from the Hebrew and Christian scriptures, Plato, and Sophocles; Augustine's Confessions; selections from Darwin; Marx and Engels' Communist Manifesto; Nietzsche's Birth of Tragedy; Freud's Interpretation of Dreams; Kafka's Metamorphosis; Mann's Death in Venice.
FALL 2010 V55.0404 Texts and Ideas: Antiquity and the 19th Century Prof. Corradi (Sociology) syllabus A guide to the intellectual heritage distinctive to the West, with special attention to the nature of the person, freedom, rationality, democracy, and the social order. The works we study continue to shape the way people understand themselves and the world. They are 'classic' in the sense that they have not finished saying what they have to say. We situate them in historical context, looking for ways in which later authors responded to themes introduced by earlier ones. From the particularity of the West, these themes show a vocation for universality. Readings include: Genesis, Exodus, Luke, Corinthians; Sophocles' Oedipus and Antigone; Plato's Apology and Republic; Aristotle's Nicomachean Ethics; Pericles' Funeral Oration; Epictetus' Discourses; Augustine's Confessions; Tocqueville's Democracy in America; Mill's On Liberty; Darwin's Origins of the Species; Marx and Engels' Communist Manifesto; Kierkegaard's Fear and Trembling; Nietzsche's Genealogy of Morality; Weber's Protestant Ethic and the Spirit of Capitalism; Lincoln's Gettysburg Address; Freud's Civilization and Its Discontents.
FALL 2010 V55.0404 Texts and Ideas: Antiquity and the 19th Century Prof. Calhoun (Sociology) syllabus A guide to the intellectual heritage distinctive to the West, with special attention to the nature of the person, faith, ethics, and the social order. The works we study continue to shape the way people understand themselves and the world. We situate them in historical context, looking for ways in which later authors responded to themes introduced by earlier ones. Readings include: Genesis, Exodus, Luke, 1 Corinthians; Sophocles' Oedipus; Plato's Apology and Crito; Aristotle's Nicomachean Ethics; Epictetus' Discourses; Augustine's Confessions; Shelley's Frankenstein; Tocqueville's Democracy in America; Mill's On Liberty; Marx and Engels' The Communist Manifesto; Kierkegaard's Fear and Trembling; Nietzsche's Genealogy of Morality; Weber's Protestant Ethic and the Spirit of Capitalism; and Dostoyevsky's Crime and Punishment.
FALL 2010 V55.0412 Texts and Ideas: Antiquity and the Renaissance - Writing Intensive Prof. Gerety (Collegiate Professor) syllabus What is the soul? Is it the conscious self or something more? Does our identity persist beyond death? What is the relation between the soul and good and evil? Some say that Socrates 'discovered' the human soul, but the idea that we have souls that outlast our bodies is as old as humanity. Our understanding of the nature of our souls often dictates the way we feel we should live. We will explore ideas from Homer and Heraclitus through Socrates himself and then on to Sophocles, Plato, Aristotle, the Hebrew Bible, the New Testament (including the Gnostics), Augustine, and Vergil. We look for the elements that make up personal identity and value in the ancient world, both religious and secular, and see how much these change from Homer's world to that of Augustine and the Roman Empire. We then turn to Dante, who provides a bridge to some of the great thinkers and artists of the Renaissance--most notably Shakespeare and DaVinci but also Montaigne and Villon. In all of these, the permanence and even presence of our souls seem more uncertain, more threatened by death and obliteration, than in Plato or Paul, and this threat reaches our morality and values as well. In this way, the Renaissance marks the beginning of the world in which all of us must now find our way.
Note: Offered in conjunction with selected sections of V40.0100, Writing the Essay.
Note: Offered in conjunction with selected sections of V40.0100, Writing the Essay.
SPRING 2011 V55.0400 Texts and Ideas: Topics: Justice and Injustice in Biblical Narrative and Western Thought Prof. Weiler (Law) syllabus Issue of justice and injustice and other normative concerns. Each week pairs a core reading from the Hebrew Bible or the New Testament with another work in the Western tradition to explore a broad range of complex normative issues. Often God will be "on trial:" Was the Deluge genocide? Is Abraham guilty of attempted murder and child abuse? Was Jesus guilty as charged? Was Socrates? The themes are all of relevance to contemporary issues: communal responsibility vs. individual autonomy, ecological crisis, ethics vs. religion, freedom of speech and thought, genocide, rule of law and civil disobedience, the Other, punishment and retribution, religious intolerance, sanctity of human life, sex and gender. The course will be taught at the Law School in Law School style—rigourous but academically and intellectually rewarding. Primary readings include: Aristophanes' Clouds; Plato's Apology; Xenophon's Apology; Sophocles' Antigone; selections from Hebrew Bible, New Testament, Aristotle, Maimonides, Aquinas, Luther, Kant, Kierkegaard, Mill, Thoreau, Kafka, Camus.
SPRING 2011 V55.0400 Texts and Ideas: Topics: Free Will in Western Thought Prof. Krabbenhoft (Spanish and Portuguese) syllabus The freedom of the human will has been a foundational premise of Western civilization from the early centuries of the Christian era to the present, and yet it has been questioned and even rejected by some of the most influential thinkers of the modern period. We look at the sources of the modern debate in passages from the Hebrew Bible and Greek philosophy, in key texts by Augustine, Luther, and Erasmus, and in the shift toward a deontological view in Kant, Schopenhauer, and nineteenth-century materialism. From this historical overview we move to contemporary theories of freedom and determinism, as well as a discussion of the intersection of neuroscience and the philosophy of free will, and read a number of literary texts in the light of theory: Sophocles' Philoctetes, Tirso de Molina's Trickster of Seville, Tolstoy's Death of Ivan Ilyich, and Stanislaw Lem's Fiasco.
SPRING 2011 V55.0400 Texts and Ideas: Topics: Literature in Wonderland Prof. Momma (English) syllabus How to Play with Language: We use language every day, and yet we do not seem to know exactly how it works. Communicating with others through language sometimes feels like playing a game. But does this mean we have only one language game to play, or that we follow only one set of rules all the time? Just like Alice, who was constantly frustrated by the logic of the inhabitants of Wonderland, we are often baffled by difficulties in communicating even the simplest idea. We explore issues on language that may be raised by reading literary and philosophical texts written by "language-conscious" authors: Is language the only way to communicate? Do we know anything about the origin of language? Do grammar and rhetoric help us communicate well or persuade others? Do etymology and the history of English tell us anything new about the language we know already? Do our minds work exactly the same way regardless of the language we speak? How do we do things with words? Readings: Carroll's Alice's Adventures in Wonderland and Through the Looking-Glass, Plato's Cratylus, Aristotle's Poetics, Shakespeare's Hamlet, Beowulf, Chaucer's House of Fame, Melville's Bartleby the Scrivener, Borges' Library of Babel, Achebe's Things Fall Apart.
