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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"
Algebra And Trigonometry - 01 edition ISBN13:978-0534434120 ISBN10: 0534434126 This edition has also been released as: ISBN13: 978-0534380298 ISBN10: 0534380298 Summary: James Stewart, the author of the worldwide best-selling calculus texts, along with two of his former Ph.D. students, Lothar Redlin and Saleem Watson, collaborated in writing this book to address a problem they frequently saw in their calculus courses. Many students were not prepared to "think mathematically" but attempted to memorize facts and mimic examples. Algebra and Trigonometry was designed specifically to help readers learn to think mathematically an...show mored to develop true problem-solving skills. Patient, clear, and accurate, the text consistently illustrates how useful and applicable mathematics is to real life. The new book follows the successful approach taken in the authors' previous books, College Algebra, Third Edition, and Precalculus, Third Edition. ...show less 0534434126
Combinatorial Problems and Exercises 9780821842621 ISBN: 0821842625 Pub Date: 2007 Publisher: American Mathematical Society Summary: The main purpose of this book is to provide help in learning existing techniques in combinatorics. The most effective way of learning such techniques is to solve exercises and problems. This book presents all the material in the form of problems and series of problems. Ships From:Boonsboro, MDShipping:Standard, Expedited, Second Day, Next DayComments:Brand new. We distribute directly for the publisher. The main purpose of this book is to provide... [more]Brand new. We distribute directly for the publisher. The main purpose of this book is to provide help in learning existing techniques in combinatorics. The most effective way of learning such techniques is to solve exercises and problems. This book presents all the material in the form of problems and series of problems (apart from some general comments at the beginning of each chapter). In the second part, a hint is given for each exercise, which contains the main idea necessary for the solution, but allo [less]
David Rubenstein Math Models With Applications This course builds on Algebra I and Geometry foundations. A variety of real life applications will be studied from various disciplines. Students use mathematical methods to model and solve real-life application problems involving money, data, chance, patterns, music, design, and science.
Download "Mathematics for Computer Scientists" by Gareth J. Janacek, Mark Lemmon Close for FREE. Read/write reviews, email this book to a friend and more... Mathematics for Computer ScientistsComments for "Mathematics for Computer Scientists" Algebra is one of the main branches in mathematics. The book series of elementary algebra exercises includes useful problems in most topics in basic algebra. The problems have a wide variation in difficulty, which is indicated by the number of stars.
MATH 104: Introduction to Mathematical Problem Solving Introduction to problem solving with emphasis on strategies applied to algebra, geometry, and data analysis. Every semester. MAY NOT BE USED TO SATISFY THE REQUIREMENTS FOR A MAJOR OR MINOR IN MATHEMATICS. MAY BE USED TO FULFULL CORE SKILL 3. Credits:3 Overall Rating:2.5 Stars N/A Thanks, enjoy the course! Come back and let us know how you like it by writing a review.
Listed below are most of the courses that mathematics majors take either as required courses or electives in mathematics. The variety of courses offered allows students to design programs to meet their individual needs. The department also teaches a number of additional courses students in the liberal arts or business take to meet general requirements. The department also offers courses at the graduate level, which mathematics majors may take in their senior year as electives. In some cases, mathematics seniors obtain dual enrollment with the MU Graduate School and receive graduate credit for some courses taken in their final undergraduate year. All prerequisite courses listed must be passed with a C- or better (whether specifically indicated or not). MATH _0110-Intermediate Algebra (3). Mathematics [MATH] 0110 is a preparatory course for college algebra that carries no credit towards any baccalaureate degree. However, the grade received in Mathematics [MATH] 0110 does count towards a student's overall GPA. The course covers operations with real numbers, graphs of functions, domain and range of functions, linear equations and inequalities, quadratic equations; operations with polynomials, rational expressions, exponents and radicals; equations of lines. Emphasis is also put on problem-solving. Prerequisites: Elementary College Algebra or equivalent. Placement in Mathematics [MATH] 0110 based on the student's ACT math score or equivalent, in addition to other criteria. MATH 1100-College Algebra (3). A review of exponents, order of operations, factoring, and simplifying polynomial, rational, and radical expres sions. Topics include: linear, quadratic, polyno mial, rational, inverse, exponential, and logarithmic functions and their applications. Students will solve equations involving these functions, and systems of linear equations in two variables, as well as inequali ties. Prerequisite: Mathematics [MATH] 0110 or a sufficient score on the ALEKS exam. This course is offered in both 3 day and 5 day versions. See the math placement website for specific requirements. A student may receive at most 5.0 credit hours among the Mathematics courses 1100, 1120, 1140, and 1160. MATH 1300-Finite Mathematics (3). A selections of topics in finite mathematics such as: basic financial mathematics, counting methods and basic prob ability and statistics, systems of linear equations and matrices. Prerequisites: Math [MATH] 1100, or Math [MATH] 1160, or both a College Algebra exemp tion and sufficient ALEKS score. Warning: without a College Algebra exemption, a sufficient ALEKS score will not suffice unless it is a proctored exam (for Math [MATH] 1100 credit). MATH 1320-Elements of Calculus (3). Introduc tory analytic geometry, derivatives, definite integrals. Primarily for Computer Science BA candidates, Economics majors, and students preparing to enter the College of BUS. No credit for students who have completed a calculus course. Prerequisite: Math [MATH] 1100, or Math [MATH] 1160, or sufficient ALEKS score. A student may receive credit for Math [MATH] 1320 or 1400, but not both. A student may receive at most 5 credit hours among the Mathemat ics courses 1320 or 1400 and 1500. MATH 1400-Calculus for Social and Life Sci ences I (3). The real number system, functions, analytic geometry, derivatives, integrals, maximum- minimum problems. No credit for students who have completed a calculus course. Prerequisite: grade of C- or better in Mathematics [MATH] 1100 or 1160, or sufficient ALEKS score. A student may receive credit for Mathematics [MATH] 1320 or 1400 but not both. A student may receive at most 5 units of credit among the Mathematics [MATH] 1320 or 1400 and 1500. Math Reasoning Proficiency Course. MATH 1800-Introduction to Analysis I (5). This course will cover the material taught in a traditional first semester calculus course at a more rigorous level. The focus of this course will be on proofs of basic theorems of differential and integral calculus. The topics to be covered include axioms of arithmetic, mathematical induction, functions, graphs, limits, continuous functions, derivatives and their applications, integrals, the fundamental theorem of calculus and trigonometric functions. Students in this class will be expected to learn to write clear proofs of mathematical assertions. Some previous exposure to calculus is helpful but not required. No credit for Mathematics [MATH] 1800 and 1320, 1400 or 1500. Prerequisites: ACT mathematics score of at least 31 and ACT composite of at least 30 or instructor's consent. Graded on A/F basis only. MATH 1900-Introduction to Analysis II (5). This course is a continuation of Mathematics [MATH] 1800. In this course we shall cover uniform convergence and uniform continuity, integration, and sequences and series. The topics will be covered in a mathematically rigourous manner. No credit for Mathematics [MATH] 1900 and 1700 or 2100. Prerequisite: Mathematics [MATH] 1800 or instructor's consent. Graded on A/F basis only. MATH 2100-Calculus for Social and Life Sciences II (3). Riemann integral, transcendental functions, techniques of integration, improper integrals and functions of several variables. No credit for students who have completed two calculus courses. Prerequisites: Mathematics [MATH] 1320 or 1400 or 1500. Math Reasoning Proficiency Course. MATH 4150-History of Mathematics (3). This is a history course with mathematics as its subject. Includes topics in the history of mathematics from early civilizations onwards. The growth of mathematics, both as an abstract discipline and as a subject which interacts with others and with practical concerns, is explored. Pre- or Co-requisite: Mathematics [MATH] 2300 or 2340. MATH 4335-College Geometry (3). Euclidean geometry from an advanced viewpoint. Synthetic and coordinate methods will be used. The Euclidean group of transformations will be studied. Prerequisite: Mathematics [MATH] 2300. MATH 4340-Projective Geometry (3). Basic ideas and methods of projective geometry built around the concept of geometry as the study of invariants of a group. Extensive treatment of collineations. Prerequisite: Mathematics [MATH] 2300. MATH 4370-Actuarial Modeling I (3). This course covers the concepts underlying the theory of interest and their applications to valuation of various cash flows, annuities certain, bonds, and loan repayment. This course is designed to help students prepare for Society of Actuaries exam FM (Financial Mathematics). It is oriented towards problem solving techniques applied to real-life situations and illustrated with previous exam problems. Prerequisites: grade of C-or better in Mathematics [MATH] 2300. MATH 4371-Actuarial Modeling II (3). This course covers the actuarial models and their applications to insurance and other business decisions. It is a helpful tool in preparing for the Society of Actuaries exam M (Actuarial Models), and it is oriented towards problem solving techniques illustrated with previous exam problems. Prerequisites: Mathematics [MATH] 2300 and 4320 or Statistics [STAT] 4750. Students are encouraged to take Mathematics [MATH] 4355 prior to this course. MATH 4540-Mathematical Modeling I (3). Solution of problems from industry, physical, social and life sciences, economics, and engineering using mathematical models. Prerequisites: 3 semesters of calculus and some exposure to ordinary differential equations or instructor's consent. MATH 4580-Mathematical Modeling II (3). Solution of problems from industry, physical, social and life sciences, economics, and engineering using mathematical models. More general classes of problems than in Mathematics 4540 will be considered. Prerequisites: 3 semesters of calculus and some exposure to ordinary differential equations or instructor's consent. Mathematics [MATH] 4540 is not a prerequisite. MATH 4800-Advanced Calculus for One Real Variable II (4). Continuation of Advanced Calculus for functions of a single real variable. Topics include sequences and series of functions, power series and real analytic functions, Fourier series. Prerequisites: Mathematics [MATH] 4700/7700 or permission of the instructor. MATH 4900-Advanced Multivariable Calculus (3). This is a course in calculus in several variables. The following is core material: Basic topology of n-dimensional Euclidian space; limits and continuity of functions; the derivative as a linear transformation; Taylor's formula with remainder; the Inverse and Implicit Function Theorems, change of coordinates; integration (including transformation of integrals under changes of coordinates); Green's Theorem. Additional material from the calculus of several variables may be included, such as Lagrange multipliers, differential forms, etc. Prerequisite: Mathematics [MATH] 4700. MATH 4970-Senior Seminar in Mathematics (3). Seminar with student presentations, written projects, and problem solving. May be used for the capstone requirement. Prerequisite: 12 hours of mathematics courses numbered 4000 or above.
Hello Everyone: I hope that you find everything you need to successfully complete these courses during this school year. I am excited about being your teacher and look forward to lots of learning and lots of laughing. If there is anything you would like to see added, please let me know. AP Calculus AB A course that provides a review of algebra and trigonometry skills as well as an in-depth look at differential calculus and its applications. In addition students will study the basic techniques and some applications of integral calculus. This course includes both Mechanics and Electricity and Magnetism and expects a high level of mathematical ability. It is the calculus-based physics course that is generally required of mathematics, physics, astronomy, and engineering majors in college.
Search Loci: Developers: How Does This Button Work? This article examines the dynamic geometry package GeoGebra from the point of view of Euclidean Constructions. Creating Mathlets with Open Source Tools In this article we present a collaborative environment of open source tools around the dynamic mathematics software GeoGebra that gives educators the freedom to create new and modify existing materials in an online community. Abstract In this article we introduce the free educational mathematics software GeoGebra. This open source tool extends concepts of dynamic geometry to the fields of algebra and calculus. You can use GeoGebra both as a teaching tool and to create interactive web pages for students from middle school up to college level. Specifically designed for educational purposes, GeoGebra can help you to foster experimental, problem-oriented and discovery learning of mathematics. We will illustrate the basic ideas of the software and some of its versatile possibilities by discussing several interactive examples. Technologies used in this article This article uses Java (1.4.2 or later) for several interactive mathlets created with GeoGebra. Please install Java from java.com if necessary.
Mathematics Quest Solutions Curriculum: Math Grade Level: 9-12 Description: The WebQuest is designed to assist students in enhancing their techniques in handling topics in Mathematics. The topics that I will be focusing on is Statistics. Keywords:Data, information, gathering, Pie Chart and Bar Chart and Pictograph Author(s): Edward Carter The Concept Of Pythagoras' Theorem Curriculum: Math Grade Level: 9-12 Description: This WebQuest outlines the concept of Pythagoras'Theorem. It shows how to find the length of a side of right angled triangle by finding the square root of the sum of the squares of the other two sides. Keywords:Pythagoras' Theorem, Rectangles, Right- angle Triangles, Area, Formula, Hypotenuse, Adjacent and Opposite Author(s): Monique Bookal Volume of a Solid of Revolution Curriculum: Math Grade Level: 9-12 Description: This WebQuest is designed for students taking AP Calculus. The topic is how to determine the volume of a solid of revolution by using the disk method and the washer method Keywords:calculus, volume, disk and washer Author(s): Will Kellogg GRAPHS AND CHARTS Curriculum: Math Grade Level: 9-12 Description: This webquest is to inform and teach students about the main types of graphs and charts Keywords:Graphs Charts Author(s): Asavari Goberdhan Unpacking the Unit Circle Curriculum: Math Grade Level: 9-12 Description: With this lesson, students will see that working with the unit circle is easy and fun. Keywords:unit circle, trigonometry, pre-calculus and algebra Author(s): James Molloy Quadratic Formula Curriculum: Math Grade Level: 9-12 Description: This Webquest is designed to help students learn the quadratic formula and how to use it to solve problems. Keywords:Algebra 2 and Quadratic Formula Author(s): Jason Wapnick Roots Can Be Complex Curriculum: Math Grade Level: 9-12 Description: Your task in this Webquest will be to gain an understanding of how imaginary numbers can be represented using trigonometry and to demonstrate this understanding by explaining with a powerpoint presentation, a poster or some other means how we can use trigonometry to find all of the nth roots of a complex number. Keywords:imaginary numbers, complex numbers, polar form, square roots, nth roots, de Moirve's formula, trigonometric form and cis Author(s): Kevin Gilliam How long ago did Otzi live? Curriculum: Math Grade Level: 9-12 Description: In this webquest you will use carbon dating to estimate when Otzi lived. This topic is covered as a part of common core curriculum CCSS.Math.Content.HSF-LE.A.4 Keywords:Exponential Decay, Math and Common Core Author(s): Tom Elwood Pythagorean Theorem Curriculum: Math Grade Level: 9-12 Description: We will look at the pythagorean theorem and how we can use this concept in every day life. Keywords:Pythagorean Theorem, Math, Pythagorean, Theorem, Fun and Life Author(s): Tyler Tavierne Scatterplots and predictions Curriculum: Math Grade Level: 9-12 Description: Students will research a trend and create a scatterplot. Through investigation of correlation and lines of best fit, the students will predict the future of their trend. This project focuses on group work, graphing, presentations, and correlation. Actuarial Science may also be introduced depending on the teacher's wishes. Keywords:correlation, scatterplots, line of best fit, math and middle school Author(s): Emily Fasen The ART of Trigonometry :-) Curriculum: Math Grade Level: 9-12 Description: In Trigonometry (trig) we learn about Polar Coordinates. This is a different way of graphing in comparison to the regular Cartesian Coordinate System or rectangular system. This circular graph presents many images that make pictures. Keywords:polar, rectangular, theta and radius Author(s): Macey Dean Prime and Composite Numbers Curriculum: Math Grade Level: 9-12 Description: This wequest sets out to teach student about prime and composite numbers. It will enable students to differentiate between prime and composite numbers. It will show children how to use the Eratosthones sieve to eliminate prime numbers there leaving the composite numbers. They will also be using their knowledge of prime numbers to generate prime factors. They will also be taught the difference between factors and prime factors. Keywords:Composite numbers, prime numbers, factors and products and eratosthones sieve Author(s): Zaneil Coley Tamantha Forbes Donna-kay Graham Lisa Davis Primary Education A Christmas Suprise Curriculum: Math Grade Level: 9-12 Description: In this webquest students will explore and calculate the real cost of giving the 12 Days of Christmas and examine some of the amazing math behind the traditional holiday carol. Keywords:Christmas, 12 Days, Triangular Numbers and Tetrahedral Numbers Author(s): James Jay Algebra 2 Functions Curriculum: Math Grade Level: 9-12 Description: Now that we have gone over functions and how to graph them, we need to make sure that we have these skills mastered! This web quest will take you through a group project to practice and master these math skills. Keywords:algebra 2 functions math Author(s): Kendra Austin Scientific Notation Curriculum: Math Grade Level: 9-12 Description: My webquest is designed to help students learn how to go about solving a scientific notation problem. Also it will show them how to write the problem in scientific notation and standard form. Keywords:Scientific notation, standart form, exponents, base and multiply Author(s): Tan' Kea Thomas Dream Vacation Curriculum: Math Grade Level: 9-12 Description: Students will be able to plan their own dream vacation. With this project they have to budget every expense that will arise on a vacation and explain what they found and how tracked all of their expenses. Keywords:budgeting, vacation, math and managing Author(s): Katie Cerveny Trigonometry with Real Life Applications Curriculum: Math Grade Level: 9-12 Description: This webquest is an activity that will increase student's knowledge about trigonometric functions in real life applications. Keywords:Trigonometry, sines and cosines and tangent functions Author(s): Esra Yaprak Bring Me to the WORLD of FRACTALS Curriculum: Math Grade Level: 9-12 Description: This webquest was designed to make learners appreciate fractals. They will discover fractals and whats incorporates them in the world. Keywords:Fractals, fractals in nature and fractals in architecture. Author(s): Hamide Akkoca The Quadratic Story Curriculum: Math Grade Level: 9-12 Description: This webquest is designed to assist students in learning the quadratic equation and to then introduce them to the calculations of using the formula Keywords:Quadratic, formula, calculations, Quadratic formula and Quadratic equation Author(s): Debbie Trejo Functions in the Real World. Curriculum: Math Grade Level: 9-12 Description: Each student in a group of three or four, choose different real world situations to research. Together the group will create a presentation about "functions in the real world." Keywords:Data Analysis, Interpretating Graphs, Functions, Modeling, Representing Change, Patterns and Relationships. Author(s): Valerie Stoffels
This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The intended audience is physicists, so the author emphasises applications and geometrical reasoning in order to give results and concepts a precise but intuitive meaning without getting bogged down in analysis. The large number of diagrams helps elucidate the fundamental ideas. Mathematical topics covered include differentiable manifolds, differential forms and twisted forms, the Hodge star operator, exterior differential systems and symplectic geometry. All of the mathematics is motivated and illustrated by useful physical examples. [via] You could just as easily call this book How to Bet at Jai-Alai and Win! But that's only half the story. While Calculated Bets might indeed help you make a buck down at the fronton, it's as much concerned with the power of mathematical modeling and computer programming. The story of accomplished mathematician Steven Skiena's longtime obsession with this obscure Basque sport, Calculated Bets uses straightforward mathematics and real-world examples to divine the statistical mysteries behind playing--and, more important, wagering on--jai alai. (Which goes a long way toward explaining why Cambridge University Press is publishing what's basically a book about gambling.) A self-styled "mild-mannered professor," the conversational Skiena (The Algorithm Design Manual) delivers on his book's many promises, from explaining how mathematical models are "designed, built, and validated" to providing lucid discussions of such topics as market efficiency and the difference between correlation and causation. Even better are his riffs on why real programmers hate Microsoft (hint: it's not jealousy) and the beauty behind interesting curves. In the end, Skiena even puts his money where his mouth is: using a modem, he sets loose an auto-dialing program called Maven that he and his grad students cooked up, sending it off in the wee hours of the morning to cull the Web for stats, play each match a half-million times, and then automatically wager a $250 stake. --Paul Hughes[via] More editions of Calculated Bets: Computers, Gambling, and Mathematical Modeling to Win:More editions of Complex Analysis: The Hitchhiker's Guide to the Plane: This well-known text provides a relatively elementary introduction to distribution theory and describes generalized Fourier and Laplace transformations and their applications to integrodifferential equations, difference equations, and passive systems. Suitable for a graduate course for engineering and science students or for an advanced undergraduate course for mathematics majors. 1965 edition. In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions. [via] A new edition of the most definitive collection of Albert Einstein's popular writings, gathered under the supervision of Einstein himself. The selections range from his earliest days as a theoretical physicist to his death in 1955; from such subjects as relativity, nuclear war or peace, and religion and science, to human rights, economics, and government. [via] This concise, undergraduate-level text focuses on combinatorics, graph theory with applications to some standard network optimization problems, and algorithms. Geared toward mathematics and computer science majors, it emphasizes applications, offering more than 200 exercises to help students test their grasp of the material and providing answers to selected exercises. 1991 edition. Prominent Russian mathematician's concise, well-written exposition considers n-dimensional spaces, linear and bilinear forms, linear transformations, canonical form of an arbitrary linear transformation, and an introduction to tensors. While not designed as an introductory text, the book's well-chosen topics, brevity of presentation, and the author's reputation will recommend it to all students, teachers, and mathematicians working in this sectorSeventy-six superlative reproductions of the enigmatic renderings of the master artist are accompanied by an introduction to the artist and his work and detailed descriptions of each piece by Escher himself. [via] A Y Khinchin was one of the great mathematicians of the first half of the twentieth century. His name is is already well-known to students of probability theory along with A N Kolmogorov and others from the host of important theorems, inequalites, constants named after them. He was also famous as a teacher and communicator. The books he wrote on Mathematical Foundations of Information Theory, Statistical Mechanics and Quantum Statistics are still in print in English translations, published by Dover. Like William Feller and Richard Feynman he combines a complete mastery of his subject with an ability to explain clearly without sacrificing mathematical rigour. In his "Mathematical Foundations" books Khinchin develops a sound mathematical structure for the subject under discussion based on the modern theory of probability. His primary reason for doing this is the lack of mathematically rigorous presentation in many textbooks on these subjects. I can remember the vague feeling of dissatisfaction I felt as a student with some of the mathematics in Frederick Reif's "Fundamentals of Statistical and Thermal Physics" and other texts. Khinchin's little book puts everything on a firm mathematical foundation and yet is very readble. I liked all three of these books but I think I liked this one best. The English translation was done by the eminent physicist and writer George Gamow. Nicely typeset in modern notation with index. This book is also a real bargain.This classic textbook, now reissued, offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The new edition has been made even more self-contained than before; it now includes a foundation of the real number system and the Stone-Weierstrass theorem on uniform approximation in algebras of functions. Several other sections have been revised and improved, and the comprehensive historical notes have been further amplified. A number of new exercises have been added, together with hints for solution. [via] Excellent study of sets in topological spaces and topological vector spaces includes systematic development of the properties of multi-valued functions. Topics include families of sets, topological spaces, mappings of one set into another, ordered sets, more. Examples included from different domains. 1963 edition. "Remarkably comprehensive." Industrial Laboratories. Here is a clear introduction to classic vector and tensor analysis for students of engineering and mathematical physics. Chapters range from elementary operations and applications of geometry, to application of vectors to mechanics, partial differentiation, integration, and tensor analysis. More than 200 problems are included throughout the book. This introductory text is geared toward engineers, physicists, and applied mathematicians at the advanced undergraduate and graduate levels. It applies the mathematics of Cartesian and general tensors to physical field theories and demonstrates them chiefly in terms of the theory of fluid mechanics. Numerous exercises appear throughout the text. 1962 edition.
