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In this book Lee Rudolph brings together international contributors who combine psychological and mathematical perspectives to analyse how qualitative mathematics can be used to create models of social and psychological...
$ 10.29
Spherical trigonometry was at the heart of astronomy and ocean-going navigation for two millennia. The discipline was a mainstay of mathematics education for centuries, and it was a standard subject in high...
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John Bird's approach, based on numerous worked examples and interactive problems, is ideal for students from a wide range of academic backgrounds, and can be worked through at the student's own pace. Basic mathematical...
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The ideal review for your probability and statistics courseMore than 40 million students have trusted Schaum's Outlines for their expert knowledge and helpful solved problems. Written by renowned experts in...
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One sun, two parents, three meals a day, four seasons, five fingers every child soon discovers that lots of things in life have an inherent number attached to them. Just as five individual fingers become...
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The ideal review for your trigonometry courseMore than 40 million students have trusted Schaum's Outlines for their expert knowledge and helpful solved problems. Written by a renowned expert in this field,...
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Mathematics scares and depresses most of us, but politicians, journalists and everyone in power use numbers all the time to bamboozle us. Most maths is really simple - as easy as 2+2 in fact. Better still it...
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Need to learn statistics for your job? Want help passing a statistics course? Statistics in a Nutshell is a clear and concise introduction and reference for anyone new to the subject. Thoroughly revised and...
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This book contains S. S. Wilks' lessons on mathematical statistics, and will make an excellent addition to the bookshelf of anyone with an interest in the subject. Preface: 'Most of the mathematical theory of...
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Originally published in 1859, this early work by English Mathematician Isaac Todhunter is both expensive and hard to find in its first edition. It contains a wealth of information on spherical trigonometry and...
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This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics...
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This book is a primer on critical thinking. Without it, the Internet is only a misinformation highway. The dark arts of untruthfulness are ubiquitous in 'official' information. The general techniques... | 677.169 | 1 |
Comment: Fewer than 5% of pages with some light marks - all other pages are entirely clean and free of any marking or notation of any kind. Covers and corners are in good overall shape; spine has a solitary crease but binding is perfect. Will be sent same or next working day - guaranteed! Buy from Bob - for an honest description, swift dispatch, proper packaging and A1 customer service!
Book DescriptionMore About the Author
Product Description
From the Back Cover
Foundation Maths has been written for students taking higher and further education courses who have not specialised in mathematics on post-16 qualifications and need to use mathematical tools in their courses. It is ideally suited to those studying marketing, business studies, management, science, engineering, social science, geography, combined studies and design. It will be useful for those who lack confidence and who need careful, steady guidance in mathematical methods. For those whose mathematical expertise is already established, the book will be a helpful revision and reference guide. The style of the book also makes it suitable for self-study and distance learning.
Features of the book
· Mathematical processes are described in everyday language – mathematical ideas are usually developed by example rather than formal proof, thereby encouraging students' learning.
· Key points highlight important results that need to be referred to easily or remembered.
· Worked examples are included throughout the book to reinforce learning.
· Self-assessment questions are provided at the end of most sections to test understanding of important parts of the section. Answers are given at the back of the book.
· Exercises provide a key opportunity to develop competence and understanding through practice. Answers are given at the back of the book.
· Test and assignment exercises (with answers provided in a separate Lecturers' Manual on the website) allow lecturers and tutors to set regular assignments or tests throughout the course.
· Extra end-of-chapter questions for students (with answers) on the website at
.
· PowerPoint slides for lecturers on the website featuring Key Points from the book with their related Worked Examples.
Anthony Croft has taught mathematics in further and higher education institutions for twenty four years. He is currently Director of the Mathematics Education Centre at Loughborough university, which has been designated a Centre for Excellence in Teaching and Learning by the Higher Education Funding Council for England. He teaches mathematics and engineering undergraduates, and has championed mathematics support for students who find the transition from school to university difficult and for students with learning difficulties. He has authored many very successful mathematics textbooks including several for engineering students.
Robert Davison has twenty five years experience teaching mathematics in both further and higher education. He is currently Head of Quality in the Faculty of Computing Sciences and Engineering at De Montfort University, where he also teaches mathematics. He has authored many very successful mathematics textbooks including several for engineering students.
About the Author
Anthony Croft has taught mathematics in further and higher education institutions for over thirty years. He is currently Professor of Mathematics Education and Director of sigma - the Centre for Excellence in Teaching and Learning based in the Mathematics Education Centre at Loughborough University. He teaches mathematics and engineering undergraduates, and has championed mathematics support for students who find the transition from school to university difficult. He has authored many very successful mathematics textbooks, including several for engineering students. In 2008 he was awarded a National Teaching Fellowship in recognition of his work in these fields.
Robert Davison has thirty years experience teaching mathematics in both further and higher education. He is currently Head of Quality in the Faculty of Technology at De Montfort University, where he also teaches mathematics. He has authored many very successful mathematics textbooks, including several for engineering students.
--This text refers to an out of print or unavailable edition of this title. | 677.169 | 1 |
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The numerical methods, formulation and parameterizations used in models of the circulation of the atmosphere and ocean will be described in detail. Widely used numerical methods will be the focus but we will also review emerging concepts and new methods. The numerics underlying a hierarchy of models will be discussed, ranging from simple GFD models to the high-end GCMs. In the context of ocean GCMs, we will describe parameterization of geostrophic eddies, mixing and the surface and bottom boundary layers. In the atmosphere, we will review parameterizations of convection and large scale condensation, the planetary boundary layer and radiative transfer | 677.169 | 1 |
must-have textbook that millions in Latin America have used for their Algebra formation. This revised edition includes a CD-Rom with exercises that will help the student have a better understanding of equations, formulas, etc.This is the must-have textbook that millions in Latin America have used for their Algebra formation. This revised edition includes a CD-Rom with exercises that will help the student have a better understanding of equations, formulas, etc.Hide
Description:Good. Ex-library book with stamps and markigns. Actual content...Good. Ex-library book with stamps and markigns. Actual content is clean. Good covers. Some small ink marks on top of the front cover. Inside has no writing or underlining | 677.169 | 1 |
Lots of real-world data, with descriptions of environmental and mathematical implications; stored in a variety of formats for easy download. Catalogued by mathematical topic and by environmental topiTeaCat is a dynamic mathematical application that aims to enable high school students to experiment with and to exercise a variety of mathematical topics. Even engineers may benefit of TeaCat for rath... More: lessons, discussions, ratings, reviews,...
WCMGrapher is a free graphing application. It is designed to enable teachers to create graphs of functions, format the graphs, then copy and paste the graph into other applications. For example, yo... More: lessons, discussions, ratings, reviews,...
Web Components for Mathematics (webcompmath or WCM) is a library used to create interactive graphing web applets for teaching mathematics. It is written in the Java programming language and is base... More: lessons, discussions, ratings, reviews,...
Winplot is a general-purpose 2D/3D plotting utility, which can draw (and animate) curves and surfaces presented in a variety of formats. It allows for customizing and includes a data table which can bStudent model a loan they would like to take out. The only mathematical concepts required are addition and multiplication. Terminology and a few basic spreadsheet concepts need to be covered. More: lessons, discussions, ratings, reviews,...
Students model a savings account and answer some thought-provoking questions. Addition and multiplication as well as a few spreadsheet concepts are all that is needed for students to use the model. More: lessons, discussions, ratings, reviews,...
This collection of free worksheets provides practice in a variety of algebra topics, generating ten problems at a time for users to solve. Each worksheet is printable and comes with an answer key.
To... More: lessons, discussions, ratings, reviews,...
For systems of three linear equations in three variables, this Formula Solver program walk you through the steps for finding the solution using Cramer's Rule (also known as the Third Order Determinant... More: lessons, discussions, ratings, reviews,...
Flash introduction to finding the equation of an ellipse centered on (0,0) and with its major axis on the x-axis. Students can use this Tab Tutor program to learn about the equation of this ellipse an | 677.169 | 1 |
mathematics at work - Achieve
Mathematics At Work - Achieve mathematics at work series following up on the work of adp achieve has produced a series of mathematics at work brochures to examine how higher-level mathematics at work - achieve
Shape of the Australian Curriculum Mathematics
Shape Of The Australian Curriculum Mathematics 4 1 purpose 1 1 the shape of the australian curriculum mathematics will guide the writing of the australian mathematics curriculum k12 1 2 this paper has been shape of the australian curriculum mathematics
Related Books About mathematics for economists pdf download
Overview
Intuitive Biostatistics is both an introduction and review of statistics. Compared to other books, it has:
Breadth rather than depth. It is a guidebook, not a cookbook.
Words rather than math. It has few equations.
Explanations rather than recipes. This book presents few details of statistical... View detail
Madelaine Hillyard is a world-famous heart surgeon at the top of her game. Her personal life is far less successful. A loving but overworked single mom, she is constantly at odds with her teenage daughter. At sixteen, Lina is confused, angry, and fast becoming a stranger to her mother—a rebel desperate... View detail
Communication Sciences and Disorders: A Contemporary Perspective introduces students to the field in a clear and succinct manner that allows readers access to the most current theories, research, and practices through rich examples, detailed case studies and engaging anecdotes. It employs a | 677.169 | 1 |
358241 / ISBN-13: 9780534358242
Introductory Algebra: Equations and Graphs
Yoshiwara's INTRODUCTORY ALGEBRA was written with two goals in mind: to present the skills of algebra in the context of modeling and problem solving; ...Show synopsisYoshiwara's INTRODUCTORY ALGEBRA was written with two goals in mind: to present the skills of algebra in the context of modeling and problem solving; and to engage students as active participants in the process of learning. Unlike other introductory algebra texts, Yoshiwara's INTRODUCTORY ALGEBRA, builds an intuitive framework for the future study of functions in intermediate algebra. This clearly differentiates Yoshiwara from standard introductory algebra texts. The text emphasizes the study of tables and graphs, and the concept of the variable is developed from that platform. Graphs are used extensively throughout the book to illustrate algebraic technique and to help students visualize relationships between variables. The numerous labeled web site by the authors believe that this skill must be learned through practice with pencil and paper.Hide synopsis
...Show more technique and to help students visualize relationships between variables. The numerous labelled website but the authors believe that this skill must be learned through practice with pencil and paper.Hide
Description:New. Yoshiwara's INTRODUCTORY ALGEBRA was written with two...New. Yoshiwara's INTRODUCTORY ALGEBRA was written with two goals in mind: to present the skills of algebra in the context of modeling and problem solving; and to engage students as active participants in the process of learning. Unlike other introduct.
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College Algebra: A Graphing Approach
9780618851881
0618851887
Summary: Part of the market-leading "Graphing Approach Series" by Larson, Hostetler, and Edwards, "College Algebra: A Graphing Approach," 5/e, is an ideal student and instructor resource for courses that require the use of a graphing calculator. The quality and quantity of the exercises, combined with interesting applications and innovative resources, make teaching easier and help students succeed.Continuing the series' empha...sis on student support, the Fifth Edition introduces "Prerequisite Skills Review." For selected examples throughout the text, the "Prerequisite Skills Review" directs students to previous sections in the text to review concepts and skills needed to master the material at hand. In addition, prerequisite skills review exercises in Eduspace (see below for description) are referenced in every exercise set.The."New!" The "Nutshell Appendix" reviews the essentials of each function, discussed in the "Library of Functions" feature, and offers study capsules with properties, methods, and examples of the major concepts covered in the textbook. This appendix is an ideal study aid for students."New!" "Progressive Summaries" outline newly introduced topics every three chapters and contextualize them within the framework of the course."New!" "Make a Decision" exercises--extended modeling applications presented at the end of selectedexercise sets--give students the opportunity to apply the mathematical concepts and techniques they've learned to large sets of real data."Updated!" The "Library of Functions,"."Updated!" The "Chapter Summaries" have been updated to include the Key Terms and Key concepts that are covered in the chapter. These chapter summaries are an effective study aid because they provide a single point of reference for review."Updated!" The "Proofs of Selected Theorems" are now presented at the end of each chapter for easy reference.The Larson team provides an abundance of features that help students use technology to visualize and understand mathematical concepts. "Technology Tips" "Technology Support" notes appear throughout the text and refer students to the "Technology Support Appendix," where they can learn how to use specific graphing calculator features to enhance their understanding of the concepts presented. The "Technology Support"notes also direct students to the "Graphing Technology Guide," on the textbook's website, for keystroke support for numerous calculator models.Carefully positioned throughout the text, "Explorations" engage students in active discovery of mathematical concepts, strengthening critical thinking skills and helping them to develop an intuitive understanding of theoretical concepts."What You Should Learn" and "Why You Should Learn It" appears at the beginning of each chapter and section, offering students a succinct list of the concepts they will soon encounter. Additionally, this fe
Larson, Ron is the author of College Algebra: A Graphing Approach, published 2007 under ISBN 9780618851881 and 0618851887. Three hundred eighty one College Algebra: A Graphing Approach textbooks are available for sale on ValoreBooks.com, one hundred forty two used from the cheapest price of $0.01, or buy new starting at $34 | 677.169 | 1 |
Beginning Algebra accessible treatment of mathematics features a building-block approach toward problem solving, realistic and diverse applications, and chapter organizer to help users focus their study and become effective and confident problem solvers. The Putting Your Skills to Work and new chapter-end feature, Math in the Media, present readers with opportunities to utilize critical thinking skills, analyze and interpret data, and problem solve using applied situations encountered in daily life. Earlier coverage of the Order of Arithmetic Operati... MOREons--now section 1.5 so that operations is now covered together before Introduction to Algebra. The discussion of solving linear equations in Chapter 2 now includes coverage of equations with no solution and equations with infinitely many solutions. Section 4.3 now offers a more thorough introduction to polynomials, with the addition of new terminology at the beginning of the section and a new lesson on evaluating polynomials at the end. Revised Ch. 7 on Graphing and Functions includes new coverage of the rectangular coordinate system and slope. The coverage of the rectangular coordinate system in Chapter 7 has been improved for greater clarity. John Tobey and Jeff Slater are experienced developmental math authors and active classroom teachers. They have carefully crafted their texts to support students in this course by staying with them every step of the way. Tobey and Slater... With you every step of the way. This 6th edtion of Beginning Algebra is appropriate for a 1-sem course in appropriate for a 1-sem course in Introductory, Beginning or Elementary Algebra where a solid foundation in algebraic skills and reasoning is being built for those students who have little or no previous experience with the topice. The utlimate goal of this text is to effectively prepare students to transition to Intermediate Algebra. One of the hallmark characteristics of B eginning Algebra 6e that makes the text easy to learn from is the building-block organization. Each section is written to stand on its own, and each homework set is completely self-testing. Beginning Algebra 6e is a worktext, meaning the design is open and friendly with wide margins so can you can encourage your students to take notes and work exercises right on the text page. Also with worktexts, images/visuals are used more frequently to convey the math concept so there are fewer words and less text for the student to read. | 677.169 | 1 |
Do Two Halves Really Make a Whole?
Really, there is no such thing as Algebra 1 and Algebra 2.
something to our children. Will it be of any more value than the material goods we have acquired? While it may be somewhat narrow in perspective, here is something to consider.
As you educate your students, can you say they are involved in concept development, or are they learning passively? Are they figuring things out for themselves, or are they learning tricks and shortcuts? Do they see the logic in what they are learning, or are they just memorizing information for a test? Are they analyzing their mistakes to find the reasons why they answered incorrectly, or are they just accepting their fate and recording a grade?
A legacy can mean many things, but helping our children learn to think may be one of the longest-lasting tools we can bequeath to our children. Of course, we need to carefully consider the educational materials we use to teach our children, and those materials need to be developed logically. Unfortunately, traditional mathematics instruction is often driven by programs that are developed topically instead of logically.
As we cover the traditional scope and sequence of algebra, I trust you will receive food for thought as you strive to leave an educational legacy to your child.
"Do two halves really make a whole?" seems like such a simple question, but is the answer that obvious? Not when it comes to high school algebra! And I'm not talking about some new way to add algebraic fractions. I'm referring to the age-old practice of teaching two years of algebra in high school, which presumably makes up a complete algebra course. They may have been called Algebra 1 and 2, or Beginning Algebra and Advanced Algebra. In either case, the implication was that each comprised one-half of a complete algebra course. However, if you look at the table of contents in any "second-year algebra" book, you will find that at least 50 percent of the book is a repeat of "first-year algebra."
So really, there is no such thing as Algebra 1 and Algebra 2. These are courses (or names for courses) that came about as a result of school scheduling. Many years ago, when it was the norm to require only two math credits to graduate from high school, a study of algebra was a natural beginning credit. Of course, since it was generally taught "mechanically," utilizing many formulas and rules, a lot of practice and repetition was involved and, in fact, the study was not even completed in one year. So, for another math credit, geometry was taught for a year. It was considered "another discipline," involving a significant amount of logical reasoning and proof, and it gave students "another math experience."
That took care of the required credits.
Then, the next year, students interested in going further in their study of mathematics were offered the opportunity to continue, and finish, their study of algebra. Of course, because of the "procedural" way it was taught initially, students simply didn't remember much of that first year. So, they started over, re-studying many of the same things. This time, however, it was called Advanced Algebra. Something of a contradiction, don't you think? In fact, the word "advanced" is a relative term anyway. Chapter 2 of an algebra book is "advanced" compared to Chapter 1, isn't it?
This has been perpetuated through the years, primarily because of that traditional implementation. When you try to memorize rules, formulas, tricks and shortcuts without really knowing why they work, it will take a lot of drill and review just to remember the material for a test. Yet, even today, that approach is often considered to be the "normal way" to teach algebra.
Therefore, I suggest that one of the most fragmenting things we have done in mathematics education is to forcibly insert a geometry course into the middle of an algebra course. Algebra is a single, "complete" course, divided only by concept areas. It is the study of relations (equations and inequalities), and it develops by degrees (as defined by the exponents). It begins, very logically, with a study of first-degree relations (all of the exponents are "1"), and continues to develop by exploring other types of exponents. Included are higher-order relations (with integer exponents), rational-degree relations (with fractions as exponents) and literal-degree relations (when the exponents are variables, or "letters").
As such, algebra is the basic language of all upper-level mathematics courses, including geometry. Not only is geometry not a prerequisite for advanced algebra (whatever that is supposed to be), but you really need a good understanding of algebra as a complete course before you can fully understand a complete geometry course. That means there is a disadvantage, from the viewpoints of instruction and subject integrity, when you study geometry in the middle of an algebra course. The analogy may be somewhat over-simplified, but it is a little like beginning to learn English, and before reaching a reasonable level of mastery in the structure and syntax of the language, being introduced to a study of classic literature. They are just not ready for that yet.
Of course, all this would be irrelevant if algebra were taught analytically, without dependence on rules and shortcuts. If students were taught the "why" of algebraic principles, less repetition and practice would be necessary, and algebra could be studied in one school year. Then, the two "halves" would truly make a "whole."
Thomas Clark is the president of VideoText Interactive and the author of Algebra: A Complete Course and Geometry: A Complete Course. His Convention workshops will go into greater detail concerning the effective teaching of mathematics. For more information, visit | 677.169 | 1 |
News Detail
Kent State Dedicates New Math Emporium on Sept. 13
Posted Sep. 7, 2011
New state-of-the art learning center equips college students with math skills needed for academic success
Members of the Kent State University community will gather Sept. 13 at 4 p.m. to celebrate the opening of the new Kent State University Math Emporium, a state-of-the-art computerized learning center designed to help students learn math. Located on the second floor of the Kent State University Library, the Math Emporium launched this fall with the start of classes on Aug. 29.
The introduction of the Math Emporium is an example of how Kent State is dedicated to the success of its students. Basic math skills are an essential foundation for many courses of study and necessary for students' overall academic success in college.
"The university has developed a specialized learning experience to equip students with the mathematical knowledge they will need on their path to graduation,†said Robert G. Frank, Kent State provost and senior vice president for academic affairs. "The students will learn math by interacting with a team of instructors and the web-based math software called ALEKS. The Math Emporium promises to make a significant impact on our first-year retention. For some students, it will give them confidence in their math skills to pursue careers that require math, such as nursing and finance.â€
At the Math Emporium, students will learn through an innovative, engaging and easy-to-use program designed to help them become comfortable and proficient in basic mathematics. The Math Emporium serves as the classroom for four classes: Basic Algebra 1, 2, 3 and 4. Prior to the beginning of school, students take a placement assessment to determine which math courses they need. Students who need additional math preparation to succeed in college will be matched with the appropriate course of study in the Math Emporium.
"Students will focus on learning exactly what they need to know at their own pace while their instructional team provides individualized coaching,†said Andrew Tonge, chair of the Department of Mathematical Sciences at Kent State. "The Math Emporium uses an adaptive software program, ALEKS, to determine what students already know. It then offers each student an individualized choice of paths forward. This enables them to complete the curriculum efficiently by always studying only material they are ready to learn. All students can then manage their study time to focus on actively learning precisely the information they need, with the aid of online help tools and an interactive e-book, together with one-on-one assistance from an instructional team.â€
The lead professor and the instructional team at the Math Emporium function as coaches, providing in-depth personalized teaching and support. Periodically, each student takes a progress assessment to check that they have fully understood the information they recently studied. Any material that has not been properly mastered is reassigned as part of the future study plan. At the end of the course, a comprehensive assessment determines the grade. This ensures students have a sufficiently rigorous grounding to have good prospects for success in subsequent courses.
"The Math Emporium's potential effect on student success is very exciting,†Frank said. "In addition to this Math Emporium on our Kent Campus, we will have similar facilities on our Regional Campuses.â€
The Math Emporium features state-of-the-art technology with 247 computer stations in an 11,154-square-foot space. The facility also features bright, vibrant colors and comfortable furniture, making it an attractive and appealing environment.
The Math Emporium is staffed from 7:30 a.m. to 9 p.m. Monday through Thursday; 7:30 a.m. to 6 p.m. on Friday; 10 a.m. to 6 p.m. on Saturday; and 12 p.m. to 8 p.m. on Sunday. Students also can access the program from any web browser.
Media Note: Members of the media are welcome to attend and cover the dedication of the Kent State University Math Emporium on Sept. 13 at 4 p.m. The Math Emporium is located on the second floor of the Kent State University Library. Parking is available in the Kent Student Center Visitor Lot.
Photo Caption: The Kent State University Math Emporium is a new state-of-the-art learning center that equips students with the mathematical knowledge they will need on their path to graduation. | 677.169 | 1 |
The Mathematics that Every Secondary School Math Teacher Needs to Know knowledge of mathematics do secondary school math teachers need to facilitate understanding, competency, and interest in mathematics for all of their students? This unique text and resource bridges the gap between the mathematics learned in college and the mathematics taught in secondary schools. Written in an informal, clear, and interactive learner-centered style, it is designed to help pre-service and in-service teachers gain the mathematical insight they need to engage their students in learning mathematics in a multifaceted way that i... MOREs interesting, developmental, connected, deep, understandable, and often, surprising and entertaining.Features include Launch questions at the beginning of each section, Student Learning Opportunities, Questions from the Classroom, and highlighted themes throughout to aid readers in becoming teachers who have great "MATH-N-SIGHT":M Multiple Approaches/RepresentationsA Applications to Real LifeT TechnologyH HistoryN Nature of Mathematics: Reasoning and ProofS Solving ProblemsI Interlinking Concepts: ConnectionsG Grade LevelsH Honing of Mathematical SkillsT Typical ErrorsThis text is ideally suited for a capstone mathematics course in a secondary mathematics certification program, is appropriate for any methods or mathematics course for pre- or in-service secondary mathematics teachers, and is a valuable resource for classroom teachers. This clear, interactive, learner-centered text and resource will help pre-service and in-service secondary mathematics teachers gain the deep mathematical insight they need to teach their students in a multifaceted way that is interesting, developmental, connected, deep, understandable, and often, surprising and entertaining. | 677.169 | 1 |
This unit explores a real-world system – the Great Lakes – where mathematical modelling has been used to understand what is happening and to predict what will happen if changes are made. The system concerned is extremely complex but, by keeping things as simple as possible, sufficient information will be extracted to allow a mathematical model of the system to be obtained.
Just as we usually take for granted the basic arithmetical operations with real numbers, so we usually assume that, given any positive real number a, there is a unique positive real number b = such that b2 = a. We now discuss the justification
This unit is from our archive and is an adapted extract from Complex analysis (M33 want you now to follow a worshipper on a 'pilgrimage in miniature' around Dakshineswar temple on the outskirts of Calcutta. Before you read further, please study carefully the plan of Dakshineswar temple in Figure 14Databases are one of the more enduring software engineering artefacts; it is not uncommon to find database implementations whose use can be traced back for 15 years or more. Consequently, maintenance of the database is a key issue.