SPRING 2011 V55.0400 Texts and Ideas: Topics: Freedom and Oppression Prof. Kunhardt (History) syllabus Examines the human quest for freedom—freedom from slavery, from sexual oppression, and from the shackling of the mind—as these three came to a crisis in nineteenth century America. We begin with a critical reading of formative biblical texts and ideas; touch down on the passionate thought-world of the American founders; and culminate in a close look at mid-nineteenth century reform efforts, and the ideas of freedom that animated them. Exploring the dawn of biblical humanism, the embrace of the secular, and efforts to widen the circles of inclusion, we pay particular attention to the writings of Abraham Lincoln and his generation, as he and others, both allies and critics, worked to eradicate slavery from American society. Why did the Bible condone slavery, helping Americans justify continuing the practice? In what ways are competing ideas of freedom to be judged? How is the idea of freedom related to that of human equality? Readings: Genesis, Exodus, Psalms, Isaiah, Matthew, Luke; and works by Paine, Jefferson, Madison, Garrison, Douglass, Sumner, Stanton, Anthony, Rose, Emerson, Thoreau, Whitman, Parker, Mill, Ingersoll, Lincoln.
SPRING 2011 V55.0400 Texts and Ideas: Topics: Mortal and Immortal Questions Professor Mitsis (Classics) syllabus A wide-ranging selection of works that have framed in memorable, though often contradictory, ways some basic questions about the nature of religion, the successes and failures of rational argument, the justification of social and political obligations, the benefits and dangers of technology and scientific knowledge, and the value of emotions and our attachments to others. Throughout the semester, students have the opportunity to become more practiced in formulating moral, political, and aesthetic arguments and in what used to be characterized as the proper use of one's solitude, that is, examining what it means to be a human being faced with death--or, perhaps, worse, faced with eternal life. Readings: Homer, Sophocles, Euripides, Thucydides, Plato, Epicureans, Stoics, Hebrew and Christian scripture, Augustine, Teresa of Avila, Hume, d'Holbach, Rousseau, Mill, Marx, Tolstoy, Freud, Proust.
SPRING 2011SPRING 2011 V55.0403 Texts and Ideas: Antiquity and the Enlightenment Prof. Rubenstein (Hebrew & Judaic Studies) syllabus Beginning with the collision of the "Judeo-Christian" and Hellenistic traditions and their encounter in the Christian Scriptures and Augustine, we see Enlightenment thinkers grapple with the fusion of these traditions they had inherited, subjecting both to serious criticism and revising them as a new tradition—science and technology—rises to prominence. Reading from the Hebrew and Christian Scriptures, Sophocles, Plato, Augustine, Montesquieu, Pope, Voltaire, and Rousseau.
SPRING 2011 V55.0403 Texts and Ideas: Antiquity and the Enlightenment Prof. Deneys-Tunney (French) syllabus The Enlightenment was a Europe-wide movement, which concerned all aspects of culture of the time: philosophy and literature, the arts (painting, music, architecture), as well as politics and society as a whole. The Enlightenment defined itself as a new birth, a subversive movement that would free mankind of all its prejudices--philosophical, religious, political, sexual, racial. In doing so, the Enlightenment appears today to be indeed the beginning of our modernity, as it invented key concepts that define or frame our contemporary representations of ourselves and the world around us: the concept of the subject or subjectivity, of nature, of origins, of equality, of critical philosophy and democracy, of pleasure, of sexuality, of happiness. It is a unique moment in history, where philosophy aims not only at interpreting the world but also at changing it to make it a better place for mankind. It culminates at the end of the 18th century in France with the French Revolution, which declared for the first time in human history that all men are born free and equal. Readings: Genesis, Plato's Symposium and Phedrus, Epicurus' Maxims and letters, Descartes' Discourse on Method, Rousseau's Discourse on Inequality and Rêveries, Diderot's Indiscreet Jewels and Jacques the Fatalist, Voltaire's Candide and Zadig, Marivaux's Dispute and Double Unfaithfulness, Kant's "What is Enlightenment?"
SPRING 2011 V55.0404 Texts and Ideas: Antiquity and the 19th Century Prof. Ertman (Sociology) syllabus Explores the ancient foundations of traditional Western culture by examining the political and social institutions, religious beliefs, and value systems of the Israelites, Greeks, Romans, and early Christians; then turns to the radical challenges to this traditional culture, in the areas of the economy, politics, religion, and morality, that arose over the course of the 19th century, challenges that continue to reverberate to this day. Readings: Genesis, Exodus, Deuteronomy, Luke, Acts, Romans; Thucydides' Peloponnesian War; Plato's Apology and Symposium; Vergil's Aeneid; Augustine's Confessions; Smith's Wealth of Nations; Marx and Engels' Communist Manifesto; Mill's On Liberty; Darwin's Origin of Species; Nietzsche's Genealogy of Morality; Freud's Civilization and Its Discontents.
Cultures and Contexts
Note: Previously listed as World Cultures
FALL 2010 V55.0502 Cultures and Contexts: Islamic Societies Prof. Chelkowski (Middle Eastern & Islamic Societies) syllabus Examines the common base and regional variations of Islamic societies. An "Islamic society" is here understood as one that shares, either as operative present or as historical past, that common religious base called Islam. For Muslims, Islam is not simply a set of beliefs or observances but also includes a history; its study is thus by nature historical, topical, and regional. Here our particular focus is on the society of Shi'i Muslims. Shi'ism has been neglected in the last 200 years of the Western study of Islam, and only since the 1978–79 Islamic Revolution in Iran has it received attention in the West. Now, with American forces in Iraq, Shi'ism is suddenly one of the main topics of interest for the news media. The Shi'is of Iraq are the majority—some 60%—of the population, but historically they have been deprived of power in the government and of access to the political and economic life of the country.
FALL 2010 V55.0505 Cultures and Contexts: Africa Prof. Gomez (History) syllabus Major issues and questions relating to Africa's development from early to contemporary times, approached through its literature. While not a formal study of the history of Africa, establishes the historical context for understanding the literary texts in the periods in which they are embedded. Examined regionally and over time are questions concerning the relationship of the production of literature to centers of power, the meaning of literature in societies espousing orality, the problematics of sustaining both content and intent upon the conversion of oral literature into written form, the specific and at times parochial uses of literature, the interplay of gender and voice, and the politics of translation into European modalities.
FALL 2010 V55.0506 Cultures and Contexts: Chinese and Japanese Traditions Prof. Roberts (East Asian Studies) syllabus Essential aspects of Asian culture—Confucianism, Taoism, Buddhism, and Shintoism—studied through careful reading of major works of philosophy and literature. A roughly equal division between Chinese and Japanese works is meant to give a basic understanding of the broad similarities and the less obvious, but all-important, differences among the cultures of Confucian Asia. One reading is a Vietnamese adaptation of a Chinese legend. The last two readings, modern novellas from Japan and China, show the reaction of the traditional cultures to the Western invasions.