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. Visual Authoring System Benefits Instruction as Well as Instructor at Ohio State Visual Authoring System Benefits Instruction As Well as Instructor at Ohio State J. Brooks Breeden was, in his words, "capital-B bored." A professor in the department of landscape architecture at The Ohio State University, he teaches courses that involve lots of mathematical problem-solving. And for a while there, in the mid-'70s, he spent virtually all his free time on campus holed up in his office constructing those math problems--horizontal and vertical curve calculations, percent of slope calculations, etc. Fresh problems for tests, student practice, classwork and homework assignments were necessary, of course, but to Breeden they were all "old-hat." Students of landscape architecture, which concerns the design of all outdoor space, study civil engineering, horticulture, ecology and the natural sciences. Math plays an important role in the discipline. Miscalculate the low point in a driveway curve, and the catch basin for run-off … The rest of this article is only available to active members of Questia
The aim of 16-19 Mathematics has been to produce a course which, while challenging, is accessible and enjoyable to all students. The course develops ability and confidence in mathematics and its applications, together with an appreciation of how mathematical ideas help in the understanding of the world and society in which we live. This unit: * helps foster a deeper understanding of rates of change; * develops an understanding of the product, quotient and chain rules; * fosters a facility in the techniques of differentiation and integration; * develops an awareness of the relative strengths and limitations of numerical and analytical techniques; * develops efficiency in the solution of problems using appropriate methods.
Microsoft Math 3.0 Review I am quite impressed with MS Math 3.0. This basic computer algebra system from Microsoft has a multitude of features and comes at a reasonable price (US$19.95). The interface is well-designed from a usability point of view. A nice feature is that it pre-empts your most likely follow-up action (eg asking if you want to find a determinant of the matrix that you just used.) Microsoft normally does not get this aspect right (it is usually too obtrusive), but in this application, they have reached a good balance. They use a graphics calculator metaphor for the user interface. This aids the input of math notation (always a problem on computers) as well as giving a certain level of familiarity. The Claims With Microsoft Math, students can learn to solve equations step-by-step, while gaining a better understanding of fundamental concepts in pre-algebra, algebra, trigonometry, physics, chemistry and calculus. Microsoft Math provides a set of mathematical tools that helps students get school work done quickly and easily. With a full-featured graphing calculator that's designed to work just like a handheld calculator, Microsoft Math offers a wide range of additional tools to help students with complex mathematics. What this means is that MS Math will show you the steps used to arrive at the solution for an equation, as follows: It gives you a choice whether you want to see the quadratic equation method (part of which is shown above) or completing the square method. What is odd is that it did not offer the factor method, which seems to be the best way to do this particular example. Anyway, the steps are well explained and they would most probably help a student who needs explanation of every step (and that seems to be the majority). I am wondering how many students will blindly copy from the Math 3.0 solution into their homework solution. Perhaps a better approach for a learning tool would have been to get students to suggest steps throughout the solution and the tool would give feedback on those steps (this could be done with multiple choice questions.) But such a suggestion adds a lot of complexity to the tool. Versatility Math 3.0 caters for both students and math instructors. Its features include: Graphing Calculator (2D and 3D) Step-by-Step Equation Solver Formulas and Equations Library Triangle Solver Unit Conversion Tool Ink Handwriting Support (designed for tablet PCs) Graphing A good graphing engine is an essential feature for a tool like this. Microsoft Math 3.0 delivers in both 2 dimensional and 3 dimensional graphs. A 3-D graph appears as follows: You can rotate the graph around any axis using a tool that looks like: From similar software, I am more used to dragging the graph itself to rotate it, but this tool allows for more precise rotation and I found myself not getting as "lost" when using this tool, compared to others. Animation Some graph features can be animated (like "constant variables", for example you can animate the a in an expression like y = ax2.) Statistics You can add a series of data points and produce a scatter plot. This is okay, but I was disappointed with the following: The data entry tool (like a simple spreadsheet) does not use [Tab] to move through the cells, as we have come to expect from spreadsheets. You can only use the arrow keys to move through cells. There is no facility to draw regression lines. Seems to me that this would not be that difficult and would make this part of the tool more useful. Calculus Math 3.0 handles differentiation and integration. It happily performed this double integral: Minor Quirks There is a lot to like about Microsoft Math 3.0. However, there were a few things that were problematic. Why the Prejudice? I do not reside in the United States and I want to download the trial. Are there any special instructions? At this time the trial of Microsoft Math 3.0 is intended for United States-based users. Why the non-availability to the rest of the world…? Anyway, I managed to download it here in Singapore with no difficulties. Font Size on Graphs Depending on your settings, it is posible to produce a graph where the axis labeling is so small that it is unreadable, as in the following actual-size screen shot. Strange Dependent-Independent Axis Choice The convention with graphs that involve time is to place the time axis as the horizontal axis. However, Math 3.0 chose the vertical axis for t in the following distance-time graph. Conclusion Microsoft has used some of the same input tools as their "Equation Writer" (designed for the tablet PC). However, Math 3.0 is a much better product and it is packed with useful features. Math 3.0 is certainly worth checking out. If you have ready access to a laptop or tablet PC, and see no need for a graphics calculator, this is a worthwhile product for a cheaper price. However, I doubt there are many educational institutions that will let students use it in class or during tests. That's the problem when education plays catch-up, rather than leading technology in education. Share this page 30 Comments on "Microsoft Math 3.0 Review" Thanks for the review. I have a few questions. When generating graphs with holes (or a piecewise non-continuous function), does it actually display the holes with an open circle? And does it have the option to display arrows at the ends of the curves? Finally, how flexible are the axes? Can you change their labels and scales easily? These are the issues I've had with all other graphing programs and they are a pain when trying to create graphs for assignments and assessments. As for flexibility of scales, this aspect is quite good. You can zoom in and out easily or set the required range exactly with a dialog box: So you can zoom in and find intersection points easily: So I guess you'll need to keep looking for those features. My favourite for use with students remains Scientific Notebook, even though it is not as good now that it uses MuPAD engine rather than Maple. I have been using it for some years and found that it was powerful enough for most situations in undergraduate mathematics. It certainly copes better with split functions than Math 3.0! For example, the Laplace chapter in Interactive Mathematics was produced entirely using SNB. However, SNB still does not give you circles at discontinuities or arrows on graphs. And at UD$99 per student, SNB is in a different league, price-wise. for example, the software has decided to replace "plus or minus" with "plus" too early in the calculation (and then finished too soon by presenting one of the two solutions as the "bottom line"). you've already mentioned that the quadratic formula isn't even the most appropriate tool in the first place. anyhow, the actual effect of all this will be to have encouraged students to avoid calculations rather than shown them how to perform 'em. you've got to move your pencil to get anywhere (also the eraser). "plugging in" problems and reading the computer-generated solution will go about as far in teaching mathematics as watching movies will in teaching drawing. Microsoft math is a really an inferior piece of software, and ads are very misleading. "Step-by-step" solutions are only give for a very selective class of problems. The software doesn't know what to do with such simple expressions such as (x^4-y^4)/(x^2-y^2), and frequently gives incorrect solutions (i.e. in x^2-1)/(x-1), it proclaims "1″ to be a valid solution!. If you need a true step-by-step solver for College ALgebra (and earlier courses) take a look at Algebrator at If you need help with calculus and above the only real alternatives are serious systems such as Maple and Mathematica. Hi Neven and thanks for your thoughts about Microsoft Math. Like any computer-based mathematics solver, there will be cases that are difficult to program for. Users should always estimate the solution (if possible) and question the results (like in your (x^2-1)/(x-1)=0 example.) Algebrator is an interesting alternative. I will try to do a review sometime soon. Yes, but the problem in educational context is that users don't have the ability to discriminate between correct and incorrect (yet plausible) solutions. In a sense this type of error is worse than the program crashing. Im really confused on drawing 3d graphs with this app I really want to know how to draw solids of revolution using this software because i am having problems in doing that. Does anybody know how to draw solids of revolution using this software pleas help me >.< I am currently having problems with printing the step-by-step solutions… I can't seem to get the full step-by-step solutions sent in one batch to the printer. For instance – while trying to solve Quadratic Equations with the software I have two steps I need to go through to get the final solutions: The first step is "Solution steps using the quadratic formula" The second step is "Solution steps for completing the square". Currently it looks like I am only capable of printing each solution separately – because when I maximize one solution, the other one minimizes. Is there any way to get both solutions sent to print at the same time? Thanks for all of your posts. It has really helped me out of bind with a (should be) easy problem. After all of the research and tips from you, I think I can do these functions in my sleep! ) My life isn't all about Math but I do like it…I like fishing too but I am sure when people need an IV bag of some medication they are hopeful that the one making it up for them can at least count. Funny how people forget how much we really do use Math in our day to day life. I am about to undertake Calculus II in a 6 week summer session, (class starts tomorrow). MM 3.0 is good until Calculus. Are there any educational programs that would work well to aid in higher maths? (i am an engineering major and can't always get to the free tutors on campus.)
Description Ratti and McWaters created their text from years of combined lecture notes and firsthand experience with students, resulting in a strong preparation for calculus. An emphasis on concept development, real-life applications, extensive exercises encourage deep understanding for students. Precalculus: A Unit Circle Approach, Second Edition, offers the best of both worlds: a fast pace approach with rigorous topics and a friendly, teacherly tone. Using the text with MyMathLab, students now have access to even more tools to help them be successful including "just-in-time" review of prerequisite topics right when they need it. Table of Contents 1. Graphs and Functions 1.1 Graphs of Equations 1.2 Lines 1.3 Functions 1.4 A Library of Functions 1.5 Transformations of Functions 1.6 Combining Functions; Composite Functions 1.7 Inverse Functions Chapter 1 Summary Chapter 1 Review Exercises Chapter 1 Practice Test A Chapter 1 Practice Test B 2. Polynomial and Rational Functions 2.1 Quadratic Functions 2.2 Polynomial Functions 2.3 Dividing Polynomials and the Rational Zeros Test 2.4 Zeros of a Polynomial Function 2.5 Rational Functions 2.6 Variation Chapter 2 Summary Chapter 2 Review Exercises Chapter 2 Practice Test A Chapter 2 Practice Test B Cumulative Review Chapters 1–2 3. Exponential and Logarithmic Functions 3.1 Exponential Functions 3.2 Logarithmic Functions 3.3 Rules of Logarithms 3.4 Exponential and Logarithmic Equations and Inequalities 3.5 Logarithmic Scales Chapter 3 Summary Chapter 3 Review Exercises Chapter 3 Practice Test A Chapter 3 Practice Test B Cumulative Review Chapters 1–3 4. Trigonometric Functions 4.1 Angles and Their Measure 4.2 The Unit Circle; Trigonometric Functions of Real Numbers 4.3 Trigonometric Functions of Angles 4.4 Graphs of the Sine and Cosine Functions 4.5 Graphs of the Other Trigonometric Functions 4.6 Inverse Trigonometric Functions Chapter 4 Summary Chapter 4 Review Exercises Chapter 4 Practice Test A Chapter 4 Practice Test B Cumulative Review Chapters 1–4 5. Analytic Trigonometry 5.1 Trigonometric Identities and Equations 5.2 Trigonometric Equations 5.3 Sum and Difference Formulas 5.4 Double-Angle and Half-Angle Formulas 5.5 Product-to-Sum and Sum-to-Product Formulas Chapter 5 Summary Chapter 5 Review Exercises Chapter 5 Practice Test A Chapter 5 Practice Test B Cumulative Review Chapters 1–5 6. Applications of Trigonometric Functions 6.1 Right-Triangle Trigonometry 6.2 The Law of Sines 6.3 The Law of Cosines 6.4 Vectors 6.5 The Dot Product 6.6 Polar Coordinates 6.7 Polar Form of Complex Numbers; DeMoivre's Theorem Chapter 6 Summary Chapter 6 Review Exercises Chapter 6 Practice Test A Chapter 6 Practice Test B Cumulative Review Chapters 1–6 7. Systems of Equations and Inequalities 7.1 Systems of Equations in Two Variables 7.2 Systems of Linear Equations in Three Variables 7.3 Matrices and Systems of Equations 7.4 Determinants and Cramer's Rule 7.5 Partial–Fraction Decomposition 7.6 Matrix Algebra 7.7 The Matrix Inverse 7.8 Systems of Inequalities Chapter 7 Summary Chapter 7 Review Exercises Chapter 7 Practice Test A Chapter 7 Practice Test B Cumulative Review Chapters 1–7 8. Analytic Geometry 8.1 Conic Sections: Overview 8.2 The Parabola 8.3 The Ellipse 8.4 The Hyperbola 8.5 Rotation of Axes 8.6 Polar Equations of Conics 8.7 Parametric Equations Chapter 8 Summary Chapter 8 Review Exercises Chapter 8 Practice Test A Chapter 8 Practice Test B Cumulative Review Chapters 1–8 9. Further Topics in Algebra 9.1 Sequences and Series 9.2 Arithmetic Sequences; Partial Sums 9.3 Geometric Sequences and Series 9.4 Mathematical Induction 9.5 The Binomial Theorem 9.6 Counting Principles 9.7 Probability Chapter 9 Summary Chapter 9 Review Exercises Chapter 9 Practice Test A Chapter 9 Practice Test B Cumulative Review Chapters 1–9 Appendix Review A1. The Real Numbers; Integer Exponents A2. Polynomials A3. Rational Expressions A4. Radicals and Rational Exponents A5. Topics in Geometry A6. Equations A7. Inequalities A8. Complex Numbers Answers to Selected Exercises Credits
Check out the New LINKS! updated November 19, 2012 Several new links have been added to my page. There is a link for the IB Studies SL textbook that will take you to a PDF of the book, AWESOME! A link to my favorite online graphing... Geometry A course that covers the building blocks of geometric shapes and theorems. We cover basic geometric proofs as well as 3-shape geometry. For juniors that scored below or just at the cut off for proficiency on the MAP test this fall or last spring. OR for juniors that have not completed Algebra 2 successfully. We are emphasising geometry for Tri 2, winter of 2011-2012 This course was designed for seniors that have yet to pass the MCA II Grad component for mathematics. An intervention is required by the state for any student that has not passed. Upon completion of this course and a students 3 attempts at the Grad exam, they are allowed to graduate. EVEN if a student does not pass the exam, as long as they are showing progress and working towards that goal and complete the intervention course, they can still graduate.
a List of Undergraduate and Basic Graduate Textbooks and Lecture Notes - the blog Stage 3 Introductory Topology Introductory Topology: Topology is an extension of geometry and built on set theory, it's about continuity. There is a joke that topologists are those who cannot distinguish between a doughnut and a coffee or tea cup. Wikipedia has a [.gif] to demonstrate this. You may have studied open sets, open neighbourhood, interior, closure, boundary, basis, continuity, compactness and connectedness etc. in the analysis course, move on to homemorphism, homotopy and fundamental group. As in abstract algebra and analysis, several selected books or notes cover more than enough. You may leave a few sections to study at the next stage.