Maintenance can take three main forms:
Operational maintenance, where the performance of the database is monitored. If it falls below some acceptable standard, then reorganisation of the database, usuall OU PGCE has been developed by The Open University and its partner schools to provide an innovative, student-teacher centred approach to initial teacher education. We aim to build on the skills, knowledge and experience that student teachers bring to the profession, and then to prepare them for a career in teaching. The course leads to the award of PGCE, and Qualified Teacher Status (QTS) conferred by the appropriate statutory body. Working with a Partner Schools Network, the OU PGCE prov joining a learned society or professional organisation. They can be very useful for conference bulletins as well as in-house publications, often included in the subscription. Don't forget to ask about student rates. Try looking for the websites of learned societies associated with your subject area (e.g. The Royal Society, the Institute of Electrical language is a complex communication system that allows the generation of infinitely many different messages by combining the basic sounds (phonemes) into words, and combining the words into larger units called sentences. The way the sounds combine is governed by phonological rules, and the way the words combine is governed by syntactic rules.
Phonemes can be divided into the vowels, which are made by vibration of the vocal folds, and consonants, which are abrupt sounds made by bri | 677.169 | 1 |
the difference is, the TI-89 is only rated up to pre-calc but has engineering capacities wheras the TI-inspire has calculus capabilities but is not rated for engineering. I don;t know if it would be better to have engineering or calculus under its list of capabilities. And if all calculators are the same, then why is it that you can't graph with a TI-30 but you can with a TI-92?Trigonometry, some pretty good stat analysis, numeric multi-variable single-equation solver, numeric derivatives and integrals are included in most of the recent TI models. (the syntax for the last ones and the computation time are terrible, but that's another subject). I guess there is some formal calculus (ie instead of computing an approx of the derivative / integral /etc. it gives you the mathematical form of it) in the new models, but I never tried it so I can't say.
After a quick internet search, I realized some of my comrades had a TI-89, so I can guarantee you it works with the features I mentioned. EDIT : including some formal calculus. I don't know about the N-spire, but it just looks to me like more expensive for similar functionalities plus a good look, which is not what most engineering students want.
I am not much more advanced by your definition of pre-calculus. Sorry, but I am no American and I cannot guess what you mean by 'advanced math' especially after naming trigo etc. in another part.
And anyways, I have to warn you : if you want to get to engineering, you will need more computing power than a calculator, you will need to learn 'real' programming not guess what you mean by that. "Algebra" is a large subject, from kids understanding theorems like "the sum of two odd numbers is an even numbers" to recent cutting-edge research in maths. And I don't think I am particularly stupid by not understanding the subtle difference between "algebra1" and "algebra2" on the basis of what you wrote. Make the effort to write so that I can understand it.
If you told me "it includes matrices products and diagonalization, arithmetic congruences, basic algorithmic, etc." I would understand | 677.169 | 1 |
at the majority of universities both in this country and abroad use the first number to designate level. First year courses are 100, second year 200 and so on. Graduate courses or dual enrolled courses are typically 500 level.
Quote:
And when used in relation to mathematics, ironically, means the exact opposite.
Proof?
Quote:
Regardless, I can only guess about the nature of your courses, they don't sound like anything serious. But that is irrelevant to the general issue here, namely, that engineering, physics, etc students don't even come close to satisfying the requirements for a mathematics degree. Heck, they are far from the minor as well. This was just as true 15 years ago as it is today. Mathematics programs haven't changed much.
As so often on this forum, you are wrong. These were graduate level courses (seniors at RU typically take the classes with the grad students). And I have met all of the requirements for a BA in mathematics as well as my two other BS degrees at RU.
Quote:
As I linked to earlier, the introductory sequence of mathematics courses includes linear algebra and differential equations. Are these subjects limited to basic courses? No.....
There is no "Bayesian math".......
15 years ago the Bayesian analysis was run by the math department and had a math course code number. It maybe run by the stats department now but it is a very real course.
At the undergrad level the introductory sequence (Calculus, linear algebra, differential eq) is all that is required of engineering students. Certainly at the grad level engineering students may take some additional, largely applied, mathematics courses. Things like numerical analysis, partial differential equations, etc.[/quote]
Again we must be an uber selective group both at IMCS and where I work now.
Actually at the majority of universities both in this country and abroad use the first number to designate level. First year courses are 100, second year 200 and so on. Graduate courses or dual enrolled courses are typically 500 level.
I agree. All the good schools (along with traditional schools) use similar numbering systems. But if you go to a school like University of Mississippi or something random, they don't always stick to the standards of education (as preset by traditional schools). But, why would you ever go to a random school?
You don't know because you don't know what you're talking about. The term advanced is not used in place of introductory. The university offers two variants of the classes. Lecture versions called Multivariable Calculus and Linear Algebra, which are available for those who opt for the AB. The Advanced variants are for engineer students and are two semesters each.
Yes....of course! What was a I thinking calling a students first courses in linear algebra introductory.
Actually at the majority of universities both in this country and abroad use the first number to designate level.
I have no idea whether the "majority" do or not, what I do know is that there is no universal numbering system. The numbering system I've seen use the most is using 2 digit numbers for lower-division, 100's for upper-division and 200's for graduate.
Regardless, like I said, I have no idea what those numbers correspond to...
Quote:
Originally Posted by lkb0714
These were graduate level courses (seniors at RU typically take the classes with the grad students). And I have met all of the requirements for a BA in mathematics as well as my two other BS degrees at RU.
BA in mathematics? I'm sure that can make some useful toilet paper, but as far as mathematics is concerned it isn't serious....
I don't care whether or not RU lets its science, etc students get a cheap "BA in mathematics" degree as a side act, I care about the requirements for a serious mathematics degree. And if you look at the requirements for in BS degree in mathematics at any good universities you'll see that the requirements extend well beyond the mathematics courses taken by physics and engineering students. Indeed, physics and engineering students don't even learn serious mathematics...... But why would they? physicists and engineers aren't in the business of doing mathematics, they simply use mathematics.
Quote:
Originally Posted by lkb0714
15 years ago the Bayesian analysis was run by the math department and had a math course code number.
And yet there is no "Bayesian mathematics", indeed, the mere utterance of that phrase demonstrates an almost no knowledge of the subject. To say it again, "Bayesian" refers to all sorts of things in mathematics, but what it doesn't refer to is a special sort of mathematics...
But Mathematicians, and this has always been the case, aren't particularly focused on Bayesianism they usually rely on the frequency interpretation of probability. Computer scientists on the other hand are very interested in Bayesian inference, which is the foundation of machine learning.
At the undergrad level the introductory sequence (Calculus, linear algebra, differential eq) is all that is required of engineering studentsMy friends who majored in engineering took the same classes as above but instead of Discrete math took Multivariable Calculus
A minor in mathematics typically requires the lower-division sequence (cal, diff eq, linear algebra) and then 5~6 upper-division courses, so usually an engineering student is only going to have around 50% (give or take) of the requirements satisfied.
The lower-division/upper-division separation in mathematics is pretty strict and partly based on the fact that the mathematics department has to spend a lot of its time educating engineering, science, etc students in introductory mathematics. Its a bit unfortunate pedagogically for the mathematics students since they should be introduced to "serious mathematics" much sooner. Regardless, the lower-division courses are really geared towards engineering, science, etc students and the mathematics students just go along for the ride and then get more serious material in the 3rd year.
Another unfortunate side effect of the above is that most people, even those that use it a lot (e.g., engineers) , don't have a good idea about what goes on in mathematics. Its also an unpleasant experience for those that mistake the introductory courses as representative of "serious mathematics" and pick mathematics as their major based on this misunderstanding, you get a lot of drop outs and mystery in the 3rd year... In contrast computer science introduces students to rigorous material in the 2nd year (after the basic programming classes) and uses its, usually murderous, 2 semester sequence in data-structures, algorithms, etc to screen out the serious from non-serious students. But they can do this because they aren't spending much time educating students outside of computer science.
BA in mathematics? I'm sure that can make some useful toilet paper, but as far as mathematics is concerned it isn't serious....
This is the summative sentence for this debate and demonstrates the breadth and depth of your ignorance. The reason Rutgers gives BA for Math is because their most selective school, Rutgers College, only gave BA degrees in everything from chemistry to math. It says literally NOTHING about their degree quality (at one point their science programs were some of the best in the country) and everything about how their 200+ year old college was originally designed.
Yet again, the math program at Rutgers is one of the top 20 in the country. Hardly, worthless, unlike your staggeringly ignorant opinion.
The reason Rutgers gives BA for Math is because their most selective school, Rutgers College, only gave BA degrees in everything from chemistry to math.
Ugh, you are focusing on things that don't matter and ignoring the real issue. I don't care how Rutgers labels things. Here is the real issue, any "mathematics degree" that is issued as a side act to studying engineering, physics, etc is not a serious mathematics degree. Any serious program in mathematics is going to require extensive course work that goes well beyond the required mathematics courses of an engineering, physics, etc student. These students only take the introductory sequence of mathematics courses that is, in reality, created for them and not mathematics students.
That is the reality of matters, engineering, physics, etc students come out of school knowing very little about real mathematics. You can continue to believe whatever you wish.
Yet again, the math program at Rutgers is one of the top 20 in the country. Hardly, worthless, unlike your staggeringly ignorant opinion.
Rutgers offers a very good math program. You can read about it on their website. The interdisciplinary programs administered by other departments 15 years ago have nothing to do | 677.169 | 1 |
Introduction to
Numerical Analysis Using
MATLAB
By
Dr Rizwan Butt
CHAPTER ONE
Number Systems and Errors
Introduction
It simply provides an introduction of numerical analysis.
Number Representation and Base of Numbers
Here we consider methods for representing numbers on
computers.
1. Normalized Floating-point Representation
It describes how the numbers are stored in the computers.
CHAPTER 1 NUMBER SYSTEMS AND ERRORS
1. Human Error
It causes when we use inaccurate measurement of data or
inaccurate representation of mathematical constants.
2. Truncation Error
It causes when we are forced to use mathematical techniques
which give approximate, rather than exact answer.
3. Round-off Error
This type of errors are associated with the limited number of digits
numbers in the computers.
CHAPTER 1 NUMBER SYSTEMS AND ERRORS
Effect of Round-off Errors in Arithmetic Operation
Here we analysing the different ways to understand the nature
of rounding errors.
1. Rounding off Errors in Addition and Subtraction
It describes how addition and subtraction of numbers are
performed in a computer.
2. Rounding off Errors in Multiplication
It describes how multiplication of numbers are performed in a
computer.
CHAPTER 1 NUMBER SYSTEMS AND ERRORS
3. Rounding off Errors in Division
It describes how division of numbers are performed in a computer.
4. Rounding off Errors in Powers and roots
It describes how the powers and roots of numbers are performed
in a computer.
CHAPTER TWO
Solution of Nonlinear Equations
Introduction
Here we discuss the ways of representing the different types of
nonlinear equation f(x) = 0 and how to find approximation of its
real root .
Simple Root's Numerical Methods
Here we discuss how to find the approximation of the simple root
(non-repeating) of the nonlinear equation f(x) = 0.
CHAPTER 2 SOLUTION OF NONLINEAR EQUATIONS
1. Method of Bisection
This is simple and slow convergence method (but convergence is
guaranteed) and is based on the Intermediate Value Theorem.
Its strategy is to bisect the interval from one endpoint of the
interval to the other endpoint and then retain the half interval
whose end still bracket the root.
2. False Position Method
This is slow convergence method and may be thought of as an
attempt to improve the convergence characteristic of bisection
method. Its also known as the method of linear interpolation.
CHAPTER 2 SOLUTION OF NONLINEAR EQUATIONS
3. Fixed-Point Method
This is very general method for finding the root of nonlinear
equation and provides us with a theoretical framework within
which the convergence properties of subsequent methods can be
evaluated. The basic idea of this method is convert the equation
f(x) = 0 into an equivalent form x = g(x).
4. Newtons Method
This is fast convergence method (but convergence is not
guaranteed) and is also known as method of tangent because
after estimated the actual root, the zero of the tangent to the
function at that point is determined.
CHAPTER 2 SOLUTION OF NONLINEAR EQUATIONS
5. Secant Method
This is fast convergence method (but not like
Newton's method) and is recommended as the best
general-purpose method. It is very similar to false
position method, but it is not necessary for the interval
to contain a root and no account is taken of signs of
the numbers f(x_n).
Multiple Root's Numerical Methods
Here we discuss how to find approximation of multiple
root (repeating) of nonlinear equation f(x) = 0 and its
order of multiplicity m.
CHAPTER 2 SOLUTION OF NONLINEAR EQUATIONS
1. First Modified Newtons Method
It can be useful to find the approximation of multiple root if the
order of multiplicity m is given.
2. Second Modified Newtons Method
It can be useful to find the approximation of multiple root if the
order of multiplicity m is not given.
Convergence of Iterative Methods
Here we discuss order of convergence of all the iterative methods
described in the chapter.
CHAPTER 2 SOLUTION OF NONLINEAR EQUATIONS
Acceleration of Convergence
Here we discuss a method which can be applied to any linear
convergence iterative method and acceleration of
convergence can be achieved.
Systems of Nonlinear Equations
When we are given more than one nonlinear equation. Solving
systems of nonlinear is a difficult task.
Newtons Method
We discuss this method for system of two nonlinear equations
in two variables. For system of nonlinear equations that have
analytical partial derivatives, this method can be used,
otherwise not.
CHAPTER 2 SOLUTION OF NONLINEAR EQUATIONS
Roots of Polynomials
A very common problem in nonlinear equations is to
find the roots of polynomial is discussed here.
1. Horner's Method
It is one of the most efficient way to evaluate
polynomials and their derivatives at a given point. It
is helpful for finding the initial approximation for
solution by Newton's method. It is also quit stable.
CHAPTER 2 SOLUTION OF NONLINEAR EQUATIONS
2. Muller's Method
It is generalization of secant method and uses quadratic
interpolation among three points. It is a fast convergence method
for finding the approximation of simple zero of a polynomial
equation.
3. Bairstow's Method
It can be used to find all the zeros of a polynomial. It is one of the
most efficient method for determining real and complex roots of
polynomials with real coefficients.
CHAPTER THREE
Systems of Linear Equations
Introduction
We give the brief introduction of linear equations, linear systems,
and their importance.
Properties of Matrices and Determinant
To discuss the solution of the linear systems, it is necessary to
introduce the basic properties of matrices and the determinant.
Numerical Methods for Linear Systems
To solve the systems of linear equations using the numerical
methods, there are two types of methods available, methods of
first type are called direct methods and second type are called
iterative methods.
CHAPTER 3 SYSTEMS OF LINEAR EQUATIONS
Direct Methods for Linear Systems
The method of this type refers to a procedure for
computing a solution from a form that is mathematically
exact. These methods are guaranteed to succeed and
are recommended for general-purpose.
1. Cramers Rule
This method is use for solving the linear systems by the
use of determinants. It is one of the least efficient
method for solving a large number of linear equations.
But it is useful for explaining some problems inherent in
the solution of linear equations.
2
CHAPTER 3 SYSTEMS OF LINEAR EQUATIONS
2. Gaussian Elimination Method
It is most popular and widely used method for solving linear
system. The basic of this method is to convert the original system
into equivalent upper-triangular system and from which each
unknown is determined by backward substitution.
2.1 Without Pivoting
In converting original system to upper-triangular system if a
diagonal element becomes zero, then we have to interchange
that equation with any below equation having nonzero diagonal
element.
CHAPTER 3 SYSTEMS OF LINEAR EQUATIONS
2.2 Partial Pivoting
In using the Gauss elimination by partial pivoting (or row
pivoting), the basic approach is to use the largest (in absolute
value) element on or below the diagonal in the column of
current interest as the pivotal element for elimination in the
rest of that column.
2.3 Complete Pivoting
In this case we search for the largest number (in absolute
value) in the entire array instead of just in the first column,
and this number is the pivot. This means we need to
interchange the columns as well as rows.
CHAPTER 3 SYSTEMS OF LINEAR EQUATIONS
3. Gauss-Jordan Method
It is a modification of Gauss elimination method and is although
inefficient for practical calculation but is often useful for
theoretical purposes. The basic idea of this method is to convert
original system into diagonal system form.
4. LU Decomposition Method
It is also a modification of Gauss elimination method and here we
decompose or factorize the coefficient matrix into the product of
two triangular matrices (lower and upper).
CHAPTER 3 SYSTEMS OF LINEAR EQUATIONS
4.1 Dollittle's method (l_ii = 1)
Here the upper-triangular matrix is obtained by forward elimination
of Gauss elimination method and the lower-triangular matrix
containing the multiples used in the Gauss elimination process
as the elements below the diagonal with unity elements on the
main diagonal.
4.2 Crout's method (u_ii = 1)
The Crout's method, in which upper-triangular matrix has unity on
the main diagonal, is similar to the Dollittle's method in all other
aspects. The lower-triangular and upper-triangular matrices are
obtained by expanding the matrix equation A = LU term by term
to determine the elements of the lower-triangular and upper-
triangular matrices.
CHAPTER 3 SYSTEMS OF LINEAR EQUATIONS
4.3 Cholesky method (l_ii = u_ii)
This method is of the same form as the Dollittle's and Crout's
methods except it is limited to equations involving symmetrical
coefficient matrices. This method provides a convenient method
for investigating the positive definiteness of symmetric matrices.
Norms of Vectors and Matrices
For solving linear systems, we discuss a method for quantitatively
measuring the distance between vectors in R^n and a measure
of how well one matrix approximates another.
CHAPTER 3 SYSTEMS OF LINEAR EQUATIONS
Iterative Methods for Solving Linear Systems
These methods start with an arbitrary first approximation to the
unknown solution of linear system and then improve this estimate
in an infinite but convergent sequence of steps. This type of
methods are used for large sparse systems and efficient in terms
of computer storage and time requirement.
1. Jacobi Iterative Method
It is a slow convergent iterative method for the linear systems.
From its formula, it is seen that the new estimates for solution are
computed from the old estimates.
2. Gauss-Seidel Iterative Method
It is a faster convergent iterative method than the Jacobi method
for the solution of the linear systems as it uses the most recent
calculated values for all x_i.
CHAPTER 3 SYSTEMS OF LINEAR EQUATIONS
Convergence Criteria
We discuss the sufficient conditions for the convergence of
Jacobi and Gauss-Seidel methods by showing l_∞-norm of their
corresponding iteration matrices less than one.
Eigenvalues and Eigenvectors
We briefly discuss the eigenvalues and eigenvectors of a matrix
and show how they can be used to describe the solutions of
linear systems.
3. Successive Over-Relaxation Method
It is useful modification of the Gauss-Seidel method. It is the best
iterative method of choice and needs to determine optimum
value of the parameter.
CHAPTER 3 SYSTEMS OF LINEAR EQUATIONS
4. Conjugate Gradient Method
It is very useful when employed as an iterative approximation
method for solving large sparse linear systems. The need for
estimating parameter is removed in this method.
Conditioning of Linear Systems
We discuss ill-conditioning of linear systems by using the
condition number of matrix. The best way to deal with ill-
conditioning is to avoid it by reformulating the problem.
Iterative Refinement
We discuss residual corrector method which can be used to
improve the approximate solution obtained by any means.
CHAPTER FOUR
Approximating Functions
Introduction
We describe several numerical methods for
approximating functions other than elementary functions.
The main purpose of these numerical methods is to
replace a complicated function by one which is simpler
and more manageable.
Polynomial Interpolation for Uneven Intervals
The data points we consider here in a given functional
relationship are not equally spaced.
CHAPTER 4 APPROXIMATING FUNCTIONS
1. Lagrange Interpolating Polynomials
It is one of the popular and well known interpolation
method to approximate the functions at arbitrary point
and provides a direct approach for determining
interpolated values regardless of data spacing.
2. Newtons General Interpolating Formula
It is generally more efficient than Lagrange polynomial
and it can be adjusted easily for additional data.
3. Aitkens Method
It is an iterative interpolation method which is based on
the repeated application of a simple interpolation
method.
CHAPTER 4 APPROXIMATING FUNCTIONS
Polynomial Interpolation for Even Intervals
The data points we consider here in a given functional relationship
are equally spaced and polynomials are based on differences which
are easy to use.
1. Newton's Forward-Difference Formula
It can be used for interpolation near the beginning of table values.
2. Newton's Backward-Difference Formula
It can be use for interpolation near the end of table values.
3. Some Central-Difference Formulas
These can be used for interpolation in the middle of the table values
and among them are Stirling, Bessel, and Gauss formulas.
CHAPTER 4 APPROXIMATING FUNCTIONS
Interpolation with Spline Functions
It is an alternative approach to divide the interval into a
collection of subintervals and construct a different
approximating polynomial on each subinterval, called
Piecewise Polynomial Approximation.
1. Linear Spline
One of the simplest piecewise polynomial interpolation for
approximating functions and basic of it is simply connect
consecutive points with straight lines.
2. Cubic Spline
The most widely cubic spline approximations are patched
among ordered data that maintain continuity and smoothness
and they are more powerful than polynomial interpolation.
CHAPTER 4 APPROXIMATING FUNCTIONS
Least Squares Approximation
Least squares approximation which seeks to minimize the
sum (over all data) of the squares of the differences between
function values and data values, are most useful for large and
rough sets of data.
1. Linear Least Squares
It defines the correct straight line as the one that minimizes
the sum of the squares of the distance between the data
points and the line.
2. Polynomial Least Squares
When data from experimental results are not linear, then we
find the least squares parabola and the extension to a
polynomial of higher degree is easily made.
CHAPTER 4 APPROXIMATING FUNCTIONS
3. Nonlinear Least Squares
In many cases, data from experimental tests are not linear,
then we fit to them two popular exponential forms y = ax^b
and y = ae^(bx).
4. Least Squares Plane
When the dependent variable is function of two variables, then
the least squares plane can be used to find the approximation
of the function.
5. Overdetermined Linear Systems
The least squares solution of overdetermined linear system
can be obtained by minimizing the l_2-norm of the residual.
CHAPTER 4 APPROXIMATING FUNCTIONS
6. Least Squares with QR Decomposition
The least squares solution of the overdetermined linear
system can be obtained by using QR (the orthogonal
matrix Q and upper-triangular matrix R) decomposition of
a given matrix.
7. Least Squares with Singular Value Decomposition
The least squares solution of the overdetermined linear
system can be obtained by using singular value (UDV^T,
the two orthogonal matrices U, V and a generalized
diagonal matrix D) decomposition of a given matrix.
CHAPTER FIVE
Differentiation and Integration
Introduction
Here, we deal with techniques for approximating numerically
the two fundamental operations of the calculus, differentiation
and integration.
Numerical Differentiation
A polynomial p(x) is differentiated to obtain p′(x), which is taken
as an approximation to f′(x) for any numerical value x.
Numerical Differentiation Formulas
Here we gave many numerical formulas for approximating the
first derivative and second derivative of a function.
CHAPTER 5 DIFFERENTIATION AND INTEGRATION
1. First Derivatives Formulas
For finding the approximation of the first derivative of a
function, we used two-point, three-point, and five-point
formulas.
2. Second Derivatives Formulas
For finding the approximation of the second derivative of a
function, we used three-point and five-point formulas.
3. Formulas for Computing Derivatives
Here we gave many forward-difference, backward-difference,
and central-difference formulas for approximating the first and
second derivative of the function.
CHAPTER 5 DIFFERENTIATION AND INTEGRATION
Numerical Integration
Here, we pass a polynomial through points of a function and
then integrate this polynomial approximation to a function. For
approximating the integral of f(x) between a and b we used
Newton-Cotes techniques.
1. Closed Newton-Cotes Formulas
For these formulas, the end-points a and b of the given
interval [a, b] are in the set of interpolating points and the
formulas can be obtained by integrating polynomials fitted to
equispaced data points.
1.1 Trapezoidal Rule
This rule is based on integration of the linear interpolation.
CHAPTER 5 DIFFERENTIATION AND INTEGRATION
1.2 Simpson's Rule
This rule approximates the function f(x) with a quadratic
interpolating polynomial.
2. Open Newton-Cotes Formulas
These formulas contain all the points used for approximating
within the open interval (a, b) and can be obtained by
integrating polynomials fitted to equispaced data points.
3. Repeated use of the Trapezoidal Rule
The repeated Trapezoidal rule is derived by repeating the
Trapezoidal rule and for a given domain of integration, error of
the repeated Trapezoidal rule is proportional to h_2.
CHAPTER 5 DIFFERENTIATION AND INTEGRATION
4. Romberg Integration
The Romberg integration is based on the repeated
Trapezoidal rule and using the results of repeated
Trapezoidal rule with two different data spacings, a more
accurate integral is evaluated.
5. Gaussian Quadratures
The Gauss(-Legendre) quadratures are based on
integrating a polynomial fitted to the data points at the
roots of a Legendre polynomial and the order of
accuracy of a Gauss quadrature is approximately twice
as high as that of the Newton-Cotes closed formula
using the same number of data points.
CHAPTER SIX
Ordinary Differential Equations
Introduction
We discussed many numerical methods for solving first-order
ordinary differential equations and systems of first-order ordinary
differential equations.
Numerical Methods for Solving IVP
Here we discuss many single-step numerical methods and multi-
step numerical methods for solving the initial-value problem (IVP)
and some numerical methods for solving boundary-value
problem (BVP).