FALL 2010 V55.0509 Cultures and Contexts: Caribbean Prof. Khan (Anthropology) syllabus Examines the impact of the Caribbean's long colonial history from the perspective of its diverse populations, through race, class, culture, gender, and sexuality. Known for its beauty, cultural vitality, and mix of peoples, cultures, and languages, the Caribbean is where today's global economy began, some 500 years ago. Its sugar economy and history of slave labor and colonialism made it the site of massive transplantations of peoples and cultures from Africa for more than four centuries and from Asia since the mid-19th century, and of a sizable influx of peoples from Europe all along. Readings examine the history of the region's differing forms of colonialism; the present postcolonial economic and political structures; anthropological material on family and community life, religious beliefs and practices, gender roles and ideologies; and ways in which national, community, and group identities are expressed today.
FALL 2010 V55.0514 Cultures and Contexts: Ancient Israel Prof. D. Fleming (Hebrew & Judaic Studies) syllabus The people of the Hebrew Bible understood themselves to be united as an ancient tribe called Israel, a name that lay behind even the eventual state. Working backward from the fullest early definition of Israel, when the Hebrew Bible was taking final form, toward the time of older origins, we push back in time, using the Bible as the primary point of reference, while examining various independent evidence. Writing projects focus mainly on interpretation of biblical texts.
Fall 2010 V55.0515 Cultures and Contexts: Latin America Prof. Abercrombie (Anthropology) syllabus Spanish, African, and Amerindian Sources of Latin American Identities. Explores the emergence of contemporary Latin America through the past and present doings of its persons and their representations, religious manifestations, song, dance, and literature. Through in-depth treatment of selected cases, and via the perspectives of history, anthropology, and cultural criticism, focusing on texts but also film, dance, music, and performance, the aims is both to uncover the roots of Latin-Americanness (and of global modernity) in the historical confluence of Europe, Africa, and America, and to discover how those roots are continually remade as each generation strives to rise from the ashes of its forebears. Case studies include the samba schools and Candomble religion in Brazilian carnival, the role of Vodou in the Haitian revolution and in New York City, the Mexican burlesques of death in the Day of the Dead, and "Indian" saints whose processions are associated with rites to underworld beings as well as to national integration. At base, we seek to answer more fundamental questions: What does it mean to have an identity, Latin American or Gringo, White, Black, Indian, or Mixed? How are the collectivities called nations, ethnicities, races, and classes brought into being and sustained? How is the vanished past resuscitated to serve the needs of the present? What does it mean to be Latin American in the age of so-called globalization? Includes frank and explicit discussion of race, sex, and religion.
FALL 2010 V55.0534 Cultures and Contexts: The Black Atlantic Prof. Morgan (Social and Cultural Analysis) syllabus A range of intersecting questions concerning the African Diaspora and what it produces: What does the trans-Atlantic slave trade create in the early modern and modern world? How is our understanding of trade, culture, capitalism, justice, race, gender, and work shaped by the histories of dispersal that characterize the Atlantic World? What aspects of culture, politics, identity, and social formations are illuminated when we think critically about the African Diaspora and the forces that propel it?
FALL 2010 V55.0537 Cultures and Contexts: Modern Israel Prof. Zweig (Hebrew & Judaic Studies) syllabus Modern Israel—Society and Culture: Despite its small size and population, Israel is a diverse, dynamic, and complex society. To understand its ethnic, religious, and political divisions, the different ethnic origins of the Jewish population over the last 150 years will be examined, and the growing role of the Arab population (approaching 20%) in Israeli society will be discussed. The special role of religion in the secular state, the development of Hebrew speaking culture, the political system, the settlement movement and the peace movement, gender issues, and the role of the army in everyday life are all addressed, concluding with a survey of the debate on whether Israel is a Jewish state or a state of all its citizens. Although the controversial issues that keep Israel in the headlines are touched on, the focus is the character of Israeli society and the impact on everyday life of living in the international limelight.
FALL 2010 V55.0539 Cultures and Contexts: Asian Pacific American Cultures Prof. Tu (Social and Cultural Analysis) syllabus Major issues in the historical and contemporary experiences of Asian Pacific Americans, including migration, modernization, racial formation, community-building, and political mobilization, among others. Asian Pacific America encompasses a complex, diverse, and rapidly changing population of people. As an expression/reflection of their cultural identities, historical conditions, and political efforts, we pay particular attention to Asian Americans' use of cultural productions-films, literature, art, media, and popular culture.
Fall 2010 V55.0541 Cultures and Contexts: New World Encounters Prof. Lane (Spanish & Portuguese) syllabus What was America before it was called America? How did indigenous cultures understand and document their first encounters with Europeans? We focus on peoples, events, and cultural expressions associated with the conquest and colonization of the Americas, concentrating on three key areas: central Mexico, home to a several pre-Columbian societies, most notably the Aztec Empire, and later the seat of Spanish power in northern Latin America (the Viceroyalty of New Spain); the central Andes, home of the Incas and later the site of Spanish power in southern Latin America (the Viceroyalty of Peru); and finally, early plantation societies of the Caribbean, where the violent history of enslaved Africans in the new world unfolded. On one hand, we explore how those subjugated by conquest and colonialism interpreted, resisted, and recorded their experience. On the other, we ask what new cultural forms emerged from these violent encounters, and consider their role in the foundation of "Latin American" cultures. Readings balance a range of primary documents and art created during the "age of encounter," including maps, letters, paintings, and testimonials, along with historical and theoretical texts.
FALL 2010 V55.0545 Cultures and Contexts: Egypt of the Pharaohs Prof. Morris (ISAWFALL 2010 V55.0546 Cultures and Contexts: Global Asia Prof. Ludden (History) syllabus Explores the expansive transformation of Asian cultures from ancient times to the present, focusing on networks of mobility, interaction, social order, and exchange that form the particularity of Asian cultures through entanglements with others. Beginning in the days of Alexander the Great and the formation of the Afro-Eurasian ecumene, follows tracts of Buddhist, Confucian, Hindu, and Muslim expansion; then turns to the age of early modern landed empires, Ottoman-Safavid-Mughal-Ming/Ching, and their interactions with seaborne European expansion. Studies truly global formations of culture in the flow of goods, ideas, and people among world regions, during the age of modern empires and nationalism, including the rise of the nation as a cultural norm, capitalism in Asia, and Japanese expansion around the Pacific rim. Concludes by considering cultural change attending globalization since the 1950s, focusing on entanglements of Asian cultures with the globalizing culture of the market, consumerism, and wage labor, and transnational labor migration as well as Asian cultural spaces in and around New York City, including our nearby Chinatown.
SPRING 2011 V55.0505 Cultures and Contexts: Africa Prof. Hull (History) syllabus Focuses on several major African cultures that influenced each other's development from the pre-colonial through the postcolonial eras. These multi-dimensional cultures are examined through a variety of films, primary and secondary sources, and museum artifacts, with emphasis on concepts of cultural identity and interchange, modernization, and cosmopolitanism. Africa is examined not only within the context of indigenous cultures but within the context of the world at large. In this vein, we weigh the contributions African cultures made to each other but also to the wider world.