Murderous Maths107135","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":4.49,"ASIN":"140710716X","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":4.49,"ASIN":"1407107119","isPreorder":0}],"shippingId":"1407107135::zm7ZSp%2BN5mXjWCwVllYdRAq868rDr25AwN6B7lOunjIfsl%2Ftiuzg3Sd%2Bwno9ceKqbEUgwh1kc5%2FeJ0ezZ9458lNDLTEcrhj5,140710716X::ds2RIYYZsCVOvnf8PzVw6V1J60JuhC82m8O%2Bg6va4xtVVIYGdAdqsYkUfMuEcQFqhykQR2Z9B8iahV9zCnHekKvU8rZQjkUb,1407107119::PbV1n0AVsNs9%2Bl8%2FnI%2BdqsWNRnm%2FyQUOg%2FwiQ%2BntDDvH9PQViqGCFQE10of0%2Bk68TFU%2BAUbHP9dXPbEdEclFiZexe4OkgRC The secret weapon 2. What is algebra? 3. The Slaught-o-Mart equations 4. The father of algebra 5. Packing, unpacking and the panic button 6. The mechanics of magic 7. The Murderous Maths testing laboratory 8. The bank clock 9. Axes, plots and the flight of the loveburger 10. Double trouble 11. The zero proof written in a variety of fonts in the usual Kjartan Poskitt entertaining style, e.g.:- 'You haven't seen me before and, after this book, I hope for your sake we never meet again, because I'm dangerous to be seen with. In fact, just to be safe, before you read on check there's no one looking over your shoulder. All clear? Right then, here's the situation. Maths is one long fierce battle in which we're all being attacked by an army of different problems. Luckily, most of them are little sums that you can solve in your head. Then for the really tough sums, you can bang the numbers into a calculator and read off the answer. But sometimes you have to do sums and you aren't told what the numbers are! How can you put a number into a calculator when you don't know what it is? What do you do when you're facing the UNKNOWN? It's usually a job for ...... the Phantom X..........'
The aim of this lecture is to introduce students to the principles and practice of Finite Element analysis. The analysis of complex static and dynamic problems involves, in essence, three steps: - Selection of a mathematical model. - Computation of a numercila solution of the model. - Interpretation of the predicted response. Main themes The objective of this course is to teach the student the theory and practical use of modern finite element methods for the solution of static problems. On completion of the course the student should - have a basic understanding of FE analysis and what can be achieved through its use, - be able to select an element type, materials, loading and boundary conditions, - be aware of the limitations and potential errors of FE modelling, - have a basic knowledge of how to interpret results provided by FE analysis, - be able to operate a standard FE analysis packages, - be aware of the range of applications of FE analysis. Content and teaching methods Nowadays, finite element methods are used successfully for the analysis of very complex problems in various areas of engineering. A finite element analysis is now frequently imperative to reach a safe and cost-effective design. However, the appropriate and efficient use of finite element procedures is only possible if the basic assumptions employed in the mathematical model, the numerical FE discretisation and the computer implementation are known.
Mathematics As the world and the economy become more reliant on technology, the need for people with strong mathematical backgrounds will only increase. Mathematicians have the ability to think through problems in a logical and rigorous manner, to see patterns in data, and to formulate models and strategies to solve problems. Mathematicians are employed in almost every sector of the economy. In finance, they help create financial instruments and determine the amount of risk in investments. In manufacturing, they design quality control procedures and streamline processes. In medicine, they design models to see the effects of drugs and to help decide the proper dosages. The Mathematics program at Martin Methodist gives each student a wide base of knowledge to start their mathematical careers. Leaving the program, students should be ready for graduate school, an entry-level job in mathematics, or a job as a teacher. Because the Mathematics program at Martin Methodist is small, we are able to give every student personal attention. The Special Topics course allows us to offer majors a course that piques their interests. The Senior Project gives students an opportunity to explore some topic of their own choosing, expanding their knowledge and view of mathematics.
Integration theory For all studies of analysis in higher mathematics it is fundamental to understand the concept of integration. Our intuitive idea of the integral of a function is as the area under its graph, and this can be turned into a formal definition through approximating Riemann sums. This leads to the Riemann integral which works fine in many circumstances, but has its limitations. One problem with the Riemann integral is that it does not manage functions with too many discontinuities, for example the function f(x) which is 1 if x is rational and 0 if x is irrational cannot be integrated. Morally the integral should have the value zero since the rationals form a countable set which should not contribute to the integral. A more serious problem is that the Riemann integral does not behave nicely when one studies sequences of functions, such as the partial sums of a Fourier series approximating a periodic function. When can one move the limit inside the integral? In this course we will study the Lebesgue integral, and more general concepts of integrals and measure. Among other things we will see how the above problems are resolved and we will study the important L^p spaces of functions. The material in this course is fundamental also for the study of probability theory. Foundations of analysis Chaotic dynamical systems For a number of years now, chaotic dynamical systems have received a lot of scientific attention. One aspect is chaos, fractals, etc., often illustrated with the fantastic pictures -- the Mandelbrot set, Julia sets, etc. -- that computer simulations of iterations of complex polynomials give rise to. Another aspect is formed by the so-called "strange attractors", that occur in conjunction with computer simulations of ordinary differential and difference equations. Some of the best known mathematical experiments were carried out by the meteorologist E. Lorenz and the astronomer M. Hénon, and here at the department precisely these models have been studied rigorously and chaotic behaviour was proved for them. D. Ruelle and F. Takens have proposed that turbulent phenomena might at least partially be explained via strange attractors. The physicist M. Feigenbaum made the fundamental discovery that many systems first go through a characteristic period doubling and then behave in a random (chaotic) way, even though they are deterministic. Later, one has shown that such period doublings occur in liquid helium flow. From a mathematical viewpoint, the course is quite special. On a relatively elementary level, one obtains insight in phenomena that lie quite close to current research. One or two computer experiments will probably be part of the course. However, the course's main emphasis will be on the mathematical theory, which in itself has a long history with names such as Poincaré, Fatou, Birkhoff, and Smale, and which lately has developed quickly, partly in symbiosis with computer experiments. Elementary differential geometry In this course we study curves and surfaces. This subject has the beauty that one can start from knowing only basic calculus, and reach many deep and interesting facts. An important concept is that of curvature, which appears in many different forms, with the common property that it measures how much an object differs from being flat (for example an ordinary sphere has constant positive curvature, and the curvature becomes smaller as the radius is increased). One of the important results covered in the course is the Gauss-Bonnet theorem, which relates the curvature of a surface to a topological quantity (the Euler characteristic). Two books that will be used in the course are: "Differential Geometry of Curves and Surfaces" by Manfredo P.do Carmo "Differential Geometry:curves-surfaces-manifolds" by Wolfgang Kuehnel Topology SU, SF2721, Rikard Bögvad Topology is the study of spaces from an abstract viewpoint. One is interested both in the fine structure of a space and in global features such as the number of holes. A fundamental concept is that of a continuous function, or continuous map, and the goal is to understand what properties such a map can have without using ideas like distance or derivative. For instance, it might seem obvious that a simple closed curve in the plane divides the plane into an "inside" and an "outside" region. This observation is correct, but to really prove it assuming only that the curve is continuous is not an easy task. In fact, this was a hard problem for a long time, studied by many mathematicians in the 19th century. In the course we will see a proof of this "Jordan curve theorem", and other results such as the "Ham sandwich theorem" (one can always divide a three layer sandwich into two equal pieces with just one cut) and the "Hairy ball theorem" (one cannot comb a hedgehog). A classical example in topology is that, in a world of perfect rubber, a coffee cup cannot be distinguished from a doughnut, but is fundamentally different from a ball. What does this observation mean? And how can one turn it into computable mathematics? The answer, perhaps surprisingly, involves group theory and abstract algebra. In the course we will see how to find and classify all two-dimensional surfaces. The doughnut and the ball are two of them. Discrete mathematics Commutative Algebra and Algebraic Geometry Geometry and algebra might appear to be two totally unrelated subjects. The truth is, however, that affine algebraic geometry and commutative algebra are perfectly dual to each other. Grasping this duality is very satisfactory and rewarding. The main purpose of the course is to initiate the fermenting process needed to achieve this understanding. Commutative algebra is about the structure of commutative rings. A commutative ring is a set with two operations, sum and multiplication, satisfying some natural conditions. The ring of integers and the polynomial rings are typical examples to have in mind. The notion of ideals arises when one tries to form quotients of a ring. Prime ideals are a particular class of ideals that, as the name suggests, generalize the notion of prime number. The set of prime ideals in a ring naturally form a topological space; the spectrum of a commutative ring. The spectrum of prime ideals is a geometric object where the ideals correspond to closed subsets. In the course we will give an introduction to these two subjects, and we will stress how to use the dictionary between algebraic geometry and commutative algebra. In particular we will focus on how algebraic notions and results are to be understood and implemented in the geometric context. Topics in mathematics III: The mathematical theory of option pricing An option is a security/contract giving the right to buy or sell an asset subject to certain conditions, within specified period of time. Trading option in a more organized and controlled way dates back to the founding of Chicago Board Option Exchange (CBOE) in 1973. The same year also saw a breakthrough in the theory of option pricing, with publication of the famous result of Fischer Black and Myron Scholes in the Journal of Political Economy. The mathematical model of Black-Scholes is still the most widely used tool for pricing financial derivatives. Although uncertainty underpins the valuation of any financial instrument, the derivation of the Black-Scholes model is heavily relied on partial differential equations rather than stochastic calculus. This model is also used for valuation of almost all financial derivatives: pricing options, pricing commodities (mines), warrants, index, ... Since its birth, this theory has evolved to embrace very complicated phenomena beyond financial markets: Political decisions, Operating strategies, Decision under uncertainty. In this course we shall discuss the most basic facts of this theory, using tools from PDE. Functional analysis The main goal is to give an introduction to the basics of functional analysis and operator theory, and to some of their (very numerous) applications. First lecture will be on Tuesday January 18 between 14:15-16:00 in the seminar room 3721, institutionen för matematik. We continue our lectures every second Tuesday, please for more details see the course homepage. Applied combinatorics The course will cover several topics of modern combinatorics. One important question is how many are there of a certain object? We will learn techniques, such as recursions, power series and tools from algebra, to answer this question. Important objects will be permutations and partitions. We will also study some applications of graph theory, in particular flows in networks. An other interesting area is error correcting codes, where we will learn som of the basic theory. Finally we will also discuss the mathematics of voting procedures. Prerequisite: A basic course in Discrete Mathematics. A basic course in linear algebra. The history of mathematics Groups and rings As James Newman once said, algebra is "a branch of mathematics in which one does something to something and then compares the results with the result of doing the same thing to something else, or something else to the same thing". Abstract algebra is the area of mathematics that investigates algebraic structures. By defining certain operations on sets one can construct more sophisticated objects: groups, rings, fields. These operations unify and distinguish objects at the same time. Adding matrices work similarly to adding integers while matrix multiplication is quite different from multiplication modulo n. Because structures like groups or rings are richer than sets we cannot compare them using just their elements, we have to relate their operations as well. For this reason group and ring homomophisms are defined. These are functions between groups or rings that "respect" their operation. This type of function are used not only to relate these objects but also to build new ones, quotients for example. Although at this point it may seem like the study of these new and strange objects is little more than an exercise in a mathematical fantasy world, the basic results and ideas of abstract algebra have permeated and are at the foundation of nearly every branch of mathematics. Galois theory Galois theory is a beautiful and fundamental part of algebra dealing with field extensions and field automorphisms. The main theorem gives a 1-1 correspondence between the subextensions of a given field extension satisfying certain properties and the subgroups of a group of automorphisms associated to the extension. Galois theory has many applications. Some of the best known applications are the proof of the impossibility of the trisection of a general angle with ruler and compass only and the proof that the solutions of a general algebraic equation of degree five or higher cannot be given only in terms of n-th roots and the basic algebraic operations. Topics in mathematics IV: Applied topology How can a topological space and its properties be described? One could try to use geometric and descriptive language. For example one might write: a 2 dimensional bounded subspace of the 3 dimensional Euclidean space without a boundary with 2 holes. Such a descriptive language however is often imprecise and may lead to wrong conclusions. For example same description could be visualize in different ways by different people. To remedy this problem, Algebraic Topology uses the precise language of algebra to describe geometry. Homology and cohomology are one of the most important tools in this translation process. It has been a great achievement in mathematics to realize that some important geometric properties of spaces can be described by these invariants. In this course we will study two specific cohomology theories: K-theory and De Rham cohomology. They both have the advantage of being elementary, and can be studied with no particular previous knowledge. K-theory deals with vector bundles over a space. An example of a vector bundle is the Möbius band which consists of a family of lines twisting around the circle. De Rham cohomology uses ideas well known from vector analysis. We will see how these theories are used to compute invariants of spaces, and we will try to give several applications. Game Theory Game theory provides mathematical tools for the analysis of strategic interactions, with applications to many fields, ranging from political science and economics to biology and computer science. One half of this course is devoted to classical game theory and deals with "games" in a very broad sense of the word. The other half is devoted to combinatorial game theory, where we restrict our attention to a class of two-player games with perfect information, including many well-known board games like chess and go.
Linear Algebra Done Right Sheldon Axler Preface to the Student You are probably about to begin your second exposure to linear algebra. Unlike your first brush with the subject, which probably emphasized Euclidean spaces and matrices, we will focus on abstract vector spaces and linear maps. These terms will be defined later, so don't worry if you don't know what they mean. This book starts from the beginning of the subject, assuming no knowledge of linear algebra. The key point is that you are about to immerse yourself in serious mathematics, with an emphasis on your attaining a deep understanding of the definitions, theorems, and proofs. You cannot expect to read mathematics the way you read a novel. If you zip through a page in less than an hour, you are probably going too fast. When you encounter the phrase "as you should verify", you should indeed do the verification, which will usually require some writing on your part. When steps are left out, you need to supply the missing pieces. You should ponder and internalize each definition. For each theorem, you should seek examples to show why each hypothesis is necessary.
This is the homepage for MATH 1150 (Mathematics of Games). This page will be updated throughout the term with important information for our course, including homework assignments, review materials, and more. Most of us have played games such as Tic-Tac-Toe, chess, Go, checkers, and poker. Many games can be studied mathematically using a branch of mathematics called game theory. We will discuss various facets of elementary game theory, including (but not limited to!) how to formulate strategies, what makes some strategies "better" than others, what makes some games difficult or impossible to analyze, and applications to real-world concepts. Specific topics we may cover include the Nash equilibrium, the prisoner's dilemma, and bluffing in poker. The class will not be purely theoretical; we will spend lots of time applying the course concepts by playing various games. A homework assignment might involve analyzing a simple game, devising a winning strategy, and then trying it out during class. The course will be roughly broken up into two halves. The first half will be devoted to games where both players move simultaneously, without knowledge of the other player's move. (These are also called matrix games.) In the second half, we will focus on games where the players move sequentially, taking turns, until the game ends. (These are also called sequential games.) Grading scheme Your term grade will consist of homework assignments (which may include problems from the text, problems I make up, or slightly longer open-ended projects), one midterm exam, and one final exam, broken down in the following way: Assignment 6 and solutions. (NOTE: the bottom line on page 2 was cut off during scanning. It only says that every remaining position can reach the "big L" shape, which is a L(oss), so all remaining positions are W(ins).) Students in this course are expected to abide by the University of Denver's Honor Code and the procedures put forth by the Office of Citizenship and Community Standards. Academic dishonesty - including, but not limited to, plagiarism and cheating - is in violation of the code and will result in a failing grade for the assignment or for the course. As student members of a community committed to academic integrity and honesty, it is your responsibility to become familiar with the DU Honor Code and its procedures: see
Graph Partitioners - Guy Blelloch Three algorithms written in NESL for finding separators of graphs, for the purpose of comparing the quality of the cuts. From the Scandal Project on developing a portable, interactive environment for programming a wide range of supercomputers (see Implementations ...more>> GraphSight - CradleFields.com A graphing tool to plot and interactively explore 2D math functions in the coordinate plane. Drag, click, and move graphed objects. The site offers a gallery of math-related graphics and help documentation. Download a trial version of GraphSight, or purchase ...more>> Graph Theory and Its Applications - Gross, Yellen Pages designed to provide information about the textbook Graph Theory and Its Applications and to serve as a comprehensive graph theory resource for graph theoreticians and students. See also Graph Theory Resources, a support page maintained by Daniel ...more>> Graph Theory - Dave Rusin; The Mathematical Atlas A short article designed to provide an introduction to graph theory. A graph is a set V of vertices and a set E of edges - pairs of elements of V. This simple definition makes Graph Theory the appropriate language for discussing (binary) relations on ...more>> Graph Theory Tutorials - Chris K. Caldwell A series of short interactive tutorials introducing the basic concepts of graph theory, designed with the needs of future high school teachers in mind and currently being used in math courses at the University of Tennessee at Martin. An Introduction to ...more>> Great Circle Mapper - Karl L. Swartz Enter two locations on Earth (latitude and longitude, or airport codes) and see a map depicting the great circle path between them and a computation of the distance along that path. The Great Circle Mapper also displays the area within a given range of ...more>> Great Math Programs - Xah Lee A listing about 40 excellent recreational math programs for Macintosh that do: polyhedra and Rubic cubes, curves and surfaces, fractals and L-systems, tilings and symmetry, game of hex and game of life, chess and five-in-a-row, peg solitare and polyominos,Greek Letters and Math Symbols - Karen M. Strom A set of transparent gifs of the Greek alphabet (all lower case letters and the necessary upper case letters), mathematical symbols, and letters and numbers for use in subscripts and superscripts. A crib sheet describing their use has been provided. A ...more>> GreenHouse Gas Online A site devoted to greenhouse gas and climate change-related science, containing climate change news and links to the abstracts of hundreds of greenhouse gas-related scientific papers. With discussions of the main types of greenhouse gas, and the global ...more>> The Greenwood Institute - Greenwood School A dyslexia, learning disabilities, and literacy resource site, with links to Web resources and publications. Comprehensive training of literacy instructors for mainstream and specialized schools; support for home schooling; research support; and consulting ...more>> Greg Egan's Home Page Information, illustrations, and Java applets that supplement some of the works of the science fiction author. The Applets Gallery includes groups of rotations in three dimensions and in four dimensions; Escher, inspired by the artist's conflicting orientation ...more>> Gregory Buck - The New Yorker "Like everyone else I know, when I go to the beach I think mathematics....I have had people ask me what it is like to do research in mathematics, and perhaps the answer is that it is like a snowstorm...." Seasonal posts by the Saint Anselm College professor ...more>> Group Pub Forum - G. C. Smith The community pages for discussing any aspect of Group Theory, the mathematics of symmetry. Group Theory is a branch of algebra, but has strong connections with almost all parts of mathematics. Announcements, books and journals, conference information, ...more>> Groups & Graphs Home Page - Bill Kocay A software package for graphs, digraphs, combinatorial designs, and their automorphism groups. Features include automorphism group computation; graph certificate which identifies a graph uniquely up to isomorphism; Hamiltonian cycles; planarity test and ...more>> Group Theory - Dave Rusin; The Mathematical Atlas A short article designed to provide an introduction to group theory. Group theory can be considered the study of symmetry: the collection of symmetries of some object preserving some of its structure forms a group; in some sense all groups arise this ...more>> Guaranteach - Alasdair Trotter and George Tattersfield Thousands of very short video lessons, recorded by dozens of different professional teachers whose methods and styles of teaching math vary widely. The diverse perspectives and "bite-size" chunks in Guaranteach's video library let viewers stay focused ...more>> Guy Kindler - The Official Site - Guy Kindler A mathematics Ph.D. student at Tel Aviv University. Math puzzles are ranked from easy to tough. A paper on approximation and various resources for a seminar on computational models may be downloaded in PostScript format. Related PowerPoint presentations ...more>> GVU Center - Jarek Rossignac; Georgia Tech The Graphics, Visualization & Usability Center, envisioning a world in which computers are used as easily and effectively as are automobiles, stereos, and telephones, and collaborating on research projects in Visualization, Animation, VR, Design, ...more>> Habitable Planet Interactive Labs - Annenberg Media Use this set of interactive labs from the Annenberg Media course "The Habitable Planet" to explore the intersection of math and science. Labs tie together common concepts around the themes of carbon, demographics, disease, ecology, and energy. Each lab ...more>>
Math Microsoft Office 2010 text introduces students to the various applications included in this latest Microsoft Office release. The program is based upon the same curriculum as the Microsoft Office Specialist Exam to build the skills students need to succeed at work Fourth Edition of Workshop Statistics: Discovery with Data continues to emphasize collaborative learning and to require student observation. Rather than describing and explaining statistics through exposition alone, Workshop Statistics: Discover with Data offers activities designed to lead students to discover statistical concepts, explore statistical principles, and apply statistical techniques. This MOAC Microsoft Access 2010 77-885 Outlook 2010 77-884 PowerPoint 2010 77-883 Word 2010 77-881