1. Single-Step Methods for IVP
These types of methods are self-starting, refer to estimate y′(x)
from the initial condition and proceed step-wise. All the
information used by these methods is consequently obtained
within the interval over which the solution is being approximated.
CHAPTER 6 ORDINARY DIFFERENTIAL EQUATIONS
1.1 Euler's Method
One of the simplest and straight forward but not an efficient
numerical method for solving initial-value problem (IVP).
1.2 Higher-Order Taylor's Methods
For getting higher accuracy, the Taylor's methods are excellent
when the higher-order derivative can be found.
1.3 Runge-Kutta Methods
An important group of methods which allow us to obtain great
accuracy at each step and at the same time avoid the need of
higher derivatives by evaluating the function at selected points
on each subintervals.
CHAPTER 6 ORDINARY DIFFERENTIAL EQUATIONS
2. Multi-Steps Methods for IVP
This type of methods make use of information about the
solution at more than one point.
2.1 Adams Methods
These methods use the information at multiple steps of the
solution to obtain the solution at the next x-value.
2.2 Predictor-Corrector Methods
These methods are combination of an explicit method and
implicit method and they are consist of predictor step and
corrector step in each interval.
CHAPTER 6 ORDINARY DIFFERENTIAL EQUATIONS
Systems of Simultaneous ODE
Here, we require the solution of a system of simultaneous first-
order differential equations rather than a single equation.
Higher-Order Differential Equations
Here, we deal the higher-order differential equation (nth-order)
and solve it by converting to an equivalent system of (n) first-
order equations.
Boundary-Value Problems
Here, we solve ordinary differential equation with known
conditions at more than one value of the independent
variable.
CHAPTER 6 ORDINARY DIFFERENTIAL EQUATIONS
1. The Shooting Method
It is based on by forming a linear combination of the
solution to two initial-value problems (linear shooting
method) and by converting a boundary-value problem to
a sequence of initial-value problems (nonlinear shooting
method) which can be solved using the single steps
method.
2. The Finite Difference Method
It is based on finite differences and it reduces a
boundary-value problem to a system a system of linear
equations which can be solved by using the methods
discussed in the linear system chapter.
CHAPTER SEVEN
Eigenvalues and Eigenvectors
Introduction
Here we discussed many numerical methods for solving
eigenvalue problems which seem to be a very fundamental
part of the structure of universe.
Linear Algebra and Eigenvalues Problems
The solution of many physical problems require the
calculations of the eigenvalues and corresponding
eigenvectors of a matrix associated with linear system of
equations.
Basic Properties of Eigenvalue Problems
We discussed many properties concerning with eigenvalue
problems which help us a lot in solving different problems.
CHAPTER 7 EIGENVALUES AND EIGENVECTORS
Numerical Methods for Eigenvalue Problems
Here we discussed many numerical methods for finding
approximation of the eigenvalues and corresponding
eigenvectors of the matrices.
Vector Iterative Methods for Eigenvalues
This type of numerical methods are most useful when matrix
involved be comes large and also they are easy means to
compute eigenvalues and eigenvectors of a matrix.
1. Power Method
It can be used to compute the eigenvalue of largest modules
(dominant eigenvalue) and the corresponding eigenvector of a
general matrix.
CHAPTER 7 EIGENVALUES AND EIGENVECTORS
2. Inverse Power Method
This modification of the power method can be used to
compute the smallest (least) eigenvalue and the
corresponding eigenvector of a general matrix.
3. Shifted Inverse Power Method
This modification of the power method consists of by
replacing the given matrix A by (A−μI) and the
eigenvalues of (A−μI) are the same as those of A except
that they have all been shifted by an amount μ.
CHAPTER 7 EIGENVALUES AND EIGENVECTORS
Location of Eigenvalues
We deal here with the location of eigenvalues of both
symmetric and non- symmetric matrices, that is, the location
of zeros of the characteristic poly nomial by using the
Gerschgorin Circles Theorem and Rayleigh Quotient
Theorem.
Intermediate Eigenvalues
Here we discussed the Deflation method to obtain other
eigenvalues of a matrix once the dominant eigenvalue is
known.
Eigenvalues of Symmetric Matrices
Here, we developed some methods to find all eigenvalues of a
symmetric matrix by using a sequence of similarity
transformation that transformed the original matrix into a
diagonal or tridiagonal matrix.
CHAPTER 7 EIGENVALUES AND EIGENVECTORS
1. Jacobi Method
It can be used to find all eigenvalues and corresponding eigenvectors
of a symmetric matrix and it permits the transformation of a matrix
into a diagonal.
2. Sturm Sequence Iteration
It can be used in the calculation of eigenvalues of any symmetric
tridiagonal matrix.
3. Given's Method
It can be used to find all eigenvalues of a symmetric matrix
(corresponding eigenvectors can be obtained by using shifted
inverse power method) and it permits the transformation of a matrix
into a tridiagonal.
4. Householder's Method
This method is a variation of the Given's method and enable us to
reduce a symmetric matrix to a symmetric tridiagonal matrix form.
CHAPTER 7 EIGENVALUES AND EIGENVECTORS
Matrix Decomposition Methods
Here we used three matrix decomposition methods and find all the
eigenvalues of a general matrix.
1. QR Method
In this method we decomposed the given matrix into a product
orthogonal matrix and a upper-triangular matrix which find all the
eigenvalues of a general matrix.
2. LR Method
This method is based upon the decomposition of the given matrix into
a product lower-triangular matrix (with unit diagonal elements) and a
upper- triangular matrix.
3. Singular Value Decomposition
Here we decomposed rectangular real matrix into a product of two
orthogonal matrices and generalized diagonal matrix.
Appendices
1. Appendix A
includes some mathematical preliminaries.
2. Appendix B
includes the basic commands for software package MATLAB.
3. Appendix C
includes the index of MATLAB programs and MATLAB built-in-
functions.
4. Appendix D
includes symbolic computation and Symbolic Math Toolbox
functions.
5. Appendix E
includes answers to selected odd-number exercises for all | 677.169 | 1 |
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The first chapter introducting complex numbers includes applictions to electrical circuits. The last section of the chapter on Analytic Functions, on harmonic functions, covers steady state temperature distributions and Poisson's equation. The logarithmic functions section of the next chapter treats temperature distribution in the upper-half plane. After proving the Cauchy-Goursat theorem, the Cauchy integral formulas and other results Chapter 4 on complex integration concludes with a section on potential functions of conservative fields. An application for Laurent series obtains the potential flow over a perturbed circle.
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Product Details
Published: 2003
Isbn: 1-885581-45-9
Pages: 193
Math is an important part of everyday life and an integral part of the skills necessary to become certified in the safety profession. Many who pursue certification have long since completed their college math courses and have not actively pursued the math skills they once had. Background Math provides the basics necessary to successfully negotiate the math included on the certification exams, as well as a handy primer for those who already have their credentials.
Topics include:
Calculator selection and use, including BCSP rules for calculators, strategies for examinations and hierarchy for operations
Fractions, reciprocals, proportions, rounding and absolute value
Exponents, roots and logarithms and antilogs
Systems of measurement, including English, metric, conversions and dimensional analysis
Notation, both scientific and engineering
Algebraic properties and simple equations, including variables, commutation, associative and distributive properties, order of operations, rules of equations, multiplying polynomials, and solving equations | 677.169 | 1 |
College Algebra - 4th edition and pop quizzes, as well as procedures, strategies, a...show morend summaries. ...show less
Systems of Linear Equations in Two Variables. Systems of Linear Equations in Three Variables. Nonlinear Systems of Equations. Partial Fractions. Inequalities and Systems of Inequalities in Two Variables. Linear Programming.
6. Matrices and Determinants.
Solving Linear Systems Using Matrices. Operations with Matrices. Multiplication of Matrices. Inverses of Matrices. Solution of Linear Systems in Two Variables. Using Determinants. Solution of Linear Systems in Three Variables Using Determinants Fair Acceptable condition and jacket is worn and taped on corners. Same day shipping. Thank you.
$9.45 +$3.99 s/h
Good
Quality School Texts OH Coshocton, OH
2005-12-29 Hardcover Good Names on inside cover and numbers on bookedge; no other internal marking/highlighting.
$1415.00 +$3.99 s/h
VeryGood
arcfoundationthriftstore Ventura, CA
0321356918 | 677.169 | 1 |
Mathematics Through Applications
KEY MESSAGE Presented in a clear and concise style, the Akst/Bragg series teaches by example while expanding understanding with applications that are ...Show synopsisKEY MESSAGE Presented in a clear and concise style, the Akst/Bragg series teaches by example while expanding understanding with applications that are fully integrated throughout the text and exercise sets. Akst/Bragg's user-friendly design offers a distinctive side-by-side format that pairs each example and its solution with a corresponding practice exercise. The concise writing style keeps readers' interest and attention by presenting the mathematics with minimal distractions, and the motivating real-world applications demonstrate how integral mathematical understanding is to a variety of disciplines, careers, and everyday situations. KEY TOPICS Whole Numbers, Fractions, Decimals, Basic Algebra: Solving Simple Equations, Ratio and Proportion, Percents, Signed Numbers, Basic Statistics, More on Algebra, Measurement and Units, Basic Geometry MARKET For all readers interested in Basic Mathematics32150058X Annotated Instructor. Same as the student...New. 032150058X Annotated Instructor. Same as the student edition. Cannot guarantee the availability of CD/DVD/Access codes. Ships now if ordered before 2pm CST 4th Edition. Pre-loved books for the budget...Acceptable 0321500113 Student Edition. Missing up to 10 pages. Heavy...Fair. 0321500113 | 677.169 | 1 |
Algebra
(25)
Winner
1998 We designed our web page to meet three educational objectives: To apply math to real-life situations; To make math interesting and stimulating; To share interactive math experiences over the Internet. We show that math is part of our daily life by applying it to driving a car, listening to music, using a computer and saving and investing for college funds. The mathematical concepts in each of our topics are defined with simple equations at elementary and junior high math levels. When students realize that they can use simple math to understand and solve problems relevant to their lives, they will discover that math is stimulating. We take away fear of learning math by using simple equations for complicated real-life application. We ask users to submit a quiz to share in the hope of stimulating their imagination in the real world. As more users submit their quizzes, we will build up a database of interesting real-world math applications About this site
2008 All beams of wave traveling parallel to the axis of the parabola after reflecting of he surface of the antenna will go to the same location within the antenna. This point is called the focal point of the parabola. That's where they place a receiver. We'll determine the position of the focal point given equation of the parabola. About this site
2003 Here you will find shortcuts for basic math equations. We chose this subject because we wanted to help younger students with the painstaking task that is math. We also wanted people to appreciate math. Math is used more in your everyday life than you might think (getting to school on time, budgeting spending money, calculating change, etc.). We want to make people aware of everyday math. About this site
2003 In this project, our team has been instructed to create a website that enables other people or students to read, think, and understand the principles of integers. On this website, you will find links to pages that support information on multiplying, dividing, adding, and subtracting integers, in whole numbers and in fractions. About this site
2000 The site is aimed at students ages 12-15 to teach the various topics in maqth covered by guiding students through the lessons, giving hints or suggestions along the way. The site can also be used by math teachers to supplement lessons or add a new twist to the regular teaching style. We hope that it will benefit students from all over the world who need extra help in math or who enjoy mathematical puzzles. About this site
2000 A self-teaching project suitable for everybody who wants to learn more about Maths, speacially Calculus. This site has been designed in an interactive way, in order to improve and increase your knowledge.
Since Caulculus is one of the most importante branches of mathematics, and one of the most used "techniques" for solving common problems, this site has been developed in order to have applications for it.
Mathematics are part of our daily life, you use numbers, geometrics figures, variables, etc, and we bet that you haven't realized about that. You count money, you draw any kind of object made primarly of geometric figures, you make hypotesis about your grades and calculations about them. You see? Maths are everywhere!!!
Our well known friends, the X, Y, Z variables, will go all the way together us and will explain step by step every process.
Interactive exams, online help, examples, excercises, graphics everything sou you can learn more about it.
Calculus of one varibale will be revised in this project.
Just like we say: "... The greatest men are not who fight other men in battle, but those who fight the ignorance... " About this site
1999 The purpose for this site is to provide students with a guide through the topic of quadratics in Algebra 1. This site discusses and illuminates the main concepts in an engaging and playful manner. About this site
1999 Our web site is about graphs. It is called Graphing from
a 5th Grader's Point of View. We put in interactive games to
make the web site interesting. We also included a quiz and
survey because we feel that it will hep people who visit our
web site understand graphs better.
Most people think graphs would not help them in their life,
but we thought differently. We realized that people use
graphs everyday. In jobs, some people use them to see how
much money they are making. We decided to make this web site
to show how important graphs really are. About this site
1999 Math Mania has two important applications. One application is the use of math lessons to teach formulas and other methods of solving various math problems. The other application is to predict the outcome of certain problems based on given data with the Math Mania Math Solver. Math Mania is full of useful information to help one learn the language of mathematics. This site incorporates the principles of math and presents them using a collection of math lessons. These math lessons are assisted by a mailing list, a message board, and chat. These tools provide an interactive line of communication between Math Mania and the online users. Math Mania also includes an online search and sitemap to allow users to quickly navigate the site and find desired information. With Math Mania, we hope users will develop a greater appreciation for math and a greater knowledge of math and its applications. About this site
1999 The idea behind our entry was to explore some areas of math commonly only skimmed over in high school math and science. The mathematical implications of music are rarely, if ever, covered, and the significance of some constants is often not fully realized, so in developing this site we looked to fill these voids. It also attempts to explain a variety of conic sections, as well as the more mathematical parts of physics. About this site
1999 "The Fibonacci Series: The Series, The Applications, The Web Page" is an educational webpage dedicated to the exploration of and sharing of knowledge about the Fibonacci Series, a sequence of numbers constructed first by Leonardo Fibonacci in 1202. Topics covered include formulae for finding terms of the series, Golden mathematics, practical applications of the series, the appearance of the series in nature and art, and biographies of Fibonacci and his contemporaries. There is also a forum provided for the discussion of the series and sharing of knowledge thereof. The site uses a lesson-by-lesson format as well as interactive Flash animations to teach about this fascinating series and to foster in its readers a sense of wonder about mathematics. About this site
1999 This web page will teach middle school students Pre-Algebra and Algebra I concepts using step by step tutorials and interactive pages. The tutorial pages will teach the formulas and concepts involved in Pre-Algebra and Algebra. Using VB Script and Java Script, the interactive pages will generate problems that will test what the student has learned, check answers for correctness, and provide feedback. About this site
1998 Welcome to the Math Tour, an interesting and entertaining site. This is a place to discover original math problems, humorous proofs of theorems, and interesting facts about math and mathematicians. Designed for all ages, both for beginners and those with developed math skills, there is something here for everyone. About this site
1998 We want kinds in eighth and ninth grade to get help on Algebra. This will help them in school and in future years. This page is also great for mathematically advanced students. They can learn some Algebra and impress their teacher! Another objective is to have people discuss questions and get involved. Our main purpose is for students to learn! About this site
1998 This site explains the logic system of Boolean algebra. The three main logic gates AND, OR, and NOT are presented and explained. The site argues that binary logic isn't enough. Enter the "trinary" logic system that the authors have created themselves, and explore possible uses for the new trinary logic. Is their argument for a trinary system a good one? You decide.
About this site
1997 Mathematics with A.L.I.C.E is a fun way to study mathematics. A biography of Lewis Carroll is a feature of the site that borrows his most famous character, Alice, as a tour guide. Alice enters the rabbit hole to learn about linear equations and polynomials. An activities section discusses math problems and provides a chat room for you to enter the conversation.
About this site | 677.169 | 1 |
A First Course in Discrete Mathematics (Springer Undergraduate Mathematics Series)
Kurzbeschreibung Drawing on many years' experience of teaching discrete mathematics to students of all levels, the author Eulerian circuits in graphs are described, Latin squares are defined and Hall's theorem is proved. The book concludes with chapters on the constructions of schedules and a brief introduction to block designs. Each chapter is supported by a number of examples, with straightforward applications of ideas alongside more challenging problems.
Synopsis This work... | 677.169 | 1 |
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Math 111: Homework
The following assignment sheets indicate all of the readings and textbook problems
that you need to do each week. Just clink on the link (week number) to access the
assignment sheet. Each homework set is worth 5 points and is self-graded. When handing
it in, please include a cover sheet containing the following information:
Name and week number.
A list of problems you did NOT complete.
The percentage of problems, p, assigned that you completed correctly.
Your grade, H, on the homework where H = (p+10)/20. Be sure to round H down to the nearest integer (0, 1, 2, 3, 4, or 5)
I will drop your lowest homework score when calculating your grade at the end of
the quarter.
NOTE: You will earn a 0 on any homework assignment that is too hard to read; or if
you seem to have mindlessly copies another student's homework (or the solutions manual);
or if you allowed another student to mindlessly copy your work.
Also note that if you are going to hand in your HW outside of class, you have two
options:
You can bring it to the secretary in the science (2800) building by 4:30p. You'll
need to put my name (Wendy Hurley) on it and a date stamp and put it in the HW box
on the left side of the secretary's counter. DO NOT try to slip it under my office
door.
You can scan it (or take pictures of it) and email it to me at [email protected]. The homework needs to be sent to me by Tuesday at 12 midnight to receive credit
for the assignment.
If at all possible, please get your homework in during class time. This makes my
job much easier and will better prepare you for the quiz/test taken in class. | 677.169 | 1 |
Basic Topology
9780387908397
ISBN:
0387908390
Pub Date: 1983 Publisher: Springer Verlag
Summary: In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for calculating them. Students with knowledge of real analysis, elementary group theory, and linear algebra will quickly become familiar with a wide variety of techniques and applications involving point-set, geometric, and algebraic topology. Over 139 illustrations and more than 350 problems of ...various difficulties will help students gain a rounded understanding of the subject.
Armstrong, M. A. is the author of Basic Topology, published 1983 under ISBN 9780387908397 and 0387908390. Six hundred nine Basic Topology textbooks are available for sale on ValoreBooks.com, one hundred six used from the cheapest price of $21.65, or buy new starting at $55 | 677.169 | 1 |
Trigonometry Demystified 2MYSTiFieD is your solution for tricky subjects like trigonometry
If you think a Cartesian coordinate is something from science fiction or a hyperbolic tangent is an extremeexaggeration, you need Trigonometry DeMYSTiFieD, Second Edition, to unravel this topic's fundamental concepts and theories at your own pace.
This practical guide eases you into "trig," startingwith angles and triangles. As you progress, you willmaster essential concepts such as mapping, functions,vectors, and more. You will learn to t... MOREransform polar coordinates as well as apply trigonometry in the real world. Detailed examples make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce key ideas.
It's a no-brainer! You'll learn about:
Right triangles
Circular functions
Hyperbolic functions
Inverse functions
Geometrical optics
Infinite-series expansions
Trigonometry on a sphere
Simple enough for a beginner, but challenging enough for an advanced student, Trigonometry DeMYSTiFieD,Second Edition, helps you master this essential subject. | 677.169 | 1 |
Trigonometry Review for Calculus Students
All calculus students need to know and understand unit circle trigonometry,
which includes know radians, the relationship between the unit circle and the
sine and cosine functions, knowing tangent, cotangent, secant, cosecant, and
the inverse trig functions: Arcsine, Arccosine etc. You need to know the
value of the sum of the sqares of sine and cosine, the
law of cosines, the double angle formulas, the formulas for
cos(a+b), sin(a+b) and should
have seen the proofs of all these identities.
The best way to review this for your calculus courses, is to read the textbook
you learned this material from and to practice problems. The textbook used
at Lehman College is Cohen's Precalculus with Unit Circle Trigonometry.
Keep in mind that it is possible that the class you took might not have covered
all the necessary material or that you may not have learned all of it correctly. Be sure to review all the topics mentioned above and do practice problems.
Tutorring is availble at the MATH LAB. | 677.169 | 1 |
Students should be familiar with algebraic manipulation, graphical representation of data (including logarithmic scales) and simple calculus. They should be able to use Microsoft Excel for data analysis (including some basic statistics, i.e., mean, mode, standard deviation). | 677.169 | 1 |
Introduayn Martin-Gay firmly believes that every student can succeed, and her developmental math textbooks and video resources are motivated by this belief.Introductory Algebra, Fourth Editionwas written to provide students with a solid foundation in algebra and to help stuents make the transition to intermediate algebra. The new edition offers new resources like theStudent Organizerand now includesStudent Resourcesin the back of the book to help students on their quest for success.
4.5 Factoring Perfect Square Trinomials and the Difference of Two Square
4.6 Solving Quadratic Equations by Factoring
4.7 Quadratic Equations and Problem Solving
Chapter 5 Rational Expressions
5.1 Simplifying Rational Expressions
5.2 Multiplying and Dividing Rational Expressions
5.3 Adding and Subtracting Rational Expressions with the Same Denominator and Least Common Denominator
5.4 Adding and Subtracting Rational Expressions with Different Denominators
5.5 Solving Equations Containing Rational Expressions
5.6 Proportions and Problem Solving with Rational Equations
5.7 Simplifying Complex Fractions
Chapter 6 Graphing Equations and Inequalities
6.1 Reading Graphs and the Rectangular Coordinate System
6.2 Graphing Linear Equations
6.3 Intercepts
6.4 Slope and Rate of Change
6.5 Equations of Lines
6.6 Introduction to Functions
6.7 Graphing Linear Inequalities in Two Variables
6.8 Direct and Inverse Variation
Chapter 7 Systems of Equations
7.1 Solving Systems of Linear Equations by Graphing
7.2 Solving Systems of Linear Equations by Substitution
7.3 Solving Systems of Linear Equations by Addition
7.4 Systems of Linear Equations and Problem Solving
Chapter 8 Roots and Radicals
8.1 Introduction to Radicals
8.2 Simplifying Radicals
8.3 Adding and Subtracting Radicals
8.4 Multiplying and Dividng Radicals
8.5 Solving Equations Containing Radicals
8.6 Radical Equations and Problem Solving
Chapter 9 Quadratic Equations
9.1 Solving Quadratic Equations by the Square Root Property
9.2 Solving Quadratic Equations by Completing the Square
9.3 Solving Quadratic Equations by the Quadratic Formula
9.4 Graphing Quadratic Equations in Two Variables
Appendix A Factoring Sums and Differences of Cubes
Appendix B Mean, Median, and Mode
Appendix C Sets
Appendix D Review of Angles, Lines, and Special Triangles
Appendix E Tables
Student Resources
An award-winning instructor and best-selling author, Elayn Martin-Gay has taught mathematics at the University of New Orleans for more than 25 years. Her numerous teaching awards include the local University Alumni Association's Award for Excellence in Teaching, and Outstanding Developmental Educator at University of New Orleans, presented by the Louisiana Association of Developmental Educators.
Prior to writing textbooks, Elayn developed an acclaimed series of lecture videos to support developmental mathematics students in their quest for success. These highly successful videos originally served as the foundation material for her texts. Today, the videos are specific to each book in the Martin-Gay series. Elayn also pioneered the Chapter Test Prep Video to help students as they prepare for a test–their most "teachable moment!"
Elayn's experience has made her aware of how busy instructors are and what a difference quality support makes. For this reason, she created the Instructor-to-Instructor video series. These videos provide instructors with suggestions for presenting specific math topics and concepts in basic mathematics, prealgebra, beginning algebra, and intermediate algebra. Seasoned instructors can use them as a source for alternate approaches in the classroom. New or adjunct faculty may find the videos useful for review.
Her textbooks and acclaimed video program support Elayn's passion of helping every student to succeed. | 677.169 | 1 |
Elementary Linear Algebra, 10th Edition
Elementary Linear Algebra 10th edition gives an elementary treatment of linear algebra that is suitable for a first course for undergraduate students. The aim is to present the fundamentals of linear algebra in the clearest possible way; pedagogy is the main consideration. Calculus is not a prerequisite, but there are clearly labeled exercises and examples (which can be omitted without loss of continuity) for students who have studied calculus. Technology also is not required, but for those who would like to use MATLAB, Maple, or Mathematica, or calculators with linear algebra capabilities, exercises are included at the ends of chapters that allow for further exploration using those tools.
This title is available with WileyPLUS. This online teaching and learning environment integrates the entire digital textbook with the most effective instructor and student resources to fit every learning style.
With WileyPLUS:
Students achieve concept mastery in a rich, structured environment that's available 24/7
Instructors personalize and manage their course more effectively with assessment, assignments, grade tracking, and more.
WileyPLUS can complement the textbook or replace the printed text altogether
Highlights Relationships among Concepts – By continually revisiting the web of relationships among systems of equations, matrices, determinants, vectors, linear transformations, and eigenvalues, Anton helps students to perceive linear algebra as a cohesive subject rather than as a collection of isolated definitions and techniques.
Proof Sketches – Students sharpen their mathematical reasoning skills and understanding of proofs by filling in justifications for proof steps in some exercises.
Emphasizes Visualization – Geometric aspects of various topics are emphasized, to support visual learners, and to provide an additional layer of understanding for all students. The geometric approach naturally leads to contemporary applications of linear algebra in computer graphics that are covered in the text.