SPRING 2011 V55.0505 Cultures and Contexts: Africa Prof. Beidelman (Anthropology) syllabus Key concepts for understanding sub-Saharan African cultures and societies, and ways of thinking critically and consulting sources sensibly when studying non-Western cultures. Topics include: problems in the interpretation of African literature and history, gender issues, the question of whether African thought and values constitute a unique system of thinking, the impact of the slave trade and colonialism on African societies and culture, and the difficulties of and means for translating and interpreting the system of thought and behavior in an African traditional society into terms meaningful to Westerners. Among the readings are novels, current philosophical theory, and feminist interpretations of black and white accounts of African societies.
SPRING 2011 V55.0507 Cultures and Contexts: Japan Prof. Solt (History) syllabus Postwar Japan, 1945 to Present. An inquiry into Japan's social, political, and economic transformation since World War II. Examines the role of the Cold War, the U.S. Occupation, the "Peace" Constitution, the symbolic monarchy, the economic "miracle," corporate structure, the gendering of labor, and the legacy of war in shaping the history of postwar Japan. An underlying theme is the connection between political economy and culture. As such, we focus on the geopolitical and economic structures underpinning the visible transformations in everyday life and try to connect these transformations in Japanese history to broader themes in global history.
SPRING 2011 V55.0510 Cultures and Contexts: Russia—between East and West Prof. Borenstein (Russian & Slavic Studies)syllabus What is Russia? What does it mean to be "Russian"? These questions have troubled Russians for centuries. Certainly, most nations engage in such soul-searching at one time or another; but Russia, thanks to special historical circumstances, has been obsessed with the problem of its own identity. Central to this concern is an issue that would appear to be more geographical than cultural: Is Russia a part of Europe (the West), or of Asia (the East)? Or, is it some hybrid that must find its own unique destiny? As we trace the development of this problem throughout Russia's history, we also become acquainted with the major characteristics and achievements of Russian culture, from its very beginnings to the present day.
SPRING 2011 V55.0512 Cultures and Contexts: China Prof. Button (East Asian Studies) syllabus However one might choose to define the nature of human being, no one is ever merely human. Apart from whatever common essence we may be said to share, we are always also a combination of racial, ethnic, national, and gender differences. Over the course of several millennia Chinese culture has produced different conceptions of human being. We explore the variety of ways those conceptions have changed over time. Central to our inquiry is the question of how contending visions of the human are expressed and contested in different kinds of philosophical and literary texts, as well as artistic works in other media, including visual culture and film. Our guiding focus is on how ideas about human being in China have shaped gender roles and relations, the discourses of spirituality and the supernatural, as well as modern problems of race, nationalism, and revolution.
SPRING 2011 V55.0516 Cultures and Contexts: India Prof. Ganti (Anthropology) syllabus Utilizing a variety of sources—novels, films, and academic scholarship—students are introduced to the history, culture, society, and politics of modern India. Home to one billion people, eight major religions, twenty official languages (with hundreds of dialects), histories spanning several millenia, and a tremendous variety of customs, traditions, and ways of life, India is almost iconic for its diversity. We examine the challenges posed by such diversity as well as how this diversity has been understood, represented, and managed, both historically and contemporarily.
SPRING 2011 V55.0529 Cultures and Contexts: Contemporary Latino Cultures Prof. Rosaldo and Prof. Gaytan (Social and Cultural Analysis) syllabus Addresses immigration, social movements, figures of resistance, testimonials, identities, popular culture, and language. Using an interdisciplinary approach that draws on readings from imaginative literature to social science, we explore Latino communities in the United States and the issues that divide and unite them.
SPRING 2011 V55.0533 Cultures and Contexts: Iran Prof. Chelkowski (Middle Eastern & Islamic Societies) syllabus From Ancient Persia to Contemporary Iran: For 2500 years, the culture and civilization of Iran, (known in the West prior to World War II as Persia), has survived innumerable attacks and vicissitudes, which swept away many other cultures, languages, and nations. The first empire in human history to be multiracial, multicultural, and multi-religious, based on tolerance, expanded ultimately to encompass all the lands from the Hindu Kush to North Africa. Emphasizing the growth of ancient Iranian culture--particularly art, architecture, literature, and their influence--we investigate the traditional myths and religions of ancient Iran, the rebirth of Iranian self-consciousness, the establishment of Shi'i Islam as the state religion, and the conflict of the vision and mysticism of traditional Iranian culture with that of the West. We survey the political organization of the Empire, Alexander the Great's conquest of Iran and its aftermath, and the impact of the Arab-Islamic conquest. We examine the rebirth of Iranian self-consciousness after World War II, and the transformation of the country during the Islamic Revolution.
SPRING 2011 V55.0545 Cultures and Contexts: Egypt of the Pharaohs Prof. Roth (Hebrew and Judaic StudiesSPRING 2011 V55.0549 Cultures and Contexts: Multinational Britain Prof. Ortolano (History) syllabus Introduces students to the peoples, cultures, and histories of the British Isles. Today home to a pair of European states, the United Kingdom and the Republic of Ireland, this grouping of islands off the northwestern coast of Europe has historically been home to an astonishing variety of peoples, kingdoms, religions, nations, and states. Rather than collapsing this diversity into a study of the English people or the British state, we think about the United Kingdom as a multinational formation, produced through the experience of repeated invasions, encounters, and migrations. Our ultimate goals are twofold: to learn about the peoples of the British Isles, and to use this knowledge to think critically about claims regarding national characteristics, ethnic stability, or cultural homogeneity--in Britain, and beyond.
Expressive Culture
FALL 2010 V55.0722 Expressive Culture: Images - Architecture in New York Field Study Prof. Broderick (Art History) syllabus New York's rich architectural heritage offers a unique opportunity for firsthand consideration of the concepts and styles of modern urban architecture, as well as its social, financial, and cultural contexts. Meets once a week for an extended period combining on-campus lectures with group excursions to prominent buildings. Attention is given both to individual buildings as examples of 19th- and 20th-century architecture and to phenomena such as the development of the skyscraper and the adaptation of older buildings to new uses0751 Expressive Culture: Television Prof. Polan (Cinema Studies) syllabus The Twilight Zone and Expressive Culture of the 1950s and 1960s. According to cliché, the 1950s in America were a period of conformity and consensus, but it is clear that there were many signs of discontent with and within the image of cheerful homogeneity. For example, at the end of the decade, the television program The Twilight Zone, showed everyday life as a source of paranoia in which ordinary existence revealed its frightening underside. Then, as the nation engaged with the New Frontier of the Kennedy 1960s, the show used science fiction to represent dreams as American nightmares. We look at The Twilight Zone in terms of its expressive rendition of 1950s and 1960s America. Along the way, we examine the shift in American television from East Coast production of liberal drama to West Coast production of escapism and entertainment and will situate Rod Serling's career within that shift. We also examine other renditions of paranoia (and symbolic resolutions of it) across the popular culture and politics of the moment. Most broadly, we attempt to examine the medium of popular television as an expressive cultural form which enlightened liberals like Serling tried to use as a mode of moral and aesthetic uplift. Critical methods that might help us understand the potentials of television as expressive culture are emphasized.
