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Find a Picacho ...Start any word problem with labeling the unknown, "Let x = the number of ...." It is this great art that has so greatly advanced all the modern sciences. Think of it as the art that supports the sciences! Algebra 2 comes after Algebra 1,which is the science of linear and quadratic equations (the building blocks of all polynomials)in order to solve problems. ...It is important to understand the basic concepts of algebra before continuing to Algebra II. Students will learn to solve equations and inequalities. They will become proficient in factoring and simplifying algebraic fractions
Helping Students Pre-AlgebraFacilitate students transition from arithmetic to algebra! Includes step-by-step instructions with examples, practice problems using the concepts, real-life applications, a list of symbols and terms, tips, and answer keys. Supports NCTM standards.
My Advice to a New Math 175 Student: Go to every single class!!!! Missing one class will put you behind. Sleeping an extra hour is not worth the hours you will have to put in to catch up. However, just being in class isn't enough. Pay attention and follow along. Don't be afraid to ask questions even if you think you are the only one that doesn't know the answer. You are in the class for your benefit, not your classmates. Also, make sure you attempt all of the assignments and do them the day that you talked about that particular subject. Don't tell yourself you'll do it some other time because you will only fall behind and all of the assigned sections will start piling up on you. If you get stuck on a problem, just ask him to go over it in class the next day. It may take awhile to do the assigned problems and you probably won't feel like doing them, but push through it anyway because it pays off in the end. It's a great feeling to encounter a problem on an exam that you actually know how to do. In addition to all of the above, there is always extra help. I was only able to attend one Tuesday night review session but it is very beneficial if you have any questions on assigned problems that weren't covered in class. What helped me the most though was utilizing his office hours to ask him questions. Going over a problem one- on-one made me a lot more confident that I knew what I was doing because I was forced to listen. He was always available during his office hour times and you could also make an appointment if you needed to. Using these outside resources gets you more involved in the class and your chance of succeeding increases. One more thing...be prepared to put a lot of time and effort into this class. It isn't easy, but it is possible to do well. It's also kind of amazing how all of the application problems that you encounter can actually be used in real life. It's even more rewarding when you actually know how to solve those problems!
TRIANGLE Triangle that are not on the standard keyboard may be entered using a braille keyboard option or several menu selection options. This scientific math program features a math/science word processor, a graphing calculator, a viewer for y versus x plots, a table viewer, and a program for audio and/or braille-assisted reading of tactile figures on an external digitizing pad (the Touch-and-Tell program). The graphing calculator feature displays graphs and functions in visual, auditory, and tactile formats. It permits evaluation of most standard math expressions. Results are returned to the scratchpad buffer and may be cut and pasted to other documents. The calculator will also evaluate functions y versus x that can be viewed in audio using a tone graph viewer that provides the user with a quick semi-quantitative overview. A moving icon on the screen provides similar information for a deaf blind user. The table viewer feature allows users to read, navigate, and edit complex tables in an easy-to-use manner. Tables can be read cell by cell or line by line. The latter option is useful for small tables being read in braille, but the first is usually preferable when speech synthesis is used or when tables are large. Tables may also be created or edited in this viewer. The word processor has five different document buffers that provide basic editing capabilities, including search and cut and paste operations. In the word processor, the keyboard or any assistive device/software that emulates a keyboard may be used for input. Output may be viewed visually on the DOS text screen; audibly using a screen-reading program and external voice synthesizer for text and the PC speaker or a SB16-compatible sound output for other audio; tactually using a braille screen access program and external refreshable braille display; or using any combination of the above simultaneously. The Touch-and-Tell program provides alternate-mode display for information presented visually in figures. The user selects an object or region on a figure that is mounted on a digitizing tablet. The touch-and-tell program then displays textual information about that object or region. This information can be read visually, audibly, or in braille. This scientific math program supports the Nomad tablet, the Edmark Touch Window, and the MagicTouch touch screen digitizing tablets. The Objectif program was made to facilitate preparation of the files and tactile figures used with this viewer. COMPATIBILITY: For use with IBM and compatible computers. SYSTEM REQUIREMENTS: For voice output, a DOS screen reading program such as Vocal-Eyes versions 2.2 and 3.0 or JAWS for DOS 2.3; a speech synthesizer such as Apollo, DECtalk Express, DoubleTalk, Keynote Gold, or MultiVoice, or a device with a speech synthesizer built into its functionality such as Freedom Scientific's Type 'n Speak and Braille 'n Speak devices or the American Printing House for the Blind's Nomad touch tablet; and drivers for the synthesizer. For braille output, a braille screen reader that supports a dictionary option for all 256 DOS screen characters and a braille display that permits downloading of braille tables. The GS8 braille table for representing the GS braille code in DOS characters may be loaded into the TSI Gateway screen reader that is included, with the permission of TSI, in the Triangle distribution files, and this screen reader can be used with any 8-dot TSI Navigator or Power Braille refreshable braille display. OPTIONS: A CD version of this software is available from the manufacturer on request, or it may be downloaded from the the manufacturer's web site. Notes: Primary funding for the Science Access Project comes from the National Science Foundation. ** Triangle may be freely distributed as long as no fee is charged and all of the files are kept together and intact
Rent Textbook Buy Used Textbook eTextbook 180 day subscription $108.5922 Student Support Edition of Introductory Algebra: An Applied Approach, 7/e, brings comprehensive study skills support to students and the latest technology tools to instructors. In addition, the program now includes concept and vocabulary review material, assignment tracking and time management resources, and practice exercises and online homework to enhance student learning and instruction. With its interactive, objective-based approach, Introductory Algebra provides comprehensive, mathematically sound coverage of topics essential to the beginning algebra course. The Seventh Edition features chapter-opening Prep Tests, real-world applications, and a fresh design--all of which engage students and help them succeed in the course. The Aufmann Interactive Method (AIM) is incorporated throughout the text, ensuring that students interact with and master concepts as they are presented. Table of Contents Note: Each chapter begins with a Prep Test and concludes with a Chapter Summary, Review Exercises, and a Chapter Test Chapters 2-12 include Cumulative Review Exercises AIM for Success Prealgebra Review Introduction to Integers Addition and Subtraction of Integers Multiplication and Division of Integers Exponents and the Order of Operations Agreement Factoring Numbers and Prime Factorization Addition and Subtraction of Rational Numbers Multiplication and Division of Rational Numbers Concepts from Geometry Focus on Problem Solving: Inductive Reasoning Projects and Group Activities: The +/- Key on a Calculator Variable Expressions Evaluating Variable Expressions Simplifying Variable Expressions Translating Verbal Expressions into Variable Expressions Focus on Problem Solving: From Concrete to Abstract Projects and Group Activities: Prime and Composite Numbers
By Linda Smail - Mathematics is the foundation of all sciences, but most students have problems learning mathematics. Although Students' success in life is related to their success in learning, many of them would not take a course in math if they didn't need to satisfy the university' core requirement. Teaching mathematics doesn't depend on geographical regions or gender; it depends on good math teachers. Based on conversations with hundreds of students over many years from different regions, I have observed that poor understating of mathematics begins when a student goes two or three years in a row without an excellent math teacher. Many students can survive bad teaching for a year, but very few can go longer. Students who have continued to enjoy math can remember excellent teachers and describe their lessons, usually back to the mid-elementary years; I certainly can. I believe that any educative adult can do mathematics and that everyone can learn but may learn differently. There is no difference in understanding mathematics between males and females, and as a female, I must say that once all chances are given and barriers are removed, females can show themselves to be equal, and perhaps even better, to men in quantitative reasoning. I love mathematics and I love teaching students courses from elementary algebra to differential equations. I have often found myself filling napkins with computations while discussing math over dinner or lunch. I do talk a lot about math, think and write about math, but students rarely do. For this reason and many others, I advise you, as students, to not let unpleasant experiences in mathematics prevent you from understanding mathematics, keep positive attitudes towards math, ask questions, practice regularly, and not to just read over notes but actually do the math. I hope that my knowledge, my love of math, and my love of teaching mathematics will result in students who will appreciate studying and understanding mathematics. Seeing the smile on my students' faces when they finally understand mathematics is my reward.
This book is designed for teachers of children in grades 3 to 7. It shows how Vedic Mathematics can be used in a school course but does not cover all school topics (see contents). The book can be used for teachers who wish to learn the Vedic system or to teach courses on Vedic mathematics for this level. The Manual contains many topics that are not in the other Manuals that are suitable for this age range and many topics that are also in Manual 2 are covered in greater detail here. Please note that these Manuals do not form a sequence: there is some overlap between the three books. PREFACE This Manual is the first of three (elementary, intermediate and advanced) Manuals which are designed for adults with a basic understanding of mathematics to learn or teach the Vedic system. So teachers could use it to learn Vedic Mathematics, though it is not suitable as a text for children (for that the Cosmic Calculator Course is recommended). Or it could be used to teach a course on Vedic Mathematics. The sixteen lessons of this course are based on a series of one week summer courses given at Oxford University by the author to Swedish mathematics teachers between 1990 and 1995. Those courses were quite intensive consisting of eighteen, one and a half hour, lessons. All techniques are fully explained and proofs are given where appropriate, the relevant Sutras are indicated throughout (these are listed at the end of this Manual) and, for convenience, answers are given after each exercise. Cross-references are given showing what alternative topics may be continued with at certain points. It should also be noted that the Vedic system encourages mental work so we always encourage students to work mentally as long as it is comfortable. In the Cosmic Calculator Course pupils are given a short mental test at the start of most or all lessons, which makes a good start to the lesson, revises previous work and introduces some of the ideas needed in the current lesson. In the Cosmic Calculator course there are also many games that help to establish and promote confidence in the ideas used here. Some topics will be found to be missing in this text: for example, there is no section on area, only a brief mention. This is because the actual methods are the same as currently taught so that the only difference would be to give the relevant Sutra(s). INTRODUCTION Vedic Mathematics is an ancient system of mathematics which was rediscovered early last century by Sri Bharati Krsna Tirthaji (henceforth referred to as Bharati Krsna). The Sanskrit word "veda" means "knowledge". The Vedas are ancient writings whose date is disputed but which date from at least several centuries BC. According to Indian tradition the content of the Vedas was known long before writing was invented and was freely available to everyone. It was passed on by word of mouth. The writings called the Vedas consist of a huge number of documents (there are said to be millions of such documents in India, many of which have not yet been translated) and these have recently been shown to be highly structured, both within themselves and in relation to each other (see Reference 2). Subjects covered in the Vedas include Grammar, Astronomy, Architecture, Psychology, Philosophy, Archery etc., etc. A hundred years ago Sanskrit scholars were translating the Vedic documents and were surprised at the depth and breadth of knowledge contained in them. But some documents headed "Ganita Sutras", which means mathematics, could not be interpreted by them in terms of mathematics. One verse, for example, said "in the reign of King Kamse famine, pestilence and unsanitary conditions prevailed". This is not mathematics they said, but nonsense. Bharati Krsna was born in 1884 and died in 1960. He was a brilliant student, obtaining the highest honours in all the subjects he studied, including Sanskrit, Philosophy, English, Mathematics, History and Science. When he heard what the European scholars were saying about the parts of the Vedas which were supposed to contain mathematics he resolved to study the documents and find their meaning. Between 1911 and 1918 he was able to reconstruct the ancient system of mathematics which we now call Vedic Mathematics. He wrote sixteen books expounding this system, but unfortunately these have been lost and when the loss was confirmed in 1958 Bharati Krsna wrote a single introductory book entitled "Vedic Mathematics". This is currently available and is a best-seller (see Reference 1). There are many special aspects and features of Vedic Mathematics which are better discussed as we go along rather than now because you will need to see the system in action to appreciate it fully. But the main points for now are: 1) The system rediscovered by Bharati Krsna is based on sixteen formulae (or Sutras) and some sub-formulae (sub-Sutras). These Sutras are given in word form: for example By One More than the One Before and Vertically and Crosswise. In this text they are indicated by italics. These Sutras can be related to natural mental functions such as completing a whole, noticing analogies, generalisation and so on. 2) Not only does the system give many striking general and special methods, previously unknown to modern mathematics, but it is far more coherent and integrated as a system. 3) Vedic Mathematics is a system of mental mathematics (though it can also be written down). Many of the Vedic methods are new, simple and striking. They are also beautifully interrelated so that division, for example, can be seen as an easy reversal of the simple multiplication method (similarly with squaring and square roots). This is in complete contrast to the modern system. Because the Vedic methods are so different to the conventional methods, and also to gain familiarity with the Vedic system, it is best to practice the techniques as you go along. CONTENTS PREFACE LESSON 1COMPLETING THE WHOLE Introduction The Ten Point Circle Multiples of Ten Deficiency from Ten Deficiency and Completion Together Mental Addition Completing the Whole Columns of Figures By Addition and By Subtraction Subtracting Numbers Near a Base Digit Sum Check for Division The First by the First and the Last by the Last The First by the First The Last by the Last Divisibility by 4 Divisibility by 11 Remainder after Division by 11 Another Digit Sum Check LESSON 9BAR NUMBERS Removing Bar Numbers All from 9 and the Last from 10 Subtraction Creating Bar Numbers Using Bar Numbers LESSON 10SPECIAL MULTIPLICATION Multiplication by 11 Carries Longer Numbers By One More than the One Before Multiplication by Nines The First by the First and the Last by the Last Using the Average Special Numbers Repeating Numbers Proportionately Disguises VEDIC MATHEMATICS MANUAL ELEMENTARY LEVEL ¯Vedic Mathematics was reconstructed from ancient Vedic texts early last century by Sri Bharati Krsna Tirthaji (1884-1960). It is a complete system of mathematics which has many surprising properties and applies at all levels and areas of mathematics, pure and applied. ¯It has a remarkable coherence and simplicity that make it easy to do and easy to understand. Through its amazingly easy methodscomplex problems can often be solved in one line. ¯The system is based on sixteen word-formulae (Sutras) that relate to the way in which we use our mind. ¯The benefits of using Vedic Mathematics include more enjoyment of maths, increased flexibility, creativity and confidence, improved memory, greater mental agility and so on. ¯This Elementary Manual is the first of three designed for teachers who wish to teach the Vedic system, either to a class or to other adults/teachers. It is also suitable for anyone who would like to teach themselves the basic Vedic methods.
Specification Aims To prove some basic results in number theory. Brief Course Description The distribution of the prime numbers appears to be rather irregular, although they certainly thin out as x increases. How can we describe the distribution? How many primes are there less than x? The key to all this is the Riemann Zeta function, the Riemann zeros, and the famous Explicit Formulas in Number Theory. The Riemann Formula counts up precisely the number of primes less than x. This formula contains oscillatory terms corresponding to the Riemann zeros, and gives rise to the "music of the primes". Syllabus The Euler product. The Hadamard product. The functional equation. The trivial zeros of the zeta function. [6] The von Mangoldt explicit formula. The oscillatory terms. [6] The Riemann explicit formula. The oscillatory terms. The Riemann approximation to π(x). The prime number theorem. The largest known prime. The distribution of prime numbers. The music of the primes.[6] Textbooks J. Stopple, A Primer of Analytic Number Theory. Cambridge, 2003 M. du Sautoy, The Music of the Primes. Fourth Estate 2003. Teaching and learning methods Two lectures each week and a weekly examples class. In addition students should expect to do at least four hours private study each week for this course unit (and seven for MATH41022).
Math Composer is a powerful yet easy to use tool for creating all your math documents. It is a simple way for math teachers and instructors to create math worksheets, tests, quizzes, and exams. This...
Mathematics at Huntington The Mathematics Department believes that there is a level of mathematics study available to every student. The mathematics program emphasizes computational skills, problem-solving techniques, and mathematical structure. Students learn skills and concepts, and practice analytical and critical thinking. They study the uses of the computers, statistics and measurement. Algebraic and geometric structure, logic, and analysis provide a sequential program for the college-bound. The decisions made about the courses taken in high school affect each student for the rest of their lives. The teaching faculty, the school counselor, the school administrators, and parents can all advise in the course selection process, but the student should be fully involved in the final decision and be ready to bear the responsibility for that decision. For this reason it is imperative to read course descriptions with considerable thought and care. In selecting your courses for next year, several factors should be considered. These factors include graduation requirements and your job or school plans for the future. All students are required to complete successfully three credits of mathematics and demonstrate a minimum level of proficiency on a New York State exam.
This paper can be used by students in Mathematics as an introduction to the fundamental ideas of MATHEMATICA PACKAGE and as a foundation for the development of more advanced concepts in MATHEMATICA. Study of this paper promotes the development of Basic Programming skills in Mathematica.
Real Analysis A First Course 9780201437270 ISBN: 0201437279 Edition: 2 Pub Date: 2001 Publisher: Addison-Wesley Summary: Real Analysis, 2/e is a carefully worded narrative that presents the ideas of elementary real analysis while keeping the perspective of a student in mind. The order and flow of topics has been preserved, but the sections have been reorganized somewhat so that related ideas are grouped together better. A few additional topics have been added; most notably, functions of bounded variation, convex function, numerical met...hods of integration, and metric spaces. The biggest change is the number of exercises; there are now more than 1600 exercises in the text.[read moreReal Analysis, 2/e is a carefully worded narrative that presents the ideas of elementary real analysis while keeping the perspective of a student in mind. The order and flow [more] Real Analysis, 2/e is a carefully worded narrative that presents the ideas of elementary real analysis while keeping the perspective of a student in mind. The order and flow of topics has been preserved, but the se Edition. Great for students on budget.
An introduction to the various branches of mathematics within the historical framework of their origin. Such topics as sets, systems of numeration (ancient and modern), logic (Aristotelian and symbolic), geometry (Euclidean plane and solid, non-Euclidean, analytic), arithmetic (simple and modular), probability, statistics and computers are explored from the standpoint of their development and impact on modern living. Does not fulfill the mathematics requirement for elementary education majors. Does not satisfy the general education requirement for mathematics. Prerequisite: Satisfactory math placement test score or a grade of P4 in DVM 0050 [DVM 005] or DVM 0070 [formerly DVM 007]. Book: As determined by the Mathematics Department. Outcomes: Upon successful completion of the course, each student should be able to: 1. Compare and/or contrast the mathematics of the ancient civilizations of Egypt, Mesopotamia, Greece, India and Persia with that of the present, especially with respect to the foundations of arithmetic, algebra, geometry, trigonometry, number theory, logic and calculus. 2. Discuss the relationship between mathematics and the natural biological sciences, the social sciences and the humanities. 3. Apply mathematics to daily existence, in skill areas such as probability, statistics, calculus and analytic geometry. 4. Use the hand-held calculator and the microcomputer to solve appropriate mathematical problems.
Matrices -- Identity and Inverse Matrices1.12008/12/15 07:09:09.311 US/Central2009/01/09 07:26:27.592 US/CentralKennyFelderKFelder@RaleighCharterHS.orgKennyFelderKFelder@RaleighCharterHS.orgAlgebra 2FelderIdentityInverseMatricesTeacher's GuideA teacher's guide to identity and inverse matrices.This may, in fact, be two days masquerading as one—it depends on the class. They can work through the sheet on their own, but as you are circulating and helping, make sure they are really reading it, and getting the point! As I said earlier, they need to know that [I] is defined by the property AIIAA, and to see how that definition leads to the diagonal row of 1s. They need to know that A-1 is defined by the property AA1A1=I, and to see how they can find the inverse of a matrix directly from this definition. That may all be too much for one day.I also always mention that only a square matrix can have an [I]. The reason is that the definition requires I to work commutatively: AI and IA both have to give A. You can play around very quickly to find that a 23 matrix cannot possibly have an [I] with this requirement. And of course, a non-square matrix has no inverse, since it has no [I] and the inverse is defined in terms of [I]!Homework:"Homework—The Identity and Inverse Matrices"
Physics: Fundamentals and Problem Solving for the iPad #physicsed #edtech I'm thrilled to announce that Physics: Fundamentals and Problem Solving has been released for the iPad today. This book, which is for the iPad only, is an algebra-based physics book featuring hundreds of worked-out problems, video mini-lessons, and other interactive elements designed for the introductory physics student. This entry was posted by admin on June 21, 2012 at 1:20 pm, and is filed under APlusPhysics. Follow any responses to this post through RSS 2.0.You can skip to the end and leave a response. Pinging is currently not allowed.
(3) . . . gain knowledge and skills to formalize their ideas and express them with a full mathematical rigour. Content:: (1) Systems of Linear Equations. (2) Matrices. (3) Determinants (4) Vector Spaces (5) Inner Product Spaces. (6) Linear Transformations. (7) Eigenvalues and Eigenvectors. Course Philosophy and Procedure: Just keep this simple principle in mind: If you are not enjoying this course, if the work is not fun, then something most be wrong. Talk to me right away! This course involves a lot of concepts that easily translate into fairly straightforward (but sometimes lengthy) calculations. Geometry, i.e., visualization is essential. There are also some topics that involve a greater level of abstraction yet there will be plenty of exercises available to check and enhance your understanding of those concepts. You will find that the concepts learned in this course can be applied to many problems in Mathematics and Science. You should plan to reserve a significant amount of time to study for this course. The material is easy, but the nature of the exercises is such that they are going to be time consuming. Being focused is of utmost importance. Don't rush in doing the problems! Grading will consist of three exams (two during the semester and the final exam) worth 100 points each. The homework and chapter projects will total to 200 points. My grading scale is A=90%, AB=87%, B=80%, BC=77%, C=70%, CD=67%, D=60%. Final Exam: Thursday, May 11, 3:00 - 5:00. Americans with Disability Act:: If you are a person with a disability and require any auxiliary aids, services or other accommodations for this class, please see me and Wayne Wojciechowski in Murphy Center Room 320 (796- 3085) within ten days to discuss your accommodation needs.
0123747511 9780123747518 0080886256 9780080886251 Elementary Linear Algebra: Elementary Ancillary list: * Maple Algorithmic testing- Maple TA- * Companion Website- * Online Instructors Manual- * Ebook- * Online Student Solutions Manual- a wide variety of applications, technology tips and exercises, organized in chart format for easy referenceMore than 310 numbered examples in the text at least one for each new concept or applicationExercise sets ordered by increasing difficulty, many with multiple parts for a total of more than 2135 questionsProvides an early introduction to eigenvalues/eigenvectorsA Student solutions manual, containing fully worked out solutions and instructors manual available «Show less Elementary Linear Algebra: Elementary Linear Algebra develops and explains in careful detail the computational techniques and fundamental theoretical results central to a first course in linear algebra. This highly acclaimed text focuses on developing the abstract
Algebra And Trigonometry With Analytic Geometry - 13th edition Summary: Clear explanations, an uncluttered and appealing layout, and examples and exercises featuring a variety of real-life applications have made this book popular among students year after year. This latest edition of Swokowski and Cole's ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY retains these features. The problems have been consistently praised for being at just the right level for precalculus students. The book also provides calculator examples, including specific keystrokes that...show more show how to use various graphing calculators to solve problems more quickly. Perhaps most important--this book effectively prepares readers for further courses in mathematics
College Algebra A study of functions, starting with the definition and focusing on the use of functions in all forms to model the real world. Includes comparing linear and nonlinear functions, transforming functions, looking at polynomial and rational functions globally and locally, models of growth and decline and systems of equations. Student needs to be proficient in Intermediate Algebra.
Sequences and Functions Unit 7 Common Core Says... In descriptive modeling, a model simply describes the phenomena or summarizes them in a compact form. Graphs of observations are a familiar descriptive model—for example, graphs of global temperature and atmospheric CO2 over time. Analytic modeling seeks to explain data on the basis of deeper theoretical ideas, albeit with parameters that are empirically based; for example, exponential growth of bacterial colonies (until cut-off mechanisms such as pollution or starvation intervene) follows from a constant reproduction rate. Functions are an important tool for analyzing such problems. F.BF.1a Write a function that describes a relationship between two quantities. (Emphasize linear, quadratic, and exponential functions). Determine an explicit expression, a recursive process, or steps for calculation from a context. Video explaination F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.? F.LE.1a Prove that linear functions grow by equal differences over equal intervals; and that exponential functions grow by equal factors over equal intervals. F.LE.1b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. F.LE.1.c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-?-output pairs (include reading these from a table). Please sign up for the newsletter to receive assessments. It is my small attempt to keep them out of the hands of the kids :)
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* The latest version of the popular encyclopedia Encarta Premium 2009 contains even more relevant and accurate background information and multimedia materials that could be useful to students in their studies. * Package Microsoft Math - an extensive set of tools, guidelines and manuals designed to address various mathematical, algebraic and trigonometric tasks. * The universal means of mathematical data visualization Graphing Calculator offers all you need to build a three-and two-dimensional graphs, and solving equations. * Library Equation Library contains more than one hundred common equations and formulas that can be used to solve various problems. * Pack Learning Essentials for Students provides a set of templates and reference materials that will expand the functionality of applications Microsoft Office Word, PowerPoint and Excel and use them to create and design written papers, presentations and reports. * The package Microsoft Student also includes a full-fledged electronic dictionary that will simplify the translation into French, German, Italian and Spanish, and allow to prepare reports, term papers and other materials on one of these languages, thanks to the special templates and tools Learning Essentials for Students.
Hey Matt, Also post a brief review of the material especially covering some aspects such as - the difficulty level, the variety, explantions - if you can! That will be indeed helpful! _________________
MATH 0900 Basic Arithmetic Lecture/Lab/Credit Hours 3 - 0 - 3 This course addresses study skills for mathematics, student learning styles, and math anxiety. Topics include operations with whole numbers, properties of the real number system, and an introduction to fractions. NOTE: MATH 09XX courses carry credit for MCC only; the credit does not transfer nor does it apply toward graduation Prerequisites (1) Within two years prior to beginning the course, MCC placement test
Art Reed has more than twelve years of Saxon teaching experience at a rural high school in Enid, Oklahoma. Using John Saxon's math books, he taught high school mathematics from Algebra ½ through Calculus . He was instrumental in raising the school's average math ACT scores from 13.4 to 21.9 in just four years. The school's scores were above the national average of 20.2 – and this was more than twenty years ago! Besides exceeding the national averages in math ACT scores, the high school also had more than ninety percent of their seniors taking math courses that were above algebra one. Additionally, the actual number of high school students taking the ACT tests had tripled! Sometime later, while teaching mathematics at the local university, he asked for and received permission from the university to use John Saxon's Algebra 2 textbook for the nontraditional students who were entering the university. These students had failed the college's math entrance exam. They needed a non-credit algebra course that would allow them to review high school algebra so they could understand and pass the credited college algebra course the following year. More than ninety percent of the adult students who enrolled in the non-credit Algebra 2 courses received a grade of C or better. They successfully passed the university's credited algebra course their first time the following year. Art Reed retired from classroom teaching in 1999. Because of his hands-on experience and success with teaching from John Saxon's math books, he was asked to assume duties as the curriculum advisor in the Home School Division of Saxon Publishers, for the upper level math textbooks from Math 76 through Calculus and Physics. His experiences and depth of knowledge regarding John Saxon's math curriculum have enabled him to advise and assist parents and educators at all levels on how to successfully get the most from their Saxon textbooks and to ensure that their students received a quality education in mathematics. During the past several decades, Art Reed has become well known for his sound curriculum advice to homeschool parents. He has come to be known as an experienced curriculum advisor for John Saxon's math textbooks from Math 76 through Calculus and Physics . Homeschool parents using Saxon math textbooks have come to ask for him by name to seek his valued advice and assistance. He has established the same professional reputation among school administrators and teachers for his assistance in helping them establish a quality Saxon math program within their school districts. Art Reed was born in Chicago, Illinois, in 1936. He attended private Lutheran schools in Chicago through high school, graduating in 1954. In the fall of that same year, he enlisted in the United States Army. He spent more than twenty-seven years in the U.S. Army, both enlisted and commissioned service, retiring as a Lieutenant Colonel in 1981. While on active duty, he served with the U.S. Army Special Forces, including two combat tours of duty with them in the Republic of Vietnam (1963 – 1965). While assigned to the 5th Special Forces Group in Vietnam, he received the Bronze Star, the Purple Heart, and the Vietnamese Cross of Gallantry with palm. He also was awarded the Air Medal and the Combat Infantryman's Badge (CIB). Among his other military decorations are the Soldiers Medal [awarded for heroism not involving direct contact with an armed enemy], the Legion of Merit, the Presidential Unit Citation, and the Meritorious Service Medal. He is a Master Parachutist with more than 200 parachute jumps. Art Reed's non-combat military assignments included duties in the U.S. Army Research Office, Office of the Chief of Research and Development, the Office of the Army Chief of Staff, and the Congressional Liaison Office in Washington, D.C. He is a qualified nuclear weapons officer, as well as an engineer and mathematician, receiving his Bachelor of Science degree from Oklahoma State University, and later earning a second degree in mathematics from Phillips University. Art and his wife Judy have been married for more than forty years. They reside in Enid, Oklahoma, as do their two daughters and their families, which include five grandchildren.