Mathematically Sound – Mathematical precision appropriate for mathematics majors is maintained in a book whose explanations and pedagogy meet the needs of engineering, science, and business/economics students.
The technology exercises that appeared in the previous edition have been moved to the web site that accompanies this text. Those exercises are designed to be solved using MATLAB, Maple, or Mathematica and are accompanied by data files in all three formats. The exercises and data can be downloaded from | 677.169 | 1 |
Algebra for All Statewide Training Session 1
Introductions, Goals and Overview
Published on August 28, 2009
First day of the statewide Algebra for All train the trainers event developed by the Michigan Mathematics and Science Centers Network in order to improve math skill among Michigan students.
This segment (1 of 9) focuses on Introductions and orientation to the course. PowerPoint review of course content and participant expectations. | 677.169 | 1 |
Math
Educational Level:
Middle School
Product Type:
Textbook Bundle
Teaching Textbooks Math 7
The Math 7 Teaching Textbook is a very popular math program. It features automated grading, step by step audiovisual solutions, and lectures that contain lively animation and sound effects. Math 7 covers all basic arithmetic, including fractions, decimals, and percents. Other topics include statistics and probability, simple graphing concepts equations, and inequalities.
This set includes the textbook, answer booklet, and set of 4 CD-Roms. The textbook has several pages of pencil markings which have been erased. Both books have minor creases on the covers. This version of Math 7 is not compatible with Mac computers. We are | 677.169 | 1 |
The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. This volume presents the results of research into such phenomena and provides a self-contained and gradual development of mathematical methods for studying successive positions of these fronts. more...
Math You Can Really Use--Every Day skips mind-numbing theory and tiresome drills and gets right down to basic math that helps you do real-world stuff like figuring how much to tip, getting the best deals shopping, computing your gas mileage, and more. This is not your typical, dry math textbook. With a comfortable, easygoing approach, it: Covers... more...
Presents and discusses the advanced research works on elementary vortices and related problems at the IUTAM Symposium in Kyoto, Japan, 26-28 October 2004. This book covers topics such as vortex dynamics, coherent structures, chaotic advection and mixing, statistical properties of turbulence, rotating and stratified turbulence, and more. more...
This text is designed to help teachers work with beginning ESL students in grades 5 to 12. It provides lessons and activities that will develop the students' vocabulary, English usage, and mathematical understanding. A balance of high-interest activit more...
Reflecting developments in the study of Saint-Venant's problem, this book focuses on the deformation of elastic cylinders for three models of continuum: classical elastic continuum, Cosserat elastic body, and porous elastic material. It includes exercises and examples that show how the methods discussed can be used to solve engineering problems. more...
Mathematics scares and depresses most of us, but politicians, journalists and everyone in power use numbers all the time to bamboozle us. Most maths is really simple - as easy as 2+2 in fact. Better still it can be understood without any jargon, any formulas - and in fact not even many numbers. Most of it is commonsense, and by using a few really simple... more...
Written by an experienced author with a strong background in applications of this field, this monograph provides a comprehensive and detailed account of the theory behind hydromechanics. He includes numerous appendices with mathematical tools, backed by extensive illustrations. The result is a must-have for all those needing to apply the methods in... more... | 677.169 | 1 |
Why would I want a TI 83 you may ask? What about the 89? It's a higher model, and has more buttons! Yes, that's exactly it, it has more buttons, and way to many features you won't use. I have a Ti 83+ (More memory than the origional, but same everything else) and it is great! It has built in Financial Apps, which is a nice addition (and helpful!) compared to the 82 (which it is also compatible with!). But the 89? Even the 85? They take greater than calculus students to even need/use those functions, and they are a much harder to learn calculator. The Calculus teacher at our school says that the 83 will get you all through calculus and most likely beyond college. My calculator,… Read more | 677.169 | 1 |
Overview: The word "discrete" means separate or
distinct. Discrete mathematics is the study of mathematical
objects that consist of separate pieces. This includes such
topics as graph theory, which is the study of relationships between
finitely many
objects, combinatorics, which uses mathematical techniques to
figure out how to count things without actually having to count and
elementary number theory, which is the study of the integers.
Course Objectives:
To develop the ability to think abstractly and creatively about
mathematical and logical problems
To develop problem-solving strategies
To learn ways to communicate mathematics to a variety of audiences
To identify and use different methods of mathematical proof
To explain and use the concepts of graphs and trees
To solve problems using counting techniques and combinatorics
Prerequisites: The formal prerequisite s are MCS-115 and
MCS-121.
More to the point, you should be comfortable
with thinking algorithmically, discovering patterns, and applying
mathematical procedures to various types of problems.
Course web site: The best source of information about
this
course is available at
There you will find a
complete
syllabus,
course description, current homework assignments, and so on.
Books: Applied
Combinatorics, fifth
edition, by Alan Tucker.
This book is intended to be read
thoroughly and thoughtfully. For each class session, you
are encouraged to read the pertinent portion of the text at least
once
beforehand and at least twice afterwards. Study the book with a
pencil
in hand. Make notes in it. Mark where you have
questions.
Do NOT try the exercises without reading the text; simply
skimming
the examples is not sufficient. You will find that it will
be necessary to read the text several times before attempting any
exercises. To survive this course, you must learn how to read a
math
book!
Count Down: Six Kids
Vie for Glory at the World's Toughest Math Competition, by Steve
Olson
This book describes several
mathematically gifted high school students and discusses issues that
are relevant to the mathematical education of all students. It
will be much easier to read than the textbook, and will provide us with
some good questions about teaching and doing mathematics.
Classes: Classes will be used for lectures,
problem solving, discussions, and other fun activities. You
should prepare for classes by doing the reading beforehand (reading
assignments are posted on the Web), thinking about the
problems
in the text, and formulating questions of your own. You should
also
participate as much as possible in class. Class meetings are not
intended to be a complete encapsulation of the course material.
You
will be responsible for learning some of the material on your own.
Attendance, both physical and mental, is required.
To help me keep attendance and to check on your preparation, you
will be expected to hand in a 3x5 index card at the beginning of each
class period. On this card, you should summarize the most
important points in the reading. If you have questions on the
reading, you should think carefully about the best way to phrase these
questions and then write them on your card. You can get three
points per class - one for being there, one for your index card and one
for participating in class. If you are not in class, you will not
get any points (even if you have a friend hand in a card).
Should you need to miss a class for any reason, you are still
responsible
for the material covered in that class. This means that you will need
to
make sure that you understand the reading for that day, that you should
ask a friend for the notes from that day, and make sure that you
understand
what was covered. If there is an assignment due that day, you should be
sure to have a friend hand it in or put it in my departmental mailbox
(in
Olin 324). Note that you can not make up any points that you normally
get for attending class. You do not need to tell me why you
missed a class unless
there
is a compelling reason for me to know.
We will be doing a lot of hands on activities in class, so you will
need to bring colored pens or pencils, a handful of pennies
and nickels, and a ruler or straightedge. You will
also find it handy to have a small stapler, paper clips, a package of
3x5 index cards, a two-pocket folder, and an eraser.
Homework: I will assign homework at the beginning of
each
chapter by posting them on the web. The problems will be designated as
``practice problems'', ``homework problems''.
Practice problems are meant to give you practice reading, writing
and doing mathematics. You should do these problems as part of
preparing for class the day they're assigned. In class, you will
be asked to present your problems to your colleagues.
Homework problems are problems which you hand in to
me. They will be graded on a scale of 0 - 10 per problem, where a
10 means that you've done a good job of solving the problem and writing
the solution up clearly. You are encouraged to work on doing
these problems with one or two other students in the class; if you do
so, then you should hand in a single set of solutions and the points
will be given to all the students in the group.
The first violation of the Honor Code will result in a score of 0 on
the assignment in question and notification of the Dean of
Faculty. Further violations will result in failing the course.
Course grade:
Attendance/participation
15%
Homework
25%
Tests
30%
Accessibility: Please contact me during the first week
of class if you have specific physical, psychiatric, or learning
disabilities
and require accommodations. All discussions will remain
confidential. You can provide documentation of your disability to the
Advising Center (204 Johnson Student Union) or call Laurie Bickett
(x7027). | 677.169 | 1 |
Mathematics
Mathematics and Sciences
Congratulations! San Jose City College placed 8th out of 179 participating two-year colleges in the AMATYC mathematics contest during the 2007 – 2008 school year.
San Jose City College offers a comprehensive selection of both developmental and transfer level mathematics courses. The program includes a comprehensive tutoring service, programs for a diverse student body, including the Transfer Express Program, a course with hands on experience for future mathematics teachers, service learning opportunities, some online courses, and opportunities to participate in a nationwide mathematics contest during both the Fall and Spring semesters.
Developmental Program
Basic Mathematics, Elementary Algebra, and Intermediate Algebra, are offered either in the traditional lecture format or in a variable unit format using Plato Interactive Mathematics. With Plato, students learn the mathematics through a combination of lectures and an interactive software program. Teachers and student aids are present during the labs to help instruct the students. With Plato, the student is allowed to work at his or her own pace to master the material – taking more than one semester if needed.
Pre-Algebra and Geometry are offered in a regular classroom setting. Additionally, at least one Intermediate Algebra section is offered as an online course each semester. Intermediate Algebra and sometimes Geometry as well are prerequisites to all of the transfer level classes.
Transfer Program (General major, Education major, Business major)
Mathematics for General Education and Math for Elementary Education are offered in the traditional classroom setting. Finite Mathematics, and Elementary Statistics are offered both in the traditional classroom setting and online. Problem solving skills are developed through the use of manipulatives, the discovery method to develop critical thinking, group collaboration, individual projects, as well as classroom lectures. Graphing calculators and computer software may be used to aid in calculations and in understanding concepts for Statistics and Finite Mathematics.
Transfer Program (Science, Engineering)
Precalculus Algebra and Trigonometry, Calculus (differential and multivariable), Discrete Mathematics, Differential Equations, and Linear Algebra are offered in the traditional classroom setting on campus. Precalculus Algebra and Trigonometry may also be taken online. Multivariable Calculus and Differential Equations are also offered in alternate semesters at Leland High School. Graphing calculators are required for all of these courses. Some of the courses may also use the Maple mathematical software package.
Tutoring Program
A comprehensive walk-in tutoring program is available for all mathematics and science students in the Learning Resource Center (in room L-105) in the library. Tutoring is done by successful mathematics students and by teacher volunteers.
Transfer Express
The Transfer Express Program helps students complete their requirements to either receive an AA degree or to transfer to a four-year university after two years of full-time study at San Jose City College. Students enrolled in this program have priority registration in the Transfer Express courses. See your counselor for more details of this program.
Future Mathematics Teachers
In addition to the Mathematics for Elementary Education Course, a course entitled Field Experience in Math and Science is offered through the education department (Educ 014).
Students do theory and field work in mathematics and science education at local schools.
Service Learning Projects
Some instructors encourage their students to participate in a service learning project related to their course. This project links San Jose City College students to the community with real work experiences in a variety of learning experiences.
AMATYC Mathematics Contest
During the Fall and Spring semesters, San Jose City College participates in a national mathematics contest sponsored by the American Mathematics Association of Two-Year Colleges (AMATYC). Each of the two rounds consists of 20 problems to be solved within a one-hour time period, with the aid of a graphing calculator. Problems may include material up to pre-calculus mathematics, including some probability and trigonometry problems. The national winner receives a $3,000 scholarship. The mathematics department also awards prizes to San Jose City College students with the top five scores for our school. Any San Jose City College student may participate. (Only non-college degree holding students count for the national contest.) | 677.169 | 1 |
fully worked-out solutions to all of the odd-numbered exercises in the text and all the Cumulative Review exercises in the student textbook, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer. Go beyond the answers; See what it takes to get there and improve your grade! This manual provides worked-out, step-by-step solutions to the odd-numbered problems and all the Cumulative Review exercises in the text. This gives you the information you need t... MOREo truly understand how these problems are solved. | 677.169 | 1 |
An Illustrated Introduction to Topology and Homotopy explores the beauty of topology and homotopy theory in a direct and engaging manner while illustrating the power of the theory through many, often surprising, applications. This self-contained book takes a visual and rigorous approach that...
This graduate-level text discusses from first principles the background theory of various effects of quantum optics, introduces students to the main ideas of quantum optics as clearly as possible, and teaches the mathematical methods used by researchers working in the fields of quantum and atom...
This interdisciplinary book brings together quantum information concepts from quantum physics, information theory, and computer science. It distinguishes between classical and quantum physics, introduces density operators, and discusses linearity and nonlocality of quantum mechanics. The book...
This book takes a practical approach to the subject, starting with concrete problems and leading to general theory. Suitable for a graduate-level course on stochastic PDEs, this edition adds material on new developments in jump processes. Along with more problems and examples, it also includes...
Mathematical Methods for Physicists and Engineers, Second Edition
Following the style of The Physics Companion and The Electronics Companion, The Mathematics Companion: Mathematical Methods for Physicists and Engineers is a revision aid and study guide for undergraduate students in physics and engineering. It consists of a series of one-page-per-topic...
Theory, Applications and Advanced Topics, Third Edition
This book covers many important classes of difference equations, including general, linear, first, second, and Nth order, along with nonlinear equations, partial difference equations, functional equations, and Nth order equations having constant coefficients. It presents a wide range of techniques...
An Introduction to Beam Physics covers the principles and applications of differential algebra, a powerful new mathematical tool. The authors discuss the uses for the computation of transfer maps for all kinds of particle accelerators or any weakly nonlinear dynamical system, such as planetary...
In an accessible way, this text teaches general relativity and differential forms to undergraduate students in mathematics and physics. Also suitable for self-study, it requires little background in physics and no advanced mathematical background. The book uses differential forms for all... | 677.169 | 1 |
Book DescriptionEditorial Reviews
Review
"My students love this textbook for its clarity and careful organization. The book, by the way, has the highest approval rating of any textbook in any class I have ever taught. Bravo!!"
About the Author
Edward R. Scheinerman is Professor in the Department of Applied Mathematics and Statistics at The Johns Hopkins University. Dr. Scheinerman's research interests include discrete mathematics; especially graph theory, partially ordered sets, random graphs, and combinatorics, as well as applications to robotics and networks.
Discrete mathematics is now a keystone course in the computer science major and a fundamental course in the mathematics major. The mathematics covered in the course is still somewhat open to interpretation, but far less than it has been in the past. I examined this book for possible use as a textbook and ended up recommending that it be used. At this time, it is the book being used for the discrete mathematics class at the college where I am employed.
It begins with a short explanation of what a mathematical proof is and some simple examples are given. Chapter 2 is called collections and covers lists, the basics of set theory and quantifiers. The next chapter covers counting and relations and chapter four is a more complex examination of the nature of mathematical proof. The remaining chapters are:
Chapter 5: Functions
Chapter 6: Probability
Chapter 7: Number theory
Chapter 8: Algebra
Chapter 9: Graphs
Chapter 10: Partially ordered sets
The coverage is complete, the writing is understandable and there are plenty of exercises at the end of the chapters. Solutions to many of the problems are found in appendices.
A sound introduction to discrete mathematics, this is a book that I can heartily recommend for use as a textbook. It covers what we in the department feel must be covered.
I had this book for my first class in the number theory & combinatorics realm, and this has been the best book I've used since. To respond to an earlier review, the errors in the proofs serve a very important function: they make you actually read the proof. The templates teach you how to recognize when a particular method of proof is required. My only regret is that I have sold the book after taking the class, and $140 is too steep to buy a fresh copy.
I can understand some of the bad reviews on this textbook, but in context of being an intro, it is outstanding.
What does intro mean? Well it is for those do not understand the fundamentals of proof or theorems, and most of the material in this book.
Most discrete math books fail at one major topic of instruction, and that is proofs and induction. The authors struggle on instructing the students both the language and how to write proofs. The authors expect a specific level of sophistication in the student. And in most cases this might be true, depending on where this course fits in the cirriculum and who the students are taking the course. Math and engineering majors have a different level of background and confidence.
This textbook is really a great intro because of the method employed by the author to instruct. He introduces each topic from a conversational level and then brings in the more formal proofs and examples. He does this with everything so it builds up the students understanding of both the how and why so that a student not only understands the topic, but understands how the proof is constructed.
His instruction on proofs and induction will teach students the language of math from a very elementary level to the point where they will be able to follow more rigourous texts.
His coverage of graphs is brilliant, his instruction really connects the students with the subtle differences in the various theorems.
Advanced students will find this a boring text, but most students will take away a profound understanding of how to think and speak like a mathematian.
I was assigned this book for a class, but instead of using it as merely a reference for the assigned problems, as I usually do, I read it nearly cover-to-cover, enjoying the author's clear, casual prose. I've never been as pleasantly surprised by a textbook. | 677.169 | 1 |
A Transition To AdvancedTRANSITION TO ADVANCED MATHEMATICS bridges the gap between calculus and advanced math in at least three ways. First, it guides students to think precisely and to express themselves mathematically?to analyze a situation, extract pertinent facts, and draw appropriate conclusions. Second, it provides a firm foundation of the basic concepts and methods needed for continued work. Finally, it provides introductions to concepts of modern algebra and analysis in sufficient depth to capture some of their spirit and characteristics. The text will improve... MORE the student's ability to think and write in a mature mathematical fashion and provide a solid understanding of the material most useful for advanced courses. Bridge the gap between calculus and advanced math with TRANSITION TO ADVANCED MATHEMATICS! This mathematics text will improve your ability to think and write in a mature mathematical fashion and provide you with a solid understanding of the material most useful for advanced courses. With a readable, concise style, discussions of sequences and real analysis concepts found throughout the text are tied to your experience in elementary calculus in order to clarify material. Worked examples and exercises throughout the text, ranging from the routine to the challenging, reinforce the concepts. | 677.169 | 1 |
760-040 PRE-ALGEBRA 3 cr
A course for students who need a review of basic mathematics or who lack the computational skills required for success in algebra and other University courses. Topics include fractions, decimals, percent, descriptive statistics, English and metric units of measure, and measures of geometric figures. Emphasis is on applications. A brief introduction to algebra is included at the end of the course. This course does count toward the semester credit load and will be computed into the grade point average. It will not be included in the 120 credits required for graduation. It may be taken for a conventional grade or on a satisfactory/no credit basis. Not available to students who have satisfied the University Proficiency requirement in mathematics.
Unreq: 760-140 or 760-141
760-041 BEGINNING ALGEBRA 3 cr
A course for those who have a sound background in basic arithmetic, but who have not been exposed to algebra, or who need to strengthen their basic algebra skills. Topics include properties of the real numbers, linear and quadratic equations, linear inequalities, exponents, polynomials, rational expressions, the straight line, and systems of linear equations. The course counts towards the semester credit load and will be computed into the grade point average. It will not, however, be included in the credits necessary for graduation. It may be taken for a conventional grade or on a satisfactory/no credit basis.
Prereq: 760-040 or equivalent demonstration of capability. Students cannot receive credit for 760-041 if they have been waived from the Mathematics Proficiency Requirement. Not available to students who have satisfied the University Proficiency requirement in mathematics. Unreq: 760-140 or 760 141.
760-111 MATHEMATICS FOR THE ELEMENTARY TEACHER I GM 3 cr
A study of sets, whole numbers, fundamental operations of arithmetic, fundamental algorithms and structural properties of arithmetic, fractions, problem solving and introduction to inductive and deductive logic stressing the structure of mathematics. All students will prepare a mathematics based activity and present it at an area elementary school. For elementary education prekindergarten-6 and elementary education elementary/middle school emphasis students.
Prereq: A grade of C or better in 760-141 or 760-141B or a waiver from the university mathematics proficiency requirement.
760-112 MATHEMATICS FOR THE ELEMENTARY TEACHER II 3 cr
Selected topics in logic. The computer as a useful tool in mathematical explorations is introduced and applied throughout the course. Topics in probability and statistics, with emphasis on descriptive techniques. Investigations in geometric figures, measurement, construction, congruent and similar geometric figures. An introduction to coordinate geometry. Problem solving, discovery, and student projects are emphasized throughout. All students will prepare a mathematics based activity and present it at an area elementary school.
Prereq: Satisfactory completion of 760-111 with a grade of C or better.
760-140 MATHEMATICAL IDEAS (PROFICIENCY) 3 cr
Designed to give students a broad understanding and appreciation of mathematics. Includes topics not usually covered in a traditional algebra course. Topics encompass some algebra, problem solving, counting principles, probability, statistics, and consumer mathematics. This course is designed to meet the University Proficiency Requirement in mathematics for those students who do not wish to take any course which has 760-141 as a prerequisite.
Prereq: Satisfactory completion of 760-041 or demonstration of equivalent capability. This course cannot be taken for credit after completing any mathematics course above 141.
760-141141BThis course covers the same material as 760-141, but meets 5 days a week143 FINITE MATHEMATICS FOR BUSINESS AND SOCIAL SCIENCES GM 3 cr
Mathematical preparation for the understanding of various quantitative methods in modern management and social sciences. Topics included are sets, relations, linear functions, interest, annuities, matrix theory, the solution of linear systems by the graphical, algebraic, Gauss-Jordan, and inverse methods, linear programming by graphical and simplex methods, counting and probability, and decision theory. College of Business and Economics majors must take this course on a conventional grade basis.
Prereq: Waiver of or a grade of C or better in 760-141.
760-177 THE LOGIC OF CHESS 1 cr
A study of logic particularly as it is used in the game of chess and, most particularly, in chess strategy and the end game of chess. The rules are taught to those who are not already acquainted with the game.
Prereq: Fulfillment of University Proficiency requirement in mathematics.
760-230 INTRODUCTORY STATISTICS 3 cr
A pre-calculus course in statistics. Descriptive statistics, probability distributions, prediction, hypothesis testing, correlation, and regression. This course does not count towards a mathematics major or minor in either liberal arts or secondary education or towards a mathematics minor in elementary education. This course may not be taken for credit if credit has been or is being earned in any other statistics course.
Prereq: Waiver or a grade of C or better in 760-141. Unreq: Any other statistics course.
760-231 UNDERSTANDING PROBABILITY AND STATISTICS GM3 cr
A pre-calculus course in probability and statistics. Descriptive statistics, classical probability, probability distributions, prediction, parametric and nonparametric hypothesis testing, correlation, regression, and use of some statistical software. This course does not count towards a mathematics major or minor in liberal arts or towards a mathematics major in secondary education. This course may not be taken for credit if credit has been or is being earned in any other statistics course.
Prereq: Completion, with a grade of C or better, of either 760-143 or 760-152. Unreq: Any other statistics course.
760-243 SHORT CALCULUS FOR BUSINESS AND SOCIAL SCIENCES GM 3 cr
A general survey of the Calculus. Topics covered include limits, differentiation, max-min theory, exponential and logarithmic functions, integration and functions of several variables. As in 760-143, business and social science applications are stressed. College of Business and Economics majors must take this course on a conventional grade basis.
Prereq: Completion with a grade of C or better in either of the courses 760-143 or 760-152. Unreq: 760-250. Students should check with their major department for advice on whether to take 760-243 or 760-250.
760-250 APPLIED CALCULUS SURVEY FOR BUSINESS AND THE SOCIAL SCIENCES GM 5 cr
An applied calculus course covering elementary analytic geometry, limits, differentiation, max-min theory, transcendental functions, integration, functions of several variables, and elementary differential equations. Some computer topics may be included. College of Business and Economics majors must take this course on a conventional grade basis.
Prerequisite: 760-143, with a grade of C or better, or equivalent preparation as determined by the Mathematics Department. Unreq: 760-243, 760-253.
760-253 CALCULUS AND ANALYTIC GEOMETRY I GM 5 cr
Review of algebraic and trigonometric functions, study of the derivative, techniques of differentiation, continuity, applications of the derivative, the Riemann integral, applications of the integral. Conventional grade basis only if course is required in the College of Business for major.
Prereq: 760-152 or equivalent high school preparation as determined by the Mathematics Department. Unreq: 760-243 and 760-250.
760-280 DISCRETE MATHEMATICS 3 cr
This course will supply a thorough grounding in the mathematical topics which are central to the study of computer science, and which form the basis for many modern applications of mathematics to the social sciences. Topics covered will include sets, logic, Boolean algebra and switching circuits, combinatorics, probability, graphs, trees, recursion, and algorithm analysis. Expressing mathematical ideas and writing proofs will be emphasized.
Prereq: 760-250 with a grade of B or better, or 760-253.
760-342/542 APPLIED STATISTICS 3 cr
This course will cover the basics of statistical testing, regression analysis, experimental design, analysis of variance, and the use of computers to analyze statistical problems.
Prereq: 760-253 or 760-250 or cons instr. Unreq: 230-245.
760-353 COLLEGE GEOMETRY I 3 cr
A course following high school geometry, especially adapted to the prospective teacher of plane geometry. The course includes the foundations of geometry, logic and proof, finite geometries, introduction to non-Euclidean geometry and topics in modern geometry such as transformations, vectors, similarities and inversion.
Prereq: 760-253 and 760-280.