SPRING 2011 V55.0721 Expressive Culture: Images - Painting and Sculpture in New York Field Study Prof. Broderick (Art History) syllabus New York's public art collections contain important examples of painting and sculpture from almost every phase of the past, as well as some of the world's foremost works of contemporary art. Meets once a week for an extended period combining on-campus lectures with group excursions to the museums or other locations where these works are exhibited.
Spring 2011 V55.0730 Expressive Cultures: Sounds Prof. Zayaruzny investigateSpring 2011 V55.0730 Expressive Cultures: Sounds Prof. MuellerSPRING 2011 V55.0750 Expressive Culture: Film Prof. Simon (Cinema Studies) syllabus American narrative films, produced primarily during the period 1965-75, considered as an innovative cycle of filmmaking in dialogue with significant historical, political, and cultural transformations in American society. Examines developments in film genre during this period especially in relation to political and cultural change. Narrative innovations are emphasized, with special attention to the specificity of film form and style (e.g., editing, mise-en-scène, sound). Provides an introduction to the methods and principles of film analysis as well as dealing with this period of filmmaking in depth. Includes films by Kubrick, Coppola, Altman, and Scorsese.
Study Abroad at NYU Global Sites
Spring 2011 V55.9549 Cultures and Contexts: Multinational Britain
Prof. Woods (NYU in London) syllabus The idea of British national identity has been built around a sense of united statehood within the confines of the four nations comprising the United Kingdom, ruling overseas territories. As such, it conveyed a sense of a multi-national empire ruled by monarchs, but developing over time into a benign, democratic, constitutional monarchy, generally through peaceful, not revolutionary change. The British have seen themselves historically as freedom-loving, independent, industrial, tolerant, Protestant and individualistic. These myths of national image have been forged partly through conflict with other nations over many centuries and reflect a nationalistic pride in military success and the maintenance of the largest empire the world has ever seen. Changes since 1945 have seen the collapse of that empire, membership in the European Union, large-scale immigration, changing gender politics, and the devolution of power to Scotland, Northern Ireland, and Wales. This has inevitably led to major challenges to traditional British views of their national identity. Includes fieldtrips to key sites.
Spring 2011 V55.9505 Cultures and Contexts: Africa
Prof. Adams (NYU in Ghana) syllabus African culture through autobiography. Texts consist of chronological life histories and memoirs, e. g., by writers of aristocratic birth and those of peasant birth, by individuals accomplished in the arts and others in the sciences, by Nobel laureates and by political leaders, by women and by men. Each narrative provides an intimate acquaintance with the traditions, aspirations, challenges, and strategies from the writer's own society. Collectively they provide the skeleton of a usefully subjective narrative of modern African history. The depicted lives include an 18th-century enslaved Nigerian child, who, ultimately, as a free man, would become a respected abolitionist; the U.S.-educated leader of Africa's first nation to gain independence from colonialism; the passionate Kenyan crusader for the preservation of Africa's environment as the source of its self-development; and the physically and morally courageous exemplar of the battle that overthrew South African apartheid.
Spring 2011 V55.9544 Cultures and Contexts: Spain—At the Crossroads of Europe, North Africa, and America
Prof. Galban (NYU in Madrid) syllabus Analyzes the ways in which historical, geopolitical, cultural, artistic, and popular views function to constitute and continuously transform a national culture. Concentrates on epistemological constructions of Spain—the idea of Spain—that emerge from competing external and internal perspectives. Students examine how this national culture is constructed, first analyzing Spain from North African perspectives through Sephardic nostalgic poetry and the Hispano-Arabic literary traditions. The American perspective pits notions of Spanish imperial power and grandeur against the Black Legend, a term that Protestant circles in Europe and the United States promoted to attack the legitimacy of Spain's New World empire. A final focus on European views analyzes the depiction of Spain as the embodiment of German and French Romantic ideals beginning at the end of the 17th century and the reemergence of the same notion during the Spanish Civil War (1933–36). Throughout, students examine principal textual and visual images that contribute to the historical and contemporary construction of a national culture that emerged at geographic and cultural crossroads.
Spring 2011 V55.9547 Cultures and Contexts: Multicultural France
Prof. Epstein (NYU in Paris) syllabus France and the U.S. have a habit of looking at one another as anti-models when it comes to discussions of assimilation and difference, "race," identity, community, and diversity. We explore this comparison as a productive means for re-considering these terms. Why is the notion of "ethnic community" so problematic in France? Why do Americans insist on the "homogeneity" of the French nation, even as, at various points throughout modern French history, France has received more immigrants to its shores than the United States? Through readings, film screenings, and site visits we study the movements and encounters that have made Paris a rich, and sometimes controversial, site of cultural exchange. Topics include contemporary polemics on questions such as headscarves, the banlieue, the new Paris museums of immigration and "primitive" art, affirmative action and discrimination positive, historic expressions of exoticism, négritude, and anti-colonialism. Occasional case studies drawn from the American context help provide a comparative framework for these ideas.
Spring 2011 V55.9548 Cultures and Contexts: Prague—In the Heart of Central Europe
Prof. Mucha (NYU in Prague) syllabus The concept of Central Europe is somewhat elusive and it is difficult to define it by geographical or political categories. Often characterized simply as a space on the edge between the West and East, many scholars see a distinct Central European culture based on historical, social, and cultural characteristics shared by the countries of this geopolitical entity, the result of complicated historical, political, ethnic, cultural, artistic, and religious interactions throughout more then thousand years of history. Identified as having been one of the world's richest sources of creative talent and thought between the 17th and 20th centuries, Central Europe was represented by many distinguished figures, such as Bach, Mozart, Beethoven, Kant, Goethe, and Hegel; later followed by Kafka, Rilke, Freud, Mendel, and Dvorak, to mention at least some. We explore characteristics of Central Europe primarily from the perspective of Prague and its cultural history, which is so typical and almost archetypal for this region. Students study geopolitical characteristics and various phenomena that co-create the idea of Central Europe. Taking advantage of Prague, students examine primary sources and artifacts (literature, music, art, film) in their contexts and environment.
Spring 2011 V55.9537 Cultures and Contexts: Modern Israel
Prof. Emmerich (NYU in Tel Aviv) syllabus Explores various aspects of the production of everydayness in Israel as it is manifested in different sites: the arts, the leisure industry, and the spatio-temporal arrangements of daily routines and practices. Given its unique geo-political circumstances and its symbolic position, Israel attracts much media coverage as well as more scholarly treatment of the Israeli-Arab or Israeli-Palestinian conflict. More often than not, Israel is portrayed through the lens of high politics or treated as an exotic anomaly. Whether popular or academic in its orientation, the study of Israeli society has thus tended to neglect everyday life in Israel. We consider aspects of Israeli politics and culture; visit art exhibitions, music venues, and the cinema; and observe street life in Tel Aviv (day and night).
Spring 2011 V55.9730 Expressive Cultures: Sounds
Prof. Cusick (NYU in Florence |
Probability : An Introduction - 87 edition
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About the book
Mathematics for Year 11 Geometry and Trigonometry 5th edition has been written
to embrace the concepts outlined in the Stage 1 Mathematics Curriculum Statement.