John Saxon's preface to Algebra 2 Preface to Saxon Algebra 2 This is the second edition of the second book in an integrated three-book series designed to prepare students for calculus. In this book we continue the study of topics from algebra and geometry and begin our study of trigonometry. Mathematics is an abstract study of the behavior and interrelationships of numbers. In Algebra 1, we found that algebra is not difficult—it is just different. Concepts that were confusing when first encountered became familiar concepts after they had been practiced for a period of weeks or months—until finally they were understood. Then further study of the same concepts caused additional understanding as totally unexpected ramifications appeared. And, as we mastered these new abstractions, our understanding of seemingly unrelated concepts became clearer. Thus mathematics does not consist of unconnected topics that can be filed in separate compartments, studied once, mastered, and then neglected. Mathematics is like a big ball made of pieces of string that have been tied together. Many pieces touch directly, but the other pieces are all an integral part of the ball, and all must be rolled along together if understanding is to be achieved. A total assimilation of the fundamentals of mathematics is the key that will unlock the doors of higher mathematics and the doors to chemistry, physics, engineering, and other mathematically based disciplines. In addition, it will also unlock the doors to the understanding of psychology, sociology, and other nonmathematical disciplines in which research depends heavily on mathematical statistics. Thus, we see that mathematical ability is necessary in almost any field of endeavor. Thus, in this book we go back to the beginning –to signed numbers—and then quickly review all of the topics of Algebra 1 and practice these topics as we weave in more advanced concepts. We will also practice the skills that are necessary to apply the concepts. The applicability of some of these skills, such as completing the square, deriving the quadratic formula, simplification of radicals, and complex numbers, might not be apparent at this time, but the benefits of having mastered these skills will become evident as our education continues. We will continue our study of geometry in this book. Lessons on geometry appear at regular intervals, and one or two geometry problems appear in every homework problem set. We begin our study of trigonometry in Lesson 43 when we introduce the fundamental trigonometric ratios—the sine, cosine, and tangent. We will practice the use of these ratios in every problem set for the rest of the book. The long-term practice of the fundamental concepts of algebra, geometry, and trigonometry will make these concepts familiar concepts and will enable an in-depth understanding of their use in the next book in the series, a pre-calculus book entitled Advanced Mathematics. Problems have been selected in various skill areas, and these problems will be practiced again and again in the problem sets. It is wise to strive for speed and accuracy when working these review problems. If you feel that you have mastered a type of problem, don't skip it when it appears again. If you have really mastered the concept, the problem should not be troublesome; you should be able to do the problem quickly and accurately. If you have not mastered the concept, you need the practice that working the problem will provide. You must work every problem in every problem set to get the full benefit of the structure of this book. Master musicians practice fundamental musical skills every day. All experts practice fundamentals as often as possible. To attain and maintain proficiency in mathematics, it is necessary to practice fundamental mathematical skills constantly as new concepts are being investigated. And, as in the last book, you are encouraged to be diligent and to work at developing defense mechanisms whose use will protect you against every humans' seemingly uncanny ability to invent ways to make mistakes. One last word. There is no requirement that you like mathematics. I am not especially fond of mathematics—and I wrote the book—but I do love the ability to pass through doors that knowledge of mathematics has unlocked for me. I did not know what was behind the doors when I began. Some things I found there were not appealing while others were fascinating. For example, I enjoyed being an Air Force test pilot. A degree in engineering was a requirement to be admitted to test pilot school. My knowledge of mathematics enabled me to obtain this degree. At the time I began my study of mathematics, I had no idea that I would want to be a test pilot or would ever need to use mathematics in any way. I thank Tom Brodsky for his help in selecting geometry problems for the problem sets. I thank Joan Coleman and David Pond for supervising the preparation of the manuscript. I thank Margaret Heisserer, Scott Kirby, John Chitwood, Julie Webster, Smith Richardson, Tony Carl, Gary Skidmore, Tim Maltz, Jonathan Maltz, and Kevin McKeown for creating the artwork, typesetting, and proofreading. I again thank Frank Wang for his valuable help in getting the first edition of this book finalized and publisher Bob Wroth for his help in getting the first edition published. John Saxon Norman, Oklahoma Beautiful. The third editions of the Saxon books seem to have done away with John Saxon's prefaces; at least, that's the case with the 3rd edition of Algebra 1/2. Thanks to our ktm Book Fairy, I have a copy of the 2nd edition of Algebra 1/2, so I'll post that preface, too. The books themselves don't seem to have been changed in other bad direction. If you're interested in buying the 2nd edition, though, Rainbow Resource seems still to have them. So does Seton Books. I'm sure other homeschooling stores do as well. ''I'm a professional mathematician, and I myself very often use mathematical methods that I understand only imprecisely,'' he said. ''It is while I use them that I begin to understand. After a while, the use and the understanding are mutually supporting.'' Carolyn has said more than once that she believes in teaching procedures first. Conceptual understanding follows. (I can't find any of her posts on this, so if I've misremembered I'll delete this.) I was always a little skeptical of this, although my working assumption is that where Carolyn and I disagree, Carolyn is right. I've now spent enough time working my way through Saxon to see what Saxon, Schmid, and Carolyn are talking about. When you practice a procedure you don't understand over and over and over again, at some point it "naturalizes." It seems right and inevitable. And it makes sense. John Saxon stresses this idea in book after book. Math isn't hard; it's different. It's unfamiliar. When you've done so much math that it no longer seems strange, it starts to seem easy — or at least not harder than other subjects. Of course, the irony is that this naturalizing process leaves me unable to explain procedures to someone for whom math is still strange. It does, however, make me understand why "math brains" tend to say things like, "It just is" when I ask for an explanation! I'll add that Saxon (and probably Carolyn & Schmid, too) rarely teaches a concept stripped of all meaning or explanation — though he does do so far more often in Algebra 1 than in the earlier books. A student using Algebra 1 must take a lot on faith. If nothing else, meaning helps memory; it's easier to remember a procedure you understand. (I have references for this observation, but don't want to spend the time to dig them up just now.) I'd be willing to bet that meaning increases student motivation, too. I recall Steve H saying that students always want an explanation if they can get one. (Steve - am I remembering that correctly?) Every one of Saxon's explanations in 6-5 through 7-6 has been pure pleasure to read, and has made me want to learn more math. In contrast, my motivation sometimes flags as I work with Saxon's highly abstract Algebra 1, my motivation sometimes flags.
7th Grade Algebra PDF7thGrade Math Placement Many parents are interested in the process of how incoming 7th graders are placed into Algebra I. More than 400 students enroll in Granite Oaks Middle School from the five feeder elementary 7thGrade Math Algebra Linear Equations (7thMathAlgebraLinearEquat) 1. 5. You are buying a sweater for your mother that is marked down 10%. If the sweater's sale price is $29.00, how much did it cost originally? A. $3.22 B. $25.78 C. $32.22 D. $36.36 6. Grade 7 Algebra & Functions a. Write as a mathematical expression: 1. 5 less than R 2. One fourth as large as the area, where the area = A 3. 25 more than Z b. Write as a mathematical equation: 1. Y is 3 more than twice the value of X 2. 2 algebra The operationthat reversesthe effect of another 3 transitive An equation of the form f(x)=0 where f is a polynomial 4 algebraic equation A diagram or graph using anumber line to show the distribution ofset data ... 7thGrade Math Vocabulary TEST 1 preparation for taking Transitional Algebra in the eighth grade and Algebra I in the ninth grade. Introduction to Pre-Algebra focuses on essential 7thgrade standards that include order of operations, operations with rational numbers, ... Honors Algebra 1 is an 8th grade honors course, open to high performing 7th graders. Students must meet both the following criteria to be eligible for this course in 7thgrade. No exceptions. * 1. ... 7thGrade Author: SDUHSD Created Date: into a more-rigorous 7thgrade (pre-algebra) curriculum and supplements with some of the Algebra standards. In 8th grade, these students take a one-year Algebra course, and take the Algebra CST. The two-year program divides the Algebra Pre-Algebra - 7thgrade math students will study Pre-Algebra. It is a transitional course designed to move students from the intermediate level of mathematics to the secondary level. This course will help to transform concrete thinking skills into abstract, him or her for Algebra 1 in 8. th grade. SCIENCE . Life Science is the text we recommend for science. In addition to the regular reading, it is full of hands-on activities and experiments to reinforce the learning. ... 7thGrade Curriculum
Math Courses It is recommended that you talk to an RVC advisor to determine which math classes are best for you to take for your program of study. The flowcharts linked to below may also be helpful when planning your schedule. MTH-086 Basic Math Skills IAI: None Basic Math Skills is designed for students who need a review of basic mathematical skills in preparation for further studies in mathematics courses. Topics include operations with whole numbers and fractions. Emphasis is placed on accurate calculations; no calculators will be used through the entire module. Study skills will be incorporated throughout the course. Placement into MTH 086 is according to placement test scores or on a voluntary basis. Credit earned does not count toward any degree, nor does it transfer. Prerequisite: None Credit: 2 semester hours Lecture: 2 Lab: 0 MTH-088 Prealgebra Part I IAI: None Prealgebra Part I includes a review of basic arithmetic skills while introducing algebra concepts. Topics include operations with integers, signed fractions and mixed numbers, solving equations, and problem solving. No calculators will be used through the entire module. Study skills will be incorporated throughout the course. Placement into MTH 088 is according to placement test scores or on a voluntary basis. Credit earned does not count toward any degree, nor does it transfer. Prerequisite: MTH 086, or equivalent, with a grade of C or better, or appropriate placement score. Credit: 2 semester hours Lecture: 2 Lab: 0 MTH-091 Beginning Algebra Part I IAI: None Beginning Algebra Part I will cover real numbers, solving linear equations and inequalities including applications, and graphing linear equations and inequalities. Study skills will be incorporated throughout the course. Placement into MTH 091 is according to placement test scores or on a voluntary basis. Credit earned does not count toward any degree, nor does it transfer. Prerequisite: MTH 088 and MTH 089, or equivalent, with a grades of C or higher in both or appropriate placement score. Credit: 2 semester hours Lecture: 2 Lab: 0 MTH-092 Beginning Algebra Part II IAI: None Beginning Algebra Part II continues work in basic algebra concepts. It will cover operations on systems of equations in two variables, polynomials, factoring, dimensional analysis, ratio and proportion. Study skills will be incorporated throughout the course. Credit earned does not count toward any degree, nor does it transfer. Prerequisite: MTH 091 with a grade of C or higher. Credit: 2 semester hours Lecture: 2 Lab: 0 MTH-093 Intermediate Algebra Part I IAI: None Intermediate Algebra Part I includes a review of factoring from beginning algebra. The course will also cover rational expressions and equations, linear equations, and an introduction to functions. Placement into MTH 093 is according to placement test scores or on a voluntary basis. Credit earned does not count toward any degree, nor does it transfer. Prerequisite: MTH 091 and MTH 092, or equivalent, with grades of C or higher in both or appropriate placement score. Credit: 2 semester hours Lecture: 2 Lab: 0 MTH-096A Mathematical Literacy-College Students IAI: None PCS: Mathematical Literacy for College Students is a one semester course for non-math and non-science majors integrating numeracy, proportional reasoning, algebraic reasoning, and functions. Students will develop conceptual and procedural tools that support the use of key mathematical concepts in a variety of contexts. Throughout the course, college success content will be integrated with mathematical topics. Credit earned does not count toward any degree, nor does it transfer. Upon successful completion of the course, students may take MTH 115, MTH 220, or MTH 096S. Prerequisite: MTH-089, or equivalent with grade of C or higher, or an appropriate math placement score, or consent of instructor. Credit: 6 semester hours Lecture: 6 Lab: 0 MTH-096S Combined Beg & Intermediate Algebra Combined Beginning and Intermediate Algebra is a one semester course covering both beginning and intermediate algebra. The topics included are real number operations and properties, linear equations and inequalities, graphing, functions, polynomials, factoring, rational expressions, systems of equations, radical expressions, and quadratic equations. The course will introduce exponential and logarithmic functions if time permits. Credit earned does not count toward any degree, nor does it transfer. Prerequisite: MTH 088 and MTH 089, or equivalent, with grades of A in both, or a sufficiently high placement test score, or consent of instructor. MTH-097 Elementary Plane Geometry IAI: None Elementary Plane Geometry is a course in the fundamental concepts of geometry intended for students who lack credit in one year of elementary geometry or desire a review of this subject matter. This course is considered equivalent to a one-year course in high school geometry. The topics included are deductive reasoning and proof, congruent triangles, parallel and perpendicular lines, parallelograms and other polygons, ratio and proportion, similarity, right triangles and the Pythagorean Theorem, circles, perimeter, area, volume, and construction. Credit earned does not count toward any degree, nor does it transfer. Prequisite: MTH 092, or equivalent, with a grade of C or higher. Credit: 3 semester hours Lecture: 3 Lab: 0 MTH-100 Technical Mathematics IAI: None Technical Mathematics is primarily for technology students. It is designed for students with a good algebraic preparation and includes basic study and applications of trigonometry. The course includes a study of exponents, radicals, and logarithms. Prerequisite: MTH 094 and MTH 097 or equivalent of both courses with a grade of C or higher in each course. Credit: 5 semester hours Lecture: 5 Lab: 0 MTH-115 General Education Mathematics IAI: M1 904 General Education Mathematics focuses on mathematical reasoning and the solving of real-life problems, rather than on routine skills and apprecation. Three or four topics are studied in depth, with at least 3 chosen from the following list: geometry, counting techniques and probability, graph theory, logic/set theory, mathematics of finance, and statistics. The use of calculators and computers is strongly encouraged. Prerequisite: MTH 094 and MTH 097 or equivalent of both courses with a grade of C or higher in each course. Credit: 3 semester hours Lecture: 3 Lab: 0 MTH-120 College Algebra IAI: None College Algebra includes a review of intermediate algebra, though it covers the overlapping material more quickly and at a deeper level. The course also develops the concept of a function and its graph, inverse functions, exponential and logarithmic functions and their applications, and systems of linear equations and the matrix methods useful in solving those systems. The course will also cover the theory of equations. Prerequisite: MTH 094 and MTH 097 or equivalent of both courses with a grade of C or higher in each course. Credit: 3 Lecture: 3 Lab: 0 MTH-125 Plane Trigonometry IAI: None Plane Trigonometry is a study of trigonometric functions of acute and general angles, inverse functions, graphs, radian measure, trigonometric identities and equations, solutions of right and oblique triangles, powers and roots of complex numbers, and may include analytic geometry. Prerequisite: MTH 120 or equivalent with a grade of C or higher. Credit: 3 semester hours Lecture: 3 Lab: 0 MTH-132 Precalculus Mathematics IAI: None Precalculus Mathematics is intended for students preparing for MTH 135 and it covers the material of MTH 120 and MTH 125 at a more rapid pace than those individual courses. Among the topics covered in this course are functions and graphs, including linear, polynomial, rational, exponential, and logarithmic functions; complex numbers and theory of equations; trigonometric functions, their basic properties and graphs; identities; inverse trigonometric functions; trigonometric equations; Law of Sines, Law of Cosines; systems of linear equations and the matrix methods useful in solving those systems; and conics. Students may not earn more than six credits for any combination of MTH 120, 125, and 132. Prerequisite: MTH 094 and MTH 097, or equivalent of both courses with a grade of C or higher in each course. Credit: 5 semester hours Lecture: 5 Lab: 0 MTH-160 Topics From Finite Mathematics IAI: M1 906 Topics From Finite Mathematics is for students enrolled in computer and information systems, business, or the social sciences. Topics include simultaneous equations, matrices, linear programming, mathematics of finance, sets, probability and statistics. This course is not intended to apply toward a major or minor in mathematics. Prerequisite: MTH 120 or equivalent with a grade of C or higher. Credit: 3 semester hours Lecture: 3 Lab: 0 MTH-164 The Computer in Mathematics C/C++ IAI: None The Computer in Mathematics C/C++ is a problem-oriented approach using the computer in the study of mathematics. Programs will be written and run to aid understanding of such topics as infinite series, logical relations, approximations, interpolation, graphing, and matrices. Problem formulation, algorithm development, and aspects of program testing and debugging will be discussed. Prerequisite: MTH 135 or equivalent with a grade of "C" or higher Credit: 4 semester hours Lecture: 4 Lab: 0 MTH-211 Calculus for Business & Social Science IAI: M1 900- 1.1 Calculus for Business and Social Sciences is an elementary treatment of topics from differential and integral calculus, with applications in the social sciences and business. Topics included are polynomial and exponential functions and their derivatives, as well as integration. Each of these topics is explored with an eye on its usefulness as a tool to answer questions in those fields of major interest to the students. This course is not intended to apply toward a major or a minor in mathematics. Prerequisite: MTH 120 or equivalent with a grade of "C" or higher. Credit: 4 semester hours Lecture: 4 Lab: 0 MTH-216 Math for Elementary Teachers I IAI: None Mathematics for Elementary Teaching I is for students intending to major in elementary education. This course focuses on mathematical reasoning and problem solving using manipulatives, calculators, and microcomputers. Topics include sets, the origin of numbers and numerals, systems of numeration, functions, whole numbers, number theory, integers, rational numbers, and irrational numbers and the real number system. The MTH 216-217 course sequence fulfills the two-course mathematical content requirement for Illinois state certification in elementary teaching. Prerequisite: MTH 094 and MTH 097, or equivalent of both courses with a grade of C or higher in each course. Credit: 3 semester hours Lecture: 3 Lab: 0 MTH-220 Elements of Statistics IAI: M1 902 Elements of Statistics is intended primarily for students enrolled in life science or social science, or others interested in elementary statistics. This course uses the graphing calculator extensively to place emphasis on conceptual understanding instead of hand calculations. Topics included are measures of central tendency and variability, graphical presentation of data, normal and binomial distributions, t- and chi-square distributions, sampling, and correlation. This course is not intended to apply toward a major or minor in mathematics. Prerequisite: MTH 094 and MTH 097, or equivalent of both courses with a grade of C or higher in each course. Credit: 3 semester hours Lecture: 3 Lab: 0 MTH-250 Modern Linear Algebra IAI: MTH 911 Modern Linear Algebra is a study of elementary topics of linear algebra, in which systems of equations and matrices are used as vehicles for the discussion of vector spaces, subspaces, independence, bases, dimension, linear transformations, and similarity. The study will also consider applications of these ideas and techniques to selected areas such as linear differential equations, approximation problems (least-squares best fit to data; Fourier series), linear programming (the simplex algorithm), Markov chains, Leontief economic models, genetics, and computer graphics. Prerequisite: MTH 236 or equivalent with a grade of "C" or higher, or concurrent enrollment in MTH 236. Credit: 3 semester hours Lecture: 3 Lab: 0
Assignments: Homework assignments will be worth 40% of your grade. You may do these with a partner, and one grade will be given to both people in each group, but you may work alone if you prefer to do so. Read our department's academic integrity guidelines before you hand in any written work. Goals: To understand the mathematics that underlies computer science, and to appreciate where it is used. This semester will concentrate on functions, number theory, recurrence equations, recursion, combinatorics, and their applications. Next semester concentrates on sets, Boolean algebra, linear algebra, and their applications. Special Dates: The Tuesdays September 18 and October 2 are Jewish holidays. I will not lecture these days but I will announce other plans for these days in class. Description: The two-semester discrete math sequence covers the mathematical topics most directly related to computer science. Topics include: logic, relations, functions, basic set theory, countability and counting arguments, proof techniques, mathematical induction, graph theory, combinatorics, discrete probability, recursion, recurrence relations, linear algebra, and number theory. Emphasis will be placed on providing a context for the application of the mathematics within computer science. The analysis of algorithms requires the ability to count the number of operations in an algorithm. Recursive algorithms in particular depend on the solution to a recurrence equation, and a proof of correctness by mathematical induction. The design of a digital circuit requires the knowledge of Boolean algebra. Software engineering uses sets, graphs, trees and other data structures. Number theory is at the heart of secure messaging systems and cryptography. Logic is used in AI research in theorem proving and in database query systems. Proofs by induction and the more general notions of mathematical proof are ubiquitous in theory of computation, compiler design and formal grammars. Probabilistic notions crop up in architectural trade-offs in hardware design. Linear algebra has a vast variety of applications including: Markov chains, cryptography, computer graphics, curve fitting, electrical circuits, and data mining. The first semester concentrates on induction, proofs, combinatorics, recurrence relations, functions, computational complexity, and number theory. The second semester concentrates on logic, sets, countability, Boolean algebra, linear algebra and applications. Note: These are long assignments so you should spread your efforts over a period of 2-3 weeks for each one. Make sure to do a few problems every few days, and not wait until the last few days. You will learn more and get better grades if you do. I will review any question before we start class on any day. I will give hints and guide you. Never give up.