760-354 COLLEGE GEOMETRY II 3 cr
A continuation of 760-353 which includes non-Euclidean geometry, synthetic and analytic projective geometry and subgeometries of projective geometry. Their relation to Euclidean geometry will also be considered.
Prereq: 760-353, or 760-253 and 760-280 and cons instr.
760-365/565 LINEAR PROGRAMMING 3 cr
A study of the vector-matrix theory and computational techniques of the simplex method, duality theorem, degeneracy problem, transportation problems and their applications to engineering and economics. Machine solution of large linear programming problems.
Prereq: 765-171 and 760-355.
760-375/575 DEVELOPMENT OF MATHEMATICS 3 cr
A study of the development of mathematical notation and ideas from prehistoric times to the present. The development and historic background of the new math will be included.
Prereq: 760-152 or cons instr.
760-380/580 PATTERNS OF PROBLEM SOLVING 3 cr
This course will expose students to a variety of techniques useful in solving mathematics problems. The experiences gained from this course can be applied to problems arising in all fields of mathematics. The student will have the chance to see how some general techniques can be used as tools in many areas. Homework for this course will consist mostly of solving a large number of mathematics problems. Consent will be given to students with substantial interest in problem solving, and adequate preparation.
Prereq: 760-280 or cons instr.
760-415/615 MODERN ALGEBRA AND NUMBER THEORY FOR THE ELEMENTARY TEACHER 3 cr
An introduction to modern algebra with special emphasis on the number systems and algorithms which underlie the mathematics curriculum of the elementary school. Topics from logic, sets, algebraic structures, and number theory.
Prereq: 760-112 and 760-152. Unreq: 760-452.
760-416/616 GEOMETRY FOR THE ELEMENTARY TEACHER 3 cr
A study of the intuitive, informal geometry of sets of points in space. Topics include elementary constructions, coordinates and graphs, tesselations, transformations, problem solving, symmetries of polygons and polyhedra, and use of geometry computer software.
Prereq: 760-112 and 760-152
760-417/617 THEORY OF NUMBERS 3 cr
A study of the properties of integers, representation of integers in a given base, properties of primes, arithmetic functions, modulo arithmetic. Diophantine equations and quadratic residues. Consideration is also given to some famous problems in number theory.
Prereq: 760-280 or 760-415 or cons instr.
760-446/646 ACTUARIAL MATHEMATICS 3 cr
This course will discuss the actuarial profession and the insurance industry, provide direction to students whishing to take the first few actuarial examinations, thoroughly cover the theory of interest, and introduce the basic concepts of actuarial mathematics.
Prereq: 760-441 or concurrent registration
760-452/652 ALGEBRAIC STRUCTURE OF THE NUMBER SYSTEMS 3 cr
An introduction to abstract algebra with emphasis on the development and study of the number systems of integers, integers mod n, rationals, reals, and complex numbers. These offer examples of and motivation for the algebraic structures of groups, rings, integral domains, fields, and polynomial rings.
Prereq: 760-280 and either 760-355 or 760-255. Unreq: 760-415.
760-471/671 NUMERICAL ANALYSIS I 3 cr
Emphasis on numerical algebra. The problems of linear systems, matrix inversion, the complete and special eigenvalue problems, solutions by exact and iterative methods, orthogonalization, gradient methods. Consideration of stability and elementary error analysis. Extensive use of microcomputers and programs using a high level language, such as PASCAL.
Prereq: 765-171 and 760-355.
760-499 PROJECT FOR MAJORS 1 cr
This course is designed to give students experience and to improve their skill in reading, writing, and understanding mathematics by requiring them to research one or more mathematical topics and then write a report about their activities and discoveries. The focus is on the learning and communication of mathematics: how to read with understanding, write with clarity and precision, and in the process discover how writing can aid in understanding.
Prereq: Jr st or cons dept chp. | 677.169 | 1 |
Knot theory is a rapidly developing field of research with many applications, not only for mathematics. The present volume, written by a well-known specialist, gives a complete survey of this theory from its very beginnings to today's most recent research results. An indispensable book for everyone concerned with knot theory.
The History of Mathematics: An Introduction, Sixth Edition, is written for the one- or two-semester math history course taken by juniors or seniors, and covers the history behind the topics typically covered in an undergraduate math curriculum or in elementary schools or high schools.
Mathematics for Economics and Business provides a thorough foundation in mathematical methods for economics, business studies and accountancy students. Assuming little prior knowledge, this informal text is a great companion for those who have not studied maths in depth before. This book truly promotes self-study as students are encouraged to tackle problems as they go along and can see fully worked examples to help their understanding. Both beginners and more advanced students will find material in this book relevant to their needs.
This revised and updated second edition maintains the content and spirit of the first edition and includes a new chapter, "Recent Experiences", that provides examples of experimental mathematics that have come to light since the publication of the first edition in 2003. For more examples and insights, Experimentation in Mathematics: Computational Paths to Discovery is a highly recommended companion.
Experience mathematics--and develop problem-solving skills that will benefit you throughout your life--with THE NATURE OF MATHEMATICS. Karl Smith introduces you to proven problem-solving techniques and shows you how to use these techniques to solve unfamiliar problems that you encounter in your day-to-day world. You'll find coverage of interesting historical topics, and practical applications to real-world settings and situations, such as finance (amortization, installment buying, annuities) and voting. With Smith's guidance, you'll both understand mathematical concepts and master the techniques
This is the philosophy behind Elementary and Middle School Mathematics: Teaching Developmentally. John A | 677.169 | 1 |
Mathematics Reader
The Nuffield Advanced Mathematics reader provided articles as background or extensions to topics covered elsewhere in the course. The aim was to encourage students to make further study of the development and applications of the ideas about which they were learning. This was one of the ways by which the course team illustrated how mathematical concepts new to the students had been used by to solve real-world problems | 677.169 | 1 |
Change the values in the left matrix and click the INVERT button. The values in the right matrix are rounded to the 4th digit...
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Change the values in the left matrix and click the INVERT button. The values in the right matrix are rounded to the 4th digit (x.xxxx) to fit the text fields. If you want to use a n x n matrix with n6 you need to set the remaining diagonal elements=1.
The following applet allows users to plot three 2x1 vectors in 2-Space and gain insight about their linear independence and...
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The following applet allows users to plot three 2x1 vectors in 2-Space and gain insight about their linear independence and linear span. Two vectors are denoted as v1 and v2. The third is b. When possible the applet shows the linear combination of v1 and v2 necessary to form b.
A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically such a...
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A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically such a student will have taken calculus, but this is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form.PDF versions are available to download for printing or on-screen viewing, an online version is available, and physical copies may be purchased from the print-on-demand service at Lulu.com. GNU Free Documentation License
The book provides a thorough introduction to "modern'' or "abstract'' algebra at a level suitable for upper-level...
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The book provides a thorough introduction to "modern'' or "abstract'' algebra at a level suitable for upper-level undergraduates and beginning graduate students. The book addresses the conventional topics: groups, rings, fields, and linear algebra, with symmetry as a unifying theme | 677.169 | 1 |
Math Resources
Links to Helpful Math Websites
Math Department Homepage - The homepage of the Math Department. Follow the link to find resources for the math classes taught at FVTC. From the Math Department Mission:
The mission of the Math Department is to provide quality educational
experiences to prepare students for employment that meets their needs and the
needs of the community they serve with a practical math foundation, so that they
may recognize and apply math concepts in their lives, their program courses, and
in their careers.
We strive to provide students with the tools to develop clear, logical,
analytical thinking skills and to foster in students an awareness of the need
for lifelong learning. We also strive to support all the program needs at FVTC
and are constantly working to upgrade the curriculum to meet the needs of the
changing workplace.
The Khan Academy is an organization on a mission. We're a not-for-profit with
the goal of changing education for the better by providing a free world-class
education to anyone anywhere.
All of the site's resources are available to anyone. It doesn't matter if you
are a student, teacher, home-schooler, principal, adult returning to the
classroom after 20 years, or a friendly alien just trying to get a leg up in
earthly biology. The Khan Academy's materials and resources are available to you
completely free of charge.
Wolfram|Alpha introduces a fundamentally new way to get knowledge and
answers—not by searching the web, but by doing dynamic computations based on
a vast collection of built-in data, algorithms, and methods.
Interact Math - A website that is tied to many of the textbooks used in the Math Department. It contains many sample exercises and includes immediate feedback on those exercises. From Interact Math's about page:
InterAct Math is designed to help you succeed in your math course!
The tutorial exercises on this site give you interactive
practice doing the end-of-section exercises in your Addison-Wesley and Prentice Hall textbooks.
Each exercise provides these learning aids:
An interactive Guided Solution (or "Help Me Solve This!") steps you
through the exercise and gives you helpful feedback if you enter an incorrect answer.
A Sample Problem or ("View an Example") steps you through a problem
similar to the exercise you are working on.
Similar Problems that refresh with new numbers. You can retry an
exercise many times and receive different numerical values each time.
Your work will be tracked for only as long as you keep your browser open. Be sure to print out your results if you want to record them!
Purplemath's algebra lessons are written with the student in mind. These lessons emphasize the practicalities rather than the technicalities, demonstrating
dependable techniques, warning of likely "trick" questions, and pointing out
common mistakes. The lessons are cross-referenced to help you find related
material, and a "search" box is on every page to help you find what you're
looking for. | 677.169 | 1 |
More About
This Textbook
Overview
"[The author's] idea is to use geometric intuition to alleviate some of the algebraic difficulties...The emphasis is on understanding rather than on detailed derivations and proofs. This is definitely the right approach in a course at this level." —MAA Reviews (Review of First Edition)
"The book certainly has its merits and is very nicely illustrated … . It should be noted that the material, which has been tested already in the classroom, aims at three potential course tracks: a course in multivariable calculus, a course in vector calculus and a course for more advanced undergraduates (and beginning graduates)." —Mathematical Reviews (Review of First Edition)
The modern subject of differential forms subsumes classical vector calculus. This text presents differential forms from a geometric perspective accessible at the advanced undergraduate level. The author approaches the subject with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually.
Each new concept is presented with a naturalpicture that students can easily grasp; algebraic properties then follow. This facilitates the development of differential forms without assuming a background in linear algebra. Throughout the text, emphasis is placed on applications in 3 dimensions, but all definitions are given so as to be easily generalized to higher dimensions.
The second edition includes a completely new chapter on differential geometry, as well as other new sections, new exercises and new examples. Additional solutions to selected exercises have also been included. The work is suitable for use as the primary textbook for a sophomore-level class in vector calculus, as well as for more upper-level courses in differential topology and differential geometry | 677.169 | 1 |
Applications Of Similarity Triangles
Investigations, explorations, and applications of right triangles. Students will employ a variety of problem-solving techniques including using Grade level Indicators – Geometry and Spatial Sense Standard. Assessment: The worksheet for the activity should be collected. answers to the activity, homework, quiz after Activity 3, and Test at end of unit. Open the file imspecial .gsp.
DEVELOPMENT AND APPLICATIONS OF CLICK CHEMISTRY INTRODUCTION. . produced in Nature contain diverse architectures with extensive carbon-carbon bond networks. These compounds such as acetylenes and olefins of azides and alkynes
Applications of Sheaf Cohomology and Exact Sequences on Network. notion introduced in this section is a network coding sheaf (NC sheaf for short), which gives a relationship between sheaf theory and network coding problems.
Applications of computer communications in education an overview. Applications of Computer Communications in Applications of computer communications in education: an overview - IEEE Communications Magazine
Applications of High Sensitivity Fluoresence. Happy holidays and a felicitous New Year! We enter 2010 with abide by our New Year resolutions. As we relax our 3) When you receive a message from the postman,
Applications of Simulation in Business Process Modelling. In addition to modelling business processes to support BPR, Process Innovation and Knowledge Management Redesigning organisations through business process re | 677.169 | 1 |
Summary: - By Judith A. Penna - Contains keystroke level instruction for the Texas Instruments TI-83 Plus, TI-84 Plus, and TI-89 - Teaches students how to use a graphing calculator using actual examples and exercises from the main text - Mirrors the topic order to the main text to provide a just-in-time mode of instruction - Automatically ships with each new copy of the text | 677.169 | 1 |
Additional answers can be found in the transcript from our 2013 Math Camp chat.
What is Math Camp?
Math Camp is an intensive review of some basic concepts of algebra and geometry and a tiny bit of calculus. The purpose of this short and intensive course is to prepare you for SPEA masters classes that require some basic background in mathematics.
Math Camp is specially designed for those students who have not taken a math class in a very long time and need a refresher course or who feel that they might need extra help mastering some basic mathematical concepts.
Is Math Camp graded?
Math Camp is ungraded; however, each day you will have some homework exercises to work that we will evaluate the next day.
How often does Math Camp meet?
We will meet every day for a week—Monday through Friday. We will meet from approximately 8:45am to 12:45pm. After class, you are encouraged to stick around SPEA to work on your homework. You can work in the atrium or in the Business/SPEA library. Every afternoon, the Teaching Assistant(s) (TA) will be available for a couple of hours in order to answer any questions you might have. Times and locations to be determined and announced at Math Camp.
What can I expect during our classes?
In class, we will have lectures and in-class exercises. We will also have guest appearances from faculty members who will tell us how the mathematical concepts we have been discussing will be helpful in your future classes and in public affairs and environmental science in general.
Which class should I attend?
To better help you decide whether or not you need to attend Math Camp, use the evaluation tool and then check your answers. If you score well on the test and feel confident that you know how to answer these questions, then you don't need to be in Math Camp. If you do not score well or cannot figure out the answers to these problems, then Math Camp is for you.
MathHow do I maximize my time in Math Camp?
To maximize your learning, come to class prepared. Read the lecture notes, then come to class and pay close attention to the lectures. Then go home and reread the lecture notes and your class notes before doing the homework assignments. Work in groups on the homework and explain difficult concepts to each other. If you still have questions, then come and see the professor or the TA.
It has been years since I have even looked at math. How can I get a jump start on Math Camp?
If you want to do further reading on the subject, these are some basic textbooks that might be helpful. A couple suggestions are below. Or you can just check out a basic algebra book from the library.
All you need to bring is a basic calculator, pencil, and paper. We will provide the course pack when you arrive on the first day.
Where can I park?
You are welcome to park in the Fee Lane Parking Garage on Fee Lane just off of 10th Street; we'll provide you with a parking pass for display in your car window that will enable you to enter and exit the parking garage during SPEA's Math Camp week. This parking privilege is only offered to registered Math Camp attendees and will end at the close of the week. You will see signage indicating "SPEA Parking" in and around the SPEA Building and garage entrance. We encourage you to park in the Fee Lane Garage on the 4th floor for easy access to the sky bridge which leads to the SPEA building. Please refer to the campus map for directions to SPEA. | 677.169 | 1 |
Mathematics in Science and Technology
The book provides the reader with the different types of functional equations that s/he can find in practice, showing, step by step, how they can be solved.A general methodology for solving functional equations is provided in Chapter 2. The different types of functional equations are described and solved in Chapters 3 to 8. Many examples, coming from different fields, as geometry, science, engineering, economics, probability, statistics, etc, help the reader to change his/her mind in order to state problems as functional equations as an alternative to differential equations, and to state new problems in terms of functional equations or systems.An interesting feature of the book is that it deals with functional networks, a powerful generalization of neural networks that allows solving many practical problems. The second part of the book, Chapters 9 to 13, is devoted to the applications of this important paradigm.The book contains many examples and end of chapter exercises, that facilitates the understanding of the concepts and applications.
Audience Undergraduate honors students in mathematics, and engineering as well as graduate students in artificial Intelligence, engineering and statistics. In addition, students in Economics programs will also be interested in this book as many of the applications illustrated are from economics fields. | 677.169 | 1 |
Al series has helped thousands of students succeed in developmental mathematics through its friendly writing style, numerous realistic examples, extensive problem sets, and complete supplements package. In keeping with its proven track record, this revision includes a new open design, more exercises and applications, and additional features to help both students and instructors succeed. KEY MESSAGE: The Lial series has helped thousands of readers succeed in developmental mathematics through its approachable w... MOREriting style, relevant real-world examples, extensive exercise sets, and complete supplements package Review of the Real Number System; Linear Equations, Inequalities, and Applications; Graphs, Linear Equations, and Functions; Systems of Linear Equations; Exponents, Polynomials, and Polynomial Functions; Factoring; Rational Expressions and Functions; Roots, Radicals, and Root Functions; Quadratic Equations and Inequalities; Additional Functions and Relations; Inverse, Exponential, and Logarithmic Functions; More on Polynomial and Rational Functions; Conic Sections; Further Topics in Algebra For all readers interested in Algebra. | 677.169 | 1 |
???U???1001 Basic Math & Pre- Algebra Practice Problems For Dummies Practice makes perfect—and helps deepen your understanding of basic math and pre-algebra by solving problems 1001 Basic Math & Pre-Algebra Practice Problems For Dummies, with free access to online practice problems, takes you beyond the instruction and guidance offered in Basic Math & Pre-Algebra For Dummies, giving you 1,001 opportunities to practice solving problems from the major topics in your math course. You begin with some basic arithmetic practice, move on to fractions, decimals, and percents, tackle story problems, and finish up with basic algebra. Every practice question includes not only a solution but a step-by-step explanation. From the book, go online and find:"The Algebra 2 Tutor is a 6 hour course spread over 2 DVD disks that will aid the student in the core topics of Algebra 2. This DVD bridges the gap between Algebra 1 and Trigonometry, and contains essential material to do well in advanced mathematics. Many of the topics in contained in this DVD series are used in other Math courses, such as writing equations of lines, graphing equations, and solving systems of equations."
Having a solid foundation in Pre-Algebra is indispensable for setting up a proper mathematical background to succeed in more advanced math and science. Professor Nancy Fung will give you the tools you need by guiding you through all the topics you will most likely see in school. | 677.169 | 1 |
MTH60 Introductory Algebra- 1st Term
Introduction to algebraic concepts and processes with a focus on linear equations and inequalities in one and two variables. Applications, graphs, functions, formulas, and proper mathematical notation are emphasized throughout the course. A scientific calculator is required. The TI-30X II is recommended. Prerequisites: MTH 20 and RD 80 (or ESOL 250). Audit available.
(For detailed information, see the Course Content and Outcome Guide ).
Credits:
4.00
Distance Education: Web Course
Information
CRN 43243
We will be using the Blitzer Text and MyMathLab (Course Compass) along with Desire2Learn for the Web course. Desire2Learn was selected by PCC as our Learning Management Software that is used to deliver online courses
To login to your course, please login to MyPCC and click on the Desire2Learn login.
Class Full? Please consider registering for the TVWEB. With these videos, the use of Desire2Learn and the optional use of MyMathLab (Course Compass) you can consider the telecourse a modified Web Course! The majority of your learning comes from viewing videos created by 3 talented PCC instructors, reading your text and working problems from your text. You can also use the optional MyMathLab that accompanies your text for computer generated problems that have video instruction and hints. Many students find this a valuable resource
INFORMATION
ABOUT ON-LINE MTH 60:
If you've already registered: You will not be able to access the course until the first day of classes. (But you can access Desire2Learn and the Resource Shell) Once you are in the Desire2Learn classroom shell follow directions for more details about how the class works. Please note the CRN number listed above to be sure you are in the right class.
Be aware that 2 proctored, hand written exams must be taken. Further details given below and in the course.
which links to more information about Math 60, your text, and resources on campus and on the web.
Here are a few things to consider:
Are you aware that learning on-line is often a bigger time commitment than on campus classes? It is not easy to learn math over the computer. There is a lot of reading, and you are really trying to teach yourself. You must be an independent learner, pretty comfortable using a computer and Microsoft Word and willing to learn the Equation Editor or Math Type.
Can you make the time to work on this class effectively? This course, like other math courses, is time-intensive. These types of classes typically require at least 5-7 hours a week reading and learning ('attending' class), and the additional 8-10 hours doing homework, studying and practicing to successfully complete all course assignments and activities (recommended for ALL math classes!), both on and offline. You need to log on to the computer at least 3 different days during the week to check for updates and participate in a mandatory discussion several times per term.
Please assess your situation before enrolling in this course, and determine if you will be able to commit this kind of time to the class.
Also think about the type of learner you are. On-line courses are a terrific option, especially for independent, self-motivated learners. If this does not describe you, consider why it is you are thinking about taking this type of class, and if it really is a choice that will allow you to experience success.
For all my math 60 students (on-line, TVWEB and on-campus) I recommend that they should be comfortable working with fractions and signed numbers without a calculator. If not, that dramatically increases the time needed for learning algebra. Make sure you have the proper pre-requisites: See Placement Info on the Math Department Web Page
If you have never had any algebra before that also increases the time needed to process and retain the new information.
If you had algebra before, and did well, it should come back relatively quickly and you will probably not need to spend as long the 2nd time around.
If you had algebra before, and did not do well you would probably need to spend the recommended time on the course
HOW THIS CLASS WORKS:
In this class, you read the text and on-line lectures. You also take frequent quizzes, do quite a bit in weekly homework, and participate in a mandatory on-line discussion with several posts for the term. Additionally, there is a proctored midterm exam, several on line exams, a proctored final exam and a possibility of written projects. More details forthcoming in the course, and below under Course Specific Requirements. Consider those factors when deciding if this course is for you
If you are trying to register, and the class is full here are some suggestions:
1) Put your name on the wait list. As spots open up, the computer automatically registers the next person on the list, then notifies you via MyPCC email. This automatic registration STOPS, the Thursday before classes begin. At that point, you need to email me if you are still interested in enrolling. Usually some spaces become available, so your persistence may pay off. ESPECIALLY THE FIRST WEEK OF THE TERM! There is no guarantee, however, that you will get into the class, but this is your best chance.
2) Consider other Distance Learning modes such as TVWEB courses, if available.
Course Specific Requirements:
There are two proctored no calculator, paper-and-pencil exams (Midterm Exam and the Final). There will be scheduled times to take those exams at the Sylvania Campus, but if you cannot make those times you can make alternative arrangements to take them at the Sylvania Testing center if you live in the district or at an accredited college testing center if you do not.. Otherwise, the entire course can be completed from a computer that has internet access.
You need to have access to a computer connected to the Internet. In order to make sure that you view the correct formatting of the modules in the course, you should use Internet Explorer version 6.0 (or higher) as your browser.
You will need Microsoft Word with the Equation Editor or Math Type so that you can submit homework containing proper mathematical symbols electronically. For information about obtaining a button for the Equation Editor and on using the Equation Editor see Steve Simonds website. (If you want to use other software for homework assignments you will need to obtain permission from the instructor.)
You will need Macromedias *free* Shockwave Player to access some of the multimedia in this course. It only takes a moment to install if you dont already have it on your computer. While you are there, you may as well download the *free* Flash Player as well.
To read some of the equations written by the equation editor in the course you will also need to download the *free* Java software.
Students with disabilities should notify their instructor if accommodations are needed to take this class. For information about technologies that help people with disabilities in taking Web based distance learning classes please visit the Office for Students with Disabilities website. | 677.169 | 1 |
Kenwood Academy Math Department
Algebra Syllabus 2011-2012
Mr. Im E-mail: [email protected]
Phone number: 535-1409 Tutoring Hours: MWF 3:00-4:30
Course Description/Objective:
Algebra1 is a study of the language, concepts and techniques of Algebra that will prepare students to approach and solve problems
following a logical succession of steps. Skills taught in the course lay groundwork for upper level math and science courses and have
practical uses. The course focuses on linear functions and equations, which provide the mathematical tools necessary for consolidating
and representing ratios and proportional reasoning. The course will involve a study of quadratic functions and equations. Throughout
the course there will be an emphasis on learning how to use basic algebraic tools to represent problem situations and to solve
important classical problems.
Learn to use basic algebraic tools to represent problem situations
Gain sound understanding of functions and their multiple representations
Develop a solid understanding of rate of change
Model and solve important problems with linear, exponential, and quadratic functions and related equations
Textbook and Resources:
Algebra 1: Illinois Edition
Publisher: Glencoe
Date: 2005
Standards
This class addresses the following standards as mandated by the Illinois Board of Education. We use the College Readiness Standards
produced by the ACT as well as the Illinois Learning standards. A full list is available at
A detailed breakdown of the Illinois standards is available at
College Readiness Standards Illinois Learning Standards
Basic Operations and Applications State standard 6: Demonstrate and apply a knowledge and
Numbers: Concepts and Properties sense of numbers, including numeration and operations,
Expressions, Equations and Inequalities patterns, ratios and proportions
Graphical Representations State standard 7: Estimate, make and use measurements of
objects, quantities and relationships and determine
acceptable levels of accuracy
State standard 8: use algebraic and analytical methods to
identify and describe patterns and relationships in data, solve
problems and predict results
State standard 9: Use geometric methods to analyze,
categorize and draw conclusions about points, lines, planes
and space.
Materials Needed:
Pencils Textbook 3 ring binder
Pencil sharpener Loose-leaf paper Dividers
Colored pen (not black or blue) Scientific/graphing calculator
Fee: Students are required to pay a $10 mathematics fee. Students who do not return a textbook will be charged a $65 fee.