It is not our intention to define a course.
This package is the first step in a new approach to mathematics education. You
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The book is language rich and technology rich. Whilst some of the exercises are
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The book contains many problems, from the basic to the advanced, to cater for
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on the gradual development of concepts with appropriate worked examples. However,
we have also provided extension material for those who wish to go beyond Stage
1 and look towards further studies or applications of mathematics for their career
choices. It is not our intention that each chapter be worked through in full.
Time constraints will not allow for this. Consequently, teachers must select exercises
carefully, according to the abilities and prior knowledge of their students, in
order to make the most efficient use of time and give as thorough coverage of
work as possible.
The extensive use of graphics calculators and computer packages throughout the
book enables students to realise the importance, application and appropriate use
of technology. No single aspect of technology has been favoured. It is as important
that students work with a pen and paper as it is that they use their calculator
or graphics calculator, or use a spreadsheet or graphing package on computer.
The interactive features of the CD-Rom allow immediate access to our own specially
designed geometry packages, graphing packages and more. Teachers are provided
with a quick and easy method of demonstrating concepts, or students can discover
for themselves, and revisit when necessary.
Teachers should note that instructions appropriate to each graphics calculator
problem are available on the CD-Rom and can be printed for students. These instructions
are written for Sharp, Texas Instruments, Casio and Hewlett-Packard calculators.
In this changing world of mathematics education, we believe that the contextual
approach shown in this book, with the associated use of technology, will enhance
the students' understanding, knowledge and appreciation of mathematics. |
Next: Definition of a Limit
Previous: Binomial Theorem and Expansions
Chapter 8: Introduction to Calculus
Chapter Outline
Loading Content
Chapter Summary
Description
Students explore and learn about limits from an intuitive approach, computing limits, tangent lines and rates of change, derivatives, techniques of differentiation, conceptual basis for integration and The Fundamental Theorem of Calculus. |
At Lawrence North High School, the entire hand-picked team of Algebra 1 instructors believes passionately that mastering these skills and concepts will have a stronger influence on your future success throughout high school and beyond than any other single course in which you may choose to enroll. Algebra 1 skills and conceptual relationships are the foundation of the CORE 40 graduation exam but will also prepare you for future math and science courses. We are committed as a team to providing quality instruction and appropriate materials and supporting you with plenty of attention, patience, and other resources. We understand the importance of the content of this class and we truly want you to succeed.
Some of the "big ideas" we emphasize in Algebra 1 include properties of real numbers, solving equations and inequalities and proportions, functions and graphs, understanding lines and slope, polynomials and factoring, radicals and quadratic functions.
Our measuring sticks are that darn CORE 40 test and your future success in Algebra 2, but our focus is on mastering those "big ideas" along the way. Some of these skills will be difficult for you to understand at first. I encourage you to keep these three P's in mind:
1)Practice! Math is a skill and can only be mastered through routine,
rigorous and disciplined practice.
2)Pace! Don't try to rush or skip ahead until you fully understand what we have already done.
Take breaks and ask lots of questions.
3)Perspective! This class is imperative regardless of your goals. I encourage you to
take a step back from the mechanical steps of the arithmetic and try to understand
the concepts and relationships. When you understand why certain steps are required
Congratulations! You made it to the second semester of Algebra 1. Only the students who have demonstrated a solid understanding of the concepts in the first semester are here right now. Yes, it's that important. The second semester is notable more difficult than the first, but we're confident you'll make it through or it would not have been recommended that you be here. We have two goals this semester: 1) to make sure everyone is prepared for the Algebra 1 End-of-Course Assessment (ECA) graduation exam in May, and 2) to help ensure your future success in Algebra 2.
Our seventh unit explains the rules for exponents and multiplying and dividing factors with the same base. We'll follow that up with a unit on polynomials to get comfortable adding and subtracting like terms with exponents, then multiply polynomial groups together using the Distributive Property. In the next unit we will change directions and go backwards through the distributive process to factor polynomial expressions, especially quadratic trinomials. As the quarter draws to a close, we'll be breaking down and solving quadratic equations. |
Differential Equations Workbook For Dummies
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(More) skills you need to master differential equations!Need to know how to solve differential equations? This easy-to-follow, hands-on workbook helps you master the basic concepts and work through the types of problems you'll encounter in your coursework. You get valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-step solutions to every equation. You'll also memorize the most-common types of differential equations, see how to avoid common mistakes, get tips and tricks for advanced problems, improve your exam scores, and much more!The Dummies Workbook WayQuick refresher explanationsStep-by-step proceduresHands-on practice exercisesAmple workspace to work out problemsTear-out Cheat SheetA dash of humor and funGo to Dummies.com®for videos, step-by-step photos, how-to articles, or to shop the store!More than 100 problems!Detailed, fully worked-out solutions to problemsThe inside scoop on first, second, and higher order differential equationsA wealth of advanced techniques, including power series
(Less) |
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Pre-Algebra Mathematics (DVMT 095) and Intermediate Algebra (DVMT 100) help students develop mathematics abilities that enable them to complete mathematics courses necessary for their plan of study. Personalized instruction, self-pacing, and mastery learning characterize the instruction in these classes.
In addition to the regular teacher-based course instruction sections, FSU offers computer-mediated sections of DVMT. These sections are conducted using interactive computer software and are supervised by an instructor. Each of the DVMT courses described below are offered in both a computer-mediated and instructor-based format.
DVMT 095: Pre-Algebra Mathematics
The primary focus of this course is to improve students' basic math skills: arithmetic concepts of whole numbers, integers, fractions, and decimals; problem solving skills dealing with ratios, rates, proportions, and percentages; concepts of linear, area, volume measurement in both the English and metric systems; and introductory algebra topics of solving linear equations and graphing. Completion of this course will meet the prerequisites for MATH 104, MATH 209, or DVMT 100. This course is graded on a Pass/Fail basis. It is worth three (3) credits; however, it may not be used to satisfy the requirements for a major or minor in mathematics, fulfill the Basic University Requirement in mathematics, nor count toward the 120 credit hour minimum required for graduation.
NOTE: Students are placed in this course based upon results of the Mathematics Placement Test administered by the University.
An introduction to the fundamental aspects of algebra, including properties of the real number system; integer arithmetic; operations with positive and negative exponents; variables and linear equations; graphing; second degree equations; factoring; operations with positive, negative, and fractional exponents; and quadratic equations. Completion of this course will meet the prerequisites for MATH 102, 103, and 106. This course is graded on a Pass/Fail basis. It is worth three (3) credits and is offered every semester. However, it does not fulfill the Basic University Requirement in mathematics, nor may the credits be used to fulfill the 120 credit hour minimum required for graduation.
Prerequisite: A passing score on the Mathematics Placement Test administered by the University or successful completion of DVMT 095. |
This course provides a non-rigorous introduction to the basic ideas and techniques of
differential and integral calculus, especially as they relate to applications in business,
economics, life sciences, and social sciences.
Expected Educational Results
As a result of completing this course, the student will be able to:
1. Locate and describe discontinuities in functions.
2. Evaluate limits for polynomial and rational functions.
3. Compute and interpret the derivative of a polynomial, rational, exponential,
or logarithmic function.