Grade 8 While our Form II (eighth grade at Haverford) liberal arts curriculum remains very similar to the Form I year, our expectations have changed. Our Form II boys are the leaders of the division and they lead by modeling to our younger boys the opportunity for academic excellence, sportsmanship, respect, and behavior that we expect of all our students. We teach them the difference between giving and taking, rights and privileges, expected actions and exceptional ones, so they can learn to make decisions on their own and not based on some stereotypical belief. They are young men, and after two full years in our building, they know the culture, the tone and the honor code. They know when they make a mistake and how to own it. They are accountable for their actions and understand the consequences for their behavior, both good and bad. They are young men who are prepared to learn, lead and listen as they leave us and enter the Upper School. Math Algebra I This course is a comprehensive Algebra I course. It assumes that the students have the prerequisite knowledge of operations with whole numbers, integers, fractions, decimals and percents. It emphasizes solutions of single variable equations, systems of linear equations in two variables, basic operations with polynomials, factoring, and the solution of quadratic equations using various methods. Considerable focus will be placed on multiple representations of these solutions, especially graphs. Students will become familiar with handheld technology tools, like the TI 83/84 family of calculators. We employ the Prentice Hall text, Algebra I. Geometry This course emphasizes the development of visual/spatial thinking skills. Beginning with the building blocks of geometry, the students will investigate the properties of points, lines and planes, and their relationships to real-world models. With the use of concrete models and puzzles, the geometry student will investigate the unique characteristics of both two- and three-dimensional shapes and figures. Time will be spent on constructions with the use of math tools and the derivation of formulas and theorems. Students will gain valuable experience with dynamic math technology, like Geometer's Sketchpad, and the TI 83/84 family of handheld calculators. We employ the Key Curriculum Press text, Discovering Geometry: An Investigative Approach. Science This is a yearlong introductory course focusing on the life sciences. The fall term emphasizes a deeper understanding of the scientific method, characteristics that all organisms share, the classification system, the cell, cell structure and processes, and the cell project. The winter term continues on with an introduction to nutrition and digestion with the nutrition project, and cell division and DNA. The spring term introduces stem cell research and regenerative medicine, and an introduction to diseases through the study of viruses and bacteria along with the childhood disease project. Social Studies World Cultures This course examines non-Western culture areas as each evolved from ancient times to the present. The culture area approach provides a vehicle for correlating the social sciences. Consequently, five factors are emphasized - historical, geographical, sociological, economic and political. As countries within each culture area are studied, the student becomes acquainted with the geographical characteristics, their effect on the economic life of the people, the customs of the country and the current political status. Through the use of Skyping and in-class guest speakers, students have the opportunity to interact with individuals that live in the current cultures they are studying. Further, students use a bulk packet compiled from writings from around the world and study current events from various nations of each region. Finally, similarities and diversities within each culture area are examined as well as what distinguishes them from other cultures. English In preparation for Upper School, Form II English emphasizes consistent refinement of reading comprehension, writing and speaking/presentation through engagement with a variety of texts. This includes, but is not limited to, novels, short stories, film/video, art, music, and technology. Each year, young men in Form II will critique how a major theme has influenced authors' decisions about voice, character, setting, style, and other literary components through ongoing and in depth literature analysis, discussion and creation. Students can expect several collaborative and independent projects, formal research (papers/presentations), and creative writing opportunities. By the end of the year, young men in Form II can expect to have furthered their analytic/persuasive essay writing skills and poise in public speaking. Texts for Form II English may include: Romeo and Juliet (Shakespeare), Animal Farm (Orwell), The Absolutely True Diary of a Part-Time Indian (Alexie), Of Mice and Men (Steinbeck), and To Kill a Mockingbird (Lee) among others. Foreign Language Latin Form II Latin continues what the student learned in the prerequisite first year of Latin study. Vocabulary, grammar, and syntax of increasing complexity encourage the student to maintain a disciplined approach to language and to analyze logically. Translation of passages provides constant practice and rewarding challenge. Roman history, mythology, and culture are explored in increasing depth with emphasis on the classical Greek hero. He learns about government, law, military attitudes, technology and literature. Increasing emphasis is put on art through the ages, even to commercial art and movies of today. The successful Form II student completes a very full and enriched first year Latin course. As he enters his Form II year, he is prepared to join a Latin II class, perhaps add a second language, or select a new language option that he will continue through high school. Spanish In Middle School we begin with the instruction of Spanish and Latin in the Prima Lingua class in sixth grade. The students then decide in 7th grade whether to continue with Spanish or Latin. They take two years of Spanish in Middle School, 7th and 8th grade. During those two years the students receive a solid foundation in the structure of the Spanish language as well as an understanding of the cultural background of the many Spanish speaking countries. On the introductory level there is an emphasis on basic vocabulary and fundamental grammatical concepts. The students of Spanish should be able to engage in an easy conversation, speaking in complete and grammatically correct sentences. They are also able to read easy texts, summarize them in their own words and narrate a story in front of the class. We use BUEN VIAJE as a textbook to study all the grammatical concepts and to read easy passages. In addition we study some readers with stories and fables the boys are familiar with: The Dschungelbook, The turtle and the hare, Goldilocks etc. Visual Arts 2D and 3D The eighth grade art program is a combination of two-dimensional and three-dimensional work with a sprinkling of art history thrown in. Projects tend to be more challenging in this course as students are asked to follow specific guidelines and processes. The 8th grade student may expect to be given a long-term sculpture project in clay, plaster or wood as well as an in depth self-portrait painting. One art project will be directly related to their academic study of World Cultures and History or Greek Mythology. Suggestions, from the art and photography teachers, will be made to the students and parents regarding art course decisions for Upper School. Video Production and Multi-Media Eighth graders boys begin the year with an in depth unit in Video Production. They cover shot types, camera angles and movement, lighting, composition, and sound. The boys move through the three processes of video: Pre-production (scripting and storyboarding), Production (treatment and filming), and Post-production (sequencing, editing, and sound). Eighth grade boys then move on to a unit that blends the traditional arts (drawing, painting, and sculpting) with new media: Animation. Through animation the boys learn technical aspects like the math and science behind a film's frame rate, its key frames, tweening, shots, and scenes. Both through video and animation the boys learn how to tell stories through sequence and montage. They will write and develop characters learning about arcs and linear / non-linear storytelling. Drama Elective* Students will walk away from this course with the knowledge of different methods and systems of acting from diverse cultures. They will create an ensemble and begin to perform as a troupe in sketch comedy, original works and in published dramatic plays. Music Students explore a variety of musical styles in their Form II year. They learn to use guitar strumming techniques that are idiomatic to music of many world cultures. They learn to identify, play and compose using the components of popular, classical and multi-cultural music. They learn to use complex chords, refine their tablature reading, and play in class ensembles. They use music technology as a tool in the study of the basic music theory of Western music, and to compose and arrange music of many styles. Repertoire for the Form II runs the gamut from Bach to Rock. Health and Physical Fitness Boys are taught skills, provided drill work, and have the opportunity to play the following: touch football, soccer, cross-country, floor hockey, basketball, wrestling, track and field, baseball, and lacrosse. The Presidential Fitness Program is administered during the Fall and Spring semesters of each middle school year. The "Presidential Award" is given to those students who score 85% or above in all tests. The "National Award" recognizes those boys scoring 50% or above in all tests. Parents will receive individual fitness profiles from curl-ups (abdominal strength), shuttle run (quickness and speed), one-mile run/walk (endurance), pushups (upper body strength), and V-sit reach (flexibility). Eighth Grade Team Each teacher is also an adviser to a small group of students and a member of at least one Grade Level Team. The Grade Level Teams meet weekly to discuss the progress of the boys which results in proactive problem solving and efficient decision making for our students and their families.
Brief Calculus With Applications: Solving Problems In Business, Economics, And The Social And Behavioral Sciences-text Only - 2nd edition Summary: For courses in Mathematics for Business, Finite Mathematics, and Applied Calculus. This text, modern in its writing style as well as in its applications, contains numerous exercises -- both skill oriented and applications --, real data problems, and a problem solving method. Its exercises are based on data from the World Wide Web, and allow students to see for themselves how mathematics is used in everyday life. Features : Problem solving method --Occurs in worked out examples throughout the entire text in the steps entitled Understand the Situation and Interpret the Solution. Provides students with the necessary preliminary thought processes needed when attacking a problem. Real data modeling --Features problems based on data culled from the WWW. Impresses upon students that mathematics can be used to solve a multitude of rich real world problems. Serves instructors with an abundance of examples and exercises enabling students to see where they could use this mathematics in the real world. Technology options -- Follows worked examples for students and instructors who wish to use graphing calculator technology. Shows students how the graphing calculator may be used to solve the example just presented. Flashbacks -- Revisits an example from a prior section and extends the content to introduce new topics. Allows students to concentrate on a new topic using familiar applications. Enables instructors to use students' prior knowledge and extend it naturally to new material. From Your Toolbox boxes -- Reviews a previously introduced key definition, theorem, or property required in the development of a new topic. Allows students to stay on a task with the material being presented without having to flip back several pages. Notes feature follows definitions, theorems, and properties. Provides students with additional insight by clarifying the just presented mathematical idea verbally. Checkpoints -- Reinforce the topics, skill, or concept at hand. Helps students take ownership of their learning and the course material, and gives them confidence in their ability to do so. Chapter openers -- Includes photos, graphs, What We Know, and Where Do We Go sections. Guides students through the text by highlighting what the have already learned and what they are about to cover. Chapter-end narratives -- Features Why We Learned It sections, extensive review exercises, and a chapter project. Outlines the major chapter topics and how they are used in various careers, and offers students the chance to test their understanding of the material they have learned -- and their understanding of it. 1. Functions, Modeling and Average Rate of Change. Coordinate Systems and Functions. Introduction to Problem Solving. Linear Functions and Average Rate of Change. Quadratic Functions and Average Rate of Change on an Interval. Operations on Functions. Rational, Radical and Power Functions. Exponential Functions. Logarithmic Functions. Regression and Mathematical Models (Optional Section). 2. Limits, Instantaneous Rate of Change and the Derivative. Limits. Limits and Asymptotes. Problem Solving: Rates of Change. The Derivative. Derivatives of Constants, Powers and Sums. Derivatives of Products and Quotients. Continuity and Nondifferentiability. 3. Applications of the Derivative. The Differential and Linear Approximations. Marginal Analysis. Measuring Rates and Errors. 5. Further Applications of the Derivative. First Derivatives and Graphs. Second Derivatives and Graphs. Graphical Analysis and Curve Sketching. Optimizing Functions on a Closed Interval. The Second Derivative Test and Optimization. 7. Applications of Integral Calculus. Average Value of a Function and the Definite Integral in Finance. Area Between Curves and Applications. Economic Applications of Area between Curves. Integration by Parts. Numerical Integration. Improper Integrals6.77
Numbers Guide (Paperback \| ISBN : 9781861975157, 1861975155) Description Suitable for those who want to be competent, and able to communicate effectively, this book offers advise on basic numeracy, points out common errors and explains the recognized techniques for solving financial problems, analyzing information of any kind and effective decision making.
:: 2013 AP* Summer Institutes at UT Austin Pre-AP High School Math: Algebra I and Geometry Focus Institute Code AP13011 This class is full and closed for registration. Topics covered include: The Rule of Four Rigor: The Key to Success in Pre-AP Limits for courses prior to calculus Rate of Change Accumulation Optimization Rational Functions Polynomial Approximations Distance, Velocity, Speed, and Acceleration Parametric Equations Univariate Data Bivariate data Probability Algebra Skills Needed for Calculus Homework in Pre-AP Vertical Teams Assessment: Testing AP Style in Pre-AP Classes Data Collection (CBR2 & CBL2) Mathematics Internet Sites Participants should bring: A favorite lesson to share. Teachers will share lessons with other workshop participants. A graphing calculator (if available). A laptop or tablet. Textbooks using next year. Lead Consultant: Robert Cole Robert Cole has presented at numerous APSIs and College Board One-Day, Two-Day and Mathematics Vertical Teams workshops. A veteran of over 30 years in the public schools, Robert has taught everything from 7th grade math to calculus, including below-level, on-level, Pre-AP, G/T and AP classes. His current assignments at Hill Country Christian School of Austin and Odyssey School in Austin include Algebra, Geometry, Algebra 2, Precalculus and AP Calculus AB. * Trademark Notice: College Board, AP, Advanced Placement Program, AP Vertical Teams, Pre-AP, and the acorn logo are registered trademarks of the College Board. Used with permission.
Chalkdust Math Chalkdust offers math instruction on videos (DVDs) and textbooks that go along with the video lessons, for basic math through calculus (grades 7-12). The textbooks they recommend are written by Ron Larson, published by Houghton Mifflin. Each course (such as algebra, geometry, or trigonometry) includes a DVD set with a total of a few dozen hours of instruction, a textbook, and a solutions guide. Prices vary. A full set is typically around $350 - $550 per course. Reviews of Chalkdust Time: two years Your situation: My son, 16, is a homeschooled high school sophomore. My strengths and skills are in the humanities areas, not in the math and science area. My son prefers humanities to math and science but is considered \'advanced\' in math in that he is taking pre-cal as a sophomore and some non-science / non-math students do not reach pre-cal until their junior or senior year of high school if at all. Why you liked/didn't like the book: Dana Mosley is an excellent math teacher. His DVDs are comprehensive and his lesson plan makes it easy on the parent and student to figure out how much work to do each day. If the student should need additional help, Dana is available by phone or by email and he answers requests promptly. i especially like that the instructor goes through the use of the scientific calculator and uses textbooks that are standard to the best high schools and colleges in the country. Any other helpful hints: More expensive than most math curricula for home schoolers, but worth every penny. Remember that students need only do every 3rd or every 5th odd numbered problem.
The grades 8-10 Patterns, Functions and Algebra Benchmark J: Describe and interpret rates of change from graphical and numerical data is one of the benchmarks most frequently tested on the 8th grade Ohio Achievement Assessment (OAA). The lesson materials and assessment items in this mini-collection support instruction related to this benchmark. week-long unit, students examine the problem of space pollution caused by human-made debris in orbit to develop an understanding of functions and modeling. The unit provides students an opportunity to use spreadsheets, graphing calculators, and computer graphing utilities. One important outcome for this unit is helping students develop an appreciation for the power and limitations of mathematical modeling. They should realize that the two most basic expectations of models are (1) the ability to account for or represent known phenomena and (2) the ability to predict future results. The unit also illustrates the critical importance of mathematics in space science. Several Internet and teaching extensions are included. This unit was adapted from Modeling Orbital Debris Problems in Mission Mathematics, Linking Aerospace and the NCTM Standards, 9-12, a NASA/NCTM project, NCTM 1997. The user can easily forgive some typos in view of the detailed notes to the teacher and the highly informative and challenging student activity sheets. (author/sw) This three-part activity illustrates the use of iteration, recursion, and algebra to model and analyze the changing amount of medicine in an athlete's body. The activity is adapted from High School Mathematics at Work, a publication from the National Research Council. In the first part, Modeling the Situation, an interactive environment is used to show the parameters involved and the range of results that can be obtained with different dosages of medicine. In the second part, Long-Term Effect, the interactive environment is used to investigate how changing parameter values affects the stabilization level of medicine in the body. In the third part, Graphing the Situation, an interactive graphical analysis provides a visual interpretation of the results. Through multiple representations of a common concept, better insight into, and a deeper understanding of, the problem situation can be achieved. (author/sw) This lesson is a nicely creative extension of the lesson in which students measure the diameter and circumference of several circular objects to arrive at an approximation of pi. In this extension, students use strips of masking tape to measure the diameter and circumference of various circular objects, create a graph using the strips pf) This. Step-by-step instructions, activity sheets, questions for reflection, and suggestions for assessment are included. (author/sw) Students must identify the slope of a line segment shown on a coordinate graph 43. (author/sw) Students must compute the distance between two points on a coordinate plane 30. (author/sw) Students must find the slope of the line connecting two points in the coordinate plane 25. (author/sw)
Mathematics 130 is a "standard" first semester calculus course. A plan for our progress through the topics of this course is shown in the table below. You should enter this course with a solid foundation in precalculus: algebra, general function topics (e.g., composition, graphs), and knowledge of particular function types: trigonometric, exponential, and logarithmic. Our goal is to develop your capacity for reading, writing, and speaking mathematics. The venue for this effort is calculus. You should complete this course with the background to be a successful student in the succeeding course, Calculus II. There will be two evening reviews and and three take-home writs as indicated below. Reviews are scheduled on Thursday evenings, 8-10 pm, in Chambers TBA. If a Thursday evening review presents a particular burden for your schedule, see me and we will negotiate an alternative time (preferably on Thursday afternoon). Writs will be due at the start of the next class. Collaboration on homework is encouraged, though anything you present or turn in should represent your understanding of the material. Although homework is not a formal part of your evaluation, a record is kept of your participation in this necessary ingredient of a successful mathematical experience. Homework will be collected on Mondays (by 12:30 pm) and on Thursdays (in class). (A fuller statement on homework evaluation is in a web-based memo.) Come to every class meeting and come on time. Missing class deprives both you of a first-hand class experience, and your classmates of your particular perspectives. I monitor attendance; missing 20% of class meetings can trigger action to encourage more faithful attendance. In any event, you are responsible for all material discussed in class, whether you are present or absent. The major components of your grade are 3 writs, 2 reviews, the final examination, and 2 or 3 "extended assignments." An "extended assignment" may be a more substantial and carefully presented problem set, perhaps around a theme, or may be a short paper. With a "writ" being the unit of measure, extended assignments will accumulate to the equivalent of 1 writ, reviews will be worth about 2 writs each, and the Final Examination will carry the weight of approximately 3 writs. Other considerations (e.g., participation and effort on homework assignments) may provide extra seasoning in this mix. Thus, the recipe for your grade in this course is distributed as roughly 3 parts writs, 1 part extended assignments 4 parts reviews, 3 parts examination, and a pinch of "other." (An explanation of my grading system is available in a web-based memo.)
Title Information This book can be used individually or as a set with Chenier's Practical Math Dictionary. This book is designed to parallel and enhance any practical math class from general education through college level programs. Many of the math concepts are left out of traditional math books and are relevant to many different trades, occupations, do-it-yourselfers, home owners, home schoolers, etc. It includes testing material economical hands-on projects that simulate industry (use with sticks of wood, chalk lines, flip cart paper, etc.), the answers, and many different unique modules for projects, classroom situations, self-study, industry, etc. All have been proven in the classroom and on-the-job. There are drilling tricks, drill and tap charts (english and Metric), drill numbers, American Standard pipe chart, shimming tricks, draw circles with a layout square, plus much, much more. This book wins the Medal of Honor in the world of math books. No other book or online resource is more useful, beneficial, and practical for everyday use in the real world. This book also put me through college algebra, geometry, and trigonometry and blew the hundred dollar text books out of the water. Since it is many years since school/univ. I find that I have the need for a "refresher" in maths. This book is IT!!!! Straightforward, concise and written in simple language, this little gem covers it all. From basic arithmetic through elementary trig, with plenty of examples, tables and illustrations. It's all here. Simplifies those things you have long been afraid of when it comes to numbers. Get it along with the companion application workfook and you'll be set whether you're a tradesman or student. Praise for the Practical Math Application Guide I work as an exhibitions installer/fabricator for a fine arts museum. I recently purchased both Chenier's books, The Practical Math Application Guide and the Practical Math Dictionary as a personal enrichment/refesher course for construction math. I wich I'd known about these books 20 years ago! The way the concepts are explained and the way the books show practical applications for everyday construction problems using traditional tools is better than in any other books I've used. Follow them cover to cover from page 1, even if you already know the math, and work the problems in the tests. It'll refresh your memory and probably teach you some new and easy methods you weren't even aware of for problem solving. Since beginning practice two weeks ago, my dependence upon my construction caclculator has diminished to near zero, and the speed and confidence with which I work has increased along with the accuracy and quality of the finished products I make. Thank you Chenier's for a truly great set of books! This is hands down one of the most practical real life math books available. As a full time carpenter for 30 years, I've used solutions to problems illustrated in this book many times, and it's a great teaching aid to ones new to the trade. Worth keeping in the truck as a reference.