Foundations of Mathematical & Computational Economics 9780324235838 ISBN: 0324235836 Edition: 1 Pub Date: 2006 Publisher: Thomson Learning Summary: Economics doesn't have to be a mystery anymore. FOUNDATIONS OF MATHEMATICAL AND COMPUTATION ECONOMICS shows you how mathematics impacts economics and econometrics using easy-to-understand language and plenty of examples. Plus, it goes in-depth into computation and computational economics so you'll know how to handle those situations in your first economics job. Get ready for both the test and the workforce with this ...economics textbook.[read more] Ships From:Multiple LocationsShipping:Standard, Expedited, Second Day, Next Day
Mathematics The Mathematics Department requires all students to take four years of mathematics. Students who take Algebra I or Honors Algebra I as freshmen and Geometry as Sophomores have the opportunity to take Calculus on the Honors or AP level as seniors if they meet the criteria for enrollment in a course entitled Honors Algebra II/Pre-Calculus as juniors. Another option is Algebra I, Geometry, Algebra II and Pre-Calculus on the Honors or Standard level. Also, any student who places into Geometry or Honors Geometry as a freshman may also take Honors Algebra II/Pre-Calculus as a sophomore if she meets the criteria for enrollment. The use of the graphing calculator and a variety of computer programs in math is an essential component of each course. Upon enrollment, all freshman will be required to have a TI84+ Graphing Calculator which they will use for all their math and science classes. 517alg IH Honors Algebra I GR 9 \| QP 4.67 \| 1 CREDIT \| YEAR This course covers the same topics as Algebra I (515), but problems of a higher difficulty level are presented as well as theoretical explanations of greater depth. Prerequisite: Student must be invited to enroll in this course based on results from the Mathematics Placement Exam administered in May before freshman year. 524geom Geometry GR 10 \| QP 4.33 \| 1 CREDIT \| YEAR This course is an axiomatic approach to the Euclidean geometry. Logical reasoning is used to explore the relationships between lines, planes, triangles, and polygons. Trigonometry, coordinated geometry and exploration of solid figures are also studied; theory and application are equally considered. The course has a strong integration with Algebra I. Prerequisite: Algebra I (515 or 517) 527geomH Honors Geometry GR 9-10 \| QP 4.67 \| 1 CREDIT \| YEAR This course is an in-depth axiomatic approach to Euclidean geometry. Topics include parallel lines and planes, triangles, polygons, circles, trigonometry, constructions, solid figures, and coordinate geometry. Abstract reasoning is developed in an advanced use of theory and application. Prerequisite: [3.67 in Algebra I (515/517) and (B+ on all SHA midterm and final exams in 515/517 or departmental approval)] OR Student may be invited to enroll in this course based on results from the Mathematics Placement Exam administered in May before freshman year. 534algII Algebra II GR 10-11 \| QP 4.33 \| 1 CREDIT \| YEAR This course stresses the structure of Algebra and the development of computational and problem-solving skills. Topics include a review of Algebra I, the real number system and its properties, complex numbers, polynomial and rational expressions, functions and relations. A theoretical approach is used with emphasis given to the application of theorems and formulas. Prerequisite: Algebra I (515 or 517) and Geometry (524 or 527) 537algIIH Honors Algebra II GR 10-11 \| QP 4.67 \| 1 CREDIT \| YEAR This course stresses the structure of Algebra and the development of computational and problem-solving skills. Topics include a brief review of Algebra I, the real number system and its properties, functions and relations, systems of linear equations in three variables, complex numbers, polynomials, and rational expressions. An in-depth theoretical approach is used and emphasis is given to the application of theorems and formulas. Prerequisite: [3.67 in Algebra I (515/517) and 3.67 on the final exam in 515/517in Grade 9 and 3.33 in Geometry (524 or 527) in Grade 10] OR 3.67 in Honors Geometry (527) in Grade 9 539 algIIpcH Honors Algebra II/ Pre-Calculus GR 10-11 \| QP 4.67 \| 1 CREDIT \| YEAR This course is designed to allow freshman and sophomores currently in Geometry or Honors Geometry to enroll in Calculus, AP Calculus and any other advanced math class as juniors and seniors. Sophomores who studied Algebra I or Honors Algebra I as freshmen may enroll in this class to prepare for Calculus or AP Calculus as seniors. Present freshman Geometry students may enroll in this class as sophomores to prepare for Honors Calculus as juniors and BC Calculus as seniors. The focus of this course is an extensive and in-depth study of functional analysis, mathematical analysis and analytical geometry. This integration of Algebra II, trigonometry and functional analysis intends to broaden the students' mathematical background and provide the mathematics needed for success in Calculus. Graphing calculators will be used for graphical investigations and explorations hence a TI83+ or TI84+ graphing calculator is required. Prerequisite: [4.0 in Algebra I (515 or 517) in Grade 9 and 4.33 in Geometry (524 or 527) in Grade 10] OR 4.33 in Honors Geometry (527) in Grade 9. In addition, all enrolled students must have an A exam average in Algebra and Geometry courses at SHA or departmental approval. 542func Functions, Statistics and Trigonometry GR 11-12 \| QP 4.33 \| 1 CREDIT \| YEAR This course serves either as a transition between Algebra II and Pre-Calculus (546) or as the final course in the math sequence. This course integrates work with functions and trigonometry to introduce the student to the topics in Pre-Calculus (546). It also challenges the student to think mathematically. The Statistics part of the curriculum is done with the technology available at Sacred Heart Academy: the laptops, the internet and the graphing calculator will be utilized to complete this section of the course. The use of functions and statistics to model real world situations is a major theme, and will provide the students with the tools to see how seemingly abstract mathematical ideas are meaningful in the world around them. Required: TI83+ or TI84+ Graphing Calculator. Prerequisite: Algebra II (534 or 537) 544statAP AP Statistics (Advanced Placement) GR 11-12 \| QP 5.0 \| 1 CREDIT \| YEAR Collecting, representing and processing data are activities of major importance to contemporary society. Topics covered in this course include the description and analysis of population distributions, change and growth of data, correlation, experiment design, probability models, linear regression, hypothesis testing and confidence intervals. Graphing calculators and computers are used as tools for the facilitation of statistical tests on significant bodies of data. Advanced Placement Statistics acquaints students with the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Ideas and computations presented in this course have immediate links and connections with actual events. Computers and calculators will allow students to focus deeply on the concepts involved in statistics. The TI83+ or TI84+ calculator is required and is used as the technical tool to allow the student to calculate any tests or data required. AP exam fee applies. Prerequisite: 4.0 in 534, 3.67 in 537 or 3.33 in 539. In addition, all enrolled students must have an A- exam average in Algebra II OR departmental approval. 123engnrg Introduction to Engineering GR 11-12 \| QP 4.33 \| ½ CREDIT \| SEM 1 OR 2 This course focuses on the fundamentals of modern engineering and technology. Students explore the engineering design process as they learn and apply math and science concepts to design and test an array of high-tech digital devices. The course will show students how engineers use advanced development tools in everyday engineering work: Designing, developing, testing, debugging, and finally producing a finished product that works. Prerequisite: 3.67 in Algebra II (534, 537, or 539) Note: This course may be used to fulfill the science or math graduation requirement. 545finance Personal Finance GR 11-12 \| QP 4.33 \| ½ CREDIT \| SEM 1 OR 2 This course explores the mathematics of personal and business matters with an emphasis on rational decision making. Topics in personal finance include analyzing budgets, banking, insurance, credit, taxes, real estate and investments. Students research a range of investment opportunities and financial instruments from a variety of sources including the Internet. Book fee applies. Note: This course counts toward the four-credit math requirement. 546precalc Pre-Calculus GR 11-12 \| QP 4.33 \| 1 CREDIT \| YEAR This course covers the advanced techniques of Algebra as well as the integration of functional analysis, analytic geometry and trigonometry. The trigonometric functions are thoroughly presented, including graphing, solving identities, and applications. This course also includes an introduction to probability and counting problems. Technology allows the focus of the course to be on functional investigations and exploration. Heavy emphasis is on the use of the overhead graphing calculator-projector and digital lesson investigations with the Smart Board. Since this course includes in-depth use of hand-held graphing calculators, the TI83+ or TI84+ graphing calculator is required. Prerequisite: 2.67 in Algebra II (534, 537, or 539) Note: Students taking this course may qualify for Honors Calculus (590) or AP Calculus AB (593). 547precalcH Honors Pre-Calculus ECE(UCONN ECE MATH 1030Q) GR 11-12 \| QP 4.67 \| 1 CREDIT \| YEAR UCONN COURSE 1030Q: 3 Spring college credits This course is an integration of an intensive study of trigonometry, geometry, and advanced algebra intended to broaden the student's mathematical background prior to the study of calculus. This course also includes an introduction to Discrete Mathematics. The three fundamental areas of functional analysis, mathematical analysis and analytic geometry are investigated in depth through the use of a myriad of technological aids such as the overhead graphing calculator, the Smart Board and digital lessons. Each student is required to have either a TI83+ or TI84+ graphing calculator since extensive use of graphing technology is incorporated as an investigative tool. Prerequisite: 4.0 in Honors Algebra II (537) AND A- exam average in 537 or departmental approval. There is an ECE change fee if a qualified student requests to be added in June. Note: All students enrolled in this course will have mandatory Spring concurrent enrollment in the University of Connecticut Early College Experience Program that allows students to earn 3 college credits. UConn will bill students separately for UConn ECE tuition in the Spring. 549stat Introduction to Statistics GR 11-12 \| QP 4.33 \| 1 CREDIT \| YEAR The importance of Statistics in both academic and personal settings has grown at a tremendous rate recently. Intro to Statistics is designed to introduce fundamental statistical knowledge that students will be able to use in college and throughout their lives. Statistics is currently taken by over 85% of all undergraduates at the university level. Topics covered in this course include; data collection, regression, probability, sampling distributions, and inference. The student who successfully completes this course will have the tools for collecting, analyzing, and interpreting data in academic settings and her everyday life. Required: TI83+ or TI84+ Graphing Calculator. Prerequisite: Algebra II (534 or 537) 590calc Honors Calculus GR 11-12\| QP 4.67 \| 1 CREDIT \| YEAR This course is designed for students who want to have preparation for and experience with calculus especially those planning to enter fields of medicine, nursing, business, economics, management, and the social sciences. It focuses on the development of conceptual understanding of real-life situations involving change so the material is data driven and technology based. Topics include functions and linear models, non-linear models, rates of change, derivatives, analysis of change, limits and integration. Extensive use of graphing technology is incorporated hence a TI83+ or TI84+ graphing calculator is required. Overhead graphing-calculator projectors, the Smart Board and digital lessons via the projector are used in most classes. Prerequisite: [4.0 in 546, 3.67 in 547 or 3.33 in 539] AND [For 546: 4.0 average on exams or departmental approval; For 539/547: 3.0 average on exams or departmental approval]. Students who are interested in taking Honors Calculus and exceed the exam average component but fall just short of the overall average required may be eligible subject to departmental approval. These cases will be considered on an individual basis and students should approach the respective teachers well in advance. 593calcAP AP Calculus AB (Advanced Placement and UCONN ECE MATH 1131) GR 11-12 \| QP 5.0 \| 1 CREDIT \| YEAR UCONN COURSE MATH 1131: 4 Fall college credits This course provides an intuitive understanding of the concepts of calculus, and experience with its applications and methodology. Course content generally follows the AP syllabus for Calculus AB, which is more extensive, and of greater breadth and depth than the 590 Calculus curriculum. UCONN will grant 4 college credits for all the Calculus covered in the first semester. This two semester course includes the study of elementary functions, limits, the derivative and its applications, and integral Calculus including anti derivatives and their applications. Overhead graphing calculators, the Smart Board and digital lessons are used in most classes. The TI83+ or TI84+ graphing calculator is required. This challenging course is meant only for the serious math student. AP exam fee applies. Prerequisite: [4.0 in 539/547 or 4.33 in 546] AND [For 546: 4.0 on the midterm and final exams or departmental approval; For 539/547: 3.33 average on exams]. There is an ECE change fee if a qualified student requests to be added in June. Note: All students enrolled in this course will have mandatory concurrent enrollment in the University of Connecticut Early College Experience Program that allows students to earn 4 college credits. UConn will bill students separately for UConn ECE tuition in the Fall only. 594calcAP AP Calculus BC (Advanced Placement) GR 12 \| QP 5.0 \| 1 CREDIT \| YEAR Calculus BC is a full-year course in the calculus of functions of a single variable. It includes all topics covered in Calculus AB plus additional topics. Both the AB and BC courses represent college-level mathematics for which most colleges grant advanced placement and college credits. The Calculus BC exam has a Calculus AB sub-score so the students enrolled in this class will be receiving two AP scores. The content of Calculus BC is designed to qualify the student for college placement and credit in Calculus II, which is one course beyond that granted for Calculus AB. AP exam fee applies. Prerequisite: [A- on the midterm exam in 590/593 or departmental approval] AND [4.33 in 590 or 4.0 in 593]. 191compsciH Honors Computer Science GR 10-12 \| QP 4.67 \| ½ CREDIT \| SEM 1 OR 2 In today's innovation-driven economy, complex problem solving and analytical reasoning skills are important for building a foundation for numerous careers, including jobs in math, science, engineering, and technology-related fields. This course provides an introduction to the intellectual enterprises of computer science and the art of programming. This course teaches students how to think algorithmically and solve problems efficiently. Students will be able to design and implement computer-based solutions to problems in several application areas, including mobile apps for Android and iOS (for iPhones, iPod touches, and iPads), two of today's most popular platforms; to learn well-known algorithms and data structures; to develop and select appropriate algorithms and data structures to solve problems; and to code in a well-structured fashion. Prerequisite: Geometry; 3.67 in a previous full-year math class, including an A- or higher on the final exam. Note: This course counts toward the four-credit math requirement. 550mathsat SAT Math Review GR 11 \| QP 4.33 \| ½ CREDIT \| SEM 2 This course provides juniors with the opportunity to prepare for the math section of the early spring SAT and the advanced math topics in the Subject tests SAT-I and SAT-II administered in early June. In this course, students are introduced to the content and format of the standardized test, learn fundamental test-taking strategies and are provided with ample opportunity to implement these strategies by taking multiple practice tests and correction tests. This course will provide test taking strategies for multiple choice problems and open answer questions, as well as TI 84+ and TI83 calculator tips for successful time management. The four major topics covered in this course are: Numbers and Operations, Algebra and Functions, Geometry and Measurement, and Data Analysis, Statistics and Probability. Each unit of study includes comprehensive instruction on the given topic, followed by guided practice and, finally, individual completion of timed practice tests. Note: This course counts toward the 27-credit graduation requirement. However, this course does not count toward the four-credit math requirement.
Secondary Mathematics III [2011] Create equations that describe numbers or relationships. For A.CED.1, use all available types of functions to create such equations, including root functions, but constrain to simple cases. While functions used in A.CED.2, 3, and 4 will often be linear, exponential, or quadratic the types of problems should draw from more complex situations than those addressed in Mathematics I. For example, finding the equation of a line through a given point perpendicular to another line allows one to find the distance from a point to a line. Note that the example given for A.CED.4 applies to earlier instances of this standard, not to the current course. Mathematical Modeling A.CED.1 - A.CED.4 Curriculum Guide The Utah State Office of Education (USOE) and educators around the state of Utah developed these guides for the Secondary Mathematics III Cluster "Create Equations that Describe Numbers or Relationships" / Standards A.CED.1, A.CED.2, A.CED.3 and A.CED.4. Optimization Problems: Boomerangs This lesson unit is intended to help educators assess how well students are able to interpret a situation and represent the constraints and variables mathematically, select appropriate mathematical methods to use, explore the effects of systematically varying the constraints, and interpret and evaluate the data generated and identify the optimum case, checking it for confirmation
Custom Classes for Mathematics in ActionScript 3 In this section we give links to Flash and Math tutorials and the MathDL Flash Forum articles that provide custom AS3 classes and templates for building math applications. We also list AS2 articles whose AS3 version is coming soon. All graphing applications listed below use our custom math formula parser, MathParser. NEW! Sketching Derivatives Applet in AS3 Flash - The Code We present a math applet for sketching derivatives with complete AS3 source code. The applet uses a large collection of custom AS3 classes developed by the Flash and Math team over the past few years. The newest of the classes are related to an interesting drawing and smoothing techinique. The user draws by dragging and shaping a curve. Function Grapher with Zooming and Panning In this tutorial, we present a math function grapher which has a drag and drop panning and mouse click zooming functionality. Panning has a cool easing effect, too. All the source code including parsing and graphing custom AS3 classes available for download. Contour Map Plotter and 3D Function Grapher in Flash Combined We use our custom AS3 classes in the package flashandmath.as3.* to build an applet which combines a contour diagram plotter and a 3D function grapher. The user's can input formulas for functions and variables ranges. The applet uses our custom classes: MathParser, GraphingBoard, GraphingBoard3D, and many helper classes. We provide complete, well-commented source code and a pdf guide of custom classes. Custom AS3 Math Classes, Implicit Plotter in Flash The implicit equations grapher presented in this tutorial is another example of how the custom AS3 math classes provided at flashandmath.com can be used to easily create custom math applets. In this tutorial, we use our custom MathParser and GraphingBoard classes that do all the work for you. The tutorial contains complete, well-commented source code. The SimpleGraph class An alternate title for this tutorial could be, "How to make a functional grapher in 30 lines of code." With the custom SimpleGraph class available from flashandmath.com, creating a graph of an expression in one variable is a snap! Visualizing Regions for Double Integrals This article in the Sharing Area of the MathDL Flash Forum presents a mathlet for students learning double integrals in rectangular and polar coordinates. The mathlet draws regions of integration corresponding to the limits entered by the user and provides many practice problems. We welcome your comments, suggestions, and contributions. Click the Contact Us link below and email one of us.
Exponential Functions In this lesson, Professor John Zhu gives an introduction of the exponential functions in the general form as well as the special exponential function. He goes through several example problems utilizing the exponential properties. This content requires Javascript to be available and enabled in your browser. Exponential Functions Useful identities: Sometimes helpful to think of numbers as exponents: , , etc
Student Responsibilities: One cannot benefit from or contribute to a class discussion or activity unless one is physically present (this a necessary condition, not a sufficient one). Attendance is required. Call me (796-3658) if you will not be in class. A valid excuse is necessary to miss class. Unexcused absences may lower your grade for the course. Assigned readings of the texts and handouts need to be done if meaningful discussion can occur. Your active participation makes the course go. Math is not a spectator sport. Assigned problems and textbook exercises are ways for you to develop problem solving skills and reflect on your learning. Do the problems when they are assigned. Content I. Logic and Proofs A. Propositions and Connectives B. Conditional and Biconditionals C. Quantifiers D. Basic Proof Methods I E. Basic Proof Methods II F. Proofs Involving Qunatifiers II. Set Theory A. Basic Concepts B. Set Operations C. Extended Operations and Indexing D. Induction III. Relations A. Cartesian Products B. Equivalence Relations C. Renaming D. Partitions IV. Functions A. Functions as Relations B. Constructions C. One-to-One, Onto Functions V. Cardinality (if time permits) A. Equivalent Sets B. Infinite Sets C. Countable Sets Evaluation I will use a 90 – 80 – 70 – 60 framework for grading. I will give you written assignments on Thursday and these will be due to the following Thursday. You may consult each other but the write-up is your responsibility. I suggest you go to separate rooms to write up your answers. There will be three exams in class. I need to see what you can do all by yourself. The dates will be determined during the first week of class. A Note to You Mathematics can be an intellectual adventure, a powerful tool, and a creative experience Some of you may have had mathematics courses that were based on the transmission, or absorption, view of teaching and learning. In this view, students passively It is one way to make sense of the world. Consequently, I have three goals when I teach. The first is to help you develop mathematical structures that are more complex, abstract, and powerful than the ones you currently possess so that you will be capable of solving a wide variety of meaningful problems. The second is to help you become autonomous and self- motivated Hopefully. As So You may find this experience frustrating at times. Persevere! Eventually I hope you will own personally the mathematical ideas you once knew unthinkingly or only peripherally (and sometimes anxiously). I want you to become competent and confident using mathematical ideas and techniques. In training a child to activity of thought, above all things we must beware of what I will call "inert ideas" - that is to say, ideas that are merely received into the mind without being utilized, or tested, or thrown into fresh combinations . . . Education with inert ideas is not only useless: it is, above all things, harmful. Except at rare intervals of intellectual ferment, education in the past has been radically infected with inert ideas . . . Let us now ask how in our system of education we are to guard against this mental dryrot. We enunciate two educational commandments, "Do not teach too many subjects," and again, "What you teach, teach thoroughly." . . . Let the main ideas which are introduced into a child's education be few and important, and let them be thrown into every combination possible. The child should make them his own, and should understand their application here and now in the circumstances of his actual life. From the very beginning of his education, the child should experience the joy of discovery. (Alfred North Whitehead, The Aims of Education) Americans With Disability Act. If you are a person with a disability and require any auxiliary aids, services or other accommodations for this class, please see me or Wayne Wojciechowski (MC 320, 796-3085) within ten days to discuss your accommodation needs.
Traditionally, an Algebra 1 course focuses on rules or specific strategies for solving standard types of symbolic manipulation problems-usually to simplify or combine expressions or solve equations. For many students, symbolic rules for manipulation are memorized with little attempt to make sense of why they work. They retain the ideas for only a short time. There is little evidence that traditional experiences with algebra help students develop the ability to "read" information from symbolic expression or equations, to write symbolic statements to represent their thinking about relationships in a problem, or to meaningfully manipulate symbolic expressions to solve problems. In the United States, algebra is generally taught as a stand-alone course rather than as a strand integrated and supported by other strands. This practice is contrary to curriculum practices in most of the rest of the world. Today, there is a growing body of research that leads many United States educators to believe that the development of algebraic ideas can and should take place over a long period of time and well before the first year of high school. Developing algebra across the grades and integrating it with other strands helps students become proficient with algebraic reasoning in a variety of contexts and gives them a sense of the coherence of mathematics. Transition to High School in Implementing CMP. The Connected Mathematics program aims to expand student views of algebra beyond symbolic manipulation and to offer opportunities for students to apply algebraic reasoning to problems in many different contexts throughout the course of the curriculum. The development of algebra in Connected Mathematics is consistent with the recommendations in the NCTM Principles and Standards for School Mathematics 2000 and most state frameworks. Algebra in Connected Mathematics focuses on the overriding objective of developing students' ability to represent and analyze relationships among quantitative variables. From this perspective, variables are not letters that stand for unknown numbers. Rather they are quantitative attributes of objects, patterns, or situations that change in response to change in other quantities. The most important goals of mathematical analysis in such situations are understanding and predicting patterns of change in variables. The letters, symbolic equations, and inequalities of algebra are tools for representing what we know or what we want to figure out about a relationship between variables. Algebraic procedures for manipulating symbolic expressions into alternative equivalent forms are also means to the goal of insight into relationships between variables. To help students acquire quantitative reasoning skills, we have found that almost all of the important tasks to which algebra is usually applied can develop naturally as aspects of this endeavor. (Fey, Phillips 2005) There are eight units which focus formally on algebra. Titles and descriptions of the mathematical content for these units are: Variables and Patterns Introducing Algebra Representing and analyzing relationships between variables, including tables, graphs, words, and symbols Frogs, Fleas, and Painted Cubes Quadratic Relationships Examining the pattern of change associated with quadratic relationships and comparing these patterns to linear and exponential patterns, recognizing, representing, and analyzing quadratic functions in tables graphs, words, and symbols; determining and predicting important features of the graph of a quadratic functions, such as the maximum/minimum point, line of symmetry, and the x-and y-intercepts; factoring simple quadratic expressions Say It With Symbols Making Sense of Symbols Writing and interpreting equivalent expressions; combining expressions; looking at the pattern of change associated with an expression; solving linear and quadratic equations Linear Systems and Inequalities Even though the first primarily algebra unit occurs at the start of seventh grade, students study relationships among variables in grade 6. There also are opportunities in 6th and in 7th grade for students to begin to examine and formalize patterns and relationships in words, graphs, tables, and with symbols. In Shapes and Designs (Grade 6), students explore the relationship between the number of sides of a polygon and the sum of the interior angles of the polygon. They develop a rule for calculating the sum of the interior angle measures of a polygon with N sides. In Covering and Surrounding (Grade 6), students estimate the area of three different- size pizzas and then relate the area to the price. This problem requires students to consider two relationships: one between the price of a pizza and its area and the other between the area of a pizza and its radius. Students also develop formulas and procedures-stated in words and symbols-for finding areas and perimeters of rectangles, parallelograms, triangles, and circles. In Bits and Pieces I, II and III (Grade 6), students learn, through fact families, that addition and subtraction are inverse operations and that multiplication and division are inverse operations. This is a fundamental idea in equation solving. They use these ideas to find a missing factor or addend in a number sentence. In Data About Us (Grade 6), students repre- sent and interpret graphs for the relationship between variables, such as the relationship between length of an arm span and height of a person, using words, tables, and graphs. In Accentuate the Negative (Grade 7), students explore properties of real numbers, including the commutative, distributive, and inverse properties. They use these properties to find a missing addend or factor in a number sentence. In Filling and Wrapping (Grade 7), students develop formulas and procedures-stated in words and symbols-for finding surface area and volume of rectangular prisms, cylinders, cones, and spheres. Developing Functions In a problem-centered curriculum, quantities (variables) and the relationships between variables naturally arise. Representing and reasoning about patterns of change becomes a way to organize and think about algebra. Looking at specific patterns of change and how this change is represented in tables, graphs, and symbols leads to the study of linear, exponential, and quadratic relationships (functions). Linear Functions In Moving Straight Ahead, students investigate linear relationships. They learn to recognize linear relationships from patterns in verbal, tabular, graphical, or symbolic representations. They also learn to represent linear relationships in a variety of ways and to solve equations and make predictions involving linear equations and functions. Problem 1.3 illustrates the kinds of questions students are asked when they meet a new type of relationship or function-in this case, a linear relationship. In this problem students are looking at three pledge plans that students suggest for a walkathon. Moving Straight Ahead. p. 9 Whereas many algebra texts choose to focus almost exclusively on linear relationships, in Connected Mathematics students build on their knowledge of linear functions to investigate other patterns of change. In particular, students explore inverse variation relationships in Thinking With Mathematical Models, exponential relationships in Growing, Growing, Growing, and quadratic relationships in Frogs, Fleas, and Painted Cubes. Examples are given below which illustrate the different types of functions students investigate and some of the questions they are asked about these functions. By contrasting linear relationships with exponential and other relationships, students develop deeper understanding of linear relationships. Inverse Functions In Thinking With Mathematical Models, students are introduced to inverse functions. Thinking With Mathematical Models. p. 32 Exponential Functions In Growing, Growing, Growing, students are given the context of a reward figured by placing coins called rubas on a chessboard in a particular pattern, which is exponential. The coins are placed on the chessboard as follows. Place 1 ruba on the first square of a chessboard, 2 rubas on the second square, 4 on the third square, 8 on the fourth square, and so on, until you have covered all 64 squares. Each square should have twice as many rubas as the previous square. In this problem students use tables, graphs, and equations to examine exponential relationships and describe the pattern of change for this relationship. Growing, Growing, Growing. p. 7 Quadratic Functions In Problem 1.3 from Frogs, Fleas and Painted Cubes, students use tables, graphs, and equations to examine quadratic relationships and describe the pattern of change for this relationship. Frogs, Fleas and Painted Cubes. p. 10 As students explore a new type of relationship, whether it is linear, quadratic, inverse, or exponential, they are asked questions like these: What are the variables? Describe the pattern of change between the two variables. Describe how the pattern of change can be seen in the table, graph, and equation. Decide which representation is the most helpful for answering a particular question. (see Question D in Problem 1.3 Frogs and Fleas and Painted Cubes above) Describe the relationships between the different representations (table, graph, and equation). Compare the patterns of change for different relationships. For example, compare the patterns of change for two linear relationships, or for a linear and an exponential relationship. After students have explored important relationships and their associated patterns of change and ways to represent these relationships, the emphasis shifts to symbolic reasoning. Equivalent Expressions Students use the properties of real numbers to look at equivalent expressions and the information each expression represents in a given context and to interpret the underlying patterns that a symbolic statement or equation represents. They examine the graph and table of an expression as well as the context the expression or statement represents. The properties of real numbers are used extensively to write equivalent expressions, combine expressions to form new expressions, predict patterns of change, and to solve equations. Say It With Symbols pulls together the symbolic reasoning skills students have developed through a focus on equivalent expressions. It also continues to explore relationships and patterns of change. Problem 1.1 in Say It With Symbols introduces students to equivalent expressions. Say It With Symbols. p. 6 In Problem 2.1 students revisit Problem 1.3 from Moving Straight Ahead (see above) to combine expressions. They also use the new expression to find information and to predict the underlying pattern of change associated with the expression. Say It With Symbols. p. 24 Solving Equations Equivalence is an important idea in algebra. A solid understanding of equivalence is necessary for understanding how to solve algebraic equations. Through experiences with different functional relationships, students attach meaning to the symbols. This meaning helps student when they are developing the equation-solving strategies integral to success with algebra. In CMP, solving linear equation is an algebra idea that is developed across all three grade levels, with increasing abstraction and complexity. In grade six, students write fact families to show the inverse relationships between addition and subtraction and between multiplication and division. The inverse relationships between operations are the fundamental basis for equation solving. Students are exposed early in sixth grade to missing number problems where they use fact families. Below is a description of fact families and a few examples of problems where students use fact families to solve algebraic equations in grades 6 and 7. These experiences precede formal work on equation solving. In Bits and Pieces II (Grade 6), Bits and Pieces III (Grade 6), and Accentuate the Negative (Grade 7), students use fact families to find missing addends and factors. Bits and Pieces II. p. 22 Bits and Pieces III. p. 28 Accentuate the Negative. p. 30 In Variables and Patterns (Grade 7), students solve linear equations using a variety of methods including graph and tables. As students move through the curriculum, these informal equation- solving experiences prepare them for the formal symbolic methods, which are developed in Moving Straight Ahead (Grade 7), and revisited throughout the five remaining algebra units in eighth grade. Moving Straight Ahead. p. 85 Say It With Symbols (Grade 8), pulls together the symbolic reasoning skills students have developed through a focus on equivalent expressions and on solving linear and quadratic equations. Say It With Symbols. p. 42 Shapes of Algebra (Grade 8), explores solving linear inequalities and systems of linear equations and inequalities. By the end of Grade 8, students in CMP should be able to analyze situations involving related quantitative variables in the following ways: identify variables identify significant patterns in the relationships among the variables represent the variables and the patterns relating these variables using tables, graphs, symbolic expressions, and verbal descriptions translate information among these forms of representation Students should be adept at identifying the questions that are important or interesting to ask in a situation for which algebraic analysis is effective at providing answers. They should develop the skill and inclination to represent information mathematically, to transform that information using mathematical techniques to solve equations, create and compare graphs and tables of functions, and make judgments about the reasonableness of answers, accuracy, and completeness of the analysis.
This is a theoretical course focusing of fundamental topics in modern integer programming. The course will be based on lectures by the instructor, with homework projects involving proofs. The course will also include a comprehensive survey of linear programming. Materials
Odyssey Algebra 04/01/05 CompassLearning ( has expanded its entire suite of Odyssey products, including Odyssey Algebra for middle schools and secondary education. The browser-based curriculum will help teachers offer a comprehensive approach to math education, while providing a platform that supports a variety of instructional strategies and learning styles. Odyssey Algebra has 13 chapters and 131 objectives to cover in an entire school year. The curriculum's online features include interactive tutorials that are woven throughout the program and aids such as online calculators, graph paper, number lines, protractors, spreadsheets and rulers. The program also provides additional offline materials for students that are designed to extend learning beyond the classroom
Calculus and Its Origins David Perkins Calculus and Its Origins is primarily a collection of results that show how calculus came to be, beginning in ancient Greece and climaxing with the discovery of calculus. Other books have traveled these paths, but they presuppose knowledge of calculus. This book requires only a basic knowledge of high school geometry and algebra. Exercises introduce further historical figures and their results, and make it possible for a professor to use this book in class.
eBook Category:Technology/Science eBook Description: Taught at junior level math courses at every university, Linear Algebra is essential for students in almost every technical and analytic discipline.
Precalculus Book Description: Get a better grade with PRECALCULUS and accompanying technology! With a focus on teaching the essentials, this mathematics text provides you with the fundamentals necessary to be successful in this course and your future calculus course. Exercises and examples are presented the way that you will encounter them in calculus so that you are truly prepared for your next course. Tools found throughout the text, such as exercises, calculus connections, and true and false questions also help you master difficult concepts.