4. Write the equations of lines tangent to the graphs of polynomial, rational,
exponential, and logarithmic functions at given points.
5. Compute derivatives using the product, quotient, and chain rules on polynomial,
rational, exponential, and logarithmic functions.
6. Solve problems in marginal analysis in business and economics using the derivative.
7. Interpret and communicate the results of a marginal analysis.
8. Graph functions and solve optimization problems using the first and second
derivatives and interpret the results.
9. Compute antiderivatives and indefinite integrals using term-by-term integration
or substitution techniques.
10. Evaluate certain definite integrals.
11. Compute areas between curves using definite integrals.
12. Solve applications problems for which definite and indefinite integrals are
mathematical models.
13. Solve applications problems involving the continuous compound interest formul
General Education Outcomes
I. This course addresses the general education outcome relating to communication by providing
additional support as follows:
A. Students develop their listening skills through lecture and through group problem
solving.
B. Students develop their reading comprehension skills by reading the text and by
reading the instructions for text exercises, problems on tests, or on projects.
Reading the mathematics text requires recognizing symbolic notation as well as
analyzing problems written in prose.
C. Students develop their writing skills through the use of problems which require
written explanations of concepts.
II. This course addresses the general education outcome of demonstrating effective individual
and group problem solving and critical thinking skills as follows:
A. Students must apply mathematical concepts previously mastered to new problems
and situations.
B. In applications, students must analyze problems and describe problems with either
pictures, diagrams, or graphs, then determine the appropriate strategy for
solving the problem.
III. This course addresses the general education outcome of using mathematical concepts to
interpret, understand, and communicate quantitative data as follows:
A. Students must demonstrate proficiency in problems-solving skills. These include
business applications of the derivative and the integral.
B. Students must apply calculus concepts to marginal analysis and optimization
problems, using their results to make business decisions and predictions.
Course Content
1. The derivative, derivative formulas, and marginal analysis
2. Graphing and optimization
3. Special derivatives: exponential and logarithmic functions
4. Integration and applications in business and economics
ENTRY-LEVEL COMPETENCIES
Upon entering this course, the student should be able to do the following:
1. Analyze problems using critical thinking skills.
2. Construct meaningful mathematical statements using algebraic symbols and notation.
3. Solve the following kinds of equations
a. Rational (leading to linear and quadratic)
b. Logarithmic
c. Exponential
4. Solve the following kinds of inequalities
a. Rational
b. Factorable polynomial of degree 2, 3, or 4
5. State the definition of a function and use function notation.
6. Identify and graph the following types of functions in two variables
a. Linear
b. Quadratic
c. Exponential
d. Logarithmic
7. Define exponential and logarithmic functions; use the properties of logarithms.
8. Evaluate expressions involving exponential and logarithmic functions of x
using a calculator.
Assessment of Outcome Objectives
I. COURSE GRADE
The course grade will be determined by the individual instructor using a variety
of evaluation methods such as tests, quizzes, projects, homework, and writing
assignments. A comprehensive final examination is required that must count at
least one-fourth and no more than one-third of the course grade.
II. DEPARTMENTAL ASSESSMENT
The course will be assessed every 5 years. The assessment instrument will consist
of a set of free-response questions included as a portion of the final exam for
all students taking the course. The assessment instrument will be graded by a
committee appointed by the Academic Group.
USE OF ASSESSMENT FINDINGS
The Math 1433 committee, or a special assessment committee appointed by the Chair of the
Executive Committee, will analyze the results of the assessment and determine implications
for curriculum changes. The committee will prepare a report for the Academic Group
summarizing its findings. |
Note: Citations are based on reference standards. However, formatting rules can vary widely between applications and fields of interest or study. The specific requirements or preferences of your reviewing publisher, classroom teacher, institution or organization should be applied.
Functions of Several Variables and Their Derivatives: Points and Points Sets in the Plane and in Space; Functions of Several Independent Variables; Continuity; The Partial Derivatives of a Function; The Differential of a Function and Its Geometrical Meaning; Functions of Functions (Compound Functions) and the Introduction of New Independent Variables; The mean Value Theorem and Taylor's Theorem for Functions of Several Variables; Integrals of a Function Depending on a Parameter; Differentials and Line Integrals; The Fundamental Theorem on Integrability of Linear Differential Forms; Appendix.- Vectors, Matrices, Linear Transformations: Operatios with Vectors; Matrices and Linear Transformations; Determinants; Geometrical Interpretation of Determinants; Vector Notions in Analysis.- Developments and Applications of the Differential Calculus: Implicit Functions; Curves and Surfaces in Implicit Form; Systems of Functions, Transformations, and Mappings; Applications; Families of Curves, Families of Surfaces, and Their Envelopes; Alternating Differential Forms; Maxima and Minima; Appendix.- Multiple Integrals: Areas in the Plane; Double Integrals; Integrals over Regions in three and more Dimensions; Space Differentiation. Mass and Density; Reduction of the Multiple Integral to Repeated Single Integrals; Transformation of Multiple Integrals; Improper Multiple Integrals; Geometrical Applications; Physical Applications; Multiple Integrals in Curvilinear Coordinates; Volumes and Surface Areas in Any Number of Dimensions; Improper Single Integrals as Functions of a Parameter; The Fourier Integral; The Eulerian Integrals (Gamma Function); Appendix
Reviews
Editorial reviews
Publisher Synopsis
From the reviews: "These books (Introduction to Calculus and Analysis Vol. I/II) are very well written. The mathematics are rigorous but the many examples that are given and the applications that are treated make the books extremely readable and the arguments easy to understand. These books are ideally suited for an undergraduate calculus course. Each chapter is followed by a number of interesting exercises. More difficult parts are marked with an asterisk. There are many illuminating figures...Of interest to students, mathematicians, scientists and engineers. Even more than that." Newsletter on Computational and Applied Mathematics, 1991 "...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students." Acta Scientiarum Mathematicarum, 1991Read more... |
The famous mathematical cat Penrose takes us on a trip though puzzleland, while sharing fascinating and challenging puzzles in this uniquely designed mini book. Each page's puzzle is introduced by our star Penrose or one of his quirky friends. Readers are treated to page after page of Penrose antics and problems, while the over 100 mind teasers... more...
There are many texts and handbooks available describing tribological processes, effects
of additives on lubrication, tribochemistry, surface engineering, and heat treating
methodologies involved in surface modification. However, few of these texts provide a
thorough integration of surface modification reactions and processes to achieve a
tribological... more...
The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. This volume presents the results of research into such phenomena and provides a self-contained and gradual development of mathematical methods for studying successive positions of these fronts. more...
Math You Can Really Use--Every Day skips mind-numbing theory and tiresome drills and gets right down to basic math that helps you do real-world stuff like figuring how much to tip, getting the best deals shopping, computing your gas mileage, and more. This is not your typical, dry math textbook. With a comfortable, easygoing approach, it: Covers... more... |
A very thorough introduction to some now classical topics can be found in James D. Murray's
now two-volume book published by Springer. Expect lots of ODE's and PDE's in that one.