Assignments:
Assignments will be given daily. Assignments are essential to the study and mastery of this course. Assignments are viewed as a
reinforcement of the concepts discussed in class daily and will be factored into the final grade. It is the student's responsibility to
record these assignments in their student planner. Students are responsible for having all assignments completed on time however, not
all assignments will be collected. It is the student's responsibility to make up and turn in assignments one day after returning from an
absence. Late assignments are not acceptable. Students will receive full credit on written assignments if the assignment is
completed. Refer to Kenwood Academy Website for updated assignments.
Format for Assignments
Complete all assignments on loose-leaf notebook paper ONLY
The heading should look as follows:
Name Period Date
Page# and Problems #s
To receive full credit
o Write problem number
o Show all necessary work for each problem
o Draw any diagrams that go with the problem
o Graded and Corrected in colored ink (not blue or black)
Failure to follow proper procedure will result in a reduction of points on the assignments.
Scoring Rubric for Assignments
10 All problems attempted, problem number is written, all necessary work is shown, diagrams are
drawn and corrections are made in red pen
5 Not all problems attempted and problem number is written, or most necessary work is shown, or not
all diagrams are drawn and corrections are made in red pen
0 Less than half the problems attempted and problem number is written or not all necessary work is shown, or diagrams are
missing, or no work at all
How to be successful with homework
Homework is graded based on effort. Each assignment is worth ten points. It is in your best interest to do the homework because it
enables you to apply the concepts you've learned, participate in class, and ask questions. If you are assigned twenty problems for
homework, you are responsible for all twenty problems. If you complete half the work don't expect full credit. If you have difficulty
with a problem while doing your homework, then try to follow the tips below.
Tips:
Find a quiet place with bright lighting to complete your assignment
Before you start your homework, read the section and study the examples presented.
Work out the problem as far as you can. You must make a good faith attempt for every problem.
If you encounter difficulty with a problem, look in your notes to see if you can find a similar problem that was done in class
If you still can't find the solution, come to class the next day and ask questions
Tests/Quizzes:
Tests are generally given at the end of a chapter and at the teacher's discretion. Quizzes are given regularly. There is to be no
talking during a test or quiz. If you have a question please direct it to Mr. Im. If caught talking we will assume the student is
cheating. Students are also expected to show all work to receive full credit on exam problems. If there is an exam scheduled on the
day that you have a field trip, you should make arrangements ahead of time to take the exam. Make-up exams are only given if you
have a legitimate absence. It is the student's responsibility to make arrangements within one day after returning from an absence to
make up a quiz or test. If arrangements are not made students will not be allowed to make up the exam and will receive a zero.
There will be opportunities for test re-takes or test corrections.
How to study and be successful in this class
Come to class on a regular basis and be prepared to learn and do your best
Complete the bellringers diligently
Take neat and organized notes as instructed by teacher
Do not hesitate to ask questions if you need to.
Do your homework every night. Homework Assignments are listed on agenda as well as the Kenwood website.
Since 70% of your grade comes from tests and quizzes, you must study for these exams.
To prepare for exams, redo some problems from bell ringers and class notes. If there are concepts that you still do not feel
confident about do problems from the chapter review that apply to these concepts.
If a study guide or practice test is provided, complete every problem and use this as your guide for the type of problems that
will be on the exam.
If you feel that you are struggling with the material and need one-on-one assistance or just some extra practice, please feel
free to come to me for tutoring after school.
Test retake/correction policy- You will have the opportunity to retake or make corrections on some tests PROVIDED ALL
your homework for the chapter is complete. This will allow you to raise your test score by up to 50% of the credit you did
NOT earn. Also, this will take place after school on teacher decided days.
Absences/Tardiness:
Students are expected to come to class regularly and on time. They are expected to enter the class respectfully, be seated and get out
homework and proper materials for taking notes. Students will not be allowed to enter class without an ID or after the tardy bell
without a pass. It is the students responsibility to get the assignments and notes missed when absent within one day of returning.
Missed assignments are due one day after the student returns.
Final Grade: Grading Scale:
Students will be graded on: 90% -100% = A
Assignments 15% 80% - 89% = B
Class Activities 15% 70% - 79% = C
Quizzes 20% 60% - 70% = D
Tests/Final Exam 50% below 60% = F
Overall Average = (assignment avg.)(.15) + (class activities avg.)(.15) + (quiz avg.)(.20) + (tests/final exam avg.)(.5)
Students are expected to take responsibility for their grade. It is important to spend time on this class daily. Feel free to confide in
your instructor if you are having difficulty and need extra help or tutoring. You are probably not alone, so do not feel embarrassed.
Students should keep an organized binder, stay aware of assignment and project due dates and check Gradebook regularly.
Timeline and Course Units (State Goal numbers are in parentheses)
Quarter 1
Unit1 – Fractions and Decimals (6), Rational Numbers (6), Order of Operations (6)
Unit 2 - Solving Linear Equations (7, 8, 9)
Quarter 2
Unit 3- Variables and Functions (6,7), Multiple Representations in the Real World (6,7,8) , Linear Patterns (8)
Unit 4- Constructing Graphs (8, 9), Exploring Graphs (10), Exploring Rate of Change in Motion Problems (6,7, 10),
Exploring Rate of Change in other Problems (6,8, 10), Understanding Slope (10), Understanding Y-Intercept (10), Creating
Linear Models for Data (10), writing the equation of a line and graphing a line (6,7,8)
Unit 5- Solving and graphing inequalities (6,7,8)
Quarter 3
Unit 6- Formulating and Solving Systems (7, 8)
Unit 7 – Laws of Exponents (7,8,9), Operations on Polynomials (8, 9), Solving Quadratic Equations (7, 10)
Quarter 4
Unit 8 - Graphs of Quadratic Functions (8, 10), Modeling with Quadratic Functions (10), , The Quadratic Formula (6, 7, 10),
Modeling with Exponential Functions (10), Modeling with Inverse Variation (6, 7)
Unit 9 – Simplifying Radicals and Radical equations (6,7,8), Pythagorean theorem (6,7)
Classroom Policies and Procedures
Respect for one another and classroom decorum will be maintained at all times. Students are expected to adhere to the
Chicago Public Schools Uniform Discipline Code and Kenwood Policy of conduct regarding academics, behavior and
dress. The following policies will be consistently enforced to ensure that every student receives the instructional time and
atmosphere that he/she deserves.
1. Be in class when the tardy bell rings.
2. Wear ID at all times.
3. Students will not be allowed to wear coats, hats, or other items that are on the Kenwood list of prohibited dress.
4. Students who come late to class are very disruptive to the rest of the class. If you are unavoidably late, please enter the room
quietly and with a pass. You may not enter class without a pass.
5. Come to class prepared to learn. (sharpened pencil, colored pen, paper, calculator, notes, book)
6. Take notes daily.
7. Do not get out of your seat without permission.
8. Do not blurt out questions or answers. Raise your hand and wait to be called on.
9. Ask questions if you do not understand what is on the board.
10. Respect all property. (School property, personal property, and other's property)
11. Respect all ideas given in class and do not criticize anybody's ideas or thoughts.
12. There will be limited restroom breaks. Students should go to the restroom before class and return before the bell rings. If
students are late they have to get a tardy pass. (This is not a suggestion it is a rule.)
13. Students leaving and returning to class during class is also very disruptive. Please take care of any personal business before
or after class. Students may not leave the classroom during class time unless there is a true emergency. If such an emergency
occurs, raise your hand, present a pass from your agenda book, collect your belongings and leave the room quietly.
14. All exams have a time limit. Students must turn in assignments and exams within the allotted time. Keep all graded work. If
questions arise, it is your responsibility to produce the original document for verification.
15. Cheating and/or plagiarism of any kind will not be tolerated. Evidence of such will result in a grade of 0 on the assignment
or exam and possible disciplinary action
16. Cell phones and other electronic devises must be turned off or silenced during class. Phones may not be visible during exams
and can not be used as a calculator. Cell phones that are visible or heard will be confiscated and can only be retrieved by a
parent or guardian.
17. Eating and drinking is not permitted in the classroom at any time.
------------------------------------------------------------------------------------------------------------------------------------------------------------------
This form is considered the first homework assignment and will be collected. Please read and sign your names
below.
I have read the syllabus and understand it. I will honor it.
__________________________________________ _____________
Students Signature Date
__________________________________________
Print Name of Student
I have read and discussed this syllabus with my child. I understand it and will support it.
________________________________________ ______________
Parent/Guardian Signature Date
________________________________________
Print Name of Parent/Guardian
Parent email: _____________________________________
Parent phone number | 677.169 | 1 |
0131444417
9780131444416
Intermediate Algebra:For college-level courses on intermediate algebra. El ·Explain key concepts clearly with an excellent, accessible writing style. ·Build problem-solving skills with thoroughly integrated problem solving techniques and explanations. ·Relate to students through real-life applications that are interesting, relevant, and practical. Martin-Gay believes that every student can: ·Test better: The new Chapter Test Prep Video shows Martin-Gay working step-by-step video solutions to every problem in each Chapter Test to enhance mastery of key chapter content. ·Study better: New, integrated Study Skills Reminders reinforce the skills introduced in section 1.1, "Tips for Success in Mathematics" to promote an increased focus on the development of all-important study skills. ·Learn
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Rent Intermediate Algebra 4th edition today, or search our site for K. Elayn textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Pearson. | 677.169 | 1 |
QBUS 100 Math for Decision Making I Course Guide
Course Description
A wide variety of problems from business may be solved using equations. Managers and economists use equations and their graphs to study costs, sales, national consumption, supply and demand, the time value of money, market equilibrium points, and optimum production levels.
All managers must understand the methods used to determine the interest and the future value (principal plus interest) resulting from savings plans and the methods used in the repayment of debts. These computations are made using formulae for computing compound interest, the future and present value of annuities, amortization of debts, and the amount paid into a sinking fund to discharge a debt.
Manufacturing firms require several components for the manufacture of items they produce, and there are usually several stages for each item's assembly and final shipment. A manufacturing firm's costs and profits depend on the availability of the components (for example, labor and raw materials), the costs of these components, the unit profit for each product, and how many products are required. The manager is able to use equations to model these components and determine optimal levels of production.
Specific, Assessable Learning Outcomes
The student will be able to:
Have a firm understanding of time value of money through compound interest, annuity calculations and bond valuations.
Develop cost and revenue functions and understand their role in profit and break-even analysis.
Develop supply and demand functions and understand their role in market equilibrium analysis.
Understand the role of matrix algebra in the solution of a system of linear equations.
Have the ability to optimize an objective function subject to a system of linear constraints via the method of graphical analysis in two dimensions.
Course Outline
The development of linear equations and graphs and their use in solving common business problems.
The development of quadratic equations and their use in solving common business problems.
Storing data in matrices and making business decisions by performing mathematical operations on matrices.
Using graphical methods to solve linear programming problems for allocating limited resources from various activities in the best possible way.
Measuring the time value of money with compound interest, annuity, amortization calculations and bond valuations.
Recommended Teaching Methodology
This course will be structured in such a way as to facilitate the use of different methods of instruction. Readings, lectures, multimedia presentations, group discussions, and written assignments will be used throughout the course. Work will be done individually and/or in small groups.
The readings will come from the required text as well as additional material to be provided by the instructor. Lectures and group discussions will enable the instructor and students to expand on the material presented in the readings. For all testing situations, a departmentally designed formula sheet will be the only supplemental material accompanying any exam.
Students will be exposed to computer algebra systems (CAS), currently a graphics calculator (TI-83 plus), to facilitate his or her knowledge and critical thinking skills to common business situations. In testing situations, each student will be required to reset all memory to manufacturer's default.
Recommended Assessment Measures
The following assessment measures will be used.
Assessment devices (quizzes, homework, exams, etc.) should be given throughout the semester, building up to a comprehensive final exam. The final exam will be used to measure the level of understanding in the areas of time value of money and bond valuation, profit analysis, market equilibrium analysis, break-even analysis, solution to a system of linear equations and optimization of an objective function subject to a system of linear constraints.
Writing and/or oral presentation(s) focusing on major areas of study will be given to students to assess their understanding of mathematics and the ability to communicate quantitative results.
Statement of Expectations
This course satisfies the quantitative reasoning (CAQ) core requirement for the college and is a pre-business core requirement for the School of Business. As such, any student in the course is required to show a D- level proficiency in the course in order to attain credit for the college core and/or attain credit towards the business major. It is normally taken during the student's first semester of full-time studies.
To attain these levels of proficiency it is required that students attend class with the physical materials needed for in-class success (such as the TI-83 and textbook). Students should remain actively engaged in the material covered during class.
Of course this is not all that is needed, as classroom success is also influenced by student preparation outside the class. It is therefore imperative that students complete out of class assignments and textbook reading in a timely fashion. Students will develop and retain the knowledge and skill set described above by continual practice, thereby slowly building and adding onto their knowledge base. "Cramming" in the days before a test is not an effective way to learn the skills necessary to employ mathematical reasoning in the business environment.
Lastly, it is expected that if you have a question about any course material you will ask those questions so that they may be answered. There are a variety of sources from which answers will come, including (but by no means limited to) the textbook, the QBA Help Lab, a tutor, classmates and MOST IMPORTANTLY the professor, either in-class or during their office hours. Remember that an unasked question is an answer never given.
Prerequisite Knowledge
Students should have a thorough understanding of general math skills (especially algebra) and at
least three units of high school math or its equivalent.
The Quantitative Business Analysis department will annually review assessment results for this course. Specifically, assessment results in each of the five learning outcome areas will be analyzed to determine the level of success in achieving these learning outcomes. Any deficiencies in achieving learning outcomes will be addressed and appropriate changes designed to improve the success in achieving these learned outcomes. | 677.169 | 1 |
Elementary Linear Algebra - 10th edition
Summary: When it comes to learning linear algebra, engineers trust Anton. The tenth edition presents the key concepts and topics along with engaging and contemporary applications. The chapters have been reorganized to bring up some of the more abstract topics and make the material more accessible. More theoretical exercises at all levels of difficulty are integrated throughout the pages, including true/false questions that address conceptual ideas. New marginal notes provide a fuller explanat...show moreion when new methods and complex logical steps are included in proofs. Small-scale applications also show how concepts are applied to help engineers develop their mathematical reasoning. ...show less
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Series
1. Understanding the nature of power series and the radius of convergence
2. Ability to undertake simple calculations using the geometric, binomial, exponential and trigonometric series
3. Ability to construct Maclaurin and Taylor series
Vector geometry
1. Ability to calculate the equations of lines and planes in 3D
2. Ability to calculate the vector product and the scalar and vector triple products
3. Ability to solve various intersection problems involving lines and planes
Descriptive Statistics
1. Ability to calculate quartiles, means and standard deviations from sample data and understanding the meaning of these measures
2. Understand the use of least squares for line fitting.
Probability
1. Ability to apply simple counting methods to determine probabilities
2. Understanding the addition and multiplication rules of probability and using them in simple calculations
3. Ability to calculate using conditional probabilities
4. Understanding the importance of statistical independence
Distributions
1. Understanding simple discrete distributions and the ability to calculate means and variances
2. Ability to calculate probabilities from the binomial distribution
3. Understanding simple continuous distributions and the ability to calculate means and variances.
4. Ability to calculate using uniform, Poisson and exponential distributions
5. Ability to calculate Normal distribution probabilities using a table of the Standard Normal
6. Ability to calculate confidence intervals for means | 677.169 | 1 |
Popular Pages
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common core state standards for mathematics overview the common core state standards ccss for mathematics are organized by grade level in grades k8 at the high school level the standards are organized by conceptual category number and quantity algebra functions geometry modeling and probability and statistics showing the body of knowledge students should learn in each category to be college and career ready and to be prepared to study more advanced mathematics as states consider how to implement the high school standards an important consideration is how the high school ccss might be organized into courses that provide a strong foundation for post-secondary success to address this need achieve in partnership with the common core writing team has convened a group of experts including state mathematics experts teachers mathematics faculty from two and four year institutions mathematics teacher educators and workforce representatives to develop model course pathways in mathematics based on the common core state standards in considering this document there are four things important to note 1 the pathways and courses are models not mandates they illustrate possible approaches to organizing the content of the ccss into coherent and rigorous courses that lead to college and career readiness states and districts are not expected to adopt these courses as is rather they are encouraged to use these pathways and courses as a starting point for developing their own appendix a designing high school mathematics courses based on the common core state standards all college and career ready standards those without a are found in each pathway a few standards are included to increase coherence but are not necessarily expected to be addressed on high stakes assessments the course descriptions delineate the mathematics standards to be covered in a course they are not prescriptions for curriculum or pedagogy additional work will be needed to create coherent instructional programs that help students achieve these standards units within each course are intended to suggest a possible grouping of the standards into coherent blocks in this way units may also be considered critical areas or big ideas and these terms are used interchangeably throughout the document the ordering of the clusters within a unit follows the order of the standards document in most cases not the order in which they might be taught attention to ordering content within a unit will be needed as instructional programs are developed while courses are given names for organizational purposes states and districts are encouraged to carefully consider the content in each course and use names that they feel are most appropriate similarly unit titles may be adjusted by states and districts 2 3 4 5 while the focus of this document is on organizing the standards for mathematical content into model pathways to college and career readiness the content standards must also be connected to the standards for mathematical practice to ensure that the skills needed for later success are developed in particular modeling defined by a in the ccss is defined as both a conceptual category for high school mathematics and a mathematical practice and is an important avenue for motivating students to study mathematics for building their understanding of mathematics and for preparing them for future success development of the pathways into instructional programs will require careful attention to modeling and the mathematical practices assessments based on these pathways should reflect both the content and mathematical practices standards 2
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common core state standards for mathematics the pathways four model course pathways are included 1 2 3 an approach typically seen in the u.s traditional that consists of two algebra courses and a geometry course with some data probability and statistics included in each course an approach typically seen internationally integrated that consists of a sequence of three courses each of which includes number algebra geometry probability and statistics a compacted version of the traditional pathway where no content is omitted in which students would complete the content of 7th grade 8th grade and the high school algebra i course in grades 7 compacted 7th grade and 8 8th grade algebra algebra i course more manageable a compacted version of the integrated pathway where no content is omitted in which students would complete the content of 7th grade 8th grade and the mathematics i course in grades 7 compacted 7th grade and 8 8th grade mathematics mathematics i course more manageable ultimately all of these pathways are intended to significantly increase the coherence of high school mathematics 4 appendix a designing high school mathematics courses based on the common core state standards 5 the non-compacted or regular pathways assume mathematics in each year of high school and lead directly to preparedness for college and career readiness in addition to the three years of study described in the traditional and integrated pathways students should continue to take mathematics courses throughout their high school career to keep their mathematical understanding and skills fresh for use in training or course work after high school a variety of courses should be available to students reflecting a range of possible interests possible options are listed in the following chart based on a variety of inputs and factors some students may decide at an early age that they want to take calculus or other college level courses in high school these students would need to begin the study of high school content in the middle school which would lead to precalculus or advanced statistics as a junior and calculus advanced statistics or other college level options as a senior strategic use of technology is expected in all work this may include employing technological tools to assist students in forming and testing conjectures creating graphs and data displays and determining and assessing lines of fit for data geometric constructions may also be performed using geometric software as well as classical tools and technology may aid three-dimensional visualization testing with and without technological tools is recommended as has often occurred in schools and districts across the states greater resources have been allocated to accelerated pathways such as more experienced teachers and newer materials the achieve pathways group members strongly believe that each pathway should get the same attention to quality and resources including class sizes teacher assignments professional development and materials indeed these and other pathways should be avenues for students to pursue interests and aspirations the following flow chart shows how the courses in the two regular pathways are sequenced the in the chart on the following page means that calculus follows precalculus and is a fifth course in most cases more information about the compacted pathways can be found later in this appendix 3
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common core state standards for mathematics appendix a designing high school mathematics courses based on the common core state standards some teachers and schools are effectively getting students to be college and career ready we can look to these teachers and schools to see what kinds of courses are getting results and to compare pathways courses to the mathematics taught in effective classrooms a study done by act and the education trust gives evidence to support these pathways the study looked at highpoverty schools where a high percentage of students were reaching and exceeding act s college-readiness benchmarks from these schools the most effective teachers described their courses and opened up their classrooms for observation the commonality of mathematics topics in their courses gives a picture of what it takes to get students to succeed and also provides a grounding for the pathways there were other commonalities for more detailed information about this study search for the report on course for success at 1 implementation considerations as states districts and schools take on the work of implementing the common core state standards the model course pathways in mathematics can be a useful foundation for discussing how best to organize the high school standards into courses the pathways have been designed to be modular in nature where the modules or critical areas units are identical in nearly every manner between the two pathways but are arranged in different orders to accommodate different organizational offerings assessment developers may consider the creation of assessment modules in a similar fashion curriculum designers may create alternative model pathways with altogether different organizations of the standards some of this work is already underway in short this document is intended to contribute to the conversations around assessment and curriculum design rather than end them effectively implementing these standards will require a long-term commitment to understanding what best supports student learning and attainment of college and career readiness skills by the end of high school as well as regular revision of pathways as student learning data becomes available supporting students one of the hallmarks of the common core state standards for mathematics is the specification of content that all students must study in order to be college and career ready this college and career ready line is a minimum for all students however this does not mean that all students should progress uniformly to that goal some students progress 1 the study provides evidence that the pathways high school algebra i geometry algebra ii sequence is a reasonable and rigorous option for preparing students for college and career topics aligned almost completely between the ccss topics and topics taught in the study classrooms the starting point for the pathways high school algebra i course is slightly beyond the starting point for the study algebra i courses due to the existence of many typical algebra i topics in the 8th grade ccss therefore some of the study algebra ii topics are a part of the pathways high school algebra i course specifically using the quadratic formula a bit more with exponential functions including comparing and contrasting linear and exponential growth and the inclusion of the spread of data sets the pathways geometry course is very similar to what was done in the study geometry courses with the addition of the laws of sines and cosines and the work with conditional probability plus applications involving completing the square because that topic was part of the pathways high school algebra i course the pathways algebra ii course then matches well with what was done in the study algebra ii courses and continues a bit into what was done in the study precalculus classrooms including inverse functions the behavior of logarithmic and trigonometric functions and in statistics with the normal distribution margin of error and the differences among sample surveys experiments and observational studies all in all the topics and the order of topics is very comparable between the pathways high school algebra i geometry algebra ii sequence and the sequence found in the study courses 4
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common core state standards for mathematics more slowly than others these students will require additional support and the following strategies consistent with response to intervention practices may be helpful · · · · · creating a school-wide community of support for students providing students a math support class during the school day after-school tutoring extended class time or blocking of classes in mathematics and additional instruction during the summer watered-down courses which leave students uninspired to learn unable to catch up to their peers and unready for success in postsecondary courses or for entry into many skilled professions upon graduation from high school are neither necessary nor desirable the results of not providing students the necessary supports they need to succeed in high school are well-documented too often after graduation such students attempt to continue their education at 2or 4-year postsecondary institutions only to find they must take remedial courses spending time and money mastering high school level skills that they should have already acquired this in turn has been documented to indicate a greater chance of these students not meeting their postsecondary goals whether a certificate program two or fouryear degree as a result in the workplace many career pathways and advancement may be denied to them to ensure students graduate fully prepared those who enter high school underprepared for high school mathematics courses must receive the support they need to get back on course and graduate ready for life after high school furthermore research shows that allowing low-achieving students to take low-level courses is not a recipe for academic success kifer 1993 the research strongly suggests that the goal for districts should not be to stretch the high school mathematics standards over all four years rather the goal should be to provide support so that all students can reach the college and career ready line by the end of the eleventh grade ending their high school career with one of several high-quality mathematical courses that allows students the opportunity to deepen their understanding of the college and career-ready standards with the common core state standards initiative comes an unprecedented ability for schools districts and states to collaborate while this is certainly the case with respect to assessments and professional development programs it is also true for strategies to support struggling and accelerated students the model course pathways in mathematics are intended to launch the conversation and give encouragement to all educators to collaborate for the benefit of our states children appendix a designing high school mathematics courses based on the common core state standards 5
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common core state standards for mathematics how to read the pathways each pathway consists of two parts the first is a chart that shows an overview of the pathway organized by course and by conceptual category algebra functions geometry etc these charts show which clusters and standards appear in which course see page 5 of the ccss for definitions of clusters and standards for example in the chart below the three standards n.q.1 2 3 associated with the cluster reason quantitatively and use units to solve problems are found in course 1 this cluster is found under the domain quantities in the number and quantity conceptual category all high school standards in the ccss are located in at least one of the courses in this chart courses domain appendix a designing high school mathematics courses based on the common core state standards clusters notes and standards conceptual category 6
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common core state standards for mathematics the second part of the pathways shows the clusters and standards as they appear in the courses each course contains the following components · · · an introduction to the course and a list of the units in the course unit titles and unit overviews see below units that show the cluster titles associated standards and instructional notes below it is important to note that the units or critical areas are intended to convey coherent groupings of content the clusters and standards within units are ordered as they are in the common core state standards and are not intended to convey an instructional order considerations regarding constraints extensions and connections are found in the instructional notes the instructional notes are a critical attribute of the courses and should not be overlooked for example one will see that standards such as a.ced.1 and a.ced.2 are repeated in multiple courses yet their emphases change from one course to the next these changes are seen only in the instructional notes making the notes an indispensable component of the pathways unit title and overview appendix a designing high school mathematics courses based on the common core state standards standards associated with cluster cluster instructional note 7
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common core state standards for mathematics overview of the traditional pathway for the common core state mathematics standards this table shows the domains and clusters in each course in the traditional pathway the standards from each cluster included in that course are listed below each cluster for each course limits and focus for the clusters are shown in italics domains high school algebra i · xtend the properties e of exponents to rational exponents geometry algebra ii fourth courses the real number system n.rn.1 2 · se properties of u rational and irrational numbers n.rn.3 · eason quantitatively r and use units to solve problems appendix a designing high school mathematics courses based on the common core state standards quantities foundation for work with expressions equations and functions n.q.1 2 3 · erform arithmetic p operations with complex numbers n.cn.1 2 · erform arithmetic p operations with complex numbers n.cn.3 · epresent complex r numbers and their operations on the complex plane n.cn.4 5 6 · epresent and model r with vector quantities n.vm.1 2 3 · perform operations on vectors number and quantity the complex number system · se complex numbers u in polynomial identities and equations polynomials with real coefficients n.cn.7 8 9 vector quantities and matrices n.vm.4a 4b 4c 5a 5b · perform operations on matrices and use matrices in applications n.vm.6 7 8 9 10 11 12 the standards in this column are those in the common core state standards that are not included in any of the traditional pathway courses they would be used in additional courses developed to follow algebra ii 8
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common core state standards for mathematics traditional pathway high school algebra i the fundamental purpose of this course is to formalize and extend the mathematics that students learned in the middle grades because it is built on the middle grades standards this is a more ambitious version of algebra i than has generally been offered the critical areas called units deepen and extend understanding of linear and exponential relationships by contrasting them with each other and by applying linear models to data that exhibit a linear trend and students engage in methods for analyzing solving and using quadratic functions the mathematical practice standards apply throughout each course and together with the content standards prescribe that students experience mathematics as a coherent useful and logical subject that makes use of their ability to make sense of problem situations critical area 1 by the end of eighth grade students have learned to solve linear equations in one variable and have applied graphical and algebraic methods to analyze and solve systems of linear equations in two variables now students analyze and explain the process of solving an equation students develop fluency writing interpreting and translating between various forms of linear equations and inequalities and using them to solve problems they master the solution of linear equations and apply related solution techniques and the laws of exponents to the creation and solution of simple exponential equations critical area 2 in earlier grades students define evaluate and compare functions and use them to model relationships between quantities in this unit students will learn function notation and develop the concepts of domain and range they explore many examples of functions including sequences they interpret functions given graphically numerically symbolically and verbally translate between representations and understand the limitations of various representations students build on and informally extend their understanding of integer exponents to consider exponential functions they compare and contrast linear and exponential functions distinguishing between additive and multiplicative change students explore systems of equations and inequalities and they find and interpret their solutions they interpret arithmetic sequences as linear functions and geometric sequences as exponential functions critical area 3 this unit builds upon prior students prior experiences with data providing students with more formal means of assessing how a model fits data students use regression techniques to describe approximately linear relationships between quantities they use graphical representations and knowledge of the context to make judgments about the appropriateness of linear models with linear models they look at residuals to analyze the goodness of fit critical area 4 in this unit students build on their knowledge from unit 2 where they extended the laws of exponents to rational exponents students apply this new understanding of number and strengthen their ability to see structure in and create quadratic and exponential expressions they create and solve equations inequalities and systems of equations involving quadratic expressions critical area 5 in this unit students consider quadratic functions comparing the key characteristics of quadratic functions to those of linear and exponential functions they select from among these functions to model phenomena students learn to anticipate the graph of a quadratic function by interpreting various forms of quadratic expressions in particular they identify the real solutions of a quadratic equation as the zeros of a related quadratic function students expand their experience with functions to include more specialized functions absolute value step and those that are piecewise-defined appendix a designing high school mathematics courses based on the common core state standards 15 | 677.169 | 1 |
More About
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Overview
This introduction to linear algebra by world-renowned mathematician Peter Lax is unique in its emphasis on the analytical aspects of the subject as well as its numerous applications. The book grew out of Dr. Lax's course notes for the linear algebra classes he teaches at New York University. Geared to graduate students as well as advanced undergraduates, it assumes only limited knowledge of linear algebra and avoids subjects already heavily treated in other textbooks. And while it discusses linear equations, matrices, determinants, and vector spaces, it also in-cludes a number of exciting topics that are not covered elsewhere, such as eigenvalues, the Hahn-Banach theorem, geometry, game theory, and numerical analysis.