Excerpted from Patterns, ratios, equality, algebraic functions, and variables are some of the concepts covered in this printable book for elementary students. You'll find a variety of materials to encourage your young students to learn math
David Lippman's Page Latest ActivityWednesday, November 18, 3pm PACIFIC TIMEPart 1: "Open Textbooks from an Author's Perspective" (30 min)Abstract: What motivates someone to write an open textbook? How much of the editorial and production process is within reach of an individual? How is the experience different from writing a traditional textbook? What is different about teaching from an open textbook? I will answer these questions with examples from my experiences writing and publishing a mathematics textbook, "A First Course in…See More I'm happy to announce the first edition release of a "survey of math" textbook appropriate for college level math courses targeted towards liberal arts majors, sometimes titled "Contemporary Mathematics" or "Math in Society". In the Washington state community college system, this course has a common course number of Math& 107.This text was designed to be fairly compatible with the two "major players" in this market: For all Practical Purposes (COMAP) and Excursions in Modern Math…See More "Yes, the issue of no-return policies by print-on-demand vendors presents a challenge and you have made an interesting suggestion. But before adding middleman to the whole open textbook adoption/dissemination process, I like us to first figure out a…" "Please consider posting a link to your math exercise sets in MERLOT. Find out how by visiting their site at As a MERLOT Member, (free) you can: Contribute learning materials, Create a personal collection,…" I posed this question as a reply to an earlier discussion, but think this might warrant its own discussion.How do people using open texts negotiate things with your bookstores? My bookstore is willing to have the books run off loose-leaf at our print shop and sell them, but when I proposed buying them through Lulu.com or Qoop to get a better quality product (at a cheaper price) they didn't seem to like that idea since they can't return unsold books. Basically, they said they'd charge our…See More I have been reviewing the open math textbooks out there (thanks for compiling a great list), and have found that while there are several great ones out there, like Collaborative Stats and the Burzynski books, many open texts are not printable, either by design or by license. I don't think my students are ready for online-only texts. So that brings me to my point :)How do we get quality, complete, printable open texts where they don't currently exist? Is the best solution to:1) Convince authors…See More Comment Wall (1 comment) You need to be a member of College Open Textbooks Community to add comments! Hi David, Hope you are well ... thanks again for sharing your open textbook experience at the workshop ... it was much appreciated by the participants and me. We have just started a new group for adopters on this Ning and it would be great if you could join since questions are coming up from faculty who are new to this process and even though you are an author -- you also have lots of experience as a faculty who uses an open textbook. Also, we're about to start accessibility reviews of open textbooks and I'd like to include your book in the list but we don't yet have a peer-review which is one of our suggested requirements to be on the accessibility list. Vicky Moyle from Bellingham indicated that she is going to adopt your book. I will ask her about the possibility of doing a peer-review that we can post later but do you know anyone who has already done a review of your book so I can be sure to add your book to the list. As an author of a book on the accessibility list, you will get information customized to your book on how to make it more accessible, etc.
MATH V055: Elementary Algebra This course covers the concepts of working with Algebraic Expressions, Equations of Equality and Inequality, Graphing, Polynomials and Factoring, Rational Expressions and Equations, and finally, Functions and their Graphs. Credits:3 Overall Rating:0 Stars N/A Thanks, enjoy the course! Come back and let us know how you like it by writing a review.
Introduction Introduction Master Math: Trigonometry is part of the Master Math series, which includes Master Math: Basic Math and Pre-Algebra, Master Math: Algebra, Master Math: Pre-Calculus, Master Math Geometry, and Master Math: Calculus. Master Math: Trigonometry and the Master Math series as a whole are clear, concise, and comprehensive reference sources providing easy-to-find, easy-to-understand explanations of concepts and principles, definitions, examples, and applications. Master Math: Trigonometry is written for students, tutors, parents, and teachers, as well as for scientists and engineers who need to look up principles, definitions, explanations of concepts, and examples pertaining to the field of trigonometry. Trigonometry is a visual and application-oriented field of mathematics that was developed by early astronomers and scientists to understand, model, measure, and navigate the physical world around them. Today, trigonometry has applications in numerous fields, including mathematics, astronomy, engineering, physics, chemistry, geography, navigation, surveying, architecture, and the study of electricity, light, sound, and phenomena with periodic and wave properties. Trigonometry is one of the more interesting and useful areas of mathematics for the non-mathematician. This book provides detailed, comprehensive explanations of the fundamentals of trigonometry and also provides applications and examples, which will hopefully provide motivation for students to learn and become familiar with this truly interesting field of mathematics.
Prerequisite: "C" or better in MATH 091 or minimum ACT Math subscore of 18. A course providing the student with experiences designed to improve the ability to make decisions and solve a variety of problems. Emphasis is on learning to investigate, organize, observe, question, discuss, reason, generalize and validate. Mathematical content includes topics which are related to consumer mathematics, geometry, graphs, probability and statistics. This course satisfies the required core-math reasoning for general education.
MAT 091: Elementary Algebra Introduction This course is suitable for any student who needs to build algebra skills before entering the math courses that earn college-level credits. Students may need this course because they have simply never had the chance to study algebra before. Students may have had algebra in high school several years ago and need to rediscover skills they used to have. Other students may be more recently out of high school but, for various reasons, their scores on the UWC Math Placement Exam suggest that they need the Elementary Algebra course. Regardless of the student's individual background, this course will build and improve the skills necessary for success in a future algebra course. These skills include only three basic types of tasks: evaluate variable expressions, solve equations, and simplify variable expressions. In fact, all algebra courses work on these same skills, only increasing the level of difficulty. If students can master these three skills, and consistently perform them accurately, they will be well positioned for success in their next course. The key to learning in an online course in Elementary Algebra is the same for every math student: practice. This means, of course, that students must do the assigned homework. Students learn math best by doing math; the more they practice, the better they will get. Students must plan sufficient time to work through the full assignment every week. Through personal motivation, organization, and effort, they can master this subject. Students might even begin to like math more than they ever thought possible. Description UW Colleges Catalog Course Description for MAT 091: Elementary Algebra - 3 non-degree credits. Elementary Algebra is intended for students with little or no previous algebra experience. Topics include the real number system, operations with real numbers and algebraic expressions, linear equations and inequalities, polynomials, factoring, and an introduction to quadratic equations. A grade of C or better in Math 091 is required before advancing to Math 105. There is no prerequisite for Elementary Algebra. This is a non-degree credit course. Proficiencies Institutional proficiencies assigned to this course Successful completion of this course will enhance the student's ability to: Interpret and synthesize information and ideas Select and apply scientific and other appropriate methodologies Solve quantitative and mathematical problems Interpret graphs, tables, and diagrams Department-specific proficiencies assigned to this course By completing this course, students will: Be able to perform arithmetic calculations on real numbers and understand the order of operations Be able to use variable notation and be able to simplify and evaluate algebraic expressions Be able to solve linear equations in one variable Know the rules of exponents as applied to variable terms Be able to add, subtract, and multiply polynomials Know how to factor polynomials using greatest common factoring, the grouping method, trinomial factoring, and difference of perfect squares Be able to graph linear equations with two variables in the rectangular coordinate system Requirements Students must be able to use Equation Editor and Drawing (in Microsoft Word) to assist with correct mathematical notation on assignments. Software Microsoft Word with Equation Editor The most current edition of MS Office (containing MS Word and Word's Equation Editor and other valuable programs) is available to University of Wisconsin students at discounted prices through the Wisconsin Integrated Software Catalog.
Plus, you can be assured your student will be learning the quality academics he needs to know to succeed in future math courses. This in-depth math course covers topics like pre-calculus, relations and functions, trigonometry, and quadratic equations. Filled with valuable information, Switched-On Schoolhouse is a must-have for today's homeschool parent and student. Teacher-friendly, time-saving tools like automatic grading and lesson planning are also included! Plus, this Alpha Omega curriculum includes integrated, step-by-step solution keys available from the SOS Teacher application. Discover how fun teaching math to your high school student can be. Simply order Switched-On Schoolhouse 12th Grade Math
AP Statistics is a college-level introductory class taught at Centennial High School. Stats is much more than making graphs & calculating the mean, median, & mode. Rather, it is using data to evaluate claims and make predictions. The first chapters that we will study (Ch 1 & 5) will develop 4 main ideas: -The principles of experimental design -The principle of survey construction -The analysis of data distribution -The principle of statistical inference This is a fresh start: This is not a typical math classs! You will need good critical thinking & communication skills. Students taking this class should have completed math analysis, precalculus, or calculus OR have a strong finish in algebra 2 (A or high B). Since college credit is available, STRONGLY consider either concurrent credit or AP Credit. Stats is great preparation for college--it will help you in a wide variety of fields of study: psychology, business, science, biology, engineering,nursing, accounting, economics, sociology, animal & veterinary sciences, medicine, sports-- to name a few. Semester 2: This cyber class finishess the Algebra 1 Algebra 1 quizzes for each section ca be found at: Semester 1: This cyber class paces the geometry course of the Meridian School District. Students register through the District Office for high school credit. Your assignments and links will be posted here. Figure out your timeline for the course. You will need to pace about a chapter a week or so. Let me know how your schedule will look. Your online geometry quizzes for each section ca be found at: SEMESTER 2: This cyber class finishes the geometry geometry quizzes for each section ca be found at:
Course Math 3 Major Topics Covered This is the third in a sequence of mathematics courses designed to prepare students to enter college at the calculus level. It includes exponential and logarithmic functions, matrices, and polynomial functions of higher degree, conic sections, and normal distributions. (Prerequisite: Instruction and assessment should include the appropriate use of manipulatives and technology. Topics should be represented in multiple ways, such as concrete/pictorial, verbal/written, numeric/data-based, graphical, and symbolic. Concepts should be introduced and used, where appropriate, in the context of realistic phenomena.
CAAP Math Results In this edition of the DATAWave, CAAP math results will be analyzed by student performance in general education mathematics classes. According to the philosophy of general education (ENMU 1995-97 Undergraduate Catalog), students should "understand and apply basic mathematical principles." The CAAP mathematics test is designed to measure student's proficiency and mathematical reason. The test assesses student's proficiency in solving mathematical problems encountered in most post-secondary curricula, emphasizing quantitative reasoning rather than the memorization of formulas. The content areas include pre-, elementary, intermediate, and advanced algebra, coordinate geometry, trigonometry, and introductory calculus. Complete descriptions of the scale scores are available in the Assessment Resource Office. MATH 107 Intermediate Algebra MATH 110 College Algebra MATH 113 Mathematics for General Education MATH 123 Calculus STAT 213 Statistical Methods There are eleven courses listed in the general education distribution for understanding and applying mathematical principles. The students' CAAP results (n=891) were matched with grades earned in those classes. An appropriate number of matches were found for five classes. Care was taken to ensure that students had completed the math course prior to being assessed by the CAAP. In this edition of the DATAWave, the CAAP results, by courses completed by students, will be examined. In a future edition of the DATAWave, a number of other variables, such as student gender, ethnicity, and preparedness, will be explored. The national average, according to the fall of 1995 CAAP user norms, was 58.0 (standard deviation = 3.8). The average score for Eastern New Mexico University, since 1993, is a 56.18 (s.d.=3.47). For students who passed Math 107, that is earned a letter grade of "C" or better, the average score was a 56.12 compared to a 56.20 for students who did not take or pass Math 107. Students who passed Math 110 scored 57.86 on average compared to a 55.66. Students who passed Math 113 scored on average a 55.76, which was lower than a 56.21 scored by students who did not attempt Math 113. Students who passed Math 123 scored a 60.88, compared to a 55.77. Students who took Stat 213 scored a 57.53, compared to a 55.92. Of the 272 students who completed Math 107, 71 earned A's, 107 earned B's, and 94 earned C's. Respectively, the mean CAAP math scores for these groups were 57.39, 56.01, and 55.29. Two hundred and six students earned a C or better in Math 110 (58 A's, 74 B's, and 74 C's). The mean CAAP math scores were: A=58.97, B=57.99, and C=56.88. In Math 113, 58 students earned a C or better. Students who earned A's (n=16) averaged 56.31 on the CAAP math test, B's (n=16) averaged 56.81, and students with C's (n=26) averaged 54.77. Seventy students earned a C or better in Math 123. "A" students (n=14) averaged 61.58, "B" students (n=28) averaged 61.29, and "C" students (n=28) averaged 59.75. Of the 138 students in the cohort who passed Stat 213, 52 earned A's (CAAP math score=58.85), 54 earned B's (56.76), and 32 earned C's (56.72). These distributions of scores were not significant for Math 107 and Math 113; however, they were significant for the other three courses—Math 110, Math 123, and Math 213. It is most interesting to note that students who passed Math 123 scored well above the national mean and students who passed Stat 213 scored very near the national mean. For the purposes of this article it is assumed that these courses are more rigorous, and that students who select these courses perhaps have better beginning skills. However, with regards to outcomes assessment, the institution can only be responsible for learning that occurs in the classes which students take. In the three examples, the Math Department performed quite well. However, in two examples, Math 107 and Math 113, students don't do quite as well. In particular, students who have taken Math 113 scored worse than students who had not. This certainly does not mean that Math 113 had a negative effect on mathematical abilities, but rather, the people who selected to take that class perhaps were not as confident in mathematical abilities. Pages 2 and 3 contain a number of box whisker charts which show the distribution of mean scores for the courses. In these charts, the boxes represent the middle 50% of all scores while the lines that extend from the boxes (the "whiskers") show the full distribution of the scores. (For the purposes of this article, outliers have been eliminated from the charts.) The heavy line represents the median for the distribution. For the majority of students who have taken math classes at Eastern, ACT scores were not available. However, were they available, the mean scores of students who passed Math 107 were lower than those who did not attempt Math 107 (17.98 versus 20.83). Similarly for Math 113, ACT scores of students who passed were lower than those who did pass (19.21 versus 19.68). In all other cases, the math scores of students who successfully attempted and completed the courses were higher than those who did not. Of the 891 students who have participated in the CAAP at Eastern, 406 have not taken any math classes. Two hundred sixty-four have taken one, 179 have taken 2, and 42 have taken 3 or more. For those who have not taken any math classes their mean CAAP math score was a 55.14, those who have taken one class or more with a "C" or better earned a 56.50, two or more a 57.67, and three or more a 57.81. n ¯x S.D. x Passed x Did not take/ Pass National --- 58 3.8 ENMU 891 56.18 3.47 Math 107 272 56.12 56.20 Math 110 206 57.86 55.66 Math 113 58 55.76 56.21 Math 123 70 60.88 55.77 Stat 213 138 57.53 55.92 0 Math Classes 406 55.14 3.41 1 Math Class 264 56.50 3.41 2 Math Classes 179 57.67 2.92 3 or more Math Classes 42 57.81 3.23 In conclusion, students who have successfully passed (a "C" or better) math courses at Eastern scored slightly below the national average. These students do, however, score higher than students who have not completed courses in mathematics at Eastern. Because of the low number of students who have completed the ACT, it is not possible to conduct a regression analysis. However, if asked whether Eastern's math classes contribute to overall performance on the CAAP math scale, it seems that the evidence is yes. Members of the campus community are invited to forward their own conclusions and observations to the Assessment Resource Office, ext. 4313 or email at testaa@ziavms.enmu.edu.
Everything in math can be represented as a function. Whether it is the surface area of a cylinder, its volume, or area of a square, it can be all represented by Calculus. It is safe to say that everything you learn up to Algebra 2 is leading up to Calculus. Invented by Sir Isaac Newton and William Gottfried Leibniz Calculus is the math of change. Consider any function that's quadratic, or more than 2nd degree, the function could be an inverse function, it could be logarithmic function, what ever. If the function is curved, mathematicians are faced with the challenge of finding the derivative of a function – in simple terms its slope, which shows the rate of change of that function and the area under the curve of that function – simply the anti-derivative found through integration. The whole meat of calculus lies in the limit process. The limit process sets the ground rules for finding the area and the slope of any function. The limit process is the making of a calculus. The limit of anything that is changing can be found if you get smaller and smaller to infinity and find the function. This is where the limit process comes in. You can get complex with the applications of calculus in Engineering courses, or Physics courses. These are places where you extensively apply the theory of Calculus. It is advisable that few years of Calculus be taken before getting into these courses, simply because it takes a lot of getting used to Calculus before you can be successful at the courses. It will also be an amazing observation that most of the concepts of physics and other math-based sciences are developed by the same people who invented Calculus, or worked with it a lot. A few popular names such as Sir Isaac Newton – invented basics of physics and Newton' Laws; and Albert Einstein – theory of relativity and other major cosmological research – come to mind. Now-a-days Calculus is applied in all types of Engineering and Computer Science and all fields requiring design. It is easy to use if you are well versed in Algebra and all the basic Mathematics from K-12, or up to Algebra 2. In a nut-shell, Calculus makes life simple at the expense of extensive Algebra!
A child with a strong foundation takes much less time to understand a subject as compared to other students. MATHEMATICS FOUNDATION CLASS 10 aims at providing the right foundation to the students as they enter the Secondary School from Middle School. This book will prove to be a stepping stone to success in higher classes and competitive exams like Olympiads, IIT-JEE, PMTs etc. The book covers a very broad syllabus so as to build a strong base. The USP of the book is its style and format. The book is supplemented with Do You Know, Knowledge Enhancer, Checkpoints and Idea Box. Another unique feature is the Exercise Part which is divided into 2 levels. The broad variety of questions covered are Short, Very Short, Long, Fill in the Blanks, True/ False, Matching, HOTS, Chart/ Picture/ Activity Based, MCQ's - one option correct, multiple options correct, Passage based, Assertion-Reason, Multiple Matching etc. Solutions to selected questions has been provided at the end of each chapter. Specifications Book Details ISBN 9789381250631 Edition Latest Edition Language English Pages 532 Subject Mathematics Binding Softback Additional Information Author Disha Experts Publisher Disha Experts Special Features ·Recommended for class 10. ·Variety of questions are short, long, very short, fill in the blanks, true/false, matching, MCQs.
One of a series of practical references for teachers, this handbook provides general information on the background of the environmental studies curriculum in the United States. It contains current information on publications, standards and special materials for the curriculum, and is designed to be adapted to suit particular schools. A topological embedding is a homeomorphism of one space onto a subspace of another. The book analyzes how and when objects like polyhedra or manifolds embed in a given higher-dimensional manifold. The main problem is to determine when two topological embeddings of the same object are equivalent in the sense of differing only by a homeomorphism of the ambient manifold. Knot theory is the special case of spheres smoothly embedded in spheres; in this book, much more general spaces and much more general embeddings are considered. A key aspect of the main problem is taming: when is a topological embedding of a polyhedron equivalent to a piecewise linear embedding? A central theme of the book is the fundamental role played by local homotopy properties of the complement in answering this taming question. The book begins with a fresh description of the various classic examples of wild embeddings (i.e., embeddings inequivalent to piecewise linear embeddings). Engulfing, the fundamental tool of the subject, is developed next. After that, the study of embeddings is organized by codimension (the difference between the ambient dimension and the dimension of the embedded space). In all codimensions greater than two, topological embeddings of compacta are approximated by nicer embeddings, nice embeddings of polyhedra are tamed, topological embeddings of polyhedra are approximated by piecewise linear embeddings, and piecewise linear embeddings are locally unknotted. Complete details of the codimension-three proofs, including the requisite piecewise linear tools, are provided. The treatment of codimension-two embeddings includes a self-contained, elementary exposition of the algebraic invariants needed to construct counterexamples to the approximation and existence of embeddings. The treatment of codimension-one embeddings includes the locally flat approximation theorem for manifolds as well as the characterization of local flatness in terms of local homotopy properties.. The Art of Teaching Science is a science-teaching handbook designed for the professional development of middle- and high-school science teachers. The experiential tools in the book make it useful for both pre- and in-service teacher education environments, easily adapted to any classroom setting. Profound changes in our understanding of the goals of science teaching-as evidenced by the emphasis on inquiry-based activities advocated by the National Science Education Standards-underscore the need to equip a new cadre of educators with the proper tools to encourage innovation and science literacy in the classroom. Providing meaningful learning experiences and connections with the most recent research and understanding of science teaching, The Art of Teaching Science sets the standard for the future of science education. Are you webmaster? Go to webmaster forum to get as much as website building knowledge and free tools.
A Portrait of Linear Algebra uses a unified approach that gives the reader an integrated view of topics in this subject. It covers all the material in a standard introductory course on linear algebra, with enough material for two full semesters. Unique Features: Emphasizes the importance of learning how to read and write proofs. Key definitions and theorems found in the discussions are restated in the section and chapter summaries for easy reference. Linear algebra is developed by generalizing the field axioms for the real numbers to Euclidean spaces. A vector-centered approach is used throughout the book. Fundamental concepts such as spanning, linear independence, basis, dimension, one-to-one and onto linear transformations and isomorphisms are discussed in the first two chapters. Permutation Theory is developed and applied to the construction of determinants. Covers the eigentheory of matrices, as well as linear transformations of finite-dimensional vector spaces, along with the related concept of similarity. Several key theorems which are not usually found in introductory books are thoroughly developed and proved: The Isomorphism Theorems of Emy Noether, Schur's Lemma, The Spectral Theorem for Normal Matrices, The Fundamental Theorem of Linear Algebra, and The Singular Value Decomposition. Creative and unusual examples and exercises are found throughout the book. The exercises include a wide range of computational problems, as well as proofs of theorems. Difficult proof exercises are outlined for the student, and hints are provided. The book is written in a reader-friendly conversational style, ideal for independent study. An optional, introductory chapter discusses common logical techniques that can be used to prove theorems in linear algebra, such as, how to apply axioms and definitions to prove basic properties of any mathematical structure, case-by-case analyses, proof by contradiction, proof by contrapositive, and mathematical induction. This is of particular importance to students who have never had a course on proofs before. The text discusses existential and universal quantifies and how to write the inverse, converse and contrapositive of an implication. Examples are motivated by an axiomatic development of the real number system. Most are analogous to similar statements later seen in the context of vectors. A discussion of the complete set of axioms of the real number system is also presented in Appendix A. Linear Algebra is defined as the study of vector spaces, their structure, and the linear transformations that map one vector space to another. Euclidean spaces and their linear transformations are introduced in the first two main chapters. This easily allows all constructions to be rewritten for general vectors spaces in the third chapter, the main examples being matrix spaces and function spaces (polynomials, continuous functions and differentiable functions). To explore the subspace structure of vector spaces, cosets and quotient spaces of vector spaces are constructed. How to construct a basis for the join and intersection of two subspaces given a basis for each subspace, as well as how to construct a basis for the image or preimage of a subspace under a linear transformation is also shown. Some of these constructions are rarely seen in introductory textbooks, but they will allow students to explore the consequences of the three Isomorphism Theorems. The capstone of the book is the development of the theory of positive-definite and semi-definite matrices, which allows students to prove the Fundamental Theorem of Linear Algebra and The Singular Value Decomposition, or SVD. The Fundamental Theorem neatly wraps up several key ideas in one beautiful package: rowspace, columnspace and nullspace, eigenspaces and orthogonality. The SVD is one of the most important workhorses in modern computing and data compression.
Explore the main algebraic structures and number systems that play a central role across the field of mathematics Algebra and number theory are two powerful branches of modern mathematics at the forefront of current mathematical research, and each plays an increasingly significant role in different branches of mathematics, from geometry and topology to computing and communications. Based on the authors' extensive experience within the field, Algebra and Number Theory has an innovative approach that integrates three disciplines--linear algebra, abstract algebra, and number theory--into one comprehensive and fluid presentation, facilitating a deeper understanding of the topic and improving readers' retention of the main concepts. The book begins with an introduction to the elements of set theory. Next, the authors discuss matrices, determinants, and elements of field theory, including preliminary information related to integers and complex numbers. Subsequent chapters explore key ideas relating to linear algebra such as vector spaces, linear mapping, and bilinear forms. The book explores the development of the main ideas of algebraic structures and concludes with applications of algebraic ideas to number theory. Interesting applications are provided throughout to demonstrate the relevance of the discussed concepts. In addition, chapter exercises allow readers to test their comprehension of the presented material. Algebra and Number Theory is an excellent book for courses on linear algebra, abstract algebra, and number theory at the upper-undergraduate level. It is also a valuable reference for researchers working in different fields of mathematics, computer science, and engineering as well as for individuals preparing for a career in mathematics education. Details ISBN: 9780470640531 Publisher: Wiley Imprint: John Wiley & Sons, Inc. Date: July 2011 Creators Author: Martyn Dixon Bio:MARTYN R. DIXON, PhD, is Professor in the Department of Mathematics at the University of Alabama, Tuscaloosa. He has authored more than sixty published journal articles on infinite group theory, formation theory and Fitting classes, wreath products, and automorphism groups. Author: Igor Subbotin Bio:IGOR YA. SUBBOTIN, PhD, is Professor in the Department of Mathematics and Natural Sciences at National University (California). Dr. Subbotin is the author of more than 100 published journal articles on group theory, cybernetics, and mathematics education. Author: Leonid Kurdachenko Bio:LEONID A. KURDACHENKO, PhD, is Distinguished Professor and Chair of the Department of Algebra at the Dnepropetrovsk National University (Ukraine). Dr. Kurdachenko has authored more than 150 journal articles on the topics of infinite-dimensional linear groups, infinite groups, and module theory. Reviews "The book is well-written and covers, with plenty of exercises, the material needed in the three aforementioned courses, albeit in a new order." (Zentralblatt MATH, 1 December 2012)"However, instructors contemplating such a unified approach should give this book serious consideration. Recommended. Upper-division undergraduates through researchers/faulty." - Choice , 1 April 2011
How it works Algebra.com is an interactive website. Our solvers generate formulae "on the fly". It is also a "people's math" website, where tutors who know math share their knowledge by writing lessons, solvers, and tutor children on homework problems. Besides that, our needs require a capacity of our software not only to draw, but also ot "understand" expressions. That's needed for the universal simplifier, as well as for plotting graphs. All of that requires a simple way of potting dynamically generated formulae, graphs, number lines, and geometric diagrams. That's what my system does. A formula or a drawing can be described in a format that everyone could understand. There is much less (in a normal case, none) learning that's involved compared to TeX. How it works A tutor writes a solution, a lesson or a solver. He types in (or has his/her solver generate) a formula, and marks it using a {{{ }}} notation. Example: As you know, a proportion is a relation such as {{{x/a=c/d}}}, where x is the unknown and a, c and d are constants. My system would notice the curly brackets and replace the text between them with a call to a script to plot the formula. The script would do the following Check to see if the result is already available in the cache If not, parse the formula and understand what it means Determine the size of the formula and of each of its components Plot the formula. if graphs or animations are requested, draw them Return the generated image to the browser. The result would be seen as As you know, a proportion is a relation such as , where x is the unknown and a, c and d are constants.
Mathematical concepts such as probability, statistics, geometric constructions, measurement, ratio and proportion, pre-algebra, and basic tests and measurements concepts including interpretation of data. Use of manipulatives in learning mathematical concepts. Only applicable to graduation requirements of elementary education students.
P D Barry, National University of Ireland, Ireland Geometrical thinking is still very much alive. Dr Barry's pragmatic approach in a combination of Euclidean treatment of geometry is pitched at university degree level. Students who take trouble to become familiar with the tools introduced will find the spirit of geometry logically unfolded in a fascinating challenge. The Mathematical Gazette A fascinating book that reminded me of a time when geometry played a more central and cohesive role. Primarily for post A-level students, it should be considered for the library shelves of mathematics departments where 'old style' geometry is still appreciated and enjoyed. Mathematics Teaching - provides a modern and coherent exposition of geometry with trigonometry for varying levels in mathematics, applied mathematics, engineering mathematics and other areas of application - describes computational geometry, differential geometry, mathematical modelling, computer science, computer-aided design of systems in mechanical, structural and other engineering, and architecture - provides many geometric diagrams for a clear understanding of the text and includes problem exercises for each chapter This book addresses a neglected mathematical area where basic geometry underpins undergraduate and graduate courses. Its interdisciplinary portfolio of applications includes computational geometry, differential geometry, mathematical modelling, computer science, computer-aided design of systems in mechanical, structural and other engineering, and architecture. Professor Barry, from his long experience of teaching and research, here delivers a modern and coherent exposition of this subject area for varying levels in mathematics, applied mathematics, engineering mathematics and other areas of application. Euclidean geometry is neglected in university courses or scattered over a number of them. This text emphasises a systematic and complete build-up of material, moving from pure geometrical reasoning aided by algebra to a blend of analytic geometry and vector methods with trigonometry, always with a view to efficiency. The text starts with a selection of material from the essentials of Euclidean geometry at A level, and ends with an introduction to trigonometric functions in calculus. Very many geometric diagrams are provided for a clear understanding of the text, with abundant Problem Exercises for each chapter. Students, researchers and industrial practitioners would benefit from this sustained mathematisation of shapes and magnitude from the real world of science which can raise and help their mathematical awareness and ability.
