Dataset Viewer (First 5GB)
text
stringlengths 8
1.01M
|
|---|
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.
...
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.
...
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 (wenersamy@engineer.com) - 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:
- To enter one or several functional...parameters of functions with simultaneous display of new graphs that allows to define influence of parameters of...example, ellisoid, cardioid, Bernoulli lemniscate and other similar graphs (where abscissa and ordinate depend on one parameter...- To solve the equations, system of the equations and inequalities by graphic way;...
...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:
*Any user-defined equations of up to nine parameters and eight variables....for properly fitting high order polynomials and rationals.
...any function. Math Mechanixs includes the ability to graph data on your computers display. You can save...and export the graph data to other applications as well. You can...create numerous types of beautiful 2D and 3D graphs from functions or data points, including histograms and...
...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.
...This euqation grapher can draw any 2D or 3D mathematical equation....an equation with y= or z= because the graphing software is programmed to handle any combination of...x y z variables. Equations can be as simple as y=sin(x) or as...slope calculation, x-y-z value tables, zooming, and tracing.
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.
$4.86 +$3.99 s/h
VeryGood
Extremely_Reliable Richmond, TX
Buy with confidence. Excellent Customer Service & Return policy.
$58.61 +$3.99 s/h
VeryGood
AlphaBookWorks Alpharetta, GA
0321442547 |
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. |
Post navigation
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!
Post navigation
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. |
Need Algebra I Help? No Fear, Yourteacher.com is Here!
Whether you are trying to figure out if you have enough gallons of gas in your car to make it to the next gas station while driving on the interstate or trying to figure out how many chocolate bars you can purchase at 65 cents a piece with the $3.25 in change you found in your jacket pocket, you need algebra to arrive at the correct answer. Both of these examples can be expressed as algebraic equations. For example, the chocolate situation can be visualized by the equation 0.65x = 3.25. In case you were dying to know, the answer is 5.
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.
If you are student struggling with your Algebra I homework, or your reviewing for a math placement exam/standardized test for college, or even if you are a parent who can't quite remember how to find common factors to help your child with his/her homework, then you have come to the right place. We have all the tools you need to learn Algebra I for the first time or review your Algebra I skills.
One of our newest authors, Yourteacher.com, has a comprehensive collection of easy-to-follow Algebra I tutorials available for purchase. The founders of Yourteacher.com have been teaching algebra through online tutorials since 1998 so we know we are putting you in good hands. Their instructional content has helped tens of thousands of students worldwide.
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. |
End of preview. Expand
in Data Studio
ClimbLab is a high-quality pre-training corpus released by NVIDIA. Here is the description:
ClimbLab is a filtered 1.2-trillion-token corpus with 20 clusters. Based on Nemotron-CC and SmolLM-Corpus, we employed our proposed CLIMB-clustering to semantically reorganize and filter this combined dataset into 20 distinct clusters, leading to a 1.2-trillion-token high-quality corpus. Specifically, we first grouped the data into 1,000 groups based on topic information. Then we applied two classifiers: one to detect advertisements and another to assess the educational value of the text. Each group was scored accordingly, and low-quality data with low scores was removed.
But it is released in gpt-2 tokens which is not easy-to-use. Therefore,we use gpt-2 tokenizer to detokenize them into raw texts.
⚠️ Please note: This version is not officially released or maintained by NVIDIA. We are not responsible for the content, accuracy, or updates of this dataset.
Citation:
If you find this dataset helpful, please cite the following paper:
@article{diao2025climb,
author = {Shizhe Diao and Yu Yang and Yonggan Fu and Xin Dong and Dan Su and Markus Kliegl and Zijia Chen and Peter Belcak and Yoshi Suhara and Hongxu Yin and Mostofa Patwary and Celine Lin and Jan Kautz and Pavlo Molchanov},
title={CLIMB: CLustering-based Iterative Data Mixture Bootstrapping for Language Model Pre-training},
journal = {arXiv preprint},
year = {2025},
archivePrefix = {arXiv},
primaryClass = {cs.CL},
url={https://arxiv.org/abs/2504.13161},
}
- Downloads last month
- 615