(Note: The actual Algebra Buster is software, instantly downloadable to your PC; it is not a "web-service". Only the demos are shown on the web. For more details click on the image below.) Below you will find a large number of demos explaining different aspects of Algebra Buster software . If you have Flash plug-in installed, click on the corresponding Flash Demo button; if you don't, click on the Screenshot button. If you have no idea what Flash is, click on the Flash Demo button anyway - most likely your browser supports it. If it doesn't, you can download it from here. You can go through demos in or out of order - most are self-contained. Let us know if you have any problems viewing them, or if you would want us to add some other topics. Topic Animated Static Adding and subtracting fractions Basic trigonometry Calculating proportions Circle equation Complex numbers Composition of functions Domain of a function Entering logarithmic expressions Entering rational expressions Entering square roots Factoring expressions Finding the LCM Graphing curves and points Graphing inequalities Levels of visibility Multiplying and dividing fractions Perpendicular line equation Point slope line equation Simplifying exponential expressions Simplifying radical expressions Solving quadratic equations Solving systems of equations Synthetic division Vertex of a parabola Working with formulas
There is no required text for the course. Much of the material covered so far (root finding, Taylor polynomials, autonomous DE, Euler's method) can be found in any slightly advanced calculus text such as Robert Adams' "Calculus, a complete course" (later editions with co-author Christopher Essex). Assignment #1, due Friday, January 11. Part A is to be handwritten and turned in during class. Part B is to be submitted electronically as a maple worksheet (.ws file) to the slate system Correction: Assignment #10. Note that there is an error in the numbering in the example for #3. One of the rows I show is numbered the wrong direction. When done correctly, 17 should be in the (4,4) position. The MATLAB file for question #3 is here: slxy.m; question #4 display_board.m; and question #5 energySolutions to Lab Quiz #8 are give in two MATLAB files: first.m and second.m. Solutions to Lab Quiz #9 are give in two MATLAB files: dice.m and vanMATLAB exercise: Snakes and Ladders. We are working our way through a longer example of the use of MATLAB to identify some statistics of the game, Snakes and Ladders. Since there are many board variants, we are making a general code that takes in the board information in a structure. So far, we have done the following: Specified the board information structure. A sample structure is shown in board1.m for a small test board shown in SandL.pdf. Wrote a dice rolling function that allows for the game to be played with different sized dice: roll.m.
Algebra -------- operations on sets, Arithmetic and Geometric sequences, complex numbers and how to transform between its different forms (Cartesian,Polar,Exponential,Trigonometric) and De Moivre theorem, mathematical induction and its applications(series,recursive,divisibility,matrices,derivative and inequality problems),Graph theory,matrices and its applications(solving equations,division and the other operations),number systems(decimal,binary,ternary,octal,hexadecimal) and the transformation from each one to the other and the operations on each system, Fourier series , how to calculate it and its applications in real life.
Created by Share this course An extensive repetition of an introductory numerics lecture for undergraduate students (math/physics/computer science): (German). The difficulty level varies from trivial notation conventions or prerequesites to theorems which may appear abstract if you are not used to this kind of math. Teaching of concepts is not intended, just active memorization of terms and passive repetition of formulas. Choose levels according to interests.
Volume 7, Number 12 25 March 2002 Vol. 7, No. 12 THE MATH FORUM INTERNET NEWS Math Awareness Month - April 2002 \| eTAP - Math PROMYS: The Program in Mathematics for Young Scientists Summer Math Camps and Programs for High School Students (AMS) MATH AWARENESS MONTH - APRIL 2002 Mathematics Awareness Month provides the mathematical sciences community with opportunities for promoting the importance and versatility of mathematics, and its relationship to our daily lives. The theme of MAM 2002 is Mathematics and the Genome. -\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|- eTAP - MATH The math section of eTAP, the electronic Teaching Assistance Program, provides mathematics instructional material designed to assist students in grades 6-10 and their parents. Materials include lesson plans, instructions with examples and exercises, and assessments similar to those used on standardized tests such as the SAT, state high school exit and equivalency exams. 1. The Language of Mathematics 2. Basic Operations 3. Order of Operations and Combining Terms 4. Fractions 5. Multiplying and Dividing Fractions 6. Operations with Decimals 7. Geometric Lines, Figures and Relationships 8. Powers, Roots and Radicals 9. Geometric Formulas 10. Basic Operations with Literal Numbers 11. Solving Basic Equations 12. Solving Problems with Algebra 13. Using Functions in Solving Right Triangle Problems 14. Further Applications of Formulas and Functions 15. Simultaneous Linear Equations 16. Quadratic Equations 17. Graphs 18. Statistics and Probability 19. High School Exit Exam 20. Glossary -\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|-\-/-\|- PROMYS: THE PROGRAM IN MATHEMATICS FOR YOUNG SCIENTISTS PROMYS encourages ambitious high school students to explore the creative world of mathematics. From July 7 to August 17, approximately 60 high school students from around the country will gather on the campus of Boston University for six weeks of rigorous mathematical activity. Through their intensive efforts to solve an assortment of challenging problems in number theory, participants practice the art of mathematical discovery. PROMYS for Teachers supports current efforts in Massachusetts to enhance problem-solving and open-ended exploration in high school mathematics classrooms. The 2002 Student, Counselor, and Teacher applications are now available. \\|/ SUMMER MATH CAMPS AND PROGRAMS FOR HIGH SCHOOL STUDENTS (AMS) The American Mathematical Society has a listing of titles, locations, and links of summer programs that provide high school students experience in the world of mathematics research. \\|/ MATH CAMPS & SUMMER PROGRAMS The Math Forum maintains an annotated list of math camps and summer programs
accompanying CD A feature of the accompanying CD is our new 'self-tutoring' software where a teacher's voice explains each step in every worked example in the book. Click anywhere on any worked example where you see the icon to activate the self-tutoring software. The CD is ideal for independent study and revision. It also contains the full text of the book so that if students load it onto a home computer, they can keep the textbook at school and access the CD at home. Table of contents Symbols and notation used in this book 6 Graphics calculator instructions 11 A Basic calculations 12 B Basic functions 13 C Secondary function and alpha keys 17 D Memory 17 E Lists 19 F Statistical graphs 21 G Working with functions 22 H Two variable analysis 26 Assumed Knowledge (Number) 29 A Number types CD B Operations and brackets CD C HCF and LCM CD D Fractions CD E Powers and roots CD F Ratio and proportion CD G Number equivalents CD H Rounding numbers CD I Time CD Assumed Knowledge (Geometry and Graphs) 30 A Angles CD B Lines and line segments CD C Polygons CD D Symmetry CD E Constructing triangles CD F Congruence CD G Interpreting graphs and tables CD 1 Algebra (expansion and factorisation) 31 A The distributive law 32 B The product (a+b)(c+d) 33 C Difference of two squares 35 D Perfect squares expansion 37 E Further expansion 39 F Algebraic common factors 40 G Factorising with common factors 42 H Difference of two squares factorisation 45 I Perfect squares factorisation 47 J Expressions with four terms 48 K Factorising x2+bx+c 49 L Splitting the middle term 51 M Miscellaneous factorisation 54 Review set 1A 55 Review set 1B 56 2 Sets 57 A Set notation 57 B Special number sets 60 C Interval notation 61 D Venn diagrams 63 E Union and intersection 65 F Problem solving 69 Review set 2A 72 Review set 2B 73 3 Algebra (equations and inequalities) 75 A Solving linear equations 75 B Solving equations with fractions 80 C Forming equations 83 D Problem solving using equations 85 E Power equations 87 F Interpreting linear inequalities 88 G Solving linear inequalities 89 Review set 3A 91 Review set 3B 92 4 Lines, angles and polygons 93 A Angle properties 93 B Triangles 98 C Isosceles triangles 100 D The interior angles of a polygon 103 E The exterior angles of a polygon 106 Review set 4A 107 Review set 4B 109 5 Graphs, charts and tables 111 A Statistical graphs 112 B Graphs which compare data 116 C Using technology to graph data 119 Review set 5A 120 Review set 5B 122 6 Exponents and surds 123 A Exponent or index notation 123 B Exponent or index laws 126 C Zero and negative indices 129 D Standard form 131 E Surds 134 F Properties of surds 137 G Multiplication of surds 139 H Division by surds 142 Review set 6A 143 Review set 6B 145 7 Formulae and simultaneous equations 147 A Formula substitution 148 B Formula rearrangement 150 C Formula derivation 153 D More difficult rearrangements 155 E Simultaneous equations 158 F Problem solving 164 Review set 7A 166 Review set 7B 167 8 The theorem of Pythagoras 169 A Pythagoras' theorem 170 B The converse of Pythagoras' theorem 176 C Problem solving 177 D Circle problems 181 E Three-dimensional problems 185 Review set 8A 187 Review set 8B 188 9 Mensuration (length and area) 191 A Length 192 B Perimeter 194 C Area 196 D Circles and sectors 201 Review set 9A 206 Review set 9B 207 10 Topics in arithmetic 209 A Percentage 209 B Profit and loss 211 C Simple interest 214 D Reverse percentage problems 217 E Multipliers and chain percentage 218 F Compound growth 222 G Speed, distance and time 224 H Travel graphs 226 Review set 10A 228 Review set 10B 229 11 Mensuration (solids and containers) 231 A Surface area 231 B Volume 239 C Capacity 245 D Mass 248 E Compound solids 249 Review set 11A 253 Review set 11B 254 12 Coordinate geometry 255 A Plotting points 256 B Distance between two points 258 C Midpoint of a line segment 261 D Gradient of a line segment 263 E Gradient of parallel and perpendicular lines 267 F Using coordinate geometry 270 Review set 12A 272 Review set 12B 273 13 Analysis of discrete data 275 A Variables used in statistics 277 B Organising and describing discrete data 278 C The centre of a discrete data set 282 D Measuring the spread of discrete data 285 E Data in frequency tables 288 F Grouped discrete data 290 G Statistics from technology 292 Review set 13A 293 Review set 13B 295 14 Straight lines 297 A Vertical and horizontal lines 297 B Graphing from a table of values 299 C Equations of lines (gradient-intercept form) 301 D Equations of lines (general form) 304 E Graphing lines from equations 307 F Lines of symmetry 308 Review set 14A 310 Review set 14B 311 15 Trigonometry 313 A Labelling sides of a right angled triangle 314 B The trigonometric ratios 316 C Problem solving 322 D The first quadrant of the unit circle 327 E True bearings 330 F 3-dimensional problem solving 331 Review set 15A 336 Review set 15B 337 16 Algebraic fractions 339 A Simplifying algebraic fractions 339 B Multiplying and dividing algebraic fractions 344 C Adding and subtracting algebraic fractions 346 D More complicated fractions 348 Review set 16A 351 Review set 16B 352 17 Continuous data 353 A The mean of continuous data 354 B Histograms 355 C Cumulative frequency 359 Review set 17A 364 Review set 17B 365 18 Similarity 367 A Similarity 367 B Similar triangles 370 C Problem solving 373 D Area and volume of similar shapes 376 Review set 18A 380 Review set 18B 381 19 Introduction to functions 383 A Mapping diagrams 383 B Functions 385 C Function notation 389 D Composite functions 391 E Reciprocal functions 393 F The absolute value function 395 Review set 19A 398 Review set 19B 399 20 Transformation geometry 401 A Translations 402 B Rotations 404 C Reflections 406 D Enlargements and reductions 408 E Stretches 410 F Transforming functions 413 G The inverse of a transformation 416 H Combinations of transformations 417 Review set 20A 419 Review set 20B 420 21 Quadratic equations and functions 421 A Quadratic equations 422 B The Null Factor law 423 C The quadratic formula 427 D Quadratic functions 429 E Graphs of quadratic functions 431 F Axes intercepts 438 G Line of symmetry and vertex 441 H Finding a quadratic function 445 I Using technology 446 J Problem solving 447 Review set 21A 451 Review set 21B 453 22 Two variable analysis 455 A Correlation 456 B Line of best fit by eye 459 C Linear regression 461 Review set 22A 466 Review set 22B 467 23 Further functions 469 A Cubic functions 469 B Inverse functions 473 C Using technology 475 D Tangents to curves 480 Review set 23A 481 Review set 23B 481 24 Vectors 483 A Directed line segment representation 484 B Vector equality 485 C Vector addition 486 D Vector subtraction 489 E Vectors in component form 491 F Scalar multiplication 496 G Parallel vectors 497 H Vectors in geometry 499 Review set 24A 501 Review set 24B 503 25 Probability 505 A Introduction to probability 506 B Estimating probability 507 C Probabilities from two-way tables 510 D Expectation 512 E Representing combined events 513 F Theoretical probability 515 G Compound events 519 H Using tree diagrams 522 I Sampling with and without replacement 524 J Mutually exclusive and non-mutually exclusive events 527 K Miscellaneous probability questions 528 Review set 25A 530 Review set 25B 531 26 Sequences 533 A Number sequences 534 B Algebraic rules for sequences 535 C Geometric sequences 537 D The difference method for sequences 539 Review set 26A 544 Review set 26B 545 27 Circle geometry 547 A Circle theorems 547 B Cyclic quadrilaterals 556 Review set 27A 561 Review set 27B 562 28 Exponential functions and equations 565 A Rational exponents 566 B Exponential functions 568 C Exponential equations 570 D Problem solving with exponential functions 573 E Exponential modelling 576 Review set 28A 577 Review set 28B 578 29 Further trigonometry 579 A The unit circle 579 B Area of a triangle using sine 583 C The sine rule 585 D The cosine rule 588 E Problem solving with the sine and cosine rules 591 F Trigonometry with compound shapes 593 G Trigonometric graphs 595 H Graphs of y=asin(bx) and y=acos(bx) 599 Review set 29A 601 Review set 29B 602 30 Variation and power modelling 605 A Direct variation 606 B Inverse variation 612 C Variation modelling 615 D Power modelling 619 Review set 30A 622 Review set 30B 623 31 Logarithms 625 A Logarithms in base a 625 B The logarithmic function 627 C Rules for logarithms 629 D Logarithms in base 10 630 E Exponential and logarithmic equations 634 Review set 31A 636 Review set 31B 637 32 Inequalities 639 A Solving one variable inequalities with technology 639 B Linear inequality regions 641 C Integer points in regions 644 D Problem solving (Extension) 645 Review set 32A 647 Review set 32B 648 33 Multi-Topic Questions 649 34 Investigation and modelling questions 661 A Investigation questions 661 B Modelling questions 669 Answers 673 Index 752 Using the interactive CD The interactive Student CD that comes with this book is designed for those who want to utilise technology in teaching and learning Mathematics. The CD icon that appears throughout the book denotes an active link on the CD. Simply click on the icon when running the CD to access a large range of interactive features that includes: spreadsheets printable worksheets graphing packages geometry software demonstrations simulations printable chapters SELF TUTOR For those who want to ensure that they have the prerequisite levels of understanding for this new course, printable chapters of assumed knowledge are provided for Number (see p. 29) and Geometry and Graphs (see p. 30). SELF TUTOR is an exciting feature of this book. The icon on each worked example denotes an active link on the CD. Simply 'click' on the (or anywhere in the example box) to access the worked example, with a teacher's voice explaining each step necessary to reach the answer. Play any line as often as you like. See how the basic processes come alive using movement and colour on the screen. Ideal for students who have missed lessons or need extra help. Graphics calculators The course assumes that each student will have a graphics calculator. An introductory section 'Graphics calculator instructions' appears on p. 11. To help get students started, the section includes some basic instructions for the Texas Instruments TI-84 Plus and the Casio fx-9860G calculators. Foreword This book has been written to cover the 'IGCSE Cambridge International Mathematics (0607) Extended' course over a two-year period. The new course was developed by University of Cambridge International Examinations (CIE) in consultation with teachers in international schools around the world. It has been designed for schools that want their mathematics teaching to focus more on investigations and modelling, and to utilise the powerful technology of graphics calculators. The course springs from the principles that students should develop a good foundation of mathematical skills and that they should learn to develop strategies for solving open-ended problems. It aims to promote a positive attitude towards Mathematics and a confidence that leads to further enquiry. Some of the schools consulted by CIE were IB schools and as a result, Cambridge International Mathematics integrates exceptionally well with the approach to the teaching of Mathematics in IB schools. This book is an attempt to cover, in one volume, the content outlined in the Cambridge International Mathematics (0607) syllabus. References to the syllabus are made throughout but the book can be used as a full course in its own right, as a preparation for GCE Advanced Level Mathematics or IB Diploma Mathematics, for example. The book has been endorsed by CIE but it has been developed independently of the Independent Baccalaureate Organization and is not connected with, or endorsed by, the IBO. To reflect the principles on which the new course is based, we have attempted to produce a book and CD package that embraces technology, problem solving, investigating and modelling, in order to give students different learning experiences. There are non-calculator sections as well as traditional areas of mathematics, especially algebra. An introductory section 'Graphics calculator instructions' appears on p. 11. It is intended as a basic reference to help students who may be unfamiliar with graphics calculators. Two chapters of 'assumed knowledge' are accessible from the CD: 'Number' and 'Geometry and graphs' (see pp. 29 and 30). They can be printed for those who want to ensure that they have the prerequisite levels of understanding for the course. To reflect one of the main aims of the new course, the last two chapters in the book are devoted to multi-topic questions, and investigations and modelling. Review exercises appear at the end of each chapter with some 'Challenge' questions for the more able student. Answers are given at the end of the book, followed by an index. The interactive CD contains software (see p. 5), geometry and graphics software, demonstrations and simulations, and the two printable chapters on assumed knowledge. The CD also contains the text of the book so that students can load it on a home computer and keep the textbook at school. The Cambridge International Mathematics examinations are in the form of three papers: one a non-calculator paper, another requiring the use of a graphics calculator, and a third paper containing an investigation and a modelling question. All of these aspects of examining are addressed in the book. The book can be used as a scheme of work but it is expected that the teacher will choose the order of topics. There are a few occasions where a question in an exercise may require something done later in the book but this has been kept to a minimum. Exercises in the book range from routine practice and consolidation of basic skills, to problem solving exercises that are quite demanding. In this changing world of mathematics education, we believe that the contextual approach shown in this book, with the associated use of technology, will enhance the students' understanding, knowledge and appreciation of mathematics, and its universal application.
(8-10) D. Use proportional reasoning and apply indirect measurement techniques, including right triangle trigonometry and properties of similar triangles, to solve problems involving measurements and rates. Patterns, Functions and Algebra Standard (8-10) D. Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations.