Unit specification Aims The programme unit aims to introduce basic ideas group theory with a good range of examples so that the student has some familiarity with the fundamental concepts of abstract algebra and a good grounding for further study. Brief description This course unit provides an introduction to groups, one of the most important algebraic structures. It gives the main definitions, some basic results and a wide range of examples. This builds on the study of topics such as properties of the integers, modular arithmetic, and permutations included in MATH10101/MATH10111. Groups are a fundamental concept in mathematics, particularly in the study of symmetry and of number theory. Intended learning outcomes On completion of this unit successful students will be able to: Appreciate and use the basic definitions and properties of groups; Command a good understanding of the basic properties for a good range of examples; Understand and find simple proofs of results in group theory. Future topics requiring this course unit This is followed by the Semester 2 unit MATH20212 Algebraic Structures 2 that focuses on rings. Together these units provide the basis for a wide range of modules in algebra and related areas at levels 3 and 4. The ideas developed in this lecture course are also used in analysis, geometry, number theory and topology.
Bonney Lake ChemistryAllowing us to begin to see numbers in a different light, algebra helps enable one to "think outside the box". There are times where a problem provides the whole, but we need to find the parts. Furthermore, algebra brings us into a different realm of numbers below zero
Definition Problem solving, in any academic area, involves being presented with a situation that requires a resolution. Being a problem-solver requires an ability to come up with a means to resolve the situation fully. Problem: A question proposed for solution; a knotty point to becleared up.Solve: To explain; to make clear; to unravel; to work out. (New Expanded Webster's Dictionary, 1988) In Mathematics, problem solving generally involves being presented with a written out problem in which the learner has to interpret the problem, devise a method to solve it, follow mathematical procedures to achieve the result and then analyze the result to see if it is an acceptable solution to the problem presented. A version of these steps are addressed in the book "How to Solve It" written by G. Polya and in the 4-Step Plan described below. Uses Typical problem solving we see in elementary-level classrooms involve word problems that present the learner with simulated situations which they can correlate to actual real-life situations. The goal is for the learner to be able to apply the strategies used to resolve the simulated situation to real-life. Instruction should cultivate the discovery of relationships, conceptuallearning, and thinking skills as well as mastery of basic facts andprocedures. ...the focus of instruction should be on meaningful learningand problem solving. (Baroody, 1989) Description of the 4-Step Plan (Glencoe/McGraw-Hill, 2001) Explore-Determine what information is given in the problem and what you need to find. (Glencoe/McGraw-Hill, 2001) In the "explore" step, students should be encouraged to read the problem carefully and determine what information is needed to solve the problem. This also requires the student to decide if there is information included that is irrelevant to solving the problem. Plan-After you understand the problem, select a strategy for solving it. (Glencoe/McGraw-Hill, 2001) In the "plan" step, the students should devise a strategy or strategies to find a solution to the problem. This may require using several mathematical methods of computation or setting up an equation. Student should also be encouraged at this point to form an estimate of the solution. The estimate will help in determining whether the final answer is reasonable. Solve-Solve the problem by carrying out your plan. (Glencoe/McGraw-Hill, 2001) In the "solve" step, the students will perform the mathematical computations necessary to determine an answer. In many cases the answer may not be acceptable at the first attempt, so the students should realize that they may have to perform their computations more than once in order to achieve the desired result. In addition, the students may find that the methods of computation they chose will not work toward the solution, therefore alternate methods may have to be used. Examine-Finally, examine your answer carefully. See if it fits the facts given in the problem. (Glencoe/McGraw-Hill, 2001) In the "examine" step, the students need to analyze their solution to see if it is an acceptable answer to their presented problem. Students should look at the estimate they formed in the "plan" step to see if it is similar to their calculated outcome. Often students should re-read the original problem to be sure that they interpretted it correctly the first time. If it is determined that the solution is not acceptable, they should return to the "plan" step and re-solve the problem. How I Teach It... When teaching the "4-Step Plan" to my sixth and seventh grade students, I ask them if they are familiar with the "plan" first. In most cases, they have studied the "plan" in a previous textbook or class. Then I ask the students if they use the "plan" to solve word problems outside of the lesson that teaches it, encouraging them to be honest. In most classes the majority of the students say they do not use the "plan". I then break the plan down by asking the following questions... 1) Do you read the word problem? 2) Do you pick out the information you need to solve the problem? If so, you just did the "explore" step. 3) Do you determine a method to solve the problem? 4) Do you form an estimate in your head? (most kids say no to this one) If so, you just did the "plan" step. 5) Do you do the math to find your answer? If so, you just did the "solve" step. 6) Do you make sure that your answer fits the problem? If so, you just did the examine step. Several of my students then decide that they do use the "4-Step Plan", at least partially. I feel that the "plan" is the basic thought process that is required to effectively solve problems. In the next section, I will connect this with Polya's 4 steps. Polya's Four Steps "How To Solve It" (Polya, 1957, p.xvi) Polya's problem solving plan is not geared for interpretation by elementary students, but has the same basic steps as the "4-Step Plan" above. Rather than give Polya's version verbatim, I will comment on each step and include his commentary when needed. I would encourage getting the book. Understanding the Problem (Polya, 1957) "You have to understand the problem." (Polya, 1957) In this step, the solver is encouraged to find the unknown, gather the data and separate the data into parts. Devising a Plan (Polya, 1957) "Find a connection between the data and the unknown. ...You should obtain eventually a plan of the solution." (Polya, 1957) In this step, the solver is encouraged to make connections to previously solved problems. Carrying out the Plan (Polya, 1957) "Carry out your plan." (Polya, 1957) In this step, the solver is encouraged to check each step along the way and think of ways of proving it's accuracy. Looking Back (Polya, 1957) "Examine the solution obtained." (Polya, 1957) In this step, the solver is encouraged to check the result, think of other methods to solve the same problem and decide if the strategy could be used for other problems. I feel encouraged by teaching the 4-Step Plan because of the connection that can be made to Polya. The same strategies are used in both, but the 4-Step Plan is easier for the elementary learner to understand. Types of Math Problems Used in Problem Solving Make a chart: Connections to Psychology Problem solving strategies, as stated in the sections above, are important to improving a student's ability to solve problems. Knowledge of a general problem-solving strategy also improvesperformance, even among children. (Bruning, Schraw & Ronning, 1999, p.211) In my reading while investigating problem-solving I encountered discussion on whether problem-solving skills should be taught as an individual course or included in the curriculum areas. Students themselves would likely benefit from both. A general problem-solving class could serve as an entry level course introducing students to basic problem-solving skills before they are encountered in the individual curriculum areas. A follow-up problem-solving course, toward the end of elementary-level teaching could serve as a way of compiling the knowledge the students have aquired and aiding in their ability to make connections to other situations. Testimonials When I taught problem solving to my junior high students, I always made my students explain HOW they solved their problems. This is required when students take the ISAT test. I wanted them to explain their process and what worked and did not work when solving the problem. I thought that this activity made the students think about problem solving. Nichole Jessup As Gifted Coordinator, it is my responsibility to oversee the special education services provided to the district's gifted population. I work very hard to give these students problem solving exercises that go beyond the typical math text word problem. If we are to encourage problem solving and critical thinking among our youth it is important that we stimulate them with problems and activities that are both intellectually challenging and conceivably possible. In real life the division problem doesn't always work out evenly and fractions don't always reduce as we would like them to. Stacy Borkgren Problem solving as a method to learn is a wonderful idea. I have used this in the library, when students are doing research. Most often they would like me (the librarian) to find the resources and the exact information that they may be looking for. As a joke, I often ask if they would like me to write their paper for them. Some would gladly allow that to happen. My point is that the research is the most exciting part of writing a paper. Students need to learn problem solving methods to gain the greatest amount of resources and knowledge of the topic they are studying. M. Youngblood I use a problem solving book in my class called Daily Mathematics which gives the students a problem of the day to solve. I require them to not only solve the problem but also to share how they solved the problem. I like that it exposes the students to so manyu different types of problems. But I wonder how effective it is to practice these problems in such a random nature. - E. Remington
Are calculus and real analysis the same thing? They are written in greek. I was wrong , the total pages are 2800 (2 theory and some problems and examples and 2 other only problems.) It uses literature from apostol,ayoub,birkhoff,comtet,ciang and lots of other[80 total].But they are extreemly hard to read. Even the most difficult textbook for calculus is easy compared to them.And they are given at engineering school
Table of contents Part I: Arithmetic as an Outgrowth of Learning to Count. From Counting to Addition. Subtraction. Multiplication. Division. Fractions. Area: The Second Dimension. Time: The Fourth Dimension. Part II: Introducing Algebra, Geometry, and Trigonometry as Ways of Thinking in Mathematics. First Notions Leading Into Algebra. Developing "School" Algebra. Quadratics. Finding Short Cuts. Mechanical Mathematics. Ratio in Mathematics. Trigonometry and Geometry Conversions. Part III: Developing Algebra, Geometry, Trigonometry, and Calculus. Systems of Counting. Progressions. Putting Progressions to Work. Developing Calculus Theory. Combining Calculus with Other Tools. Introduction to Coordinate Systems. Part IV: Developing Algebra, Geometry, Trigonometry, Calculus as Anlytical Methods in Mathematics. Complex Quantities. Making Series Do What You Want. The World of Logarithms. Mastering in the Tricks. Development of Calculator Aids. Digital Mathematics. Appendix: Answers to Questions and Problems. Author comments Stan Gibilisco is a professional technical writer who specializes in books on electronics and science topics. He is the author of The Encyclopedia of Electronics, The McGraw-Hill Encyclopedia of Personal Computing, and The Illustrated Dictionary of Electronics, as well as over 20 other technical books. His published works have won numerous awards. The Encyclopedia of Electronics was chosen a "Best Reference Book of the 1980s" by the American Library Association, which also named his McGraw-Hill Encyclopedia of Personal Computing a "Best Reference of 1996." Stan Gibilisco's Web sites are and Back cover copy The definitive self-teaching guide to learning mathematics--now fully up-to-date. Unlike other math books that make your start at page one and work your way up to the technique you need, this unique guide steers you right to your topic of interest, fully explains it within its own context, and then shows you how to use it with real-world examples. The unique jump-in-anywhere format and conversational tone of Stan Gibilisco's and Norman Crowhurst's Mastering Technical Mathematics makes this book--now thoroughly updated--a must for just about any technical professional. It's also the perfect instruction manual for independent students who want to structure their own learning. With this one-of-a-kind, case study-filled guide to all kinds of math used in technical fields, you can--find the technique you need quickly, along with easy-to-understand examples showing how it's used; skip from topic to topic in any order, and learn in your own style at your own pace; master technical math painlessly with this guide's easy-going style and example-packed format; discover new applications in logic, digital systems, and numbering systems; test yourself with quiz questions in each chapter (and complete worked-out solutions). If you work in a field where math comes with the territory, don't miss the guide that puts a multitude of math solutions right at your fingertips: Mastering Technical Mathematics, Second Edition.
Why does undergraduate discrete math require calculus? - MathOverflow most recent 30 from does undergraduate discrete math require calculus?johntantalo2010-06-04T18:32:18Z2011-01-13T02:33:19Z <p>Often undergraduate discrete math classes in the US have a calculus prerequisite.</p> <p>Here is the description of the discrete math course from my undergrad:</p> <blockquote> <p>A general introduction to basic mathematical terminology and the techniques of abstract mathematics in the context of discrete mathematics. Topics introduced are mathematical reasoning, Boolean connectives, deduction, mathematical induction, sets, functions and relations, algorithms, graphs, combinatorial reasoning.</p> </blockquote> <p>What about this course suggests calculus skills would be helpful?</p> <p>Is passing calculus merely a signal that a student is ready for discrete math?</p> <p>Why isn't discrete math offered to freshmen — or high school students — who often lack a calculus background?</p> by coudy for Why does undergraduate discrete math require calculus?coudy2010-06-04T18:45:38Z2010-06-04T18:45:38Z<p>I see three reasons.</p> <p>Generating functions is an example of tools used in discrete mathematics. Calculus definitely helps working with them.</p> <p>Binomial coefficients arise frequently in discrete math. Many formulas about these coefficients can be handled by calculus.</p> <p>Also, even if you are interested only on what happens for finite sets of size n, probably you will want to let n goes to infinity at some point, and then continuous laws, integrals and the like will appear naturally.</p> <p>Still I think that it is possible to teach a beginner course in discrete mathematics which does not rely on calculus.</p> by Andrey Rekalo for Why does undergraduate discrete math require calculus?Andrey Rekalo2010-06-04T19:11:35Z2010-06-04T19:11:35Z<p>Sometimes it's difficult even <em>to write an answer</em> to a discrete math problem without an integral or two.</p> <p><strong>Example.</strong> The number of integer lattice points that satisfy the conditions $$-n\leq x,y,z\leq n,\quad -s\leq x+y+z\leq s$$ for some $n$, $s\in\mathbb N$, is equal to $$\frac{1}{2\pi}\int\limits_{-\pi}^{\pi}\left(\frac{\sin \frac{2n+1}{2}t}{\sin\frac {t}{2}}\right)^3\frac{\sin \frac{2s+1}{2}t}{\sin \frac{t}{2}} dt. $$</p> by engelbrekt for Why does undergraduate discrete math require calculus?engelbrekt2010-06-04T19:15:12Z2010-06-04T19:15:12Z<p>Where I work, the first-semester science students are offered two mathematics courses: One-variable calculus and introductory discrete mathematics. Obviously the emphasis in the latter course cannot be on solving counting problems in terms of elementary functions, since calculus is the main tool for handling these. The course contains combinatorics, graph theory and number theory up to congruences. Calculus is not a prerequisite.</p> by Alexander Woo for Why does undergraduate discrete math require calculus?Alexander Woo2010-06-04T20:09:16Z2010-06-04T20:09:16Z<p>A significant portion (my observation was about 20-30% at Berkeley, which means it must approach 100% at some schools) of first year students in the US do not understand multiplication. They do understand how to calculate $38 \times 6$, but they don't intuitively understand that if you have $m$ rows of trees and $n$ trees in each row, you have $m\times n$ trees. These students had elementary school teachers who learned mathematics purely by rote, and therefore teach mathematics purely by rote. Because the students are very intelligent and good at pattern matching and at memorizing large numbers of distinct arcane rules (instead of the few unifying concepts they were never taught because their teachers were never taught them either), they have done well at multiple-choice tests.</p> <p>These students are going to struggle in any calculus course or any discrete math course. However, it is easier to have them all in one place so that one instructor can try to help all of them simultaneously. For historical reasons, this place has been the calculus course.</p> by Chris Phan for Why does undergraduate discrete math require calculus?Chris Phan2010-06-04T20:33:14Z2010-06-04T20:33:14Z<p>Perhaps it's done to ensure a certain level of mathematical maturity. For example, here is what one author writes in <a href=" rel="nofollow">the preface to his discrete mathematics text</a>:</p> <blockquote>This book has been written for a sophomore-level course in Discrete Mathematics. [. . .] Students are assumed to have completed a semester of college-level calculus. This assumption is primarily about the level of the mathematical maturity of the readers. The material in a calculus course will not often be used in the text.</blockquote> <p>(Eric Gossett, Discrete Mathematics with Proof, 2nd ed., John Wiley and Sons, 2009)</p> by hypercube for Why does undergraduate discrete math require calculus?hypercube2010-06-04T21:19:49Z2010-06-04T21:19:49Z<p>Although calculus is not frequently used in discrete mathematics it is nice to know that the students have had at least some exposure to sets and functions. I am teaching discrete this summer and find myself saying "you have seen this in calculus" when talking about several fundamental concepts.</p> <p>When doing proofs in a calculus course I usually try to point out the fundamental concepts from the course that are needed and in a discrete course the actual process of how do do a proof is studied more closely. Again it is nice to know that at least the students have seen proofs before and we can build on this exposure.</p> by Victor Protsak for Why does undergraduate discrete math require calculus?Victor Protsak2010-06-04T22:01:36Z2010-06-04T23:32:20Z<p>In the context of college students, I agree with Alexander Woo's explanation. By the way, the best and the brightest often place out of calculus (that's the case at Yale, and I imagine it's not that much different at Berkeley), so the percentages of weak students at best schools aren't as dire as you might think.</p> <p>Concerning the last question, </p> <p><em>"Why isn't discrete mathematics offered to high school students without calculus background?"</em> </p> <p>Not only is that possible, but it had been the norm in the past within the "New Math" curriculum, when everyone had to learn about sets and functions in high school. This ended in a PR disaster and a huge backlash against mathematics, because generations of students were lost and got turned off by mathematics for life; some of them later became politicians who decide on our funding. Consequently, it was abandoned. (Apparently, calculus in HS was introduced as a part of the same package and survived.)</p> <p>I'd be interested to know if there are any high school – college partnerships that offer discrete mathematics to H.S. students with strong analytical skills, and how do they handle the prerequisites question.</p> by Noah Snyder for Why does undergraduate discrete math require calculus?Noah Snyder2010-06-05T04:29:34Z2010-06-05T04:29:34Z<p>In the context of very bright high school students with strong mathematics backgrounds, it is typical to teach discrete math to students without requiring calculus as a prerequisite. In particular, this is the norm both at the Ross program (where 2nd year students often had a combinatorics class) and at Mathcamp (where many discrete math classes are often taught without calculus as a prerequisite). Both summer programs avoid teaching calculus because it messes up highschool students who are going to be stuck taking calculus whether they already know it or not.</p> <p>In particular, it's quite possible to teach formal differentiation and integration of power series in order to do generating functions without discussing traditional differentation or limits. In fact, the Ross problem sets had a problem set developing the basics of calculus for polynomials (linearity, Leibniz rule, etc.) without ever discussing limits. I'd already learned calculus at that point, but not all the students had. And the students who didn't know calculus didn't have too much of a difficulty with that problem set. It's certainly easier than proving that the group of units modulo p is cyclic.</p> <p>So the reason for requiring such a prerequisite for a college course is not that it's actually a logical prerequisite, but instead for sociological reasons along the lines of Alex's answer.</p> by Gerry Myerson for Why does undergraduate discrete math require calculus?Gerry Myerson2010-06-05T13:33:12Z2010-06-05T13:33:12Z<p>When I was at Buffalo 30 years ago, Tony Ralston advocated teaching discrete math instead of calculus to 1st year students. I taught it out of some notes he had prepared, and thought the students found it harder than calculus. It was easier to relate calculus topics to things they already knew about than it was to do that for the topics in his notes. </p> <p>I'm pretty sure those notes became a textbook, so you can probably get a copy and see one man's idea of what should/could be taught to students before calculus. </p> by J W for Why does undergraduate discrete math require calculus?J W2010-08-31T16:44:40Z2010-08-31T16:44:40Z<p>Today I came across the following article that might be of interest: <a href=" rel="nofollow">Has Our Curriculum Become Math-Phobic?</a> by Keleman et al. The authors address mathematics in the computer science curriculum and advocate the early introduction of discrete mathematics.</p> by kcrisman for Why does undergraduate discrete math require calculus?kcrisman2011-01-13T02:33:19Z2011-01-13T02:33:19Z<p>This has been dormant for a while, but it's worth pointing out <a href=" rel="nofollow">the ACM recommendations</a>, which essentially say what J W says - but I don't have enough rep to vote up that answer or comment on it, so I provide the link here for those searching for info. The ACM also recommended calculus in <a href=" rel="nofollow">this set of recs</a>, whereas the update is more about the core CS curriculum. It's also worth mentioning that the ACM is focused more on "sound reasoning", not "formal symbolic proof", in its guidelines. That doesn't necessarily mean less mathematical, from what I can tell.</p>
In this resource, from the Department fof Education Standards Unit, students learn to distinguish, by drawing and by using the order of the vertices, between Eulerian graphs, semi-Eulerian graphs and graphs that are neither; and to find strategies for solving the route inspection or 'Chinese postman' problem. Students should have some knowledge of what is meant by a graph, a vertex and an edge in the context of decision mathematics. (AS/A level
and computational algebraic systems might play? What is the role of paper and pencil computation in developing understanding as well as skill? These are questions that appear at every level of school mathematics. Checkpoints: Assessment Algebra represents a major challenge for many students. If more students are to succeed in meeting that challenge, it will be important to identify the points of difficulty for individual students and provide effective instructional responses before they are lost. The difficulty factors assessments of algebra reading (Koedinger and Nathan, In Press) and algebra writing (Heffernan and Koedinger, 1997, 1998) are examples of efforts to provide assessment tools for this purpose. Two features of the subject make assessing individual progress very important. Algebra requires facility with much of the mathematics that has come before. If the mathematical foundation is weak in any of its components, algebra mastery will be undermined. Determining where students need to shore up the preparatory mathematics, as well as opportunities for doing so, are critical to success. Second, algebra instruction moves toward high-level abstraction. The readiness of individual students to move from one level of difficulty to the next will differ. If the movement comes before a bridge is effectively built to a student's prior knowledge or before new knowledge is consolidated, the student will be lost. If movement toward greater difficulty does not come soon enough, a student will make less progress in higher level algebra than is possible. Indeed, precisely this is at the heart of opposing views of algebra pedagogy. If formative assessment were sophisticated enough to determine individual student readiness to move on, then trade-offs between attending to the needs and preparedness of different students would not be necessary. A research and development effort at Carnegie Melon University that generated the Algebra Cognitive Tutor has focused very productively on the second element of this problem (see Box 3.5). It began as a project to see whether a computational theory of thought, called ACT (Anderson, 1983), could be used as a basis for delivering computer-based instruction. The cognitive theory applies to problem solving more broadly. For pur-
Policies Life of Fred: Pre-Algebra with Economics $29.00 You know what arithmetic books look like. They are all pretty much alike. Using very few words, they give a couple of examples and then have the students do a hundred identical problems. Then they give another couple of examples and another hundred problems. And for students, arithmetic becomes as much fun as cleaning up their rooms, eating yams, or going to the dentist. The books in the Life of Fred series take a different approach. Note that the subtitle on each book is "as serious as it needs to be". Veteran math teacher, Stan Schmidt, has brought to life a character who will make math fun, relevant, and understandable. Don't be surprised if your child who dreads math asks to do more at the end of a lesson. Each of the books tells a story—a story of one day in the life of a five-and-a-half-year-old boy. All of the math arises out of Fred's life. Never again will students have to ask their perennial question: "When are we ever gonna use this stuff?" Don't let the nontraditional method of teaching fool you. Each of these books contains more math than is normally taught at the college level. These are not skimpy. They offer solid preparation for SAT exams and upper-division mathematics. One of the reasons is that very few arithmetic books tell you the why of various math rules—they just say that "it's a rule". Fred will give you the reasoning behind the rules making the math much more meaningful and memorable. In all of the books in the Life of Fred series, the emphasis is on how to learn by reading. Students of normal academic ability can learn mathematics from Fred without your tutoring the material though you'll enjoy reading about Fred's adventures as much as your student does. You can relax. As students progress through high school, college, and graduate school, they find that less and less is learned in the classroom lecture format. Increasingly, it's the written word that does the teaching. Let the book do the math teaching. These books are gloss-film laminated hardcovers with Smyth sewn binding. Fully indexed and illustrated. They are not workbooks to write in, and each book will be enjoyed by all your children (and grandchildren!) Fred begins his summer vacation. Learn . . . * How to get rid of snakes in sugar cane fields * The difference between freedom and liberty * Why Fred couldn't be a movie star * . . . and even some algebra and economics All fun! Just open & enjoy Domain and codomain of a function, Conversion factors, Steps in Solving Word Problems, How Not to Bore Your Horse If You Are a Jockey, One-to-one Functions, Unit Analysis, Key to a Successful Business, Five Qualities that Money Should Have, the Tulip Mania in Holland, Definitions of Capitalism, Socialism, and Communism, Payday Loans, the Tragedy of the Commons, Partnerships, Cardinality of a Set, Four Ways to Kill Competition, Freedom vs. Liberty, Why We Have a High Standard of Living, Tariffs, Demand Curves, Venn Diagrams, Ricardo's Law of Comparative Advantage.
Communiqué de presse Better student preparation needed for university maths Schools and college maths courses are paying little attention to preparing students to use maths in other areas of study according to a project funded by the Economic and Social Research Council (ESRC). Moving from sixth form, or college, into higher education (HE) can be a challenge for many students, especially those who start mathematically demanding courses. Life prior to university focuses on achieving maximum examination success to be sure of a place. Faced with this pressure, school and college maths courses pay little attention to preparing students to use maths in other areas of study according to a project funded by the Economic and Social Research Council (ESRC). A student's ability to apply mathematical reasoning is critical to their success, especially in HE courses like science, technology, engineering and medicine. The study, undertaken by Professor Julian Williams, Dr Pauline Davis, Dr Laura Black, Dr Birgit Pepin of the University of Manchester and Associate Professor Geoffrey Wake from the University of Nottingham, shows that it is important to understand how students can prepare for the 'shock to the system' they face and how they can be given support at school, college and university to help in the transition. The researchers found that students were not fully aware of the importance of the mathematical content in the courses they had joined at university, and particularly how to apply maths in practice. Associate Professor Geoffrey Wake states, "Different teaching styles of university lecturers and the need for autonomously-managed learning, where students need to learn some mathematical content of their courses on their own without input from lecturers, also came as a bit of a shock for many students. On the other hand, some of the lecturers had limited knowledge of the exam-driven priorities of A-level maths courses and were not aware of the techniques students had been taught prior to attending their university courses." The researchers also found significant problems in motivating studentsto engage with the mathematics within their chosen university coursewhere mathematics was not their main area of study. Generally, schools and colleges were found not to be preparing students for university learning practices, and the level of learning-skills support was variable once students arrived at university. "Many students felt that they would benefit from student-centred learning and greater opportunity for dialogue with their lecturers," says Associate Professor Wake. "Unfortunately, the efficiencies required of university teaching resulting in lecturing of large numbers of students makes developing such a learning culture unlikely." The findings led the researchers to consider the implications for the policies and practices of schools, colleges and universities recommending a better two-way flow of information between schools and colleges and universities to address the issues of preparation and expectation. They concluded that the sixth-form curriculum should provide 'learning to learn' skills and mathematical modelling for students following A-level maths courses.