As far as more exotic math is concerned, a complete overview would be difficult: it seems people throw everything they have and see what works. I've seen some interesting talks involving combinatorics, others involving algebraic geometry. |
The following is a summary of main duties for some occupations in this unit group:
Mathematicians conduct research to extend mathematical knowledge in traditional areas of mathematics such as algebra, geometry, probability and logic and apply mathematical techniques to the solution of problems in scientific fields such as physical science, engineering, computer science or other fields such as operations research, business or management.
Statisticians conduct research into the mathematical basis of the science of statistics, develop statistical methodology and advise on the practical application of statistical methodology. They also apply statistical theory and methods to provide information in scientific and other fields such as biological and agricultural science, business and economics, physical sciences and engineering, and the social sciences.
Actuaries apply mathematical models to forecast and calculate the probable future costs of insurance and pension benefits. They design life, health, and property insurance policies, and calculate premiums, contributions and benefits for insurance policies, and pension and superannuation plans. They may assist investment fund managers in portfolio asset allocation decisions and risk management. They also use these techniques to provide legal evidence on the value of future earnings. |
Overview
Main description
STUDENT TESTED AND APTable of contents
To the StudentAcknowledgmentsCongratulationsChapter 1: Pre-Algebra 1: Introductory terms, order of operations, exponents, products, quotients, distributive lawChapter 2: Pre-Algebra 2: Integers plus; signed numbers, basic operations, short division, distributive law, the beginning of factoringChapter 3: Pre-Algebra 3: Fractions, with a taste of decimalsChapter 4: Pre-Algebra 4: First-degree equations and the beginning of problems with wordsChapter 5: Pre-Algebra 5: point well taken; graphing points and lines, slope, equation of a lineChapter 6: Pre-Algebra 6: Ratios, proportions, and percentagesChapter 7: Prebusiness: What you need to know about surviving the real world: checks, deposits and withdrawal slips, interest, what you should know about banks and credit cards, mortgages, bonds and stocksChapter 8: Pregeometry 1: Some basics about geometry and some geometric problems with wordsChapter 9: Pregeometry 2: Triangles, square roots, and good old PythagorasChapter 10: Pregeometry 3: Rectangles, squares, and our other four-sided friendsChapter 11: Pregeometry 4: Securing the perimeter and areal search of triangles and quadrilateralsChapter 12: Pregeometry 5: All about circlesChapter 13: Pregeometry 6: Volumes and surface area in 3-DChapter 14: Pretrig: Right angle trigonometry (how the pyramids were built)Chapter 15: Precounting, Preprobability, and PrestatisticsChapter 16: Miscellaneous
Author comments
Bob Miller was a lecturer in mathematics at City College of New York for more than 30 years. He has also taught at Westfield State College and Rutgers. His principal goal is to make the study of mathematics both easier and more enjoyable for students. |
Young scholars explore the Fundamental Theorem of Calculus. In the Calculus lesson, students investigate indefinite and definite integrals and the relationship between the two, which leads to the discovery of the Fundamental Theorem of Calculus.
Students explore the concept of differential calculus. In this differential calculus lesson, students use the derivative definition as h approaches zero to find the derivative of quadratic and 4th degree functions. Students use their Ti-89 to find the gradient of the secant and tangent.
Twelfth graders investigate the limitations of the Fundamental Theorem of Calculus. In this calculus instructional activity, 12th graders explore when one can and cannot use the Fundamental Theorem of Calculus and explore the definition of an improper integral.
Students explore the concept of area under a curve. In this area under a curve instructional activity, students find integrals of various functions. Students use their Ti-Nspire to graph functions and find the area under the curve using the fundamental theorem of calculus. |
students acquire conceptual understanding of key geometric topics, work toward computational fluency, and expand their problem-solving skills. Course topics include reasoning, proof, and the creation of sound mathematical argumentsExtensive scaffolding aids below-proficient readers in understanding academic math content and in making the leap to higher-order thinking. Mathematical vocabulary is supported with rollover definitions and usage examples that feature audio and graphical representations of terms. Situational interest that promotes a relevant, real-world application of math skills serves to engage and motivate students.
The content is based on the National Council of Teachers of Mathematics (NCTM) standards and is aligned to state standards (available on request). |
High School Workshops
(1997 – present)
These day-long workshops, held on the University of Arizona campus, are designed for high school classes. (We also occasionally hold workshops designed for middle school classes, as well as workshops geared specifically towards school teachers.) The workshops cover topics that are not commonly taught in school math classes. Through an intuitive approach to each subject, students are exposed to both interesting and active areas of contemporary mathematics research.
A secondary purpose of the high school workshops is to expose high school students to what an undergraduate education in mathematics includes, and to encourage them to add math classes to their schedule when they enter college.
If you are a teacher interested in bringing your class to a workshop, please contact the current program coordinator (see below).
Workshop topics
Listed here are past workshop topics. We are always open to ideas for new topics.
Introduction to Fourier Series and Harmonic Analysis
Advanced topics in Fourier Series and Harmonic Analysis
Introduction to Cryptology
Public Key Cryptography and Digital Signature Verification
Factoring and Primality Testing
Introduction to Quantum Mechanics
Einstein's Way Cool Notion of Motion
Elasticity and Bridge Design
Rate of Change and Functions
Probability and Game Theory
The symmetric road to the Rubik's Cube
Knot Theory
Graph Theory
Biomathematics
Additional information on particular workshops (topic descriptions, dates, and participants) is available at various workshop-related websites:
Current program coordinator
History and Participants
Workshops in this outreach program are organized and run entirely by graduate students (with faculty encouragement and departmental administrative support). The program came into existence in Spring 1997 as one aspect of the SWRIMS project, when SWRIMS director Dr. William Vélez suggested this outreach program—and allocated SWRIMS funding—to graduate students Jennifer Christian-Smith, Aaron Ekstrom, and Alexander Perlis. (SWRIMS had already been involved in high school workshops on Population Biology and Honey Bees, which were organized by Dr. Joseph Watkins.)
Initially, graduate student program coordinators and workshop organizers were funded by SWRIMS. Since around 2000, the primary incentive for graduate student participation has been the vertical integration requirement for graduate students funded by the department's VIGRE Grant.
Reports
Talks about (aspects of) this outreach program
Katrina Piatek-Jimenez and Jennifer Christian-Smith. Graduate Students in the High School Classroom: Enriching the School Mathematics Curriculum and Students' Perceptions of Mathematics. Radio show interview by Dr. Patricia Kenschaft, host of radio show Math Medley, February 16, 2002.
Jennifer Christian-Smith. The Saturday Mathematics Workshop Series at the University of Arizona: An Outreach Project Connecting Undergraduate and Graduate Students to High School Students. AMS/MAA Joint Meetings, New Orleans, Louisiana, January 2001.
Aaron Ekstrom and Alexander Perlis. Fourier Series for high school students. AMS/MAA Joint Meetings, San Antonio, Texas, January 1999. |
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