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Cool Math Blogs The flipped classroom is an alternative to the standard methods of classroom instruction by completely flipping the classroom on its head. The teacher takes a step back from being the master mentor of the students and joins them in actively working through the lesson activities. The study of mathematics includes the investigation of numbers, shapes, structures, and change. It helps us to solve real world problems through logic and deduction. There are several mathematical strands including algebra, calculus and statistics. You can increase your proficiency in these strands through courses that offer online math help. Mathematical problems require a strong understanding of numeracy and the ability to perform specific operations and formulas. Math help is not always available, so you need to have your strategies for working through problems on your own. You can make the work of finding the correct solution to your problem much easier by following these three basic steps. Building a strong mathematical foundation is an important step before entering college. Mastery of foundations in math will enable you to achieve greater success in your college career. There are several steps you can take to ensure that you have developed the necessary mathematical skills and are well prepared for your college coursework. It's been said that everything old becomes new again, and so it goes with rote learning of math facts. Rote learning involves the introduction and practice of specific information to the point of complete mastery of the facts
A level maths book for self-teachingCheck out ebay, search for c1 c2 maths and c3 c4 maths as basic maths books. I have found the C1/2 by Peter Hind a good start (edexcel) but have a slightly different one for C3/4. There are also decision modules available for A level. L Bostock and S. Chandler also do a good basic book, often availble for a few pounds second hand. My school uses this for AS core and the associated one for A2. I think they're pretty good, plenty of examples, answers in the back, and a CD with extra questions. If you're not studying for exam purposes then it probably won't make a difference, but be aware that different exam boards have different topics on their modules so textbooks will cover slightly different things. Have you got a child at school with a mymaths login that you could use? Mymaths has excellent interactive lessons and worksheets on all core modules and the initial applied modules. Thank you for all your kind input. But I am still not sure these books from any exam board are suitable for 100% self-teaching? I need books can explain things deeply, not just show you how to work out the questions. Still not sure what's suitable. If I need to teach myself a new topic, (maths teacher), I would use the textbooks mentioned and if I needed more input, use the internet. There are so many resources available for free online - notes and explanations aimed at sixth formers or above and videos on YouTube and the Khan Academy - that I think are more comprehensive than any single textbook could be. My favourite alevel maths resources are mep. They are all free on the website and there is some interactive transition from GCSE to ALevel stuff there too. I echo noblegiraffe that i use youtube clips if i am struggling with a new topic. The Further Maths Support Network has online revision lectures for all (or at least most of) the A level maths modules, listed by exam board. I don't think you have to be a member of a school who's signed up with them to watch the lectures.
This book helps advanced undergraduate, graduate and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues as well as to the ways to optimize program execution speeds. Many examples are given throughout... more... Emanuel Derman was a quantitative analyst (Quant) at Goldman Sachs, one of the financial engineers whose mathematical models became crucial for Wall Street. The reliance investors put on such quantitative analysis was catastrophic for the economy, setting off the ongoing string of financial crises that began with the mortgage market in 2007 and continues... more... From rainbows, river meanders, and shadows to spider webs, honeycombs, and the markings on animal coats, the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in... more... Many problems in mathematical physics rely heavily on the use of elliptical partial differential equations, and boundary integral methods play a significant role in solving these equations. Stationary Oscillations of Elastic Plates studies the latter in the context of stationary vibrations of thin elastic plates. The techniques presented here reduce... more... This book contains suggestions for and reflections on the teaching, learning and assessing of mathematical modelling and applications in a rapidly changing world, including teaching and learning environments. It addresses all levels of education from universities and technical colleges to secondary and primary schools. Sponsored by the International* Offers a rigorous mathematical treatment of mechanics as a text or reference * Revisits beautiful classical material, including gyroscopes, precessions, spinning tops, effects of rotation of the Earth on gravity motions, and variational principles * Employs mathematics not only as a "unifying" language, but also to exemplify its role as... more... An insightful presentation of the key concepts, paradigms, and applications of modeling and simulation Modeling and simulation has become an integral part of research and development across many fields of study, having evolved from a tool to a discipline in less than two decades. Modeling and Simulation Fundamentals offers a comprehensive and authoritative... more... This volume provides recent developments and a state-of-the-art review in various areas of mathematical modeling, computation and optimization. It contains theory, computation as well as the applications of several mathematical models to problems in statistics, games, optimization and economics for decision making. It focuses on exciting areas like... more...
Elementary Statistics: A Step by Step Approach, A Brief Version is written for students in the beginning statistics course whoe mathematical background is limited to basic algebra. The book uses a nontheoretical appraoch in which concepts are explained intuitively and supported by examples for your student. There are no formal proofs in the book. The applications are general in nature and the exercises include problems from agriculture, biology, business, economics, education, psychology, engineering, medicine, sociology, and computer science. The learning system found in Elementary Statistics provides your students with a valuable framework in which to learn and apply concepts! For more information about Elementary Statistics: A Step by Step Approach, A Brief Version, click on mhhe.com/bluman
Mathematics for Computer Scientists (G51MCS) Mathematics for Computer Scientists teaches you the basic logical and mathematical theory that is necessary to become a good programmer and computer scientist. It covers some familiar fields, like Arithmetic and Algebra, but also parts of Math that are more specific to the study of data structures and algorithms. First of all, it is necessary to learn the fundamental reasoning techniques: how to prove mathematical statements and how to check that a proof is correct. Then you must become familiar with the concepts of set, function, relation and be able to work with them with confidence. All this forms the basis for specific mathematical theories. Arithmetic is the first one: the most important method of proof here is induction on natural numbers. Then comes Boolean Algebra, essential to understand the logic of circuits and data structures. Other topics of study are Combinatorics, which studies the way to count complex arrangements of objects, and Modular Arithmetic, the "Mathematics of clocks". At the end of the module you will have acquired the intellectual tools that allow you to understand the abstract nature and the workings of algorithms. Outline of lectures In this section you will find, after each lecture, a list of topics that were taught and links to additional material and lecture notes. I'm constantly trying to improve these notes, so I encourage you to tell me if you find mistakes or things that are not clearly explained. How to study Here are my suggestions on how you should study and prepare for the exam. There are three activities that will help you get the best results: Read and study the lecture notes; Try to solve the coursework assignments; Try to solve the past exam papers. You must make sure that you understand and know the material in the lecture notes. When you try to solve the coursework assignments, do it from scratch, without looking at the solutions and feedback that you received the first time that you did them. You should reach a level where you can do them without support. If this doesn't happen yet, you can go back and read your notes and study the part of the lecture notes that deal with the topic of the assignment. Then, on a different day, try it again. Repeat this process until you can do the exercises confidently. Use a similar strategy when doing the past exams. You should give yourself a couple of hours to solve a complete exam paper. Sit at your desk with it and without books or notes and try to do it. Afterwards check your answers: the complete solution to last year's exam is given above. Suggested reading The main study material for the module are the lecture notes that you find on this page. If you think you need more explanations and examples or if you want to learn more advanced topics, here are some very good books: Roland Backhouse, Algorithmic Problem Solving Steven G. Krantz, Discrete Mathematics Demystified Rowan Garnier and John Taylor, Discrete Mathematics Norman L. Biggs, Discrete Mathematics The first book is used in the module APS, which is the twin of MCS: It gives more motivation and examples of application of the theory. It uses games and puzzles to teach the material. The second book is a simple introduction to all the basic mathematical notions. It doesn't require much previous background and is written in a plain easy style. The last two books present the topics in more depth and give many useful examples; they also cover more advanced material that is not treated in this module. These texts, however, are not a replacement for the lecture notes. If you don't understand something and you find that the lecture notes are not clear enough, the right thing to do is to come to me and I will try to explain things better and expand the lecture notes. Coursework and Tutorials Every two weeks on Thursday, you will find an assignment on this page. You have to solve the given problems and hand you solutions in by the following Wednesday at 16:00 at the school office (stamp the assignment and put it in the letter box). The following week the teaching assistants will demonstrate the solutions during the tutorials. You have been divided into five groups, each having a tutorial on a different day and time. Check this timetable to see when and where your tutorial session is. If you're unable to attend the tutorial you've been assigned to, contact one of the teaching assistants, Laurence Day or Bas van Gijzel and ask to change your group. Write on the cover letter of the assignment what group you belong to. The average mark of the four assignments will be your coursework mark, which counts for 25% of you final mark. The first tutorial takes place in the week 8-12 October: It will give you a chance to ask any question about the first few lectures. Be sure to read carefully the regulations about submission of coursework and plagiarism in the student handbook. In addition to those regulations, assignments must be submitted at the latest by the end of the week of their official deadline and standard penalties apply. Contacting the teacher Please don't hesitate to ask me any question you may have about the module. You can contact me by e-mail: put G51MCS in the subject line, so I know immediately that it is about this module.
Elementary and Intermediate Algebra : Concepts and Applications Series brings proven pedagogy to a new generation of students, with updates throughout to help todays... MORE BENEFIT: TheBittinger Concepts and Applications Seriesextends proven pedagogy to a new generation of students, with updates throughout to help todayrs"s the Graph Functions and Graphs; Systems of Equations and Problem Solving; Inequalities and Problem Solving; Exponents and Radicals; Quadratic Functions and Equations; Exponential and Logarithmic Functions; Conic Sections; Sequences, Series, and the Binomial Theorem; Elementary Algebra Review MARKET: For all readers interested in algebra. Introduction to Algebraic Expressions Introduction to Algebra The Commutative, Associative, and Distributive Laws Fraction Notation Positive and Negative Real Numbers Addition of Real Numbers Subtraction of Real Numbers Multiplication and Division of Real Numbers Exponential Notation and Order of Operations Polynomials Exponents and Their Properties Negative Exponents and Scientific Notation Polynomials Addition and Subtraction of Polynomials Multiplication of Polynomials Special Products Polynomials in Several Variables Division of Polynomials Functions and Graphs Introduction to Functions Domain and Range Graphs of Functions (including brief review of graphing) The Algebra of Functions Variation and Problem Solving Systems of Equations and Problem Solving Systems of Equations in Two Variables Solving by Substitution or Elimination Solving Applications: Systems of Two Equations Systems of Equations in Three Variables Solv
Change and Motion: Calculus Made Clear, 2nd Edition & An Introduction to Number Theory (Set) Recommended based on your selection Course 1 of 2: Change and Motion: Calculus Made Clear, 2nd Edition Professor Michael Starbird, The University of Texas at Austin Ph.D., University of Wisconsin at Madison Calculus has had a notorious reputation for being difficult to understand, but the 24 lectures of Change and Motion: Calculus Made Clear are crafted to make the key concepts and triumphs of this field accessible to non-mathematicians. This course teaches you how to grasp the power and beauty of calculus without the technical background traditionally required in calculus courses. Follow award-winning Professor Michael Starbird as he takes you through derivatives and integrals—the two concepts that serve as the foundation for all of calculus. As you investigate the field's intellectual development, your appreciation of its inner workings and your skill in seeing how it can solve a variety of problems will deepen. Lecture Outline 1. Two Ideas, Vast Implications Calculus is a subject of enormous importance and historical impact. It provides a dynamic view of the world and is an invaluable tool for measuring change. Calculus is applicable in many situations, from the trajectory of a baseball to changes in the Dow Jones average or elephant populations. Yet, at its core, calculus is the study of two ideas about motion and change. 13. Achilles, Tortoises, Limits, and Continuity The integral's strategy of adding up little pieces solves a variety of problems, such as finding the volume of a pyramid or the total pressure on the face of a dam. 2. Stop Sign Crime—The First Idea of Calculus—The Derivative The example of a car moving down a straight road is a simple and effective way to study motion. An everyday scenario that involves running a stop sign and the use of a camera illustrates the first fundamental idea of calculus: the derivative. 3. Another Car, Another Crime—The Second Idea of Calculus—The Integral You are kidnapped and driven away in a car. You can't see out the window, but you are able to shoot a videotape of the speedometer. The process by which you can use information about speed to compute the exact location of the car at the end of one hour is the second idea of calculus: the integral. 3. Another Car, Another Crime—The Second Idea of Calculus—The Integral (info) 15. The Best of All Possible Worlds—Optimization Calculus is useful in many branches of mathematics. The 18th-century French scientist Georges Louis Leclerc Compte de Buffon used calculus and breadsticks to perform an experiment in probability. His experiment showed how random events can ultimately lead to an exact number. 4. The Fundamental Theorem of Calculus The moving car scenario illustrates the Fundamental Theorem of Calculus. This states that the derivative and the integral are two sides of the same coin. The insight of calculus, the Fundamental Theorem creates a method for finding a value that would otherwise be hard or impossible to get, even with a computer. 16. Economics and Architecture Zeno's Arrow Paradox concerns itself with the fact that an arrow traveling to a target must cover half the total distance, then half the remaining distance, etc. How does it ever get there? The concept of limit solves the problem. 5. Visualizing the Derivative—Slopes Change is so fundamental to our vision of the world that we view it as the driving force in our understanding of physics, biology, economics—virtually anything. Graphs are a way to visualize the derivative's ability to analyze and quantify change. 17. Galileo, Newton, and Baseball The real numbers in toto constitute a smooth, seamless continuum. Viewing the world as continuous in time and space allows us to make mathematical models that are helpful and predictive. 6. Derivatives the Easy Way—Symbol Pushing The derivative lets us understand how a change in one variable affects a dependent quantity. We have studied this relationship with respect to time. But the derivative can be abstracted to many other dependencies, such as that of the area of a circle on the length of its radius, or supply or demand on price. 18. Getting off the Line—Motion in Space Zeno's Arrow Paradox shows us that an infinite addition problem (1/2 + 1/4 + 1/8 + . . .) can result in a single number: 1. Similarly, it is possible to approximate values such as π or the square root of 2 by adding up the first few hundred terms of infinite sum. Calculators use this method when we push the "sin" or square root keys. 7. Abstracting the Derivative—Circles and Belts One of the most useful ways to consider derivatives is to view them algebraically. We can find the derivative of a function expressed algebraically by using a mechanical process, bypassing the infinite process of taking derivatives at each point. 19. Mountain Slopes and Tangent Planes We have seen how to analyze change and dependency according to one varying quantity. But many processes and things in nature vary according to several features. The steepness of a mountain slope is one example. To describe these real-world situations, we must use planes instead of lines to capture the philosophy of the derivative. 8. Circles, Pyramids, Cones, and Spheres The description of moving objects is one of the most direct applications of calculus. Analyzing the trajectories and speeds of projectiles has an illustrious history. This includes Galileo's famous experiments in Pisa and Newton's theories that allow us to compute the path and speed of projectiles, from baseballs to planets. 20. Several Variables—Volumes Galore After developing the ideas of calculus for cars moving in a straight line, we have gained enough expertise to apply the same reasoning to anything moving in space—from mosquitoes to planets. 9. Archimedes and the Tractrix Optimization problems—for example, maximizing the area that can be enclosed by a certain amount of fencing—often bring students to tears. But they illustrate questions of enormous importance in the real world. The strategy for solving these problems involves an intriguing application of derivatives. 21. The Fundamental Theorem Extended Calculus plays a central role in describing much of physics. It is integral to the description of planetary motion, mechanics, fluid dynamics, waves, thermodynamics, electricity, optics, and more. It can describe the physics of sound, but can't explain why we enjoy Bach. 10. The Integral and the Fundamental Theorem Formulas for areas and volumes can be deduced by dividing such objects as cones and spheres into thin pieces. Ancient examples of this method were precursors to the modern idea of the integral. 22. Fields of Arrows—Differential Equations Many money matters are prime examples of rates of change. The difference between getting rich and going broke is often determined by our ability to predict future trends. The perspective and methods of calculus are helpful tools in attempts to decide such questions as what production levels of a good will maximize profit. 11. Abstracting the Integral—Pyramids and Dams Archimedes devised an ingenious method that foreshadowed the idea of the integral in that it involved slicing a sphere into thin sections. Integrals provide effective techniques for computing volumes of solids and areas of surfaces. The image of an onion is useful in investigating how a solid ball can be viewed as layers of surfaces. 23. Owls, Rats, Waves, and Guitars Whether looking at people or pachyderms, the models for predicting future populations all involve the rates of population change. Calculus is well suited to this task. However, the discrete version of the Verhulst Model is an example of chaotic behavior—an application for which calculus may not be appropriate. 12. Buffon's Needle or π from Breadsticks The integral involves breaking intervals of change into small pieces and then adding them up. We use Leibniz's notation for the integral because the long S shape reminds us that the definition of the integral involves sums. 24. Calculus Everywhere There are limits to the realms of applicability of calculus, but it would be difficult to exaggerate its importance and influence in our lives. When considered in all of its aspects, calculus truly has been—and will continue to be—one of the most effective and influential strategies for analyzing our world that has ever been devised. Course 2 of 2: Introduction to Number Theory Professor Edward B. Burger, Williams College Ph.D., The University of Texas at AustinLecture Outline 1. Number Theory and Mathematical Research In this opening lecture, we take our first steps into this ever-growing area of intellectual pursuit and see how it fits within the larger mathematical landscape. 13. Fermat's Method of Ascent When most people think of mathematics, they think of equations that are to be "solved for x." Here we study a very broad class of equations known as Diophantine equations and an important technique for solving them. We also encounter one of the most widely recognized equations, x2 + y2 = z2, the cornerstone of the Pythagorean theorem. 14. Fermat's Last Theorem One of the most famous and romantic stories in number theory is the legendary tale of Fermat's last theorem. Professor Burger explicates this most mysterious of proposed "theorems" and describes how the greatest mathematical minds of the 18th and 19th centuries failed again and again in their attempts to provide a proof. 3. Triangular Numbers and Their Progressions Using an example involving billiard balls and equilateral triangles, Professor Burger demonstrates the fundamental mathematical concept of arithmetic progressions and introduces a famous collection of numbers: the triangular numbers. 15. Factorization and Algebraic Number Theory This lecture returns to a fundamental mathematical fact—that every natural number greater than 1 can be factored uniquely into a product of prime numbers—and pauses to imagine a world of numbers that does not exhibit the property of unique factorization. 4. Geometric Progressions, Exponential Growth Professor Burger introduces the concept of the geometric progression, a process by which a list of numbers is generated through repeated multiplication. Later, we consider various real-world examples of geometric progressions, from the 12-note musical scale to the take-home prize money of a game-show winner. 16. Pythagorean Triples In this lecture, Professor Burger returns to Pythagoras and his landmark theorem to identify an important series of numbers: the Pythagorean triples. After recounting an ingenious proof of this theorem, Professor Burger explores the structure of triples. 5. Recurrence Sequences The famous Fibonacci numbers make their debut in this study of number patterns called recurrence sequences. Professor Burger explores the structure and patterns hidden within these sequences and derives one of the most controversial numbers in human history: the golden ratio. 17. An Introduction to Algebraic Geometry The shapes studied in geometry—circles, ellipses, parabolas, and hyperbolas—can also be described by quadratic (second-degree) equations from algebra. The fact that we can study these objects both geometrically and algebraically forms the foundation for algebraic geometry. 6. The Binet Formula and the Towers of Hanoi Is it possible to find a formula that will produce any specific number within a recurrence sequence without generating all the numbers in the list? To tackle this challenge, Professor Burger reveals the famous Binet formula for the Fibonacci numbers. 18. The Complex Structure of Elliptic Curves Here we study a particularly graceful shape, the elliptic curve, and learn that it can be viewed as contour curves describing the surface of—of all things—a doughnut. This delicious insight leads to many important theorems and conjectures, and leads to the dramatic conclusion of the story of Fermat's last theorem. 7. The Classical Theory of Prime Numbers The 2,000-year-old struggle to understand the prime numbers started in ancient Greece with important contributions by Euclid and Eratosthenes. Today, we can view primes as the atoms of the natural numbers—those that cannot be split into smaller pieces. Here, we'll take a first look at these numerical atoms. 19. The Abundance of Irrational Numbers Ancient mathematicians recognized only rational numbers, which can be expressed neatly as fractions. But the overwhelming majority of numbers are irrational. Here, we'll meet these new characters, including the most famous irrational numbers, p, e, and the mysterious g. 8. Euler's Product Formula and Divisibility As we look more closely at the prime numbers, we encounter the great 18th-century Swiss mathematician Leonhard Euler, who proffered a crucial formula about these enigmatic numbers that ultimately gave rise to modern analytic number theory. 20. Transcending the Algebraic Numbers We move next to the exotic and enigmatic transcendental numbers, which were discovered only in 1844. We return briefly to a consideration of irrationality and the moment of inspiration that led to their discovery by mathematician Joseph Liouville. We even get a glimpse of Professor Burger's original contributions to the field. 9. The Prime Number Theorem and Riemann Can we estimate how many primes there are up to a certain size? In this lecture, we tackle this question and explore one of the most famous unsolved problems in mathematics: the notorious Riemann hypothesis, an "open question" whose answer is worth $1 million in prize money. 21. Diophantine Approximation In this lecture, Professor Burger explores a technique for generating a list of rational numbers that are extremely close to the given real number. This technique, called Diophantine approximation, has interesting consequences, including new insights into the motion of billiard balls and planets. 10. Division Algorithm and Modular Arithmetic How can clocks help us do calculations? In this lecture, we learn how cyclical patterns similar to those used in telling time open up a whole new world of calculation, one that we encounter every time we make an appointment, read a clock, or purchase an item using a scanned UPC bar code. 22. Writing Real Numbers as Continued Fractions Real numbers are often expressed as endless decimals. Here we study an algorithm for writing real numbers as an intriguing repeated fraction-within-a-fraction expansion. Along the way, we encounter new insights about the hidden structure within the real numbers. 11. Cryptography and Fermat's Little Theorem After examining the history of cryptography—code making—we combine ideas from the theory of prime numbers and modular arithmetic to develop an extremely important application: "public" key cryptography. 23. Applications Involving Continued Fractions This lecture returns to the consideration of continued fractions and examines what happens when we truncate the continued fraction of a real number. The result involves two of our old friends—the Fibonacci numbers and the golden ratio—and finally explains why the musical scale consists of 12 notes. 12. The RSA Encryption Scheme We continue our consideration of cryptography and examine how Fermat's 350-year-old theorem about primes applies to the modern technological world, as seen in modern banking and credit card encryption. 24. A Journey's End and the Journey Ahead In this final lecture, we take a step back to view the entire panorama of number theory and celebrate some of the synergistic moments when seemingly unrelated ideas came together to tell a unified story of number.