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Appendices This textbook is designed to teach the university mathematics student the basics of linear algebra and the techniques of formal mathematics. There are no prerequisites other than ordinary algebra, but it is probably best used by a student who has the "mathematical maturity" of a sophomore or junior. The text has two goals: to teach the fundamental concepts and techniques of matrix algebra and abstract vector spaces, and to teach the techniques associated with understanding the definitions and theorems forming a coherent area of mathematics. So there is an emphasis on worked examples of nontrivial size and on proving theorems carefully. This book is copyrighted. This means that governments have granted the author a monopoly --- the exclusive right to control the making of copies and derivative works for many years (too many years in some cases). It also gives others limited rights, generally referred to as "fair use," such as the right to quote sections in a review without seeking permission. However, the author licenses this book to anyone under the terms of the GNU Free Documentation License (GFDL), which gives you more rights than most copyrights (see appendix GFDL). Loosely speaking, you may make as many copies as you like at no cost, and you may distribute these unmodified copies if you please. You may modify the book for your own use. The catch is that if you make modifications and you distribute the modified version, or make use of portions in excess of fair use in another work, then you must also license the new work with the GFDL. So the book has lots of inherent freedom, and no one is allowed to distribute a derivative work that restricts these freedoms. (See the license itself in the appendix for the exact details of the additional rights you have been given.) Notice that initially most people are struck by the notion that this book is free (the French would say gratuit, at no cost). And it is. However, it is more important that the book has freedom (the French would say liberté, liberty). It will never go "out of print" nor will there ever be trivial updates designed only to frustrate the used book market. Those considering teaching a course with this book can examine it thoroughly in advance. Adding new exercises or new sections has been purposely made very easy, and the hope is that others will contribute these modifications back for incorporation into the book, for the benefit of all. Depending on how you received your copy, you may want to check for the latest version (and other news) at Topics. The first half of this text (through Chapter M:Matrices) is basically a course in matrix algebra, though the foundation of some more advanced ideas is also being formed in these early sections. Vectors are presented exclusively as column vectors (since we also have the typographic freedom to avoid writing a column vector inline as the transpose of a row vector), and linear combinations are presented very early. Spans, null spaces, column spaces and row spaces are also presented early, simply as sets, saving most of their vector space properties for later, so they are familiar objects before being scrutinized carefully. You cannot do everything early, so in particular matrix multiplication comes later than usual. However, with a definition built on linear combinations of column vectors, it should seem more natural than the more frequent definition using dot products of rows with columns. And this delay emphasizes that linear algebra is built upon vector addition and scalar multiplication. Of course, matrix inverses must wait for matrix multiplication, but this does not prevent nonsingular matrices from occurring sooner. Vector space properties are hinted at when vector and matrix operations are first defined, but the notion of a vector space is saved for a more axiomatic treatment later (Chapter VS:Vector Spaces). Once bases and dimension have been explored in the context of vector spaces, linear transformations and their matrix representation follow. The goal of the book is to go as far as Jordan canonical form in the Core (part C), with less central topics collected in the Topics (part T). A third part contains contributed applications (part A), with notation and theorems integrated with the earlier two parts. Linear algebra is an ideal subject for the novice mathematics student to learn how to develop a topic precisely, with all the rigor mathematics requires. Unfortunately, much of this rigor seems to have escaped the standard calculus curriculum, so for many university students this is their first exposure to careful definitions and theorems, and the expectation that they fully understand them, to say nothing of the expectation that they become proficient in formulating their own proofs. We have tried to make this text as helpful as possible with this transition. Every definition is stated carefully, set apart from the text. Likewise, every theorem is carefully stated, and almost every one has a complete proof. Theorems usually have just one conclusion, so they can be referenced precisely later. Definitions and theorems are cataloged in order of their appearance in the front of the book (\miscref{definition}{Definitions}, \miscref{theorem}{Theorems}), and alphabetical order in the index at the back. Along the way, there are discussions of some more important ideas relating to formulating proofs (\miscref{technique}{Proof Techniques}), which is part advice and part logic. Origin and History. This book is the result of the confluence of several related events and trends. At the University of Puget Sound we teach a one-semester, post-calculus linear algebra course to students majoring in mathematics, computer science, physics, chemistry and economics. Between January 1986 and June 2002, I taught this course seventeen times. For the Spring 2003 semester, I elected to convert my course notes to an electronic form so that it would be easier to incorporate the inevitable and nearly-constant revisions. Central to my new notes was a collection of stock examples that would be used repeatedly to illustrate new concepts. (These would become the Archetypes, appendix A.) It was only a short leap to then decide to distribute copies of these notes and examples to the students in the two sections of this course. As the semester wore on, the notes began to look less like notes and more like a textbook. I used the notes again in the Fall 2003 semester for a single section of the course. Simultaneously, the textbook I was using came out in a fifth edition. A new chapter was added toward the start of the book, and a few additional exercises were added in other chapters. This demanded the annoyance of reworking my notes and list of suggested exercises to conform with the changed numbering of the chapters and exercises. I had an almost identical experience with the third course I was teaching that semester. I also learned that in the next academic year I would be teaching a course where my textbook of choice had gone out of print. I felt there had to be a better alternative to having the organization of my courses buffeted by the economics of traditional textbook publishing. I had used TeX and the Internet for many years, so there was little to stand in the way of typesetting, distributing and "marketing" a free book. With recreational and professional interests in software development, I had long been fascinated by the open-source software movement, as exemplified by the success of GNU and Linux, though public-domain TeX might also deserve mention. Obviously, this book is an attempt to carry over that model of creative endeavor to textbook publishing. As a sabbatical project during the Spring 2004 semester, I embarked on the current project of creating a freely-distributable linear algebra textbook. (Notice the implied financial support of the University of Puget Sound to this project.) Most of the material was written from scratch since changes in notation and approach made much of my notes of little use. By August 2004 I had written half the material necessary for our Math 232 course. The remaining half was written during the Fall 2004 semester as I taught another two sections of Math 232. While in early 2005 the book was complete enough to build a course around and Version 1.0 was released. Work has continued since, filling out the narrative, exercises and supplements. However, much of my motivation for writing this book is captured by the sentiments expressed by H.M. Cundy and A.P. Rollet in their Preface to the First Edition of Mathematical Models (1952), especially the final sentence, This book was born in the classroom, and arose from the spontaneous interest of a Mathematical Sixth in the construction of simple models. A desire to show that even in mathematics one could have fun led to an exhibition of the results and attracted considerable attention throughout the school. Since then the Sherborne collection has grown, ideas have come from many sources, and widespread interest has been shown. It seems therefore desirable to give permanent form to the lessons of experience so that others can benefit by them and be encouraged to undertake similar work. How To Use This Book. Chapters, Theorems, etc. are not numbered in this book, but are instead referenced by acronyms. This means that Theorem XYZ will always be Theorem XYZ, no matter if new sections are added, or if an individual decides to remove certain other sections. Within sections, the subsections are acronyms that begin with the acronym of the section. So Subsection XYZ.AB is the subsection AB in Section XYZ. Acronyms are unique within their type, so for example there is just one Definition B, but there is also a Section B:Bases. At first, all the letters flying around may be confusing, but with time, you will begin to recognize the more important ones on sight. Furthermore, there are lists of theorems, examples, etc. in the front of the book, and an index that contains every acronym. If you are reading this in an electronic version (PDF or XML), you will see that all of the cross-references are hyperlinks, allowing you to click to a definition or example, and then use the back button to return. In printed versions, you must rely on the page numbers. However, note that page numbers are not permanent! Different editions, different margins, or different sized paper will affect what content is on each page. And in time, the addition of new material will affect the page numbering. Chapter divisions are not critical to the organization of the book, as Sections are the main organizational unit. Sections are designed to be the subject of a single lecture or classroom session, though there is frequently more material than can be discussed and illustrated in a fifty-minute session. Consequently, the instructor will need to be selective about which topics to illustrate with other examples and which topics to leave to the student's reading. Many of the examples are meant to be large, such as using five or six variables in a system of equations, so the instructor may just want to "walk" a class through these examples. The book has been written with the idea that some may work through it independently, so the hope is that students can learn some of the more mechanical ideas on their own. The highest level division of the book is the three Parts: Core, Topics, Applications (part C, part T, part A). The Core is meant to carefully describe the basic ideas required of a first exposure to linear algebra. In the final sections of the Core, one should ask the question: which previous Sections could be removed without destroying the logical development of the subject? Hopefully, the answer is "none." The goal of the book is to finish the Core with a very general representation of a linear transformation (Jordan canonical form, Section JCF:Jordan Canonical Form). Of course, there will not be universal agreement on what should, or should not, constitute the Core, but the main idea is to limit it to about forty sections. Topics (part T) is meant to contain those subjects that are important in linear algebra, and which would make profitable detours from the Core for those interested in pursuing them. Applications (part A) should illustrate the power and widespread applicability of linear algebra to as many fields as possible. The Archetypes (appendix A) cover many of the computational aspects of systems of linear equations, matrices and linear transformations. The student should consult them often, and this is encouraged by exercises that simply suggest the right properties to examine at the right time. But what is more important, this a repository that contains enough variety to provide abundant examples of key theorems, while also providing counterexamples to hypotheses or converses of theorems. The summary table at the start of this appendix should be especially useful. I require my students to read each Section prior to the day's discussion on that section. For some students this is a novel idea, but at the end of the semester a few always report on the benefits, both for this course and other courses where they have adopted the habit. To make good on this requirement, each section contains three Reading Questions. These sometimes only require parroting back a key definition or theorem, or they require performing a small example of a key computation, or they ask for musings on key ideas or new relationships between old ideas. Answers are emailed to me the evening before the lecture. Given the flavor and purpose of these questions, including solutions seems foolish. Every chapter of part C ends with "Annotated Acronyms", a short list of critical theorems or definitions from that chapter. There are a variety of reasons for any one of these to have been chosen, and reading the short paragraphs after some of these might provide insight into the possibilities. An end-of-chapter review might usefully incorporate a close reading of these lists. Formulating interesting and effective exercises is as difficult, or more so, than building a narrative. But it is the place where a student really learns the material. As such, for the student's benefit, complete solutions should be given. As the list of exercises expands, the amount with solutions should similarly expand. Exercises and their solutions are referenced with a section name, followed by a dot, then a letter (C,M, or T) and a number. The letter `C' indicates a problem that is mostly computational in nature, while the letter `T' indicates a problem that is more theoretical in nature. A problem with a letter `M' is somewhere in between (middle, mid-level, median, middling), probably a mix of computation and applications of theorems. So solution MO.T13 is a solution to an exercise in Section MO:Matrix Operations that is theoretical in nature. The number `13' has no intrinsic meaning. More on Freedom. This book is freely-distributable under the terms of the GFDL, along with the underlying TeX code from which the book is built. This arrangement provides many benefits unavailable with traditional texts. No cost, or low cost, to students. With no physical vessel (i.e. paper, binding), no transportation costs (Internet bandwidth being a negligible cost) and no marketing costs (evaluation and desk copies are free to all), anyone with an Internet connection can obtain it, and a teacher could make available paper copies in sufficient quantities for a class. The cost to print a copy is not insignificant, but is just a fraction of the cost of a traditional textbook when printing is handled by a print-on-demand service over the Internet. Students will not feel the need to sell back their book (nor should there be much of a market for used copies), and in future years can even pick up a newer edition freely. Electronic versions of the book contain extensive hyperlinks. Specifically, most logical steps in proofs and examples include links back to the previous definitions or theorems that support that step. With whatever viewer you might be using (web browser, PDF reader) the "back" button can then return you to the middle of the proof you were studying. So even if you are reading a physical copy of this book, you can benefit from also working with an electronic version. A traditional book, which the publisher is unwilling to distribute in an easily-copied electronic form, cannot offer this very intuitive and flexible approach to learning mathematics. The book will not go out of print. No matter what, a teacher can maintain their own copy and use the book for as many years as they desire. Further, the naming schemes for chapters, sections, theorems, etc. is designed so that the addition of new material will not break any course syllabi or assignment list. With many eyes reading the book and with frequent postings of updates, the reliability should become very high. Please report any errors you find that persist into the latest version. For those with a working installation of the popular typesetting program TeX, the book has been designed so that it can be customized. Page layouts, presence of exercises, solutions, sections or chapters can all be easily controlled. Furthermore, many variants of mathematical notation are achieved via TeX macros. So by changing a single macro, one's favorite notation can be reflected throughout the text. For example, every transpose of a matrix is coded in the source as {\tt\verb!\transpose{A}!}, which when printed will yield $\transpose{A}$. However by changing the definition of {\tt\verb!\transpose{ }!}, any desired alternative notation (superscript t, superscript T, superscript prime) will then appear throughout the text instead. The book has also been designed to make it easy for others to contribute material. Would you like to see a section on symmetric bilinear forms? Consider writing one and contributing it to one of the Topics chapters. Should there be more exercises about the null space of a matrix? Send me some. Historical Notes? Contact me, and we will see about adding those in also. You have no legal obligation to pay for this book. It has been licensed with no expectation that you pay for it. You do not even have a moral obligation to pay for the book. Thomas Jefferson (1743 -- 1826), the author of the United States Declaration of Independence, wrote, If nature has made any one thing less susceptible than all others of exclusive property, it is the action of the thinking power called an idea, which an individual may exclusively possess as long as he keeps it to himself; but the moment it is divulged, it forces itself into the possession of every one, and the receiver cannot dispossess himself of it. Its peculiar character, too, is that no one possesses the less, because every other possesses the whole of it. He who receives an idea from me, receives instruction himself without lessening mine; as he who lights his taper at mine, receives light without darkening me. That ideas should freely spread from one to another over the globe, for the moral and mutual instruction of man, and improvement of his condition, seems to have been peculiarly and benevolently designed by nature, when she made them, like fire, expansible over all space, without lessening their density in any point, and like the air in which we breathe, move, and have our physical being, incapable of confinement or exclusive appropriation. Letter to Isaac McPherson August 13, 1813 However, if you feel a royalty is due the author, or if you would like to encourage the author, or if you wish to show others that this approach to textbook publishing can also bring financial compensation, then donations are gratefully received. Moreover, non-financial forms of help can often be even more valuable. A simple note of encouragement, submitting a report of an error, or contributing some exercises or perhaps an entire section for the Topics or Applications are all important ways you can acknowledge the freedoms accorded to this work by the copyright holder and other contributors. Conclusion. Foremost, I hope that students find their time spent with this book profitable. I hope that instructors find it flexible enough to fit the needs of their course. And I hope that everyone will send me their comments and suggestions, and also consider the myriad ways they can help (as listed on the book's website at
spreadsheets can also be used. Activity sheets, discussion questions, lesson extensions, suggestions for assessment, and prompts for teacher reflection are included. (author/sw) Distinguish between situations that can be modeled with linear functions and with exponential functions. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. HSF-LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Estimate, compute and solve problems involving rational numbers, including ratio, proportion and percent, and judge the reasonableness of solutions. Patterns, Functions and Algebra Standard Benchmarks (8–10) B. Identify and classify functions as linear or nonlinear, and contrast their properties using tables, graphs or equations. J. Describe and interpret rates of change from graphical and numerical data. Benchmarks (11–12) A. Analyze functions by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior. Grade Level Indicators (Grade 8) 3. Identify functions as linear or nonlinear based on information given in a table, graph or equation. 16. Use graphing calculators or computers to analyze change; e.g., interest compounded over time as a nonlinear growth pattern. Grade Level Indicators (Grade 9) 5. Principles and Standards for School Mathematics Algebra Standard Understand patterns, relations, and functionsAnalyze change in various contextsapproximate and interpret rates of change from graphical and numerical data.
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While we understand printed pages are helpful to our users, this limitation is necessary to help protect our publishers' copyrighted material and prevent its unlawful distribution. We are sorry for any inconvenience. Generally speaking, humans develop skills as they mature. They will employ skills when they are competent and comfortable with them and using them will lead to an improvement in their quality of life. Children develop speech and then they can more easily tell their parents what they want; they develop dexterity and then they can more readily enjoy their toys. In this chapter we are concerned with developing certain key skills in mathematics students, skills that we describe as transferable and that will enable students to improve their quality of life. Professional mathematicians require good transferable skills, such as reading, writing, speaking and working with others, as well as subject-specific knowledge. They may be applied mathematicians, in one or more of a variety of guises such as scientists, engineers, economists or actuaries, and will be working with others, using mathematics and mathematical modelling to solve problems and answer questions that may arise in industry, commerce or a social context. If they are pure mathematicians, they will almost certainly be employed by a university with some requirement to conduct research and to teach. Those mathematics graduates who become schoolteachers will certainly need good interpersonal and leadership skills, along with several other attributes that they may not get through an undergraduate mathematics education! Some mathematics graduates will go into general employment, and they, like their peers will need all of the aforementioned transferable skills.
MAT 299 - Mathematical Proof and Problem Solving This course introduces students to the language and methods used to create and write mathematical proofs and solve problems. Methods of proof will include: direct, contrapositive, contradiction, and induction. Methods of problem solving will be based on Polya's four steps for problem solving. Students will learn about and utilize the many functions of proof including: verification, explanation, communication, discovery, justification, and inquiry. The course will also explore the relationship between problem solving and the process of proving. Students will explore fundamental abstract concepts in mathematics including: functions and relations, set theory, number theory, and logic.
Why do we need to learn algebra? Question #64340. Asked by ballparkdeeh. (Apr 06 06 11:38 AM) Brainyblonde First of all, algebra is the gateway to all the higher maths: geometry, algebra II, trigonometry, analytic geometry, calculus and beyond. Since all sciences (including biology, chemistry, physics, astronomy, engineering, computer science, architecture, design, many social sciences, economics, finance, even flying an airplane!) depend on algebra and higher math, learning algebra is essential for anyone considering working in these fields. Learning the abstract reasoning skills that algebra teaches helps students become better abstract reasoners in general. Good abstract reasoning skills improve a student's ability to write a coherent essay, for example, since essays require the writer to shift back and forth between abstract concepts and specific supporting facts. Many life skills, including choosing a career, making major purchases, running a business, and managing a family also require reasoning skills that are improved by math study. In addition, success in algebra correlates highly with success in higher education. Algebra and further math are critical to a student's chance of attending university. This was well documented in a 1990 study by the College Board. In this study, researchers found that students who take a year of algebra and follow that with a year of geometry nearly double their chances of going to college -- by doing that alone! Students should be aware that the two college entrance exams, the SAT and the ACT, are loaded with algebra I questions. It is impossible to get a decent score on these exams' math sections without a solid grasp of algebra. This is why we study algebra. Apr 06 06
0764144650 9780764144653, graphs, and graphing-calculator-based approached. Major topics covered include: algebraic methods; functions and their graphs; complex numbers; polynomial and rational functions; exponential and logarithmic functions; trigonometry and polar coordinates; counting and probability; binomial theorem; calculus preview; and much more. Exercises at the end of each chapter reinforce key concepts while helping students monitor their progress. Barron's continues its ongoing project of improving, updating, and giving contemporary new designs to its popular Easy Way books, now re-named Barron's E-Z Series. The new cover designs reflect the books' brand-new page layouts, which feature extensive two-color treatment, a fresh, modern typeface, and many more graphics. In addition to charts, graphs, and diagrams, the graphic features include instructive line illustrations, and where appropriate, amusing cartoons. Barron's E-Z books are self-teaching manuals designed to improve students' grades in many academic and practical subjects. In most cases, the skill level ranges between senior high school and college-101 standards. In addition to their self-teaching value, these books are also widely used as textbooks or textbook supplements in classroom settings. E-Z books review their subjects in detail and feature short quizzes and longer tests to help students gauge their learning progress. All exercises and tests come with answers. Subject heads and key phrases are set in a second color as an easy reference aid. «Show less
Woodmere Calculus was a math prof and worked at Cornell supporting researchers. I have IDs for NYU and Queens College.SPSS was Frank's first stat package in the '80s at Cornell where he was the Stat/data manager for a large EPA project studying dirnking water. While tutoring and consulting students and researc...The key concepts you are likely to encounter in any first algebra course include number systems, variables, functions, graphing, inequalities and polynomial equations. Calculus is the study of change, with the basic focus being on Rate of change and Accumulation. In both of these branches (Diff...
A solid understanding of mathematics, also known as numeracy, is an important component of a well-rounded education. The ability to perform basic mathematical computations is a requirement of many entry-level jobs. In addition, careers in fields such as engineering, medicine, finance and all of the sciences require a solid background in higher-level university mathematics, including calculus, statistics and linear algebra. PHOTO BY REV DAN CATT ON FLICKR WITH CC LICENSE The first thing to point out here is that the basic mathematical computations for entry level jobs are much different than the higher-level university level mathematics needed for engineering, medicine, finance and the sciences. I have to agree with Zwaagstra that a solid understanding of mathematics is an important component of a well-rounded education. However, his assertion that mathematics equals numeracy is definitely false, as I have had pointed out to me on a regular basis. Many mathematicians, engineers, doctors, economists, and scientists struggle with basic computational math, but are still fully capable of doing higher level mathematics. This has been true for a long time, far longer than the new math has been used in schools. Because math is such an important skill, schools have an obligation to ensure that students learn key math concepts. Unfortunately, schools are largely failing in this regard. First-year post-secondary students are increasingly unprepared for university-level mathematics, and this has led to a proliferation of remedial math courses at universities across Canada. Many parents choose to enrol their children in special tutoring sessions with organizations such as Kumon and the Sylvan Learning Centre to fill in the gaps left by the public school system. Unfortunately, many cannot afford extra tutoring, and this creates a two-tiered system that unfairly penalizes children whose parents cannot pay for extra math lessons. Now Zwaagstra points out that remedial math courses are on the rise in universities, but he doesn't mention a couple of key facts. First, under the old system of mathematics instruction, around 50 per cent of students failed first-year math courses, which were often included in programs as a tool with which to weed people out of university. Could it be that this issue has always been around, and universities are simply now doing something about the problem? What about the increase in students seeking a university education? Could these two issues be connected? Zwaagstra has assumed a correlation between the number of remedial math courses, and the effectiveness of K-12 math education, without actually finding research that supports his conclusion. It is also important to point out that the "new" math education techniques are themselves not very old, and are not used by all teachers equally. The most recent iteration of the elementary school math curriculum in British Columbia is only four years old, and the secondary school curriculum is only five years old, neither of which is a long enough period of time to make the kind of determinations of effectiveness that Zwaagstra is making. Further, he talks about parents enrolling their kids in after-school tutoring programs without discussing the reasons why parents are doing this. Are parents increasingly enrolling their kids for extra tutoring because they are dissatisfied with their children's current educational attainment? Or do they have other reasons for paying for these tutoring services? We don't know, and Zwaagstra doesn't provide us with any evidence for the reasons for parents to choose tutoring. He just cherry-picks this fact because it seems to support his argument. Although there is solid evidence supporting the traditional approaches to teaching math that involve mastering standard algorithms, practising skills to mastery and introducing concepts in incremental steps, most provincial math curricula and textbooks employ a different approach. Constructivism, which encourages students to come up with their own understanding of the subject at hand, is the basis for this new approach to teaching math. As a result, there is very little direct instruction of important mathematics algorithms or rigorous practising and memorization of basic math facts. The problems in our math education system are entirely due to the introduction of the new math curriculum, according to educator and author Michael Zwaagstra. There is also solid evidence showing that the longer that people are out of school, the less likely they are to use the algorithms they use in school, but the more successful they are at solving mathematical problems they encounter, as Keith Devlin points out in his book, The Math Instinct. In other words, traditional school math seems to be a hindrance to people being able to actually solve real-world mathematical problems. It's worth pointing out that Devlin's research is reasonably old, and most of the participants in the research learned mathematics in the traditional method. Is it even worth pointing out that Zwaagstra doesn't actually include any of his "solid evidence" in his paper, and the footnote here (see the original article) leads to a definition of the word algorithm? Our students deserve better. Pupils who are not taught math properly are being unfairly denied the opportunity to enter careers in many desirable fields. The public school system has an obligation to ensure that every child has the opportunity to learn the mathematics required for university-level mathematics courses. It's pretty important to note that when teachers are given proper training in effective pedagogy, their students' understanding improves. To say that the problems in our math education system are entirely due to the introduction of the new math curriculum is pretty irresponsible, given that any number of other factors could be contributing to the problem. Further, many schools use the International Baccalaureate program, which itself relies on the "new math" with a focus on students understanding mathematics and being able to communicate their understanding. These students are highly sought after by universities. If the new math was so destructive, wouldn't we see these students being turned away by universities? Zwaagstra then goes on to bash the results of the PISA examinations, citing an article (claiming it is research) written that suggests that Finnish students are not as good at math as the PISA results would claim, and that by extension, neither are Canadian students. There is a strong consensus [emphasis mine] among math professors that the math skills of these students are much weaker than they were two or three decades ago. Zwaagstra links to two articles (neither of which is a research study) that state that some professors have found a drop in numeracy skills (again, these are associated with mathematical ability, but are not equivalent), and the other of which makes no mention of math skills at all. In this case, Zwaagstra is completely misrepresenting the articles themselves. He then points to two professors who have done research on the computational abilities of graduates and noticed a decline, but he does not clarify whether or not this is correlated with a decline in their ability to do university-level mathematics. Zwaagstra continues by bemoaning the lack of standards and emphasis on accurate calculations by the National Council of Mathematics Teachers (NCTM), and the Western and Northern Canadian Protocol (WNCP). Clearly, the research these two organizations have done for decades is not sufficient for Zwaagstra. However, there is a big difference between demonstrating a conceptual understanding of mathematics and actually being able to solve equations accurately and efficiently. Just as most people would be very uncomfortable giving a driver's licence to someone who merely demonstrates a conceptual understanding of how to drive a car, we should be concerned about a math curriculum that fails to emphasize the importance of mastering basic math skills. To extend Zwaagstra's analogy, we should similarly be afraid of giving the keys to someone who has no real-world experience driving. If someone has spent all of their time in a flight simulator, but never actually driven a car, should they be allowed to do so? Does an emphasis on the mechanics of driving a car (or the mechanics of mathematics) turn someone into one who is capable of driving a car (or able to use mathematics)? Zwaagstra's solution to improving math education is to move "back to basics," which is as unoriginal an idea as I've heard. It is arrogant of Zwaagstra to assume that this approach hasn't been tried before. Perhaps he could instead address the issue of elementary school teachers often lacking support and training in how to teach math? Zwaagstra points out (correctly) that having mastered one computation, students are then better able to learn another computation, but this leaves students learning a series of computations, and not spending any time actually using them. JUMP math is mentioned in Zwaagstra's article as an antidote to the problem, but he doesn't talk about the issue of the associated training, or the lack of diverse assessment used in the JUMP