The first four chapters are devoted to the abstract structure of finite dimensional vector spaces. Subsequent chapters deal with determinants as a blend of geometry, algebra, and general spectral theory. Euclidean structure is used to explain the notion of selfadjoint mappings and their spectral theory. Dr. Lax moves on to the calculus of vector and matrix valued functions of a single variable—a neglected topic in most undergraduate programs—and presents matrix inequalities from a variety of perspectives.
Later chapters cover convexity and the duality theorem, describe the basics of normed linear spaces and linear maps between normed spaces, and discuss the dominant eigenvalue of matrices whose entries are positive or merely non-negative. The final chapter is devoted to numerical methods and describes Lanczos' procedure for inverting a symmetric, positive definite matrix. Eight appendices cover important topics that do not fit into the main thread of the book.
Clear, concise, and superbly organized, Linear Algebra is an excellent text for advanced undergraduate and graduate courses and also serves as a handy professional reference.
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An introduction to linear algebra, emphasizing analytical aspects as well as applications, for graduate and advanced undergraduate students. Early chapters are devoted to the abstract structure of finite dimensional vector spaces, and subsequent chapters treat determinants as a blend of geometry, algebra, and general spectral theory. Other subjects include calculus of vector and matrix valued functions of a single variable, matrix inequalities, Pfaff's theorem, and lattices. Includes exercises. Annotation c. by Book News, Inc., Portland, Or.
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Meet the Author
PETER D. LAX, PhD, has had a long and distinguished career in mathematics. A student and then colleague of Richard Courant, Fritz John, and K. O. Frederichs, he is considered one of the world's leading mathematicians. He teaches at New York University's Courant Institute of Mathematical | 677.169 | 1 |
To the outside world, a "supercomputer" appears to be a single system. In fact, it's a cluster of computers that share a local area network and have the ability to work together on a single problem as a team. Many businesses used to consider supercomputing beyond the reach of their budgets, but new Linux applications have made high-performance clusters... more...
Beyond Geometry describes how set-theoretic topology developed and why it now occupies a central place in mathematics. Describing axiomatic method as well as providing a definition of what a geometric property is, this new resource examines how early analysts incorporated geometric thinking into their development of the calculus. It also looks at the... more...
Mathematical Applications and Modelling is the second in the series of the yearbooks of the Association of Mathematics Educators in Singapore. The book is unique as it addresses a focused theme on mathematics education. The objective is to illustrate the diversity within the theme and present research that translates into classroom pedagogies.The book,... more...
This book is an introduction to the subject of mean curvature flow of hypersurfaces with special emphasis on the analysis of singularities. This flow occurs in the description of the evolution of numerous physical models where the energy is given by the area of the interfaces. These notes provide a detailed discussion of the classical parametric approach... more...
Until the mid-twentieth century, topological studies were focused on the theory of suitable structures on sets of points. The concept of open set exploited since the twenties offered an expression of the geometric intuition of a 'realistic' place (spot, grain) of non-trivial extent. Imitating the behaviour of open sets and their relations led... more... | 677.169 | 1 |
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Numerical analysis is an increasingly important link between pure mathematics and its application in science and technology. This textbook provides an introduction to the justification and development of constructive methods that provide sufficiently accurate approximations to the solution of numerical problems, and the analysis of the influence that errors in data, finite-precision calculations, and approximation formulas have on results, problem formulation and the choice of method. It also serves as an introduction to scientific programming in MATLAB, including many simple and difficult, theoretical and computational exercises. A unique feature of this book is the consequent development of interval analysis as a tool for rigorous computation and computer assisted proofs, along with the traditional material.
Description:
A self contained introduction to probability, exchangeability and Bayes rule
provides a theoretical understanding of the applied material. Numerous examples with R code that can be run "as is" allow the reader to perform the data analyses themselves. The ... | 677.169 | 1 |
It describes each strategy and clarifies its advantages and drawbacks. Also included is a large sample of classroom-tested examples along with sample student responses. These examples can be used "as is" - or you can customize them for your own class. This book will help prepare your students for standardized tests that include items requiring evidence... more...
Topics in Matroid Theory provides a brief introduction to matroid theory with an emphasis on algorithmic consequences. Matroid theory is at the heart of combinatorial optimization and has attracted various pioneers such as Edmonds, Tutte, Cunningham and Lawler among others. Matroid theory encompasses matrices, graphs and other combinatorial entities... more...
This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method,...Debates in Mathematics Education explores the major issues that mathematics teachers encounter in their daily lives. It engages with established and contemporary debates, promotes and supports critical reflection and aims to stimulate both novice and experienced teachers to reach informed judgements and argue their point of view with deeper theoretical... more...
Praise for the First Edition "Stahl offers the solvability of equations from the historical point of view...one of the best books available to support a one-semester introduction to abstract algebra." — CHOICE Introductory Modern Algebra: A Historical Approach, Second Edition presents the evolution of algebra and provides readers with... more...
A great for anyone looking to explore interactions within... more...
This volume, as Andrew M. Odlzyko writes in the foreword, "commemorates and celebrates the life and achievements of an extraordinary person." Originally conceived as an 80th birthday tribute to Herbert Wilf, the well-known combinatorialist, the book has evolved beyond the proceeds of the W80 tribute.Professor Wilf was an award-winning teacher,... more... | 677.169 | 1 |
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Fayetteville, GA ACT Math Professional Engineer.Algebra is about more than memorizing formulas. It offers a method of mental organization which you will use to solve problems the rest of your life. With good motivation, everyone can learn algebraYou will learn how to draw graphs of straight lines and parabolas. You will learn about the shapes of graphs for many types of equations. Algebra 1 also includes some statistics and probability and a small amount of geometry. | 677.169 | 1 |
mediate Algebra for College Students
KEY MESSAGE The Blitzer Algebra Series combines mathematical accuracy with an engaging, friendly, and often fun presentation for maximum student ...Show synopsisKEY MESSAGE The Blitzer Algebra Series combines mathematical accuracy with an engaging, friendly, and often fun presentation for maximum student appeal. Blitzer's personality shows in his writing, as he draws students into the material through relevant and thought-provoking applications. Every Blitzer page is interesting and relevant, ensuring that students will actually use their textbook to achieve success! KEY TOPICS Algebra, Mathematical Models, and Problem Solving; Functions and Linear Functions; Systems of Linear Equations; Inequalities and Problem Solving; Polynomials, Polynomial Functions, and Factoring; Rational Expressions, Functions, and Equations; Radicals, Radical Functions, and Rational Exponents; Quadratic Equations and Functions; Exponential and Logarithmic Functions; Conic Sections and Systems of Nonlinear Equations; Sequences, Series, and the Binomial Theorem MARKET for all readers interested in algebra.Hide synopsis
Description:This edition features the exact same content as the traditional...This edition features the exact same content as the traditional text in a convenient, three-hole-punched, loose-leaf version. Books a la Carte also offer a great value— this format costs significantly less than a new | 677.169 | 1 |
Modelling With Force and Motion The School Mathematics Project
9780521408912
ISBN:
0521408911
Pub Date: 1993 Publisher: Cambridge University Press
Summary: The aim of 16-19 Mathematics has been to produce a course which, while chaallenging, is accessible and enjoyable to all students. The course develops ability and confidence in mathematics and its applications, together with an appreciation of how mathematical ideas help in the understanding of the world and society in which we live. The unit: · helps develop an ability to use the concepts introduced in Newton's laws ...of motion to study projectiles, forces, circular motion at constant speed, and statics of rigid bodies; · provides insight into the potential of mathematics for modelling physical phenomena; · helps foster an appreciation of the links between mathematics and the real world; · develops a basis for further study in engineering and science; · fosters an ability to model both in familiar and unfamiliar contexts within the field of mechanics.
School Mathematics Project Staff is the author of Modelling With Force and Motion The School Mathematics Project, published 1993 under ISBN 9780521408912 and 0521408911. Fourteen Modelling With Force and Motion The School Mathematics Project textbooks are available for sale on ValoreBooks.com, six used from the cheapest price of $3.49, or buy new starting at $16.44.[read more] | 677.169 | 1 |
Product Description
Key To Algebra offers a unique, proven way to introduce algebra to your students. New concepts are explained in simple language and examples are easy to follow. Word problems relate algebra to familiar situations, helping students understand abstract concepts. Students develop understanding by solving equations and inequalities intuitively before formal solutions are introduced. Students begin their study of algebra in Books 1-4 using only integers. Books 5-7 introduce rational numbers and expressions. Books 8-10 extend coverage to the real number system. This kit contains only Books 1-10. Answers Notes for Books 1-4Books 5-7 and Books 8-10 are available separately, as well as the Key to Algebra Reproducible Tests.
Product Reviews
Key To Algebra, Books 1-10
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October 21, 2013
concise and easy to follow
i bought this set for my child who will be taking integrated algebra in the fall. unfortunately, we found this set to be too easy and elementary for my child. she's covered almost all of it in school this past year. These books weren't the right level for my child. However, Key To Algebra books are concise, easy to understand and follow. It is not overwhelming as Saxon books can be. There's plenty of reviews and problems to do to reinforce the concept learned in each "chapter"
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Book summary
Adopting a user-friendly, conversationaland at times humorousstyle, these authors make the principles and practices of discrete mathematics as stimulating as possible while presenting comprehensive, rigorous coverage. Examples and exercises integrated throughout each chapter serve to pique reader interest and bring clarity to even the most complex concepts. Above all, the book is designed to engage today's readers in the interesting, applicable facets of modern mathematics. More than 200 worked examples and problems, as well as over 2500 exercises are included. Full solutions are provided in the back of the book. More than 150 Pausesshort questions inserted at strategic pointsare included. Full solutions to Pauses are included at the end of each section. For educators in area of discrete mathematics. [via] | 677.169 | 1 |
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More About
This Textbook
Overview
This book provides a general introduction to modern mathematical aspects in computing with multivariate polynomials and in solving algebraic systems. It presents the state of the art in several symbolic, numeric, and symbolic-numeric techniques, including effective and algorithmic methods in algebraic geometry and computational algebra, complexity issues, and applications ranging from statistics and geometric modelling to robotics and vision.
Graduate students, as well as researchers in related areas, will find an excellent introduction to currently interesting topics. These cover Groebner and border bases, multivariate resultants, residues, primary decomposition, multivariate polynomial factorization, homotopy continuation, complexity issues, | 677.169 | 1 |
Although every country seeks out information on other nations, China is the leading threat when it comes to the theft of intellectual assets, including inventions, patents, and R&D secrets. Trade Secret Theft, Industrial Espionage, and the China Threat provides an overview of economic espionage
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To learn and understand mathematics, students must engage in the process of doing mathematics. Emphasizing active learning, Abstract Algebra: An Inquiry-Based Approach not only teaches abstract algebra but also provides a deeper understanding of what mathematics is, how it is done, and how
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Effective horse trainers strive to improve the performance of their horses while preserving the integrity of the musculoskeletal apparatus. Biomechanics and Physical Training of the Horse supplies an anatomical and functional overview of the topic, enabling trainers to optimize the different
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books.google.com - Was... Mathematical Analysis
Real Mathematical Analysis(Google eBook)
Was science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.
Great introductory book, especially for people who wish to self-study Real Analysis. Note that for any high school students who wish to self-study from this book should have a strong background in Mathematics. General understanding of the Propositional Calculus (a.k.a. Mathematical Logic) and Set Theory will help in the beginning, but once you get through the first chapter, the rest of the book slowly becomes accessible. | 677.169 | 1 |
Mathematik mit MATLAB: Aufgaben und Losungen
This book, written in German, provides a compact introduction to MATLAB, including matrix operations, graphical representations, M-files, and flow control. The second part of the book contains a comprehensive set of exercises dealing with mathematic fundamentals, graphics, linear algebra and geometry. All of the exercises in the last part of the book are solved using MATLAB.
Companion software: The authors have developed a set of MATLAB M-files that are available on a CD-ROM bound into the book or may be retrieved from the publisher's website.
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Explore how to use MATLAB to make advancements in engineering and science. | 677.169 | 1 |
books.google.com - This easy-to-use workbook is full of stimulating activities that will give your students a solid introduction to precalculus! A variety of lessons, puzzles, mazes, and practice problems will challenge students to think creatively as they work to build their precalculus skills. Each lesson begins with... Reproducibles | 677.169 | 1 |
acing combinatorial and graph-theoretical tools at the forefront of the development of matrix theory, this book uses graphs to explain basic matrix construction, formulas, computations, ideas, and results. It presents material rarely found in other books at this level and describes several applications of matrices in electrical engineering, physics, and chemistry. | 677.169 | 1 |
Product Description
The Algebra 2 Tutor DVD Series teaches students the core topics of Algebra 2 and bridges the gap between Algebra 1 and Trigonometry, providing students with essential skills for understanding advanced mathematics.
This lesson teaches students how to solve equations that contain polynomials that cannot be easily factored. In order to do this, the quadratic formula must be used. Students are introduced to the quadratic formula and taught how to properly apply it to the equation at hand. Grades 8-12. 15 | 677.169 | 1 |
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Algebra 3-4
Course Description
This course emphasizes modeling data and problem situations with functions, specifically linear, quadratic, polynomial, exponential, rational, radical and logarithmic functions. The course also introduces students to sequences and series, solving systems with and without matrices, complex numbers, problems in trigonometry and some descrete topics such as probability. Students deepen their understanding of these topics as they work both individually and in groups to solve problems, to apply the mathematics and to communicate their reasoning. Students will use TI-84 graphing calculator in class to study these topics | 677.169 | 1 |
Precalculus with Trigonometry and Analytical Geometry
Description
This text provides a strong foundation for work with functions that culminates with an introduction to the calculus topics of the derivative and the integral. Beginning with a review of basic trignometry, the study progresses to advanced topics including functions, identities, and trigonometric equations. Development of analytical geometry topics include a logical approach to the study of lines, conics, quadric surfaces, polar coordinates, and parametric equations. Colorful graphs in one, two, and three dimensions illustrate the concepts and provide a frame of reference for discussion. Helpful tips and example problems show step-by-step solutions that aid in understanding and problem solving. Balanced exercises in each chapter provide ample opportunity for students to understand both the algebraic solution and practical application of problem solving | 677.169 | 1 |
Advanced Algebra Regents Video Tutorials
This page is for advanced algebra students who need help, and for teachers and tutors who are looking for video tutorials on regents.
how to do june 2009 algebra regents question 35 video, algebra Regents with explanations
Advanced Algebra Regents Video Tutorials
Many students learning advanced algebra find regents difficult. They feel overwhelmed with regents homework, tests and projects. And it is not always easy to find regents tutor who is both good and affordable. Now finding regents help is easy. For your regents homework, regents tests, regents projects, and regents tutoring needs, TuLyn is a one-stop solution. You can master hundreds of math topics by using TuLyn.
At TuLyn, we have hundreds of video tutorial clips including regents videos.
Our regents videos replace text-based tutorials and give you better step-by-step explanations of regents. Watch each video repeatedly until you understand how to approach regents problems and how to solve them.
Hundreds of video tutorials on regents make it easy for you to better understand the concept.
this website is the best it really is. It is nice to see a movie and not just to study from a worksheet. And all these worksheets that you can print out and work on is the best help of all June 14, 2009, 1:27 pm | 677.169 | 1 |
Challenges in Geometry
for Mathematical Olympians Past and Present
Christopher J. Bradley
Description
The International Mathematical Olympiad (IMO) is the World Championship Competition for High School students, and is held annually in a different country. More than eighty countries are involved.
Containing numerous exercises, illustrations, hints and solutions, presented in a lucid and thought- provoking style, this text provides a wide range of skills required in competitions such as the Mathematical Olympiad.
More than fifty problems in Euclidean geometry involving integers and rational numbers are presented. Early chapters cover elementary problems while later sections break new ground in certain areas and area greater challenge for the more adventurous reader. The text is ideal for Mathematical Olympiad training and also serves as
a supplementary text for student in pure mathematics, particularly number theory and geometry.
Dr. Christopher Bradley was formerly a Fellow and Tutor in Mathematics at Jesus College, Oxford, Deputy Leader of the British Mathematical Olympiad Team and for several years Secretary of the British Mathematical Olympiad Committee. | 677.169 | 1 |
The Algebra 2 Tutor DVD Series teaches students the core topics of Algebra 2 and bridges the gap between Algebra 1 and Trigonometry, providing students with essential skills for understanding advanced mathematics.
This lesson teaches students how to graph equations on the coordinate plane. The 'x' and 'y' coordinates are presented along with the concept of an ordered pair. This information is used to teach students how to set up a table of values to plot graphs of functions. Grades 8-12. 39 minutes on DVD. | 677.169 | 1 |
Beginning Algebra
9780321784919
ISBN:
032178491X
Edition: 6th Revise Pub Date: 2011 Publisher: Pearson Education
Summary: Written by Elayn Martin-Gay, Beginning Algebra was released in 2011 in this 6th revised format. Complete with plenty of new material compared to earlier versions, you can find out more about getting to grips with algebra and learning how to start in the right way. Published by Pearson Education, this text book is available at the cheapest prices. Buy Beginning Algebra online now and take advantage of the lowest price...s on previously owned text books. Sell back your copy now if you already own it and make the most of a good deal. Try Valore Books for Beginning Algebra deals now.
Martin-Gay, Elayn is the author of Beginning Algebra, published 2011 under ISBN 9780321784919 and 032178491X. Eight hundred thirty five Beginning Algebra textbooks are available for sale on ValoreBooks.com, two hundred thirty five used from the cheapest price of $60.98, or buy new starting at $123.85 | 677.169 | 1 |
KEY MESSAGE: The KEY TOPICS: Algebra, Mathematical Models, and Problem Solving; Functions and Linear Functions; Systems of Linear Equations; Inequalities and Problem Solving; Polynomials, Polynomial Functions, and Factoring; Rational Expressions, Functions, and Equations; Radicals, Radical Functions, and Rational Exponents; Quadratic Equations and Functions; Exponential and Logarithmic...
Less
Bob Blitzer's unique background in mathematics and behavioral sciences, along with his commitment to teaching, inspired him to develop a precalculus series that gets readers engaged and keeps them engaged. Presenting the full scope of the mathematics is just the first step. Blitzer draws in the reader with vivid applications that use math to solve real-life problems. These applications help answer the question "When will I ever use this?" Readers stay engaged because the book helps them remain focused as they study. The three-step learning system—See It, Hear It, Try It—makes examples easy to follow, while frequent annotations offer the support and guidance of an instructor's voice. Every page is interesting and relevant, ensuring that readers will actually use their textbook to achieve...
LessISBN-10: 0321756266 | ISBN-13: 9780321756268 | Edition: 4 College Algebra in Context, Fourth Edition, is ideal for students majoring in business, social sciences, and life sciences. The authors use modeling, applications, and real-data problems to develop skills, giving you the practice you need to become an adept problem solver in your future courses and career. This revision maintains the authors' focus on applying math in the real world through updated real-data applications. Features such as Group Activities and Extended Applications promote collaborative learning, improve communication and research skills, and foster critical thinking. 0321900782 / 9780321900784 College Algebra: An Early Functions Approach Plus NEW MyMathLab with Pearson eText -- Access Card Package Package consists of: 0321431308 / 9780321431301 MyMathLab/MyStatL ab -- Glue-in Access Card 0321654064 / 9780321654069 MyMathLab Inside Star Sticker 0321729641 /...
Less
Gets Them Engaged. Keeps Them Engaged This text is perfect for those wanting to learn College Algebra from an exciting text that demonstrates the relevancy of math to everyday life. Blitzer's philosophy: present the full scope of mathematics, while always (1) engaging the reader by opening their minds to learning (2) keeping the readerengaged on every page (3) explaining ideas directly, simply, and clearly. Blitzer exposed the critical concept of frunctions right away in Chapter One preparing the reader for further study in mathematics College Algebra - Blitzer, Robert/ Miller, Daniel S.THIS IS A BRAND NEW UNOPENED ITEM. Buy SKU: 245998698 If you want additional info
Beecher, Penna, and Bittinger's College AlgebraDugopolski's College Algebra, Fifth Edition gives readers the essential strategies to help them develop the comprehension and confidence they need to be successful in this course. Readers will find enough carefully placed learning aids and review tools to help them do the math without getting distracted from their objectives. Regardless of their goals beyond the course, all readers will benefit from Dugopolski's emphasis on problem solving and critical thinking, which is enhanced by the addition of nearly 1,000 exercises in this edition.