Category Archives: TI-84 UPDATE: If you are interested in the TI-84+C, please check out my TI-84+C Review. I was fortunate to receive a pre-release device from TI for review purposes. After word broke last week of a possible new graphing calculator from Texas Instruments, I reached out to TI, asking if they'd be willing to make any on… Continue Reading Whether you're in the market for your first graphing calculator, or replacing an old friend, it's no small investment. Most of the popular graphers on the market today cost over $100.… Continue Reading When you are given multiple equations and multiple variables, a graphing calculator can be a lifesaver. New versions of the TI-84 come with a pre-installed app the makes these problems a snap. This video lesson covers solving systems equations by the elimination, or linear combination method, before covering how to use the TI-84 to solve.… Continue Reading If you're a student of geometry or trigonometry, you've probably come across problems involving degrees, minutes, and seconds. This is an alternative to measuring in decimal degrees, and it works a lot like time.… Continue Reading
Precalculus I, II Winter 2014 and Spring 2014 quarters This two-quarter sequence of courses will prepare students for calculus and more advanced mathematics. It is a good course for students who have recently had a college-level math class or at least three years of high school math. Students should enter the class with a good knowledge of supporting algebra. Winter quarter will include an in-depth study of linear, quadratic, exponential, and logarithmic functions. Spring will include an in-depth study of trigonometric and rational functions in addition to parametric equations, polar coordinates, and operations on functions. Collaborative learning, data analysis and approaching problems from multiple perspectives (algebraically, numerically, graphically, and verbally) will be emphasized. Registration Information Credits 4 (Winter); 4 (Spring) Class Standing Freshmen–Senior Prerequisites Entry in winter quarter requires proficiency equivalent to successful completion of college algebra. (High school algebra 2 or integrated math 3 should be equivalent.) Entry into the spring quarter requires proficiency equivalent to the successful completion of Precalculus I. Contact the instructor for an assessment of proficiency.
How to Use the New Westonmath App This app is your source of information for math courses at Weston High School. The tab right below this one lists some of its features, but here's enough to get you started: This page is called Home. You can get to it through the Home menu, which is always the first one at the top of every page. To find information about a particular course, click on the Courses menu. You will see a list of all our courses and their sections, listed by teacher and block number. Click on any course to read basic information about it, including the course description and a list of sections, each with its teacher, block, and room number. Click on any column header to sort by that column. Click again to reverse the sort. Click on a section's block to see assignments for that section. Course pages also have tabs along the top (below the three standard Westonmath menus). You can click on any tab to read about the course information, resources, policies, and news. You can also get to any section's assignments by clicking on the section in the Courses menu. The current assignment is always listed first, followed by any upcoming assignments that have already been posted, followed by all past assignments. You can choose whether to display 2, 5, 10, or all past assignments. The third menu lists all the Faculty in our Department. Clicking on the icon to the left of a name takes you to that teacher's home page, which includes a list of the courses s/he is currrently teaching. Clicking on the icon to the right opens up your favorite email program, with a new message addressed to that teacher. If you are using a machine that doesn't have an identified email client, this option will not work. The Home page also contains some general information about the Math Department, such as resources, news, and a puzzle that is often (well...occasionally) updated. Check out the tabs in the accordion! If you spot any bugs, send email to Mr. Davidson (DavidsonL@weston.org). Students keep asking, "Why doesn't the Math Department just use teacherweb?" One student even asked whether we're too cool for teacherweb. The WHS Math Department admits to being cool, but that's not what westonmath is all about. The westonmath.org website is far more than a place to find out tonight's homework assignment. Here are some of its features: The "Current Assignment" automatically rolls over every afternoon. The teacher doesn't have to remember to do so manually. Future assignments aren't confused with the current one. You have an easily accessible database of all past assignments. Even in June it stretches all the way back to September. Teachers have access to past assignments in every course going back to 2002. This is extremely helpful for experienced teachers and newcomers alike. Westonmath is course-oriented rather than teacher-oriented. Students, parents, and teachers can easily find out important information about a course, such as its syllabus and its grading policies. Even if there are four or five different teachers for a course, all the course-wide data are collected in a single place.
2-D Graphs We have all had sliced bread. It's been around since 1928. Two-dimensional graphs have been around for a while, too. While number lines are nice, we can't tell which dots go with which terms. Since we as much about 2-D graphs as we do sliced... Please purchase the full module to see the rest of this course Purchase the Sequences Pass and get full access to this Calculus chapter. No limits found here.
Grading_and_Partial_Credit_103 Course: MATH 103, Fall 2008 School: Michigan State University Rating: Word Count: 4031 Document Preview a detailed explanation of my grading philosophy. Much of this is probably shared by every math instructor. For almost every problem, grading is based on the following things (in the order indicated). The first and most important mission students must accomplish in their response to every problem is to demonstrate that they understand the purpose (goal) of the problem. Most students usually do this successfully. However, the most common way students fail to do this is to write the wrong TYPE of answer in the answer blank. For example, suppose a problem asks students to find the solutions of an equation. Solutions of an equation are numbers. So if a student writes numbers in the answer blank, that's good. If they are the correct numbers, then that's even better, but this is of much less importance. If students write something other than numbers in the answer box, then they must not have read the question to find out what the purpose (goal) of the problem was; or even worse, perhaps they read the question but did not know what the word "solution" meant. This is why it is crucial to learn the vocabulary associated with the course. The most catastrophic error a student can ever make is to give a final answer that cannot possibly be correct because it is not even the type of answer the problem asked for. NEVER write an answer on the answer blank that you know cannot possibly be correct. To avoid such catastrophic errors, try some of the following strategies. These are especially helpful when taking tests. o After you read a problem and before you do anything else, decide what type of object the answer is. Is it a number? A set? An expression? An equation? An inequality? A function? A matrix? A vector? A scalar? What type of object is it? You can tell this ahead of time in almost every problem you will ever face. o Begin every story problem by "answering the question before you have answered the question." Read the directions, then go immediately to the answer blank and write a complete sentence that will eventually serve as the final answer to the problem. Omit only the numerical portion of the answer for now. You can plug it in once you get it. o What variables appear in the given problem? Which of those variables will appear in the final answer? You can usually determine this before you actually find the answer, and by thinking about this ahead of time, you can catch many catastrophic errors. If you know ahead of time that the answer should depend on the value of h, yet h does not appear in your final answer, then something must be wrong! o If you can tell that something must be wrong, SAY SO! Sentences like "there must be something wrong, because this result shouldn't be negative" show that you know what you are talking about, but perhaps messed up something in the details. Using comments like this on your paper is good "damage control" for problems you mess up. Grading and Partial Credit MTH 103-095 The second most important part of a student's response is the method. There is usually more than one possible method that can be used to solve each problem. Did you identify one of the possible methods? Is the strategy you chose appropriate? Did you recognize which concepts are applicable to the problem? If so, your method is good. As a non-example of identifying a valid method or appropriate strategy, suppose that an algebra test asks students to find solutions of the equation x 3 - 2 x - 4 = 0 , and a student tries to use the quadratic formula. This is a grievous error, since it indicates that the student either failed to recognize that the equation was not quadratic, or perhaps did not realize that the quadratic formula is only applicable to quadratic equations (hence the name "quadratic" formula). To avoid errors like this, you must study not only methods for solving various problems, but also when those methods are applicable. The third most important part of your response is your solution. Assuming you identified a valid method and general strategy to use for the problem, did you correctly apply that method? Is your work written correctly, logically, and clearly? For many beginners, this one is the most elusive of the four parts of the response. For that reason, a detailed discussion of how to write a good solution to a math problem is given on the next few pages. Read on. One of the most common types of solution that beginning math students must write is for the following type of problem: You are given an object, and you are asked re-express it in a different form--that is, write down another representation of the same object. Factoring or expanding polynomials, simplifying or evaluating expressions, and doing basic arithmetic are examples of this situation. For example, consider the following two problems. #1. Simplify (8 + 24 ) / 2 . #2. Expand ( x + 4)( x 2 + 3 x) . (The answer is 4 + 6 .) (The answer is x 3 + 7 x 2 + 12 x .) At first glance, these two problems may appear to have nothing in common. But they do. In both cases, the final answer is exactly equal to the given object. Here's an explanation. Consider problem #1 above, for instance. The number 4 + 6 is exactly the same as the number (8 + 24 ) / 2 . If you are not fully convinced that this is indeed the case, you may want to check for yourself by using a computer to see rounded-off decimal expansions of (8 + 24 ) / 2 and 4 + 6 . You will see that their decimal expansions are the same (they begin with 6.4494897427831780981972840747059 but do not stop, since this number is irrational). Therefore, 4 + 6 is just a different representation of (8 + 24 ) / 2 . Do not think of 4 + 6 and (8 + 24 ) / 2 as different numbers--they are not different numbers! Instead, realize that 4 + 6 and (8 + 24 ) / 2 are different representations of the same number. The directions for problem #2 said "simplify". To "simplify" something does not mean to change its "identity" or "meaning"; but rather, to simplify something means to change only its form so that the new form is more concise, clear, or compact. So, for any problem that says to "simplify" some object, the first thing to know is that the final answer must be exactly equal to the given object. Grading and Partial Credit MTH 103-095 Now consider #2, which said "expand ( x + 4)( x 2 + 3 x) ". The direction "expand" can be thought of as a more specific version of the direction "simplify". To "expand" an object (which, in this case, is an algebraic expression) means to rewrite the given expression so that it contains terms (things that are added), not factors (things that are multiplied). In the sentence you just read, the important word was REWRITE. Go back to that sentence (which began with "To `expand' an object"), read it again, and this time emphasize the word "rewrite" as you read it. Again, the directions indicate that the goal is NOT to change the given object, but rather, to write down another representation of the same object. In other words, the goal of the problem is to write an expression that is exactly equal to the given expression, and more specifically, the "new" expression should have terms instead of factors. Indeed, the final answer x 3 + 7 x 2 + 12 x is exactly equal to the given expression ( x + 4)( x 2 + 3 x) . The reason these two expressions are "equal" is that no matter what value we substitute into the expressions for x, the values of the expressions are the same. For example, if we substitute (say) - 1 for x, we see that the value of the given expression x 3 + 7 x 2 + 12 x is (-1 + 4)((-1) 2 + 3(-1)) = (3)(1 - 3) = (3)(-2) = -6 and the value of the final answer expression, ( x + 4)( x 2 + 3 x) , is (-1) 3 + 7(-1) 2 + 12(-1) = -1 + 7 - 12 = -6 . So, both expressions' values were - 6 when we substituted in - 1 for x. Instead of - 1 , if we were to substitute (let's say) 2 for x, we would find that the expressions' values are (2 + 4)(2 2 + 3(2)) = (6)(4 + 6) = (6)(10) = 60 and (2) 3 + 7(2) 2 + 12(2) = 8 + 28 + 24 = 60 , which again are the same. As these "for instances" suggest, the values of the expressions ( x + 4)( x 2 + 3 x) and x 3 + 7 x 2 + 12 x are the same, no matter what value we substitute for x. Therefore the given expression ( x + 4)( x 2 + 3 x) and the final answer x 3 + 7 x 2 + 12 x are exactly equal, and again, the final answer is exactly equal to the given object. Let us summarize the explanations for why problems #1 and #2 have very similar goals. The common feature was that in both problems, the goal was to find a different representation of the given object. Therefore, the final answers were exactly equal to the given objects. It is standard practice to write solutions for problems like this in the following format, or a similar format. [Given Object] = [Another representation of the given object which is in a form "closer to" the desired form] = [Yet another repre] Grading and Partial Credit = [Same object, intermediate form #n] = [Same object, desired form #1] MTH 103-095 You can open any math book and see the above format being used. The only variation from one type of problem to the next is "desired form" is (i.e., the appearance of the final answer). This is always made clear by the directions, or the context of the problem. Grading and Partial Credit MTH 103-095 Here is another sample problem with a few different example solutions, all of which use the same method and arrive at the same answer, but have differently-written solutions. Problem Factor 2 x 3 - 8a 2 x + 24 x 2 + 72 x into prime polynomials with integer coefficients. Solution (one Solution (another Solution (still another)( x + 6 - 2a) The three versions of the same solution all have two very important commonalities: The object written at each step was EXACTLY EQUAL to the entire object written at the previous step. Equality was never lost. The solutions are complete English sentences which make complete sense when read out loud. For example, to read any of the three above solutions, you could say this: " 2 x 3 - 8a 2 x + 24 x 2 + 72 x equals 2 x 3 + 24 x 2 + 72 x - 8a 2 x , which is equal to 2 x[ x 2 + 12 x + 36 - 4a 2 ] , which equals 2 x[( x + 6) 2 - 4a 2 ] , which is equal to 2 x( x + 6 + 2a)( x + 6 - 2a) ." Grading and Partial Credit MTH 103-095 As a non-example of how to write a solution to a problem in which the goal is to give another representation of the same object, the following is an unacceptably poor solution of the same problem. Poor solution 2 x 3 - 8a 2 x + 24 x 2 + 72 x 2 x 3 + 24 x 2 + 72 x - 8a 2 x 2 x[ x 2 + 12 x + 36 - 4a 2 ] ( x + 6) 2 ( x + 6 + 2a )( x + 6 - 2a ) = 2 x( x + 6 + 2a )( x + 6 - 2a ) The above solution is poor for the following reasons: Equality was lost. The objects on the fourth, fifth, and sixth lines are obviously not equal to each other. To make matters worse, the author claimed that the object on the fifth (second-to-last) line is equal to the object on the last line. That is, the writer said that ( x + 6 + 2a )( x + 6 - 2a ) is exactly equal to 2 x( x + 6 + 2a)( x + 6 - 2a) ; but this is false. There is only one assertion (i.e., statement) in the entire solution, the namely assertion that ( x + 6 + 2a )( x + 6 - 2a ) = 2 x( x + 6 + 2a)( x + 6 - 2a) ; and this assertion is false as already mentioned. Aside from that, there are no other statements in the solution; there is only a list of objects. The reader cannot tell what the author is saying about the objects 2 x 3 - 8a 2 x + 24 x 2 + 72 x and 2 x 3 + 24 x 2 + 72 x - 8a 2 x . Did the author mean to indicate that these expressions are equal? Did the author actually know they are equal? Further, does the author even understand what it means for two algebraic expressions to be equal? The reader cannot tell. In particular, a grader who reads this solution would probably doubt that the author understands the following concept: Algebraic expressions are equal if and only if the value of the expressions are the same for any values that are substituted for the variables in the expressions (provided the values of the variables are in the domains of the expressions). So the reason why 2 x 3 - 8a 2 x + 24 x 2 + 72 x and 2 x 3 + 24 x 2 + 72 x - 8a 2 x are equal is that if we to substitute (let's say) 5.76 for x and - 1.8 for a into both expressions (or any other values of x and a that we pick), the values of the two expressions would be the same. If the solution's author had understood this, then presumably the author would have indicated his or her understanding by actually saying in the solution that 2 x 3 - 8a 2 x + 24 x 2 + 72 x and 2 x 3 + 24 x 2 + 72 x - 8a 2 x are equal. Furthermore, if the author understood what it means for algebraic expressions to be equal, then he or she would certainly not have written down the false assertion that ( x + 6 + 2a )( x + 6 - 2a ) equals 2 x( x + 6 + 2a)( x + 6 - 2a) . In summary, the poor solution on the previous page shows either a lack of mathematical understanding or a lack of effort (or both) on the part of the author; and therefore the poor solution certainly should not earn the author full credit. Grading and Partial Credit MTH 103-095 In contrast to the previous example, it is not always correct to write down the phrase "is equal to" (i.e., the symbol "=") between steps. Here is an example. Problem Solve the equation 2 x - 8 = 7 - 3 x . Poor response 2 x - 8 = 7 - 3x = 5x - 8 = 7 = 5 x = 15 = x=3 This time the author has claimed that for each of the objects 2 x - 8 , 7 - 3 x , 5 x - 8 , 7, 5 x , 15, x, 3 is equal to ALL the other objects. For example, the author has stated that 7 is equal to 15 and also equal to 3. The author also said that 2 x - 8 equals 5 x - 8 , and 5 x is equal to both of those; and so on. This is ridiculous. Had the author understood that the symbol "=" means "is equal to", and understood what it means for expressions to be equal, he or she would not have written this response. Here is a response to the problem that makes sense. An acceptable response 2 x - 8 = 7 - 3x 5x - 8 = 7 5 x = 15 x=3 The format in the above response is how tradition says we search for solutions of equations in one variable--we write down a list of equations that get simpler and simpler until we get one whose solutions are obvious. But the traditional approach is not always the most logical or best way to do things (this holds true for life in general). Below are two more responses that are (in a sense) a bit more logical. When you read the next two responses to yourself, read " " by saying "implies that" or "means that" or "which implies that", etc. Another good response 2 x - 8 = 7 - 3x 5x - 8 = 7 5 x = 15 x=3 Still another good response 2 x - 8 = 7 - 3x 5x - 8 = 7 5 x = 15 x=3 Notice that both these responses are read out loud in the same way, and both make sense when spoken in English. Grading and Partial Credit MTH 103-095 Recall that the most important part of your response to a math problem is to show that you understand the goal or purpose of the problem, and after that, the second most important part of your response is to choose a method that is appropriate to accomplish the goal, and the third most important part is to write a good solution. The solution is the aspect of the response that this lengthy discussion (which astonishingly began all the way back on page 2) has addressed. You may have noticed that the discussion of the method and the purpose parts were considerably shorter than the discussion of the solution. This is because beginners usually struggle the most with the solution part, perhaps due to the fact that in students' prior math courses, the final answer was what mattered most, and so little if any focus was placed on communicating the mathematics clearly and correctly. But here are some points of encouragement, which I hope will be pleasant reading for all serious students. First, there is no need whatsoever to memorize "the one correct" format for solving each type of problem faced. This is because no problem has only one correct strategy for solving it nor a single correct format for presenting the solution. Just as there are many legitimate ways to say the same thing in English, there is more than one way to write a perfectly good solution to a math problem. In fact, (here comes the second point of encouragement) the criteria for writing good mathematical solutions are the same as the familiar criteria for writing good English statements--in either case, the writing is "good" if it makes sense when read aloud, if it is organized logically, if it addresses the points concisely, and so forth. So, the very same mindset applies both to writing in plain English and writing solutions to math problems. In both cases, you can simply proofread what you have written, and perhaps also have another