math system. I think that the training manuals that go along with the JUMP math curriculum, for example, actually address the misconceptions of the people teaching the math (mostly elementary school teachers) rather than itself being a significantly better system. As one educator has told me, JUMP math is pretty useless without the training materials for teachers. Just as someone who does not practise the piano will never learn to play well, someone who does not practise basic math skills will never become fluent in math. Similarly, someone who has not had time to play with a piano, to improvise, and to perform music for others will never develop an appreciation for the instrument. Zwaagstra is suggesting that we should discard the extra parts of math education, like problem solving, and focus on computations, which is the musical equivalent of only learning scales, and never getting to perform music. No one would stand for that in music education, so why should we accept it in math education? People should have the freedom to express an opinion on what they feel is a problem. To do so otherwise is to be undemocratic. Opinions can draw attention to issues in our society that need to be addressed. However, such opinions should be clearly labelled as such, and not called studies. Peer reviewed research (which shows that the techniques advocated by the NCTM and WNCP are effective) carries with it a heavier weight of authority, and is a more reliable instrument with which to craft public policy. Instead of relying on uninformed opinions of people outside of the field of mathematics education to determine education policy, we should look at what the research says works for improving instruction. Our goal should be to replicate practices which work, and to extinguish practices which do not. * * * * * How can educators help students improve in math? How effective is the "new" math? Share your tips in the Comments section below. Today's students are more tech savvy than ever as they are immersed in the world of social media, "infotainment" and spectacle. As a result, many students feel they have to "power down" to succeed in a classroom environment that offers fewer options for learning than are available in the lives they live outside the classroom. In the information age, educators are faced with the pressure to stay current and come up with innovative ways to excite their students about learning. By integrating technology into the classroom, educators can make learning more engaging and present curriculum in a way that resembles the type of media that students are accustomed to consuming. As an assistant professor of education at Brock University, I believe that relevant types of technology like 3LCD projectors can be integrated into the classroom experience to enhance learning outcomes. Incorporating technology in the classroom can be as simple as creating an agenda in PowerPoint, and showing or emailing it to the entire class. It makes the agenda a little more interactive, ensures every student is on the same page and also saves paper. Many students respond better when they are shown something visual, and they can actually see how it applies to what they're learning in class. Whether it's Skyping with others around the world or viewing a video on YouTube, the entire classroom gets to participate and see the practical component of what they're learning. Today's students are leaders in the use of technology and as educators, we need to understand and adapt to their evolving learning styles. By using technology tools in lessons and projects that engage students, educators can increase classroom participation while students develop better critical-thinking and comprehension skills. I believe that projectors are a key component for 21st-century teachers – they help students retain information, cater to a variety of learning styles and create an authentic learning experience. In challenging economic conditions where schools face tight budgets, it is critical to allocate resources in ways that would make the greatest impact. Technology is the best investment for the future of our youths in a highly connected world. * * * * * How are you using technology to integrate it in class? Do you have advice on how students can balance and integrate technology in their studies? Share your tips, resources and views in the Comments section below. Dr. Maria Montessori is one of the most famous women in the world and yet a key part of her life is all but unknown. Dr. Robert Gardner, working with colleagues at Clanmore Montessori in Oakville, Ont., took a new look at a time in Maria Montessori's life that is glossed over, even by her most noted biographers. "Not to know this story is to have an incomplete understanding of one of history's most remarkable women," says Cathy Sustronk, one of the founders of Clanmore. When Maria Montessori was 30 (in 1900) her father presented her with a book filled with 200 articles he had clipped from the national and international press, all of which wrote glowingly about his unusually talented daughter. She was known as the "beautiful scholar," and in an age when women were blocked from most professions and careers she had – against all odds – become the first woman physician in Italy. She had been interviewed by Queen Victoria and had represented her country at major international conferences. She was elegant, poised and – perhaps – just a bit vain. She was at the height of her fame, and it seemed that she could achieve anything. At this heady moment she was appointed the co-director for a school in Rome. It was an unprecedented appointment for a woman in that very conservative time. Her partner was another young physician, Giuseppe Ferruccio Montesano. Italian sources suggest that he was not in robust good health, but he was elegantly handsome. He came from the south of Italy and in his family, while the sons all entered the professions, the daughters were consigned to "womanly tasks" such as lace-making and the study of music. He and Montessori fell in love and she became pregnant. At that time, especially in Italy, to have a child out of wedlock would have been disastrous to anyone. Montessori was facing the ignominy of being a scarlet woman. Montesano's mother, by all accounts a very severe dowager, refused to consider marriage. Montesano was desperate. Montessori, perhaps for the first time in a charmed life, was bewildered. Montesano had a solution. He would give the child his name, but the baby would have to be sent away to a wet nurse as soon as it was born. There was, however, no possibility of marriage. His mother, a woman who traced her ancestry to the House of Aragon, the rulers of southern Italy, was adamant. Montessori was devastated. Montesano, in trying to calm her, promised that he would never marry anyone else. She was the only one for him. Montessori made the same vow. In a sense, they would have a spiritual union which made the disastrous consequences of their affair less dismal. A Crisis, Then Remarkable Recovery A year later Montesano betrayed her and married another woman. Montessori was in complete crisis. She had sent her baby son away to live with strangers and she could not openly acknowledge the child's relationship to her. In the next decade she would see the child occasionally, but she never indicated to the boy that she was his mother. She was a tortured soul. In this moment of absolute defeat she did something remarkable. Instead of crumbling under the strain, she went into the seclusion of a convent to meditate. Before the crisis she was likely somewhat egotistical and her life had been filled with triumph after triumph. As a woman of her time, and as an Italian, she was – of course – a Roman Catholic. But her faith was the faith of a scientist and a scholar, skeptical and refined. Now this proud and brilliant woman was reduced to a state of desperation. However, during the days and weeks in seclusion something incredible happened. In fact, she underwent a complete psychological transformation and she emerged from this period of self-examination with a set of goals which seem unbelievable to the modern observer. She appeared determined to totally reinvent herself. She moved forward with a resolution that is at once baffling and inspiring. Although she was the first female medical doctor in the history of Italy, she decided to leave the practice of medicine forever. Abruptly, and without explanation, she resigned her prestigious post as co-director of an institute for developmentally challenged children. Then she enrolled at the University of Rome to master totally new areas of study. She took courses in anthropology, educational philosophy, and experimental psychology. At the same time, she made another momentous decision that changed the course of education and teaching forever. Up to this time she had been preoccupied with children who were in some ways in the language of the times, "feeble minded." Now she decided to focus all of her energies on improving pedagogy for the normal child. With that decision, Dr. Maria Montessori proceeded to revolutionize our thoughts about infancy and the incredible capacities of children from the very moment of birth. In a strange way, if there had been no Dr. Montesano there would have been no Maria Montessori. He, inadvertently, became the catalyst for a monumental emotional crisis that led Montessori, just into her thirties, to challenge every misconception about the capacities and needs of the very young. A Son's Influence on the Nobel Peace Prize Winner Dr. Montesano never recognized his child, Mario Montessori, as his own. Indeed, even Maria Montessori, on her many tours where Mario was her faithful interpreter, always introduced him as either her nephew or her adopted son. It was when she was close to death that she accepted him publicly and in her will she identified him as "Il figlio mio" – my son. Montesano, though, was never more than a footnote to history while Maria Montessori was nominated for the Nobel Peace prize three times. Among scores of honours, she was the recipient of the French Legion of Honour decoration, and she received honourary doctorates from some of the greatest universities in the world. It was a terrible crisis that forged her untiring will to help children everywhere to reach their true potential. Without that searing ordeal her name, like that of the man who betrayed her, may have been forgotten. It might be thought that the crisis that shaped her thinking might somehow have diminished her. Even generous modern readers may wonder why she abandoned her child for almost 15 years. The fact is, this terrible tragedy steeled her to recreate herself and caused her to focus her incredible talents in an effort to somehow make amends for the tragic loss of her son's presence during his formative years. One day, when he was 15, the young Mario Montessori noticed an elegant woman watching him with great interest. Something told him that this was his mother. He approached her and they were reunited. For the rest of his life, although he subsequently married, he was her constant companion and confidant. They were inseparable and together they created an approach to education that exists to this day. The remarkable ending to this story is that modern research continues to validate her findings. In a recent study by Dr. Angeline Lillard, titled The Science Behind the Genius, Dr. Lillard collects scores of modern research findings which support Dr. Montessori's earliest views on educating the child. Increasingly Dr. Montessori's observations are being employed in secondary schools with stunning results. In fact, her ideas could well be employed in the university system where students are often isolated in an arid world of abstract lectures. Maria Montessori, in some academic settings, is ignored precisely because she had such a trenchant insight into the failings of so much of what we call education. More than half a century after her death her influence is still making itself felt, still creating a sense of discomfort amongst some professional educators, and still pointing towards a more humane form of transmitting information to young children and adolescents. Smart Boards strategies for capturing the inner Brainpower of students and adults worldwide. Rewire Their Brains to Achieve Academic and Social Success… These topics opens the possibilities for how you as a Teacher, Educator, parent, student, Psychologist, Social Worker, Guidance Counsellor, Youth Worker and administrative can apply practical and technological strategies that could open the door for learners who require alternative strategies to gain personal and professional success. Come and Experience the next step in Learning and Providing support for anyone that learns differently. Hear Students and Adults speak on their experience of working with Assistive Technology to manipulate through the education and corporate environment. Hear from people who have experience the success of providing information in alternative ways for success. These successful strategies can support anyone who work with or have being diagnosed as learning differently. Learn more and register today to attend. In IT for Every Classroom, a weekly column on Dialogue Online, Paul Keery shares his practical tech advice for non-IT teachers. Photo from The York School Last week, we considered the factors involved in deciding what type of IT project to incorporate into your curriculum. This time around, let's look at examples of projects that would be appropriate for students in junior, intermediate and senior grades. I Remembrance Day Podcasts Believe it or not, Remembrance Day (Nov. 11) is fast approaching. Schools have revived and restored Remembrance Day commemorations in the last decade to recognize Canadians' service in conflicts around the world since the First World War. Students at all grades can create their own commemorative enhanced podcasts to recognize the contributions of family members (parents or grandparents) or of individual combatants. These can be played at school assemblies or in class on Nov. 11. For the Memory Project link, select WWI under Conflict, and it will take you to a list of veterans who have provided memories of the war. Find at least one other resource online; there are several good ones. Assignment: Imagine that you have survived the battle of Vimy Ridge, Canada's defining battle of the First World War. Write a short, one-minute Podcast about your experiences in the battle: in the trenches; what was life like every day as a soldier living in the trenches? describe the actions of one of four Canadians decorated at Vimy Ridge: Provate William Milne, Lance-Sergeant Ellis Sifton, Captain Thain MacDowell, or Private John Pattison. Your podcast will be an enhanced one; it must include photographs and images of the battle (actual images of the soldiers would be wonderful, but may be impossible to find) as well as appropriate sound effects and music. Procedure: Submit your script for evaluation before you record your podcast. Evaluation: The script will be worth 35 per cent of the mark; the completed podcast will be worth 65 per cent of the mark. This assignment could easily be modified to include the Second World War, Korean War, Canadian Peacekeeping Missions from the 1950s through the 1990s, the Gulf War, and the Afghanistan conflict. Students would be expected to write a proper script (as described in an earlier blog, Scriptwriting for Podcasts), and submit it as part of their completed assignment. II Dramatic Radio Show Students would be expected to write and record a radio play. Assignment: Produce a Drama or Comedy Program. Time: You have four classes to write and produce a five-minute drama or comedy program. This can be done in groups of three. Procedure You may use a script you write, a script of a student-written one-act play, or a script from an Old-Time Radio show. You must have actors, sounds and sound effects you record yourself. You must have music. Choose or write a drama that requires this amount of audio and complexity (not a one person introspective show). If what you choose lasts longer than five minutes, you must edit or clearly indicate that this is the first in a serial; you do not have to complete the entire script. Each student in the group must play a role in the play. Submit your script before recording the play. You will have four class periods to prepare the program; one of these will be used for editing your final show. Recording will take place in the third class period. You may have to convert sound files to mp3s at home to be sure that you are ready to upload them in class. The final edited version will be completed and due during the fourth class period. Evaluation: The script will be worth 35 per cent of the mark; the completed Podcast will be worth 65 per cent of the mark. Your feature will be presented in class. This project would be suitable for language arts of English classes, as well as high school drama and media classes. The new school year will be an exciting time for Civics classes throughout Canada as provincial and territorial elections ramp up. Already, is gathering and distributing materials to make this election one of the most memorable and active in the K-12 classrooms around the province. Last year, there was a municipal and federal election to keep Greenwood College School's students reading, listening and advocating for their politics, and now this year's classes will carry on that legacy of involvement and political action. (Click here for the article on their participation in the federal election.) Teachers and students can take advantage of a great learning opportunity during elections. CHRIS BOLIN/OUR KIDS MEDIA At our school, students' involvement in the election is an authentic and important way for them to learn about why getting active early in politics is so important. Moving the discussions away from the nitty-gritty of political procedure and precedents and into concrete connections to their own lives will help to raise politically active citizens. We plan on calling in to radio shows, writing letters to the editor, interviewing local candidates, and holding a mock election through Student Vote. In these ways, we will be getting students politically interested, active and engaged in the hopes that when the next election comes along, they will be an informed voter, and cast their ballot. Jack Layton's address to the youth of the country in his letter to Canadians spoke directly to the power and importance of political engagement in this demographic. Here is a link to Matt Galloway's interview with me on Metro Morning discussing his letter. Layton's letter is being met with a myriad of resources for teachers: is the government of Canada's website to explain and explore all about elections gives teachers lesson plans and hooks to get students asking questions about why politics is important to them is a place for students to read, explore and contribute to political discussions going on around the world about political issues is a vital resource for any teacher looking to hold an election in their class or school. What makes student vote unique is that they tally the votes from all schools involved and publish the data the day after the election. This shows the city, country, and now province where students, if they had the vote, would put their ballot. As a politics and history teacher, I hope that teachers and students take advantage of this great learning experience, and get involved with the election. The issues are important, personal and directly impact the future of this province. Good luck! * * * * * Do you have other tips and resources for teachers to help students get engaged in politics? Share your thoughts in the Comments section below. In IT for Every Classroom, a weekly column on Dialogue Online, Paul Keery shares his practical tech advice for non-IT teachers. Photo from The York School Choosing a subject for an IT project can be challenging. There are a number of important factors to consider when deciding where and how to add a podcast project to your curriculum. What Topics Fit Into the Course? Every course will present different opportunities for IT integration. English and Language Arts classes could easily do book reports or dramatizations of scenes from books or plays. History and Social Sciences classes would be able to do biographies of influential people or could examine controversial issues in those subjects. ESL and Second Language classes can use IT to practice speaking and pronunciation, or to do readings from second language books. Mathematics and Science classes could create reports on experiments or biographical reports about famous mathematicians or scientists. However, be sure to choose a topic that reflects your students' skills at using IT. Early projects in which students are learning to use IT should be kept relatively simple. Once they have become skilled users of particular hardware or software, their IT projects can become more complex. What Resources Are Available for Students to Use? The audio and video content of students' projects will also be affected (perhaps limited) by the resources that are available for them to add to their IT project, be it a podcast or a video project. [a] What audio files are available to be included in the project? If your History students are assigned a podcast about a modern historical figure, do you want your students to include audio clips of the person speaking? If so, are these legally available? [b] What still images and video files are available to be included in the project? If your Science students are doing a project about human space flight, what images can they legally download? Are public domain videos available? If so, how long will it take to download them – and will students be able to download them at school? Before creating a project, you must be sure that resources are readily available and can legally be used. See the blog post Recording the Autobiographical Podcast for a list of online sources that students can use to find such resources to use in their project. What Can Students Reasonably Be Expected to Produce? There is another possibility: Students can create audio and video files themselves. This is entirely possible if students are filming their own classroom work. For example, if Science students are creating a video project analyzing a classroom experiment, they could certainly film their own experiment and include it in the project. Care will have to be taken when filming the experiment, but it is certainly feasible. Similarly, Drama students could be assigned to create a video project analyzing their class play – if they are already doing a major play as part of the course and they have had to design and create costumes and sets. However, it may not be feasible to film a scene from a play as part of an English or Language Arts class: Where will the costumes and sets come from (especially if it is a Shakespeare play)? You can either set the play in a modern setting, or decide to do a podcast instead. The Final Choice It may seem, after looking at all of these factors, that it's almost impossible to design and implement an effective IT project, but it can be done. In IT for Every Classroom, a weekly column on Dialogue Online, Paul Keery shares his practical tech advice for non-IT teachers. Photo from The York School When you're starting out with IT, it's hard to resist getting carried away with the wonder of it all. There are so many possibilities. Podcasts. Enhanced visual podcasts. Movies. The trouble with getting caught up in the wonder of it all is that it is so easy to try to do too much in a first project or the only IT project for the school year (if you only have access to computers in an lab setting for a few weeks). Teachers want to get a bit of everything into the project. But trying to do too much will result in a lot of frustration for students and teachers as well as a poor learning experience. Think ahead and plan carefully must be your guide. Project Ideas – When To Do IT? IT is time intensive. IT projects will often take half as much time as you have scheduled, especially if you're just getting into IT integration. If your students have access to computers on a regular basis, avoid busy times of the year when other events are going on and schedule your IT project at a time when your students can focus on their IT work. Make sure that there is time available if the project runs long. However, if your access to a lab is pre-determined, you have no choice; you'll have to make the best of it. Keep the project short and simple to ensure that the students will finish on time. Project Ideas – How To Organize Them IT projects can best be used as summative projects (though it is very possible to do formative evaluation while the project is going on). Students should learn basic knowledge about the topic of the IT project first. Then use the IT project to have students do more research to add more specific knowledge about a particular area of the topic, as well as apply that knowledge to a problem related to the topic. For example, suppose students are learning about the War of 1812 as part of the upcoming bicentennial celebrations. In class, start off with a basic introduction to the war: Who was fighting, the major battles, the role of native peoples in the war, how civilians were affected by the war, and the outcome (who won?). After that is finished, students could be assigned more specific topics that would allow them to study an aspect of the War of 1812 in more detail: Why did the war start? Who were Isaac Brock, Laura Secord and Tecumseh, and what role did they play in the war? What happened at Queenston Heights (or any other battle)? What happened to York (now Toronto) during the war? Students could then analyze what happened and explain why it happened, or why an important person did or did not achieve their goals. Students could easily create a one or two-minute podcast or enhanced podcast about one of these topics. After the students present their podcasts to the class, all the students in the class could then be given a quiz about each podcast (or about all the podcasts). Project Ideas – What To Do? It's best that the IT project should form all or almost all of the instruction for a unit of work, given the research, writing, recording and presentation time the students will need. Try to choose a unit that lends itself to this approach. In Language Arts and Social Studies, a project could be built around a novel, short story, or a significant historical or geographical event; see the previous section for an example of such a project. In Art or Music, students could create an enhanced podcast about an artist or musician, including a biography and analysis of examples of their work. In Math and Science, students could create an enhanced podcast about a mathematician or scientist, including a biography and analysis of examples of their work; or they could examine and interpret a mathematical or scientific principle. Once students have finished their work, make sure to keep copies of their projects to show their parents, or to show future classes how IT projects can be done – and how students are combining traditional and modern literacy skills. Disclaimer: Information presented on this page may be paid advertising provided by the [advertisers/schools] and is not warranted or guaranteed by ourkidsmedia.com or its associated websites. See Terms and Conditions.
Mathematics enrichment program The Mathematics Enrichment Program(PDF350KB) has been offered by the University of Southern Queensland since 2007 and is a structured program designed to improve mathematical problem solving skills in gifted high-school students. Within Toowoomba and surrounding districts, a number of students display aptitude for mathematics beyond what is offered in the standard high school curriculum. Such students could potentially benefit from exposure to more problem solving techniques not traditionally offered. Aims of the program Interesting questions in selected topics will be tackled in lively sessions, to build students' range of techniques for solving problems. The aims of the program include: to help students perform at a high level in national mathematics competitions particularly the Australian Mathematics Competition; to encourage further study in mathematics; to enhance satisfaction for students who quickly master school level concepts. Who can attend? The program is aimed to suit the mathematical ability of Year 9 and 10 students. Interested students and schools in remote locations should contact Assoc Prof Ron Addie to discuss alternative methods of offering the program. How do I apply? Students will need to be registered through their Mathematics Teacher at school. Teachers will email names and contact details to Debbie White via sciences.engage@usq.edu.au. Cost There is no cost to attend the program. Time The program runs from 4.00 - 6.00 pm on Thursday afternoon at USQ. Refreshments are provided. Please note that the proposed topics for discussion may not necessarily be offered on the date listed. Presenters Presenters will include Ron Addie from the Department of Mathematics & Computing at USQ; Ashley Plank past member of the Department of Mathematics & Computing who now works as a consultant in statistics for medical research; Tim Dalby from Open Access College at USQ; Neville de Mestre leader in research into mathematics in sport; Peter Galbraith Honorary Professor at University of Queensland; Stephen Broderick, Head of Mathematics at St Ursula's College and President of the Toowoomba Maths Teachers Association and Bob Nelder, Head of Mathematics at Mt Lofty State High School and past president of TMTA. We look forward to creating a lively and fun Mathematics Enrichment program. This file is in Portable Document Format (PDF) which requires the use of Adobe Acrobat Reader. A free copy of Acrobat Reader may be obtained from Adobe . Users who are unable to access information in PDF should contact sciences.engage@usq.edu.auto obtain this information in an alternative format.
To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Algebra II Sal works through 80 questions taken from the California Standards Test for Algebra II ( If you struggle with these you can get more help by viewing the "algebra" topic and completing its exercises. Sal works through 80 questions taken from the California Standards Test for Algebra II ( If you struggle with these you can get more help by viewing the "algebra" topic and completing its exercises.
Algebra: A Self-Teaching Guide With a "learn-by-doing" approach, it reviews and teaches elementary and some intermediate algebra. While rigorous enough to be used as a college or ...Show synopsisWith a "learn-by-doing" approach, it reviews and teaches elementary and some intermediate algebra. While rigorous enough to be used as a college or high school text, the format is reader friendly, particularly in this Second Edition, and clear enough to be used for self-study in a non-classroom environment. "Pre-test" material enables readers to target problem areas quickly and skip areas that are already well understood. Some new material has been added to the Second Edition and redundant or confusing material omitted. The first chapter has undergone major revision. Chapters feature "post-tests" for self-evaluation. Thousands of practice problems, questions and answers make this algebra review a unique and practical
MacroeconomicsIntermediate Algebra: Connecting Concepts through Applications INTERMEDIATE ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS shows students how to apply traditional mathematical skills in real-world contexts. The emphasis on skill building and applications engages students as they master concepts, problem solving, and communication skills. It modifies the rule of four, integrating algebraic techniques, graphing, the use of data in tables, and writing sentences to communicate solutions to application problems. The authors have developed several key ideas to make concepts real and vivid for students. First, the authors integrate applications, drawing on real-world data to show students why they need to know and how to apply math. The applications help students develop the skills needed to explain the meaning of answers in the context of the application. Second, they emphasize strong algebra skills. These skills support the applications and enhance student comprehension. Third, the authors use an eyeball best-fit approach to modeling. Doing models by hand helps students focus on the characteristics of each function type. Fourth, the text underscores the importance of graphs and graphing. Students learn graphing by hand, while the graphing calculator is used to display real-life data problems. In short, INTERMEDIATE ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS takes an application-driven approach to algebra, using appropriate calculator technology as students master algebraic concepts and skillsOpen Source Training: WordPress Intermediate Class (August 2011) You need no WordPress or web design knowledge. Youll get rapid WordPress answers from teachers who have taught thousands of students. Youll have fun! The videos are entertaining and make your WordPress experience enjoyable. Youll learn from comprehensive and organized classes, not random tutorials. Youll save dozens of frustrating hours digging around the web for answers. You wont waste thousand of dollars on webdesigners. You can build WordPress websites. Exercise and Solutions Manual to Accompany Foundations of Modern Macroeconomics Second EditionApplied Survey Data AnalysisMacroeconomics: Private and Public Choice (13 edition) Macroeconomics: Private and Public Choice, the most accessible principles books on the market, has been updated to include coverage of the recent economic conditions. The new edition reflects current economic conditions, helping students apply economic principles to the world around them. You'll find analysis and explanation of measures of economic activity applied to today's markets and highlighting the recession of 2008-2009, plus text on the lives and contributions of notable economists. Common economic myths are dispelled, and the "invisible hand" metaphor is applied to economic theory, demonstrating how it works to stimulate the economy. The thirteenth edition of Macroeconomics: Private and Public Choice includes a robust set of online multimedia learning tools, with video clips and free quizzes designed to support classroom work. A completely updated Aplia interactive learning system is also available, completely with practice problems, interactive tutorials, online experiences and more. Intermediate Accounting 14 editionSolutions Upper Intermediate A clear structure, results-based lessons, extra practice, and specific exam preparation are all key elements in Solutions.The course supports students through its straightforward layout and clear presentation. Lessons are achievable and motivating, and give learners specific objectives to work towards.Speaking is integrated into every lesson, with model answers and pronunciation practice teaching students how to speak accurately. Each unit has at least one writing lesson, which includes sample texts and a 'Check your work' feature. These help students improve their critical thinking, spelling, grammar, and usage of phrases.Solutions follows the presentation-practice-production methodology: lexis and grammar is presented in context, followed by controlled practice, free practice, and applied production. Practice is reinforced from the Vocabulary and Grammar Builder in the Student's Book, tasks in the Workbook, games on the Student's MultiROM and website, and 20 additional photocopiables per level. on. Macroeconomics ( Netload - Rapidgator )Applied Survey Data Analysis ( Rapidgator - Netload )Keeping its finger on the pulse of the profession, the new twelfth edition updateEnglish Grammar in Use Fourth edition is an updated version of the worlds with answers version is ideal for self-study. An online version, book without answers, and book with answers and CD-ROM are available separately Grammar in Use with Answers 4th edition: A Self-Study Reference and Practice Book for Intermediate Students of English ( Rapidgator - Ryushare - Uploaded ) English Grammar in Use with Answers, 4th edition: A Self-Study Reference and Practice Book for Intermediate Students of English Download Filehost: Uploaded.net, Ryushare.com, Rapidgator.net By Raymond Murphy 2012 \| 390 Pages \| ISBN: 0521189063 \| PDF \| 124 MB
From time to time, not all images from hardcopy texts will be found in eBooks, due to copyright restrictions. We apologise for any inconvenience. Table of contents About this book Calculus and Differential Equations has been written with the needs of Australian students in mind. The book introduces differential equations much earlier than is done in more traditional calculus texts because it is one of the most important topics in calculus. The material has been graded into core (important and fundamental material) through to extensions which are more conceptual and finally harder more advanced material. The exercises are similarly graded. This will enable students to first focus on and master the basic ideas before tackling the harder stuff.