Appropriate for courses in College Algebra at the Freshman/Sophomor e level. Sobe l and Lerner provide teachers with a teachable text and students with a readable text that will properly prepare them for future courses, particularly precalculus. The text is designed specifically to ease the transition to precalculus and directly involve the graphing calculator.
The Eighth Edition of this highly dependable book retains its best features— accuracy, precision, depth, and abundant exercise sets— Systems of Equations and Inequalities; Exponential and Logarithmic Functions; Counting and Probability; and more. For individuals with an interest in learning algebra as it applies to their everyday lives.
Mike Sullivan's time-tested approach focuses students on the fundamental skills they need for the course: preparing for class, practicing with homework, and reviewing the concepts. In the Ninth Edition, College Algebra has evolved to meet today's course needs, building on these hallmarks by integrating projects and other interactive learning tools for use in the classroom or online.Note : Access codes and supplements are not guaranteed with rentals.
ISBN-10: 0321758935 | ISBN-13: 9780321758934 | Edition: 6 The Blitzer Algebra Series combines mathematical accuracy with an engaging, friendly, and often fun presentation for maximum appeal. Blitzer's personality shows in his writing, as he draws readers into the material through relevant and thought- provoking applications. Every Blitzer page is interesting and relevant, ensuring that students will actually use their textbook to achieve success | 677.169 | 1 |
I'm getting really bored in my math class. It's middle school math with pizzazz book b, but we're covering higher grade material. The concepts are really complicated and that's why I usually doze off in the class. I like the subject and don't want to fail , but I have a big problem understanding it. Can someone guide me?
Don't fret my friend. It's just a matter of time before you'll have no problems in solving those problems in middle school math with pizzazz book b. I have the exact solution for your math problems, it's called Algebrator. It's quite new but I assure you that it would be perfect in assisting you in your algebra problems. It's a piece of program where you can answer any kind of algebra problems with ease . It's also user friendly and shows a lot of useful data that makes you understand the subject matter fully.
Yeah, I think so too . Algebrator explains everything in such great detail that even a beginner can learn the tricks of the trade, and solve some of the most tough mathematical problems. It elaborates on each and every intermediate step that it took to reach a certain solution with such finesse that you'll learn a lot from it. | 677.169 | 1 |
Description:
Computational science is a quickly emerging field at the intersection of the sciences, computer science, and mathematics because much scientific investigation now involves computing as well as theory and experiment. However, limited educational materials exist in this field. Introduction to Computational Science fills this void with a flexible, readable textbook that assumes only a background in high school algebra and enables instructors to follow tailored pathways through the material. It is the first textbook designed specifically for an introductory course in the computational science and engineering curriculum.The text embraces two major approaches to computational science problems: System dynamics models with their global views of major systems that change with time; and cellular automaton simulations with their local views of how individuals affect individuals. While the text is generic, an extensive author-generated Web-site contains tutorials and files in a variety of software packages to accompany the text.Generic software approach in the textWeb site with tutorials and files in a variety of software packagesEngaging examples, exercises, and projects that explore scienceAdditional, substantial projects for students to develop individually or in teamsConsistent application of the modeling processQuick review questions and answersProjects for students to develop individually or in teamsReference sections for most modules, as well as a glossaryOnline instructor's manual with a test bank and solutions | 677.169 | 1 |
This free undergraduate textbook provides an introduction to proofs,
logic, sets, functions, and other fundamental topics of abstract
mathematics. It is designed to be the textbook for a bridge
course that introduces undergraduates to abstract mathematics, but it
is also suitable for independent study by undergraduates (or
mathematically mature high-school students), or for use as a very
inexpensive supplement to undergraduate courses in any field of
abstract mathematics.
The book is being released online with a Creative Commons
license (Attribution-NonCommercial-ShareAlike 2.0). Although not
in final form, it has already been
used as a textbook for 3 semesters at the University of
Lethbridge. The preliminary version posted in May 2009 is
approximately 220
pages. | 677.169 | 1 |
Kombinasi Naga Dan TrikThe Math Forum @ Drexel University. The Math Forum is the comprehensive resource for math education on the Internet. Some features include a K-12 math expert help service, an extensive database of math ....
The Math Forum @ Drexel University. The Math Forum is the comprehensive resource for math education on the Internet. Some features include a K-12 math expert help service, an extensive database of math .... | 677.169 | 1 |
• Graph up to four equations at once.
• Graphs are labeled.
• You can drag the graph or pinch to zoom in or out.
• Calculator can find roots and intersections.
3) A unit converter. With a tap, you can enter the result of your conversion into the calculator. Currently converts different units of the following: acceleration, angle, area, density, distance, energy, force, mass, power, pressure, speed, temperature, time, and volume. Great for doing physics homework!
4) Constants for scientific calculations -- speed of light, strength of gravity at Earth's surface, etc. etc. etc. Tapping on a constant will insert it into your calculation -- i.e, you don't have to key in the value. Again, great for doing physics homework!
5) It can make a table of the values of any function you care to enter. You can choose the starting x value of the table, as well as how much x increases for each successive row.
6) Forgot the quadratic formula? Or the double-angle formulas for sine and cosine? The math/science reference hits the high points of various subjects. Currently includes algebra, differential and integral calculus, geometry, trigonometry, vectors, vector calculus, and classical mechanics.
I'd love to hear your comments or suggestions. You can write me at [email protected] -- but without the xyz | 677.169 | 1 |
Editorial Reviews
Review
"[The author], through the use of a few clear metamathematical tools, offers the reader a convincing and well-documented historical reconstruction of the rise of the structural image of algebra... [The] book, by reason of its historical approach, could be associated with the so-called 'new historiography of mathematics'. But, unlike some of these works, it is a very good example of the fine balance between historical data and philosophical interpretaion. -- M. Mazzotti, British Journal of the History of Science
--This text refers to an alternate
Paperback
edition.
From the Back Cover
The notion of a mathematical structure is among the most pervasive ones in twentieth-century mathematics. Modern Algebra and the Rise of Mathematical Structures describes two stages in the historical development of this notion: first, it traces its rise in the context of algebra from the mid-nineteenth century to its consolidation by 1930, and then it considers several attempts to formulate elaborate theories after 1930 aimed at elucidating, from a purely mathematical perspective, the precise meaning of this idea.
Part one dicusses the process whereby the aims and scope of the discipline of algebra were deeply transformed, turning it into that branch of mathematics dealing with a new kind of mathematical entities: the "algebraic structures". The transition from the classical, nineteenth-century, image of the discipline to the thear of ideals, from Richard Dedekind to Emmy Noether, and culminating with the publication in 1930 of Bartel L. van der Waerden's Moderne Algebra. Following its enormous success in algebra, the structural approach has been widely adopted in other mathematical domains since 1930s. But what is a mathematical structure and what is the place of this notion within the whole fabric of mathematics? Part Two describes the historical roots, the early stages and the interconnections between three attempts to address these questions from a purely formal, mathematical perspective: Oystein Ore's lattice-theoretical theory of structures, Nicolas Bourbaki's theory of structures, and the theory of categories and functors.
More About the Author
I am a historian of mathematics working at Tel-Aviv University. You can see more about my work, here:
My research has focused on an attempt to understand the historical development of some of the main threads of twentieth-century mathematics. Among other things my research has dealt with the rise of modern algebra, the development of the idea of a mathematical structure, the rise of the modern axiomatic method, the introduction of digital computers into research in pure mathematics, and the works of some leading figures such as David Hilbert, Emmy Noether, Nicolas Bourbaki, and others.
As part of a more general academic interest in history and philosophy of science, in 1999-2009 I was editor of the journal Science in Context (Cambridge University Press), and in 2003-2009 I was director of the Cohn Institute for History and Philosophy of Science at Tel-Aviv University.
I also have a keen interest in Latin American literature. I wrote an introductory overview (in Hebrew) to the prose of Jorge Luis Borges, and also translated several books into Hebrew, including Mario Vargas Llosa's "La Casa Verde".
Corry's work is a truly amazing piece of scholarship. As appreciative as I normally am for histories of mathematics, I was utterly clueless about the techtonic shift in attitudes toward algegraic and structural/relational thinking which has become the hallmark or contemporary mathematics that occurred in the late 19th, early 20th Centuries.
This is an exceptionally careful bit of scholarship that should be of substantial interest to anyone with even a casual interest in mathematics, algebra, and logic. It does not bog the reader down with excessive mathematical detail -- it is, after all, a work in history rather than mathematics 'simpliciter.' Corry develops his argument with a meticulous attention to detail coupled with a well-crafted prose style that makes this book a "MUST HAVE" for anyone with even a tangential concern for the history &/or philosophy of mathematics, or any of the fields related to those. | 677.169 | 1 |
Introduction to Geometric Computing
Computing is quickly making much of geometry intriguing. What is the core set of topics that a practitioner needs to study before embarking on the design and implementation of a geometric system in a specialized discipline? This book attempts to find the answer.
Although geometry has been a flourishing discipline for millennia, most of it has seen either no practical applications or only esoteric ones. Computing is quickly making much of geometry intriguing not only for philosophers and mathematicians, but also for scientists and engineers. What is the core set of topics that a practitioner needs to study before embarking on the design and implementation of a geometric system in a specialized discipline? This book attempts to find the answer. Every programmer tackling a geometric computing problem encounters design decisions that need to be solved. What may not be clear to individual programmers is that these design decisions have already been contemplated by others who have gone down some system design path only to discover (usually much later) that the design decisions that were made were lacking in some respect. This book reviews the geometric theory then applies it in an attempt to find that elusive "right" design.
Table of Contents
Table of Contents
From the contents Introduction.
Euclidean Geometry.
2D Computational Euclidean Geometry.
3D Computational Euclidean Geometry.
Affine Intersections.
Numerical Precision.
Non
Euclidean Geometries.
Spherical Geometry.
Rotations and Quaternions.
Barycentric Coordinates.
Oriented Projective Geometry.
Oriented Projective Intersections.
Grassmannians.
Coordinate
Free Geometry.
Coordinate
Free Geometry.
Filtering.
Introduction to CGAL.
Raster Graphics.
Segment Scan Conversion.
Illumination and Shading.
Raster
Based Visibility.
Ray Tracing.
Graphs.
Graphs: A Comparison of Four Libraries.
Tree and Graph Drawing.
Introduction to the Boost Graph Library.
Geometric and Solid Modeling.
Boundary Representations.
The Halfedge and Euler Operators.
Binary Space Partitioning.
Constructive Solid Geometry.
Nef Polyhedra.
Tetrahedralizations.
Vector Visibility.
Visibility in the Plane.
Visibility in Space.
The PostScript Language.
OpenGL.
the GLOW Toolkit.
Generic Programming | 677.169 | 1 |
Presentations at Professional Conferences
Function Diagrams
Description: An encyclopedic introduction to function diagrams and their pedagogical applications to arithmetic, basic algebra, dynamical systems, and calculus. Much of this illustrated with the help of GeoGebra.
Three Paths to the Quadratic Formula
Description:
A sequence of lessons on parabolas, quadratic functions, and quadratic equations. The unit works well with Algebra 2 students, and includes activities with manipulatives, graphing, and symbol manipulation. These approaches lead to three distinct proofs of the quadratic formula, including a new one.
Bibliography: For the hands-on approach to quadratics and completing the square, see Lab Gear Activities for Algebra 1, by Henri Picciotto, Creative Publications. (It is currently unavailable from the publisher. Contact me if you need it.)
Common Core a closer look
Description:
The Common Core State Standards introduce significant and generally positive changes to the high school math curriculum, but they do not mandate a specific sequence in grades 9-11. This deliberate omission may allow educators to escape the tyranny of tradition, and re-sequence the high school curriculum in a way that is consistent with students' mathematical maturity and brain development, on the one hand, and with the new possibilities offered by advances in pedagogy and by new technologies, on the other. Unfortunately, the large number of standards, and the sequences suggested in the CCSS Appendix undermine these possibilities.
Reimagining High School Math
Description:
High school math classes look very much the same from year to year and from school to school. Yet, other models are possible! In addition, technological advances mean that speed and accuracy are no longer legitimate priorities. We can no longer divorce skills from understanding, nor can we consider obsolete skills to be foundational. What we need is an eclectic mix of approaches that prioritize student learning and habits of mind.
Connecting the Dots
Description:
Accessible hands-on activities on the geoboard (or dot paper) lead to many ideas in arithmetic, geometry, and algebra: equivalent fractions, slope, the Pythagorean theorem, and simplifying radicals. This session is suitable for middle school and high school math teachers who are looking for Common Core-compatible approaches and content which will work with a wide range of students.
Strengthening Mathematics Departments
Audience: This session will be of particular interest to department chairs and anyone involved in school change.
Description: How do we build a culture of teacher collaboration? How do we spread effective approaches across the department? How do we incorporate new ideas into our program? How do we respond to administrative directives, as well as to the needs of our students? What should we ask of our administrators? We will share our tentative answers, and would love to hear yours. Join us in a conversation about what it takes to strengthen a math department.
Teacher Collaboration A key to improving
math instruction
Audience: This session will be of particular interest to department chairs and anyone involved in school change.
Description: Teachers value autonomy and specialization, yet the advantages of collaboration and flexibility are many. So are the complications. Hear the rationale for one department's move to intensive mentoring and the development of a collaborative ethic. I will assess decades of experience in this practice, and reflect upon its impact on teachers, curriculum, pedagogy, and learning.
Escape from the Textbook!
Description:
Almost every off-book activity we plan is well received and leads to greater interest and motivation. Freeing ourselves from set-in-stone curricula allows us to respond to the realities of our classrooms, tackle heterogeneous classes, and implement cooperative and hands-on learning. However pressures of coverage, lack of time, external mandates, and isolation can undermine our efforts. Join an online and in-person network to help each other escape from the textbook for a lesson, a unit, or an entire course. (Co-presented with Carlos Cabana at Asilomar.)
The Geometry of Conic Sections
Description:
Most high school curricula seem to forget that the conic sections are geometric objects! I will explain in several ways that contrary to popular belief, all parabolas have exactly the same shape. I will use interactive software (both 2D and 3D) to construct the conics, prove their reflection properties, and show that they are indeed the result of slicing a cone. Finally, I will explore a question about soccer that unexpectedly leads to a hyperbola.
Nothing Works! The Art of Teaching
Mathematics
Description:
Teaching high school math is a complex endeavor, where apparently contradictory approaches can complement each other: there is no one way that works with all teachers and all students. I will present my mix of techniques for organizing curriculum, sequencing concepts, designing rich activities, working with (somewhat) heterogeneous classes, leading effective class discussions, using cooperative learning groups, assigning homework, assessing student understanding, and other day-to-day concerns.
Infinity An alternate elective after Algebra 2
Description:
Syllabus and highlights of an alternate math elective after Algebra 2, which I have been teaching biennially since 1991: paradoxes involving infinity, proof by contradiction, Cantor's discoveries, mathematical induction, chaos, fractals; connections to literature, philosophy, science, and computer programming. Readily available materials on these subjects tend to be written for either the general public or college students. My presentation will focus on how to make this content accessible in high school.
Description:
Units from a course I developed with my
colleagues in the Math Department at the Urban School of San
Francisco. Our approach is to cover fewer topics in greater depth and to use a variety of learning tools, both manipulative and electronic.
This presentation was initially created by Naoko
Akiyama and Scott Nelson as a one-hour presentation. I joined them to expand it to a three-hour minicourse. Get the
slides.
Bibliography: Much of the material is unpublished, but see
Hands-on approach to quadratics and completing the square: Lab Gear Activities for Algebra 1, by Henri Picciotto,
Creative Publications (It is currently unavailable from the publisher. Contact me if you need it.)
Description:
Make regular polygons, pyramids, prisms, and antiprisms. Explore the relationships between the dodecahedron, the icosahedron, the rhombic triacontahedron, and more... Identify the components of icosahedral symmetry.
A hands-on lab with an amazing manipulative, making connections with many traditional geometry and trigonometry topics. | 677.169 | 1 |
S. S. M. Precalculus
9780495382874
ISBN:
0495382876
Edition: 11 Pub Date: 2007 Publisher: Cengage Learning
Summary: Check your work-and your understanding-with this manual, which provides solutions for all of the odd-numbered exercises in the text. You will also find strategies for solving additional exercises and many helpful hints and warnings.
Cole, Matt is the author of S. S. M. Precalculus, published 2007 under ISBN 9780495382874 and 0495382876. Two hundred sixty S. S. M. Precalculus textbooks are available for sale ...on ValoreBooks.com, twenty eight used from the cheapest price of $5.30, or buy new starting at $32 | 677.169 | 1 |
Pre-Algebra: Equations and Other Tips
Date: 08/30/97 at 11:13:13
From: Erik Sull
Subject: Math Help
This year I am in Pre Algebra. I'm in 8th Grade; can you give me tips
on equations and other things that will be useful for me to know?
Date: 08/31/97 at 15:12:31
From: Doctor Guy
Subject: Re: Math Help
I'll try to give you a few tips about equations.
Remember that mathematics is, for most people, a way of understanding
the world better and solving real problems that come up. To me, the
essence of algebra is translating what appear to be messy problems
involving, perhaps, entire paragraphs of explanations and/or diagrams,
into short, easily-understood symbols (equations). These equations can
be manipulated, using fairly simple rules, allowing you to solve them
and to come up with answers to problems that would be otherwise
extremely difficult to answer. This is why, as a society, we want just
about everybody to have some understanding of algebra at some level.
Of course, it is also necessary that you understand the rules of
arithmetic involving whole numbers, decimals, fractions, and percents.
I'm sure that your pre-algebra class will involve that as well. I do
not know how well you perform in arithmetic, but if you have problems
with that, then be sure to pay attention to the explanations that your
teacher and your textbook give in that area.
It may help if I give an example of a relatively easy problem, to show
how it can be handled via algebra. Here is the problem:
Alfeda Baxter wants to rent a car in order to visit some business
clients in the San Francisco Bay Area next week when she flies in
for a week-long business trip. She calls up two auto-rental
agencies and gets price quotes from each. Dependable Rent-a-Car
will rent her a mid-sized sedan for $143.00 for the week, and
13 cents per mile driven; she has to pay for her own gasoline.
Reliable Automobile Rentals will rent her the same sized car
for $129.00 for the week, and charges 28 cents per mile driven.
They are equally convenient companies about which she has heard
equally good things.
Ms. Baxter is not quite sure how many miles she is going to drive
during the week, but it might be a lot. Since all of these
transportation costs are going to come out of her own pocket, she
wants to hold the cost as low as possible. The question is, at how
many miles does the car from Reliable Auto Rentals become as
expensive as the one from Dependable Rent-a-Car? Based on that,
Ms. Baxter can make a decision on which company to rent from.
That's a pretty long problem, but it can be translated into symbols
pretty easily. The first step is to ask, "what is the question?" The
question is, how many miles would she have to drive so that the RAR
car would cost the same as the DRAC car.
Since the question involves miles, we may as well now do one of the
next important steps, choosing a variable. Let's use M for miles.
Now let's look back at the information about RAR: the cost there is
$129.00 plus 28 cents per mile, or $0.28 times the number of miles.
We can translate that into an expression,
[Cost at RAR, in dollars] = 129.00 + 0.28 * M
Note that I use "*" to mean multiplication. I could also have writtten
129 + .28M (notice that I dropped unnecessary zeroes and omitted the
times sign; that is legal--it still means 28 cents times M).
Now at DRAC, the cost is $143.00 plus 13 cents per mile, or
[Cost at DRAC, in dollars]=143.00 + 0.13 * M.
Remember, the question was, at how many miles are these two costs
equal? Well, to find that out, all we need to do is to write an
equation that states that they ARE equal, and then we use some rules
of algebra (which I will explain as we go along) to find out what M
is, i.e. the number of miles. Here goes:
[Cost at RAR, in dollars] = [Cost at DRAC, in dollars]
Now we substitute equal things for equal things (important rule) and
get
129 + .28 * M = 143 + .13 * M
The next general idea is to get M on one side of the equation and all
the numbers on the other, by multiplying, dividing, subtracting, and
adding the same thing to both sides. The main rule to remember is that
you have to do the same thing to both sides of the equation. I think I
want to get M on the left-hand side of the equation, and get everything
else on the right. First I will subtract 129 from both sides.
129 - 129 + .28*M = 143 - 129 + .13 * M
which simplifies to
0 + .28 * M = 14 + .13 * M
When you add 0 to anything, it stays the same:
.28 * M = 14 + .13 * M.
Another important rule you need to know: Multiplication and division
come before addition and subtraction when evaluating an expression.
Since we do not know what M is, we cannot simply add the 14 and the
.13*M in the previous line to get 14.13*M. I want to get all the M's
on the lefthand side of the equation, so we CAN subtract .13*M from
both sides of the equation:
.28 * M - .13 * M = 14 + .13 * M - .13 * M
We can now use the distributive property (have you learned it?) and
get
(.28-.13)*M = 14 + 0 or
.15 * M = 14
Now we want to find M, so we can divide both sides by .15
.15 * M / .15 = 14/.15
On the left, .15/.15 equals 1 and 1 times M is M; so M = 14 / .15, and
I will now use a calculator to find 14/.15, or M = 93.33333333 miles.
What does this mean? It means that if Ms. Baxter drives 93 and 1/3
miles that week, then the two car companies' prices are the same. If
she drives less than that, then Reliable will be cheaper. If she
drives more than that, then Dependable will be cheaper. So all she has
to do is to estimate how many miles she thinks she will drive, and she
can take her pick.
Now you may not have understood each step; I went rather fast. Perhaps
you see why we take several months teaching this stuff to students--
there is a lot to learn. Good luck this year, and if you have a
specific question you need help with, don't hesitate to e-mail us. You
may also be able to find specific answers to questions in our
archives.
-Doctor Guy, The Math Forum
Check out our web site! | 677.169 | 1 |
Math Resources for Calculus-Based Physics
Math Handouts (pdf).
Calculus is a co-requisite (rather than a prerequisite)
for the calculus-based physics course that I teach at
Saint Anselm College. The math handouts
address calculus topics that students encounter in
the physics course before they see them in their
mathematics course.
Average with Error
Spreadsheet A spreadsheet set up to determine the mean
and standard deviation of a column of values entered by
the user and to display the distribution as a bar graph
along with a scaled gaussian curve determined from the
mean and standard deviation. The curve aids the
user in judging whether the data is part of a gaussian
distribution.
Gaussian Error
Propagation Spreadsheet A spreadsheet set up to determine the
distribution (mean and standard deviation plus a
histogram) for the case of a function of one to six
variables when each of the variables is characterized by
a guassian distribution of known mean and standard
deviation.
Math Skills Video The pdf file
contains an outline of the topics covered on the math
skills video and the mov file is a QuickTime movie in
which the pre-calculus math skills needed for either
an algebra-based or a calculus-based physics course
are reviewed. The mp4 file is the same video in a
different format. Click on the link to play
the video, RIGHT click on it to download. This
video is also avaliable on YouTube at MathSkillsVideo.YouTube.
Math Problems Video The pdf file is a set of 22 pre-calculus
mathematics problems. The mov file is a QuickTime
movie in which the solutions to the mathamatics problems
are presented. The mp4 file is the same video in a
different format. Click on the link to play the
video, RIGHT click on it to download. This video is
also avaliable on YouTube at MathProbsVideo.YouTube.
Calculus ScreenCams A set of six short Lotus ScreenCam movies in
the form of executable (.exe) files compressed into
one zip file. You need to be running Windows to
play these. The movie titles are: Derivatives,
The Chain Rule for the Function of a Function,
Taking the Derivative of a Power Function, The
Chain Rule for the Product of Two Functions,
and Finding the Extrema of a Function . | 677.169 | 1 |
Approximations and inequalities in the calculus of approximations. classification of approximate numbers
(1961)
Tools
"... The ..."
The devised earlier by the author to represent interval relations. First, the MR-diagram is defined together with appropriate graphical notions and con-structions for basic interval relations and operations. Second, diagrammatic constructions for all standard arithme-tic operations are presented. Several examples of the use of these constructions to aid reasoning about various simple, though nontrivial, properties of interval arithmetic are included in order to show how the representation facilitates both deeper understanding of the subject matter and reasoning about its properties.
"... This copy of the thesis has been supplied on condition that anyone who consults it is understood to recognise that its copyright rests with its author and that no quotation from the thesis and no information derived from it may be published without proper acknowledgement. Aston University ..."
This copy of the thesis has been supplied on condition that anyone who consults it is understood to recognise that its copyright rests with its author and that no quotation from the thesis and no information derived from it may be published without proper acknowledgement. Aston University | 677.169 | 1 |
GraphSight is a feature-rich comprehensive 2D math graphing utility with easy navigation, perfectly suited for use by high-school an college math students. The program is capable of plotting Cartesian, polar, table defined, as well as specialty graphs. Importantly, it features a simple data and formula input format, making it very practical for solving in-class and homework problems. The program comes with customizable Axis options, too | 677.169 | 1 |
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