Description of Research Given a family of graphs F, a graph G is said to be F-free if G does not contain any graph from F as an induced subgraph. G is hamiltonian if G has a cycle of length the order of G. G is pancyclic if G contains cycles of all lengths from 3 to the order of G. Thus the concept of pancyclicity is an extension of the concept of hamiltonicity. The concept of hamiltonicity has been extensively studied in terms of degree conditions, the relationship between connectivity and independence, and forbidden subgraphs. My research extends the forbidden subgraph condition to determine similar conditions that guarantee pancyclicity. For example, I have shown that graphs which are 4-connected, claw-free, and P10-free are pancyclic. Example of how my research is integrated into my GK-12 experience One example integrating my research into the classroom was a discussion of graph decompositions. I was able to define for the students a few types of graphs and discussed how to determine the minimum number of graphs of a particular type necessary to decompose another type of graph. This concept was then tied into molecular models and we discussed how this type of information could be used to determine physical properties of such molecules. This discussion showed students that mathematical modeling is useful for scientific understanding
Math Text$ Math Text$ While searching the text book stores online I noticed that Academic math books are generally super expensive, ranging price from $150 to $300. Some texts are a few hundreds, 300 pages and they cost up to $200 or more? Come one? Please don't tell me because they have the hardcover or colors and drawings they cost more than average texts. There are many counter examples and they are very excellent books on their subjects, mainly computer science texts. So my conclusion was it has nothing to do with whether the text is really hardcover or colored with nice drawings (even free mags have these features) or the publisher that is expensive...or yet another famous tale that "used book industry" is causing book price to go up. Not to mention that those expensive texts have a news edition very frequent, every year or so and no significant change from previous one except for the exercise numbers? Rip of students' money? Science texts require to be up-to-date with rapidly changing science and this costs money for reviewers? Another unrealistic argument. Changing exercises order and numbers and corrected mistypes is not a consequence of a new scientific discovery :) What about math books? Math is almost the same for many topics since many decades...so what's going on? In my opinion it's the authors' greed. Not authors greed - authors have nothing to say, publishers set the price. Publishers will tell you highly specialized books require highly specialized editing work (costly) and they never sell in amounts large enough for the effect of scale to kick in. Which is not untrue, but it is not clear if it justifies prices that we see. Even if this is the case, there should be some rules to control publishers' greed. My argument is that students have to buy the required texts, and they are many across the world. BIG NUMBER = (# of uni's) x (# of classes) x (# of students) requiring the text. And if they say it does not sell very well and often then why make the book it in the first place? I can give many examples of books that are university texts and they are: 1 - a few hundred pages, some are 300 or less 2 - content is average, with some mistakes... 3 - significant content of the subject is only made accessible online 4 - no solution accompanied provided 5 - over $200 So why I'm buying this book? Only if I were a student forced to do so? Then why make such a book? Simply because millions gonna buy it. :) As simple as this. Yep I checked Dover's and they have very good collection with excellent price. However, for someone majoring in math or engineering...having to buy expensive books, makes me wonder why not helping the students...anyway Yep I checked Dover's and they have very good collection with excellent price. However, for someone majoring in math or engineering...having to buy expensive books, makes me wonder why not helping the students...anyway Typically companies help students because they expect payback down the road. For example if you give everyone matlab to use for free/cheap as a student, when they go to work as engineers they're going to tell their companies they need matlab to do their job more efficiently. On the other hand students are basically the only people buying these books - it's very unlikely you're going to tell your company they need to buy a bunch of Dover mathematics books so you can study Fourier analysis (since the probably expect you to know this already) In addition to no student is willing to pay for a software as much as they pay for the entire semester or even more...so it makes sense to give a special price they can afford. And this is a completely different matter. Personally I think when a book is priced over $60 then it's not a book anymore. For example, several calculus books have the same content, almost identical, same TOC, but use different coloring scheme and symbols. And all have same unrealistic price. I mean what the authors have in mind they want to compete? Others are not more than a dictionary of topics, a skill from all trades...no need to name titles. Others less than 300 pages in content for $350? Really? One interesting book I had to buy is about algebra, and it's amazing how it presents the topics. No intro, no why, no origin, nothing but a definition and a few examples, then jump to exercises with no solution, (only T/F answers), and with some BIG mistakes. No colors, no drawing or illustration, no applications, no subject appreciation. Guess what it's over $200. I don't want even to think about DEs books. Creativity is missing in presenting topics. "Why" and "how" is left as an exercise, not even in the "solution manual." I suggest there should be non-university-student versions of all these super expensive books, probably from Dover. This will very likely increase the sales. I think it's strange that some publishers set the prices so high. At some point, I would expect that so many students would just download an illegal digital copy instead of buying the book, that it would actually be more profitable for the publisher to set a lower price. I also find it strange that we don't see more self-published books. The authors can probably get paid at least 5 times as much per book if they don't let a publisher take most of the money. Prices can be absurd at times. I'm a little bit interested in the book "Quantum measure theory" by Jan Hamhalter, mainly because it claims to have a nice proof of Gleason's theorem. Its price at Amazon.com: $329 for the paperback, and $259 for the Kindle edition. No way I'm ever going to pay that to see the proof of a theorem. I guess I'll just try to find a library that has it. Even if I have to fly to Germany to find it in a library, that could be cheaper than buying the book. Step 1: Go to library, get out all the books. Step 2: Determine the best to buy. Step 3: Buy. Link your book that you want HAD to buy. Used only works sometimes. Publishers put out a new edition rather frequently. Even if the revisions are minor, a class will require the new edition, simply because the old edition can't be bought new and, theoretically, you can't guarantee finding enough used versions for all of the students. I have known a few students that have rebelled against this. They spent nearly $200 or more on a Calculus book that lasted them through a couple of classes, but skipped a semester before taking the third in the sequence and got slammed with having to buy a new book for the third class (not an unusual situation for adult students that are going to school part time). Some just choose to use the old edition and borrow someone else's book to get the exercises (violating copyright laws usually only costs 10 cents a copy or so in the school library). Personally, I own three Calculus text books. I believed reisistance was futile and actually forked out the money for a new book that would be used for the last class in the sequence, plus I won a Calculus book for having the highest score on some test all the students had to take after the first two classes. (In fact, actually, it was the highest score anyone had scored on that test. Naturally, the book that I won was an old edition that the school couldn't use anymore.) I think having three Calculus books is kind of cool. It makes me look smart, plus I always have one available, even if I left my favorite one in my other suit.
The aim of this book is to present a modern treatment of the theory of theta functions in the context of algebraic geometry. The novelty of its approach lies in the systematic use of the Fourier-Mukai transform. more... Accessible Mathematics is Steven Leinwand?s latest important book for math teachers. He focuses on the crucial issue of classroom instruction. He scours the research and visits highly effective classrooms for practical examples of small adjustments to teaching that lead to deeper student learning in math. Some of his 10 classroom-tested teaching shifts... more... impressive volume is dedicated to Mel Nathanson, a leading authoritative expert for several decades in the area of combinatorial and additive number theory. For several decades, Mel Nathanson's seminal ideas and results in combinatorial and additive number theory have influenced graduate students and researchers alike. The invited survey articles... more... Markov Chain Monte Carlo (MCMC) methods are now an indispensable tool in scientific computing. This book discusses recent developments of MCMC methods with an emphasis on those making use of past sample information during simulations. The application examples are drawn from diverse fields such as bioinformatics, machine learning, social science, combinatorial... more... The selected papers in this volume cover all the most important areas of ring theory and module theory such as classical ring theory, representation theory, the theory of quantum groups, the theory of Hopf algebras, the theory of Lie algebras and Abelian group theory. The review articles, written by specialists, provide an excellent overview of the... more... Since the appearance of the authors' first volume on elliptic curve cryptography in 1999 there has been tremendous progress in the field. This second volume addresses these advances and brings the reader up to date. Prominent contributors to the research literature in these areas have provided articles that reflect the current state of these important... more... Features contributions that are focused on significant aspects of current numerical methods and computational mathematics. This book carries chapters that advanced methods and various variations on known techniques that can solve difficult scientific problems efficiently. more... Explore the main algebraic structures and number systems that play a central role across the field of mathematics Algebra and number theory are two powerful branches of modern mathematics at the forefront of current mathematical research, and each plays an increasingly significant role in different branches of mathematics, from geometry and topology... more...
M316L Syllabus FOUNDATIONS OF GEOMETRY, STATISTICS, AND PROBABILITY Prerequisite and degree relevance: Prerequisite is M 316K with grade of C or better (except for students pursuing middle grades mathematics teacher certification through the UTeach program). This course is required for students preparing to teach elementary school, and for students in UTeach Liberal Arts planning to teach in the middle grades. It is also taken by some students preparting to teach middle grades mathematics. Text: Beckmann Topics and Format: The focus is on students working on Explorations supporting learning in the following sections of the textbook. More Detailed Syllabus for Instructors: Instructors should contact Mark Daniels (mdaniels@math.utexas.edu) for details.
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Intermediate Algebra Concepts and Applications 9780201708486 0201708485 Summary: The Sixth Edition of Intermediate Algebra: Concepts and Applications continues to bring your students a best-selling text that incorporates the five-step problem-solving process, real-world applications, proven pedagogy, and an accessible writing style. The Bittinger/Ellenbogen hardback series has consistently provided teachers and students with the tools needed to succeed in developmental mathematics. With this revi...sion, the authors have maintained all the hallmark features that have made this series so successful, including its five-step problem-solving process, student-oriented writing style, real-data applications, and wide variety of exercises. Among the features added or revised are new Aha! exercises that encourage students to think before jumping in to solve a problem, 20% new and added real-data applications, and 50% more new Skill Maintenance Exercises. This series not only provides students with the tools necessary to learn and understand math, but also provides them with insights into how math works in the world around them.[read more]
Linear algebra usually deals with vectors, matrices, solving multiple equations with multiple unknowns. These concepts are applied when there are too many variable going around and you have to represent them in a more systematic way, usually through the form of matrices. In Linear Algebra, you will be able to find out that such matrices are very powerful and contain a lot of information which is useful in the analysis and design of anything represented by that matrix. Discrete Mathematics deals with the math that is not continuous--easy to say... There are many topics under DM such as set theory and topology, boolean algebra, graph theory, trees, algorithm complexity, automata. II. COURSE DESCRIPTION: An introductory knowledge of Discrete Mathematics can prove very useful, indeed. This syllabus is intended for a one – or two – term introductory course in Discrete Mathematics. Formal Mathematics prerequisites are minimal; calculus is not required. This includes examples, exercises, figures, notes and self – tests to help the students master introductory Discrete Math. In the early 1980's there were almost no books appropriate for an introductory course in Discrete Mathematics. At the same time, there was a need for a course that extends the students' mathematical maturity and ability to deal with abstraction and included useful topics such as combinatorics, algorithms, and graphs. This syllabus addressed these needs. Subsequently, Discrete Mathematics courses were endorsed by many groups for several different audiences, including mathematics and computer science majors. A panel of MAA ( Mathematics Association of America ) endorsed a year – long course in Discrete Mathematics. The Educational Activities Board of IEEE ( Institute of Electrical and Electronics Engineers ) recommended a freshman discrete mathematics course. ACM ( Association of Computing Machinery ) and IEEE accreditation guidelines mandated a discrete mathematics course. This syllabus includes topics such as algorithms, combinatorics, sets, functions, and mathematical induction endorsed by these groups and addressed the goals of those proposals, which expanding mathematical maturity.
Mathematics Course Descriptions This remedial course focuses on basic mathematical concepts and skills, including whole numbers, fractions, decimals, percents, operations with signed numbers, exponents, algebraic expressions, and the solution of simple first-degree equations. Admission to this course is based on college placement test scores. This course prepares students for the required mathematics courses in their program of study. The application of statistical methods to the analysis of business conditions and projections form the core of this course. Among the topics covered are: measures of central tendency, standard deviation, percentiles, statistical graphs, binomial and normal distribution, probability, and hypothesis testing. Computer statistical packages are used to emphasize methods discussed in the course. Mathematics for game programming is primarily an algebraic field, which is based on a set of definitions and rules. In this introductory course students will be introduced to all the definitions, rules and applications that cover the following topics: Integral Exponents and Scientific Notation, Set Theory, Functions, Domain, Range, Vertical Line Test, Polynomials, Basic Trigonometry, Analytic Geometry, Vector Mathematics, Matrix Mathematics and Quaternion Mathematics. A graphing calculator is required for this course. This course deals with concepts in algebra and trigonometry including: numerical and algebraic expressions, signed numbers, linear and quadratic equations, laws of exponents, graphing, vectors, determinants and matrices, and their application to the fields of electronic and computer technology. Analytic geometry and differential calculus are discussed. Skills acquired in Mathematical Analysis I are reinforced and enhanced. Topics include: inequalities, progressions and binomial theorem, trigonometric identities and functions, analytical geometry of the straight line and conic section, curve fitting, the derivation and applications in electronic and computer technology.
Globalshiksha is providing LearnNext ChandigarhBoard Class 10 CDs for Maths and Science. This CD contains the entire syllabus for ChandigarhBoard Class 10 Mathematics and Science for the current year. Included lessons are in audio and visual format. It includes various types of solved questions, Solved examples, practice workout, experiments, tests and many more tests related to ChandigarhBoard Class 10 Maths and Science. Different types of visual tools and activities on each Lesson with Examples, Experiments, Summary and workout are also provided which is benefit for the students. Using this CD students can understand the image concepts well; clear all doubts with ease through this Educational disc get score in the exams. This compact disk comes with a useful Exam Preparation with two types of tests like Lesson Test and Model Test, in Lesson Tests its usually 20-30 minutes in duration, which will help you to evaluate the understanding of each lesson and Model Tests of usually 150-180 minutes in duration, that cover the whole subject on the lines of final exam pattern. This package can help you sharpen your preparation for final exams, identify your strengths and weaknesses and know answers to all tests with a thorough explanation, overcome exam fear and get scores in exams.
This course is a college credit course. A student will pick up 5 college quarter credits from MSCTC-FF. Sets, factoring, fractions, linear equation in one, two, or three unknowns, exponents, radicals, quadratic equations, inequalities, determinants, progressions, complex numbers, theory of equations and variations are covered in this course. Prerequisite: Student must pass the MSCTC-FF assessment, have a Junior GPA of 3.2 or a Senior GPA of 2.8 and maintain a "C" average in the course. Trigonometry is a semester course designed to introduce the theory necessary to handle real-world applications in a realistic way. This approach allows each topic to be related to the study of a particular class of function. The students must 1. Define the function 2. Draw representative graphs -35- 3. Figure out properties of the class of function 4. Use the function as a mathematical model The resulting ability to use functions as models allows the students to draw the graphs themselves, write equations for the graphs, and use the equations to make predictions and interpretations about the real-world situation they are modeling. Since answers to real-world problems seldom come out "nicely", a calculator is called for where appropriate. This course will cover the following concepts: trigonometric functions and their graphs, circular functions and their graphs, trigonometric identities and equations, oblique triangles, vectors, and polar coordinates if time permits. Prerequisite: College Algebra. Students must pass the MSCTC-FF assessment, have a Junior GPA of 3.2 or Senior GPA of 2.8 and maintain a "C" average in the course Basic foundations of geometric concepts will pave the way to geometric reasoning and mathematical proof. Knowledge of coordinate geometry, polygons, similarity, and right triangle trigonometry will be taught and expanded to include real would problems. Prerequisite: Algebra Ib or Algebra 8+
Product Description Microsoft Math's large collection of tools, tutorials, and instructions helps students learn mathematical concepts, while quickly solving math and science problems. Students see how to solve problems step-by-step - instantly. Microsoft Math works for many grade levels, studying subjects from basic math to calculus. The core tool of Microsoft Math, the Graphing Calculator is designed to help students visualize and solve difficult math and science problems, whether trigonometry, statistics, algebra, or calculus. The Formulas and Equations Library puts more than 100 common equations and formulas in a single location. The Unit Conversion Tool makes it easy for students to quickly convert units of measure. The Step-by-Step Equation Solver gives students the support they need by providing them with complete step-by-step solutions to many math problems. Students are guided through problems in subjects ranging from pre-algebra to calculus. The Triangle Solver is a graphing tool that helps students explore triangles, and understand relationships between different components to solve sides, angles, values, and formulas. Ink Handwriting Support works with Tablet and Ultra-Mobile PCs, so students can write out problems by hand and have them recognized by Microsoft Math. Microsoft Math Videos No video available… Microsoft Math Reviews & Ratings Editor's Review Microsoft Math is the leading virtual math tutor software, offering a wide variety of educational tools that make learning math simple and fun. Students are taught math in a practical, easy-to-understand manner - learning the basics of problem of solving and logical arithmetic skills before progressing to more difficult tasks. The software is perfect for students of all grade levels, offering assistance in every mathematical topic, from addition to calculus. The main tool that aids in the simplification of complex mathematical thinking is the Graphing Calculator, which allows the student to see numbers as a visual concept that is easier to grasp. This tool is especially useful for advanced math tutoring, involving topics such as scientific problem solving, trigonometry, and other advanced forms of mathematics. Students also have access to a vast Formulas and Equations library, which contains more that one hundred commonly used equations and formulas for easy reference. Using this tool is a great way to memorize these equations through repetitive practice. Likewise, students will also have quick and easy access to Unit Conversion tools that will aid them in developing the skills needed to complete complex measurement conversions. Aside form the above resources, users are given an incredibly useful educational module known as the Step-By-Step Equation Solver, which contains in-depth solutions to virtually every kind of math problem. This is a great resource to have when the student is having trouble figuring out which angle to approach the problem with. As the student is guided through similar problems repeatedly, their problem solving skills will become second nature. One tool that is especially helpful for learning to solve geometrical problems is the Triangle Solver - a shape graphing utility that aids in the understanding and solving of various geometry problems, including angles, values, and numerous formulas. Students can even use the Ink Writer feature to write out problems on PC tablets and Ultra-Mobile PC's. This feature was added to the software as many students find it easier to learn by repeatedly writing, rather than typing. Although the features mentioned above are related to more advanced math topics, the software also does an excellent job of teaching basic math skills in a fun and visual fashion. Students are guaranteed to learn in a pressure-free, relaxed environment, with all of the tools needed to solve difficult problems. Studies have shown that the main inhibitor of learning is psychological pressure. Since the user is not pressured into figuring everything out based on a few short textbook pages, they're able to learn through repetitively solving problems with ease, with the aid of useful and easy-to-access tools. The following are the minimum system requirements for Microsoft Math 3.0: Processor: 600MHz or faster (1 GHz or faster recommended) System: Windows XP ( with SP2 or later) Memory: 256 M of RAM (512 MB or more recommended) Available Disk Space: At least 450 MB Microsoft Math: What We Liked The software explains all of the features with easy to understand instructional wizards. Students in any with any skill level can benefit as even the simplest mathematical concepts are explained in simple and fun ways. The software does an excellent job of teaching problem solving skills and logical reasoning, which proves to be a crucial component to mathematical success. The software can run on virtually any modern compute,r which makes it perfect for students with smaller notebooks that are used solely for writing and homework. The Step-by-Step equation solver removes all of the pressure form the learning experience, letting the student learn through trial and error instead of the pressure of perfection. Microsoft Math: What We Didn't Like There is so much easily accessible info within the software, it could also be used by an unscrupulous student to cheat. Microsoft Support Microsoft offers support for this product at the Encarta Solution Center. There users can find a plethora of useful information such as Frequently Asked Questions, how to fix common error messages, troubleshooting guides, and other product documentation. About Microsoft Microsoft is the largest computer software company in existence, originally founded in 1975. Microsoft has since become the most dominating name in computer technology, pioneering the operating system with MS-DOS and then Windows. Microsoft is headquartered in Redmond, Washington, USA.
Richard Beals, "Analysis: An Introduction" Cambridge University Press (September 13, 2004) \| ISBN: 0521600472 \| 272 pages \| PDF \| 1,8 Mb Review "Analysis: An Introduction is most appropriate for a undergraduate who has already grappled with the main ideas from real analysis, and who is looking for a succinct, well-written treatise that connects these concepts to some of their most powerful applications. Beals' book has the potential to serve this audience very well indeed." MAA Reviews, Christopher Hammond, Connecticut College Book Description This self-contained text, suitable for advanced undergraduates, provides an extensive introduction to mathematical analysis, from the fundamentals to more advanced material. It begins with the properties of the real numbers and continues with a rigorous treatment of sequences, series, metric spaces, and calculus in one variable. Further subjects include Lebesgue measure and integration on the line, Fourier analysis, and differential equations. In addition to this core material, the book includes a number of interesting applications of the subject matter to areas both within and outside the field of mathematics. The aim throughout is to strike a balance between being too austere or too sketchy, and being so detailed as to obscure the essential ideas. A large number of examples and 500 exercises allow the reader to test understanding, practise mathematical exposition and provide a window into further topics. Read More » This book is a compilation of approximately nine hundred problems, which have appeared on the preliminary exams in Berkeley over the last twenty years. It is an invaluable source of problems and solutions for every mathematics student who plans to enter a Ph.D. program. Students who work through this book will develop problem solving skills in areas such as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra. The problems are organized by subject and ordered in an increasing level of difficulty. This new edition contains approximately 120 new problems and 200 new solutions. It is an ideal means for students to strengthen their foundation in basic mathematics and to prepare for graduate studies. This 2nd volume in the series History of the Theory of Numbers presents material related to Diophantine Analysis. This series is the work of a distinguished mathematician who taught at the University of Chicago for 4 decades and is celebrated for his many contributions to number theory and group theory. 1919 edition. Steven G. Krantz, "Geometric Function Theory: Explorations in Complex Analysis" Birkhäuser Boston; 1 edition (September 20, 2005) \| ISBN: 0817643397 \| 314 pages \| PDF \| 2 Mb Complex variables is a precise, elegant, and captivating subject. Presented from the point of view of modern work in the field, this new book addresses advanced topics in complex analysis that verge on current areas of research, including invariant geometry, the Bergman metric, the automorphism groups of domains, harmonic measure, boundary regularity of conformal maps, the Poisson kernel, the Hilbert transform, the boundary behavior of harmonic and holomorphic functions, the inhomogeneous CauchyRiemann equations, and the corona problem. The author adroitly weaves these varied topics to reveal a number of delightful interactions. Perhaps more importantly, the topics are presented with an understanding and explanation of their interrelations with other important parts of mathematics: harmonic analysis, differential geometry, partial differential equations, potential theory, abstract algebra, and invariant theory. Although the book examines complex analysis from many different points of view, it uses geometric analysis as its unifying theme. Alexander Mielk, "Analysis, Modeling and Simulation of Multiscale Problems" Springer; 1 edition (October 19, 2006) \| ISBN: 3540356568 \| 697 pages \| PDF \| 10,4 Mb This book reports recent mathematical developments in the DFG Priority Programme "Analysis, Modeling and Simulation of Multiscale Problems", which started as a German research initiative in 2000. The field of multiscale problems occurs in many fields of science, such as microstructures in materials, sharp-interface models, many-particle systems and motions on different spatial and temporal scales in quantum mechanics or in molecular dynamics. Recently developed tools are described in a comprehensive manner. This book provides the state of the art on the mathematical foundations of the modeling and the efficient numerical treatment of such problems. Read More »
Educational Value To general education: Necessary to just function in society. For vocational purposes: In every vocation a person needs to understand basic math. Goals 1. Students will be able to add, subtract, multiply and divide with whole numbers, fractions, decimals and integers. 2. Students will understand and work with perimeter, area and volume formulas involving geometric shapes. 3. Students will be able to solve percentage, proportion and linear equations involving a single variable. 4. Students will be prepared for more advanced Mathematics courses . Description A basic course in mathematics with attention given to the operations of addition , subtraction, multiplication and division of rational numbers. Problem solving with percentage, measurement (perimeter, area, and volume) and linear equations with one variable. whole numbers you can demonstrate the ability to use the order of operations on numerical expressions involving whole numbers you can demonstrate the ability to solve application problems invilving whole numbers fractions you can demonstrate the ability to use the order of operations on numerical expressions involving fractions you can demonstrate the ability to convert between mixed numbers and improper fractions you can demonstrate the ability to solve application problems involving fractions You will demonstrate your competence: on assigned activities on written exams on a two hour cumulative final exam Your performance will be successful when: you can demonstrate the ability to perform the basic operations( adding, subtracting, multiplication and division) with decimal numbers you can demonstrate the ability to use the order of operations on numerical expressions involving decimal numbers you can demonstrate the ability to convert between decimal numbers and fractions you can demonstrate the ability to solve application problems involving decimals You will demonstrate your competence: on assigned activities on written exams on a two hour cumulative final exam Your performance will be successful when: you can demonstrate the ability to perform the basic operations ( adding, subtracting, multiplication, and division) with signed numbers you can demonstrate the ability to use the order of operations on numerical expressions involving signed numbers you can demonstrate the ability to solve applications problems involving signed numbers You will demonstrate your competence: on assigned activities on written exams on a two hour cumulative final exam Your performance will be successful when: you can demonstrate the ability to convert between decimals, fractions, and percents you can demonstrate the ability to solve application problems involving percents 6. Utilize U.S. and Metric systems of measurement Learning objectives What you will learn as you master the competency: a. Identify the basic unit equivalencies in the U.S. system b. Convert from one unit of measure to another in the U.S. system c. Identify the basic unit equivalencies in the metric system d. Convert from one unit of measure to another in the metric system e. Solve application problems involving U.S. and metric systems of measures Performance Standards You will demonstrate your competence: on assigned activities on written exams on a two hour cumulative final exam Your performance will be successful when: you can demonstrate the ability to perform conversions between American units of measure you can demonstrate the ability to perform conversions between metric units of measure you can solve application problems involving American and/or metric units measure 7. Solve application problems involving ratios and proportions Learning objectives What you will learn as you master the competency: a. Use a ratio to compare two quantitites with the same unit b. Use a rate to compare two quantities with different units c. Solve proportion equations d. Solve application problems involving ratios and proportions Performance Standards You will demonstrate your competence: On assigned activities On written exams On a two-hour cumulative final exam Your performance will be successful when: you demonstrate the ability to use ratios to compare two quantities with the same or different unit you demonstrate the ability to solve application problems involving proportions You will demonstrate your competence: On assigned activities On written exams On a two-hour cumulative final exam Your performance will be successful when: you demonstrate the ability to simplify algebraic expressions by removing parentheses and combining like terms 9. Utilize algebraic equations in solving application problems Learning objectives What you will learn as you master the competency: a. Solve algebraic equations using the basic properties of equality b. Solve algebraic equations where the variable is on both sides of the equals sign c. Solve algebraic equations with parentheses d. Translate comparisons in English into mathematical equations using variables e. Solve applications problems involving algebraic equations Performance Standards You will demonstrate your competence: On assigned activities On written exams On a two-hour cumulative final exam Your performance will be successful when: you demonstrate the ability to solve a variety of first degree equations involving parentheses and more than one variable term you demonstrate the ability to translate English to algebraic expressions you demonstrate the ability to utilize algebraic equations to solve applications problems
PLATO Course Algebra 2A/B User Feedback Purpose Statement This year long blended/hybrid course, aligned to the Mathematics standards, is designed for students in grades 8, 9, 10, 11, and 12. This online course is designed to be supplemented by a face-to-face teacher. Descriptive Summary This advanced set of Algebra 2 units are competency-based. Learners experience new situations which they practice in a real-world environment and match to previous learning from Algebra 1. Instructional strategies incorporated include math items that contain real-world applications, as well as items that support multiple learning styles. Students are expected to respond to writing prompts and utilize higher-order thinking skills to ensure understanding of specified concepts.
Unit specification Aims To give an introduction to the basic ideas of geometry and topology. Brief description This course unit introduces the basic ideas of the geometry of curves and surfaces in Euclidean space, differential forms and elementary topological concepts such as the Euler characteristic. These ideas permeate all modern mathematics and its applications. Intended learning outcomes On successful completion of this module students will have acquired an active knowledge and understanding of the basic concepts of the geometry of curves and surfaces in three-dimensional Euclidean space and will be acquainted with the ways of generalising these concepts to higher dimensions. Future topics requiring this course unit The ideas in this course unit will be developed further in third and fourth level course units in geometry and topology.
Maths with Statistics : Code ALV14 A Level Maths with Statistics Home Study Course AQA A Level Maths with Statistics Course Description Entry requirements English reading and writing skills and maths to at least GCSE grade C or equivalent are required. You will need to have general skills and knowledge base associated with a GCSE course or equivalent standard. This specification is designed to: develop the student's understanding of mathematics and mathematical processes in a way that promotes confidence and fosters enjoyment develop abilities to reason logically and to recognise incorrect reasoning, to generalise and to construct mathematical proofs extend their range of mathematical skills and techniques and use them in more difficult unstructured problems use mathematics as an effective means of communication acquire the skills needed to use technology such as calculators and computers effectively, to recognise when such use may be inappropriate and to be aware of limitations develop an awareness of the relevance of mathematics to other fields of study, to the world of work and to society in general Course Content On this course you will study six units: AS Level Unit 1 MPC1 Core 1 Unit 2 MPC2 Core 2 Unit 3 MS1B Statistics 1B A2 Level Unit 4 MPC3 Core 3 Unit 5 MPC4 Core 4 Unit 6 MS2B Statistics 2 Each unit has 1 written paper of 1 hour 30 minutes. Course Content Unit 1 MPC1 Core 1 Co-ordinate Geometry Quadratic functions Differentiation Integration Unit 2 MPC2 Core 2 Algebra and Functions Sequences and Series Trigonometry Exponentials and logarithms Differentiation Integration Unit 3 MS1B Statistics 1B Statistical Measures Probability Discrete Random Variables Normal Distribution Estimation Unit 4 MPC3 Core 3 Algebra and Functions Trigonometry Exponentials and Logarithms Differentiation Integration Numerical Methods Unit 5 MPC4 Core 4 Algebra and Functions Coordinate Geometry in the (x, y) plane Sequences and Series Trigonometry Exponentials and Logarithms Differentiation and Integration Vectors Unit 6 MS2B Statistics 2 Poisson distribution Continuous random variables The t-distribution Hypothesis Testing Chi-squared tests Qualification Information AS +A2 = A level in Maths with Statistics. Both AS and A2 level courses and examinations must be successfully completed to gain a full A level. AQA Specification 6360

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