person (with an appropriate level of experience) proofread it as well, so that you can verify your work is understandable. Of course, mathematics uses lots of symbols and abbreviations, but each symbol and each abbreviation represents an English word or phrase; so if you simply know how to read the symbols, they will present no additional difficulty to you as you proofread your writing. Now for the third and most important encouraging point: The effort you put into learning effective mathematical communication will pay you back great dividends, because a far greater understanding and appreciation of the mathematics is gained when you are able to explain the mathematics you are doing. You surely have your own personal experiences that convince you of this--whether in a mathematical setting or not, your understanding and appreciation of any subject tend to increase when you explain it to someone. This is why communicating math effectively will help you learn math better--a good solution for a math problem is (at least in part) an explanation that leads the reader logically from the problem definition to the result. Do not think of "the reader" as only "the grader". The first person who reads your solutions is always you! Thus, your solutions to math problems will function most effectively if you author them to serve as explanations (to yourself) of your own reasoning. In doing this, you will accomplish a goal far more important than pleasing a grader. You will also secure a more permanent understanding of the topic at hand, so that your mathematical abilityModel Disconfirmation of expectationsAdvantages Takes into consideration expectations as well as actual perceptionsDisadvantages The use of expectations in measuring service quality has currently come under a lot of criticism in the literat ELKHUNT12-4-96By ANGELA K. SIKKEMACapital News Service LANSING-Mancelona resident Joseph Orman literally danced for joy whenhe received his elk hunting license in the mail on the first Monday inNovember. Orman was one of only 200 h Artificial Life - SugarscapeBy Dan MillerWhat is meant by being alive? You breathe air? You act independently? Being alive is essentially a matter of patterns and processesArtificial Life AL researchers look for the distinctive behaviors of February 28, 2001 ATTN:Dear: Thank you for your interest in our products and services. We require all registered users to logon at least once every six months to their account if they wish to keep their accounts active. Our records indicate that yo 11-8-96Props. S & EBy AMY DAOUSTCapital News Service LANSING-Downtown Detroit expects to be a "happening" place now thatvoters decided to bring back the Detroit Lions and open three casinos. That's the hope, anyway, after passage of t include length in for loop or cumsum functino to sum all the lengthsnow on to assignment 7:build a function that outputs xi, yi, zi, e and n with input E,N,H, number of steps"etep and nstep code" from lecturein the function, use the griddat Lab: Pool Maintenance SystemDesigning Real Time Systems with UML and Rational Rose RealTimeVersion 1.0Copyright SEEX1Exercise In this lab, you will create a model to monitor the chlorine level of the water in a swimming pool. There are two Configuring Rose RT RTS with RSx/Eclipse1. Setup Ensure you have the appropriate compilation tools in your PATH variable. Eclipse will also want include files for standard header files. Since we are using 2. Add the RTS project to the workspace Crea Floating Grill and DinnerwareGoal: Create a set of plates, bowls, trays, spoons, knifes, forks, etc that can float in a waist high pool, hot tub, the ocean. Can also be used on land or a boat for overboard protection. Approach: use the same techn Aristotle (384 - 322 BCE)Life & TimesAristotle (384-322 BCE)Plato's student born in Macedonia about the time Plato was opening the Academy in Athens age seven went to Athens and entered the Academy-stayed on as teacher; left 20 yrs later on Plato Designing NewslettersConsider: a Audience a Cost a Frequency a Size a Artworks and formats a ShapeaAudienceWho are they a What about demographics - how do they relate to the audience and its needs a Is it a technical audience/newsletter how woul Dr. Katherine Heenan English 472 Spring 2007 Herrick Notes Herrick, James. A History and Theory of Rhetoric: An Introduction. 3rd edition. New York: Allyn and Bacon, 2005 Chapter One notes An Overview of Rhetoric Notes the resurgence in interest o Dr. Katherine Heenan English 472 Spring 2007 March 27, 2007Vatz, Richard. "The Myth of the Rhetorical Situation," Philosophy and Rhetoric 6:3 (1973): 154-161.Writing in response to Bitzer and arguing that Meaning is not intrinsic in events, K. Heenan English 218 Spring 2005 Workshop Project #1 1. The goal of the paper should be to address a question with a meaningful argument, presented forcefully and persuasively. In what ways does the writer achieve this goal? What might s/he do diffe Choose either of the two following essays to adapt into screenplay format. Essay 1: MASKS Her soft, blond hair was in piggytails, as usual, with ringlets that bounced whenever she turned her head. As if they were springs, they could stretch, then shr WELFARE10-17-96By CATHERINE HOLLINGSWORTHCapital News Service LANSING-Mary Lassila of Houghton has a success story she shares withfriends who say they no longer want to get welfare, but fear financialhardship at low paying jobs. Las Computer Video October 18 (Day); October 10 (Night)There are two necessary output for video output: a monitor and a video card. Monitor:o Most monitors use CRT (cathode ray tube) technology. With CRT technology, anelectron gun at one end fir What is an end morraine? What are tarns, kettle lakes, and eskers? What is a reservoir? What are the large hydrologic reservoirs on Earth? Know their size in order from larger to smaller. What are typical inflows and outflows of reservoirs? What is h Portfolio Assignment-English 215, Spring 2005 Duane Roen The portfolio project consists of a reflective letter, as well as supporting materials, in which you analyze your growth as a writer during the semester. The "rhetorical considerations" section MAT 342 Test 3 - Review 4.1 Know the definition of a linear transformation on a vector space V. Understand the examples and the geometric meaning of the relevant examples. Be able to find the image of a subspace of V and the kernel of the linear tran MAT 243 Test 3 Practice 1. You have 6 coins in your pocket. Find the probability that they add up to at least 50 cents.2. There are n married couples. How many of the 2n people must be selected inorder to guarantee that one has selected a married
This text offers the most geometric presentation now available, emphasizes linear transformations as a unifying theme, and is recognized for its extensive and thought-provoking problem sets. While preserving the same table of contents as the previous edition, this revision is the outcome of a read more... This best-selling book provides an accessible introduction to discrete mathematics, using an algorithmic approach that focuses on problem-solving techniques. The new edition weaves techniques of proofs into the text as a running theme. Each chapter has a special section dedicated to showingThis student-friendly text develops concepts and techniques in a clear, concise, easy-to-read manner, followed by fully-worked examples. Application problems drawn from the literature of many different fields prepares students to use the techniques covered to solve a wide variety of practical read more... This textbook offers an interesting, straightforward introduction to probability and random processes. While helping students to develop their problem-solving skills, the book enables them to understand how to make the transition from real problems to probability models for those problems. To keep read more... This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skillsthe skills needed to solve complex problems, to evaluate horrendous sums, and to read more... The books in the series adhere to the latest syllabus proposed by NCERT and all other major Boards across the country. However , there are certain additions like Maths Lab Activities within the chapters which are required to be taught as per the CBSE directives. It helps in making the students read more...
The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I. ) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included. This text is part of the Walter Rudin Student Series in Advanced Mathematics. show more show less Edition: N/A Publisher: McGraw-Hill Publishing Co. Binding: N/A Pages: 352 Size: 5.05" wide x 7.09" long x 0.61" tall Weight: 0.66
Another good book though starts at an elementary level but covers lot of fundamental topics such as geometry, topology and calculus and could be highly recommended for the honors programs is: What is Mathematics? By Richard Courant and Herbert Robbins. Another good book though starts at an elementary level but covers lot of fundamental topics such as geometry, topology and calculus and could be highly recommended for the honors programs is: What is Mathematics? By Richard Courant and Herbert Robbins.
Detail Table of Contents Buy Now Please allow 5 to 10 days for delivery. Detail Table of Contents Matrices : Chapter 5 SUMMARY: Matrix is a set of 'm × n' numbers arranged in the form of rectangular array having 'm' rows and 'n' columns. It is called an m x n matrix. Matrices play an important role in modern techniques of quantitative analysis of managerial decisions. Matrices provide a compact way of representing a system of equations. This chapter discussed about determinants, adjoint and inverse of a matrix. To the end of the chapter we have discussed how managers can use matrix methods like Cramer's Rule, matrix inversion method and Gauss - Jordan elimination method to solve linear equations related to various managerial problems. Thus, matrices play a vital role in a manager's decision making process.
This unit covers the basic concepts and language we will use throughout the course. Just like every other topic we cover, we can view vectors and matrices algebraically and geometrically. It is important that you learn both viewpoints and the relationship between them
114 Due:Problem Set # 1 7 Feb 2007Name: The following questions, although not an astronomical, illustrate the use of logarithms in representing numbers that differ by many of orders of magnitude. Refer to the table below which lists the MATH 640 Numerical Analysis Section 7.4: Error Bounds and Iterative RenementSection 7.4 is the rst to introduce us to the concept of how good is it, i.e. of how accurate the numerical approximation to the solution of Ax = b truly is. We also see wa MIE 643 Course InformationKarnaugh Map ConfigurationA Karnaugh map provides a pictorial method of grouping together expressions with common factors and therefore eliminating unwanted variables. The Karnaugh map can also be described as a special a AGRO/HORT/BOTA 339: Introduction to the molecular techniques of plant biology and biotechnologyCOURSE OBJECTIVETo provide a practical experience in the major techniques used in plant genetic analysis at the molecular and bioinformatic levels.TEX Ways of failing to live up to the maximsChris Potts, Ling 390a: Controlling the Discourse, Fall 2007 Sep 26 Background In Logic and conversation, Grice identies four ways in which speakers might fail to fulll a maxim or maxims. This handout summariz Student Information SheetLing 201 Fall 2004 Discussion SectionBelow I printed the information about you I got from SPIRE, and some additional questions. Please check the personal information and correct it if necessary. The other questions are f Math 400.1 Practice Final Exam Wednesday, December 19, 2007(1) You should be able to state all the main denitions of the course. These include, but are not limited to: group, subgroup, cyclic group, Abelian group, the center of a group, the symmetr Stat 324: Lecture 01 Descriptive statisticsMoo K. Chung mchung@stat.wisc.edu January 18, 20051. A population is a collection of object under investigation. A sample is a subset of the population. The frequency of any particular value is the number Genetics 466, Lecture 40 Quantitative Genetics II: Nature vs. NurtureObjective: Learn the concept of heritability as a way of separating the phenotypic variance into genetic and environmental components. Understand the concept of "broad-sense" herit
This isn't really a heuristic, but I hate "functions are formulas." It takes a lot of students a really long time to think of a function as anything other than an algebraic expression, even though natural algorithmic examples are everywhere. For example, some students won't think of f(n) = {1 if n is even, -1 if n is odd} as a function until you write it as f(n) = (-1)^n.
...more>> Mind Over Math - Mind Over Math, Inc. Local to Orangeville and Waterloo, Mind Over Math is a tutoring centre that offers help for students in the Ontario Curriculum. The company has specialized programs tailored to the different courses, and can make available workbooks for purchase. The ...more>> Motivating Math - Robert Bunge A math help site focusing on basic math through introductory algebra. Suitable for secondary students and adult learners. Includes tutorials, Java-based tools, and pedagogical ideas behind the presentation. ...more>> Numerical Integration Tutorial - Joseph L. Zachary A tutorial that explores rectangular and trapezoidal methods for numerical integration. Includes a Java applet that opens in a separate window, for use alongside the tutorial. From a Computer Science course at the University of Utah, and the book Introduction ...more>> Operations Research - J. E. Beasley OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research (OR). Beasley includes practice questions ("tutorials"), links to other web resources, and past exams. ...more>> Origami Mathematics - Tom Hull Information on origami and the mathematics of paper folding. With an origami math bibliography and pictures and tutorials in origami geometric construction, as well as links to other origami sites and events.Permadi.com - F. Permadi Java and Flash applets: logic games, drawing and pattern-making programs, Conway's Life, and more arcade-style offerings. Also includes tutorials in using Flash and a graphics gallery. ...more>> Plane Geometry Web Pages - David Jaffe Materials from a geometry course originally taught to future middle and high school teachers. Using definitions, theorems, proofs, and examples, the site introduces mappings; isometries and similarities; angles and trigonometry; congruence and similarity; ...more>> Please Excuse My Dear Aunt Sally - Robert Owens A step-by-step introduction to the mathematics behind the PEMDAS mnemonic. With examples, quizzes, and puzzles illustrating order of operations. A Wired@School project of The Franklin Institute Online Museum Educator programPractical Money Skills for Life - VISA For educators, parents and students to practice better money management for life. Available online or in a binder format, the free classroom curriculum consists of a teacher's guide, student worksheets and quizzes. Teacher's Guide lessons cover topics ...more>> The Precalculus Algebra TI-83 Tutorial - Mark Turner An online tutorial for using the TI-83 graphing calculator to solve the kinds of problems typically encountered in a college algebra or precalculus algebra course. Step-by-step instructions with full key sequences and animated screen images. Includes ...more>> Precalculus Tutorial - John W. Bales A tutorial for students enrolled in a precalculus, college algebra, or trigonometry course. Bates explains, "It does not, and cannot, replace the textbook or other class resources or assignments. At the instructor's discretion, all or part of this tutorial ...more>>
1. How can we earn extra credit? Extra credit is never awarded at the last minute, nor is it given in big chunks. Extra credit is occasionally offered in class, and is even awarded for coming to extra help. 2. How is my grade determined? Every assessment has a specified point value. Each marking period, the total points earned is divided by the total points possible, to determine the marking period grade. The approximate weight for each type of assessment is as follows: 70 % Tests 15 % Homework and Journals 15 % Projects Will there be homework every night? Yes!! How is my homework graded? Every once in a while there will be an open notebook pop quiz. Some of the problems will come directly from the homework. Others will be similar enough that you should be able to follow your own examples! What is the best way to do my homework? Have a calculator, pencil and lots of paper handy. Copy the diagrams and write neatly, so that you can follow your own logic. After each odd numbered problem, check the answer key in the back of the book. This way you'll know whether or not you're on the right track, before you move onto the next problem. Don't be afraid to look in the text for an example just like the problem you're trying to solve. Call or I.M. a friend and ask for a hint. If you're still not sure, ask the next day in class, or come for extra help. What tools will I need to bring to class every day? A three-ring binder with folder pockets, paper, a pencil, an eraser, your text book, and a calculator (if possible). What tools will I need at home? A ruler marked both with centimeters and inches, a protractor, a compass, a calculator, a large binder for the papers you shouldn't throw out but don't need to carry with you, and all of the same tools you need to bring to class. When can I clean out my notebook? After each chapter test, you may wish to move all materials from this chapter to a notebook that you keep at home. Do NOT discard any graded papers until after you've received your report card. Save ALL tests and quizzes to prepare you for the midterm and final exams. What if I am absent? Check the website or your syllabus for HW assignments. Ask a classmate to show you what happened in the classroom (but don't ask during class!) The next day you come to class, pick up any handouts you missed and turn in any papers that would have been collected. For each day you are absent, you have one day to make up missed work without penalty. Plan to come for extra help.
Clear, rigorous definitions of mathematical terms are crucial to good scientific and technical writing-and to understanding the writings of others. Scientists, engineers, mathematicians, economists, ... Yoshiwara's INTRODUCTORY ALGEBRA was written with two goals in mind: to present the skills of algebra in the context of modeling and problem solving; and to engage students as active participants in ...
0495387983 9780495387985 1111780714 9781111780715 them through practice. This simple and straightforward approach, in an easy-to-read format, has helped many students grasp and apply fundamental problem-solving skills. The carefully structured pedagogy includes learning objectives, detailed examples to develop concepts, practice exercises, an extensive selection of problem-set exercises, and well-organized end-of-chapter reviews and assessments. The clean and uncluttered design helps keep students focused on the concepts while minimizing distractions. Problems and examples reference a broad array of topics, as well as career areas such as electronics, mechanics, and health, showing students that mathematics is part of everyday life. Also, as recommended by the American Mathematical Association of Two-Year Colleges, many basic geometric concepts are integrated in problem-solving scenarios. The text's resource package--anchored by Enhanced WebAssign, an online homework management tool--saves instructors time while also providing additional help and skill-building practice for students outside of class. «Show less... Show more» Rent Intermediate Algebra 1st Edition today, or search our site for other Kaufmann
Search Course Communities: Course Communities Maple Worksheets on First Order Differential Equations Course Topic(s): Ordinary Differential Equations \| Analytic Methods A collection of Maple worksheets that go through analytic methods of solving first order differential equations (separable, linear, integrating factor, exact, Bernoulli). The worksheets explain the methods themselves as well as the Maple code needed to solve.
Get the confidence and the math skills. you need to get started with calculus!. Are you preparing for calculus? This easy-to-follow, hands-on workbook helps you master basic pre-calculus concepts and ... Intermediate Algebra, 5th Edition, is designed to provide students with the algebra background needed for further college-level mathematics courses. The unifying theme of this text is the development ... Gilbert Strang's textbooks have changed the entire approach to learning linear algebra -- away from abstract vector spaces to specific examples of the four fundamental subspaces: the column space and ...
Prerequisite: Algebra II or higher with a grade of "C" or better or consent of professor, and satisfactory score on placement test. This course is a dual-enrollment course, which also earns four college credit hours in Precalculus Algebra. The purpose of the course is to emphasize the skills necessary for the study of calculus. A review of algebraic techniques and operations, exponents, radicals, complex numbers, and absolute value is also included. Major course topics are: linear equations and inequalities; quadratic equations and inequalities; relations, functions, and graphs; exponential and logarithmic functions; systems of equations and inequalities; higher degree polynomial equations; matrices and determinants; applications; sequences, series, and the binomial theorem; and mathematical proof.
Scalar posted on: 18 Jun, 2012 \| updated on: 24 Sep, 2012 ScalarMath is studied in linear Algebra where real number is considered as scalar and we can also relate the term scalar math with the vectors in vector space by using the operation known as Scalar Multiplication. In this operation a scalar or a number is multiplied by a vector to get back another vector. We generally define a vector space with use of some field instead of using real number or scalar, and such field is known as Complex Numberplane or field. The vector space or the Complex Plane has many scalar on its plane and these scalars are the elements of the field. In scalar math, we have a matrix called scalar matrix which is used to denote a matrix in the form KI where k denotes a scalar and I is the identity matrix. There is a big difference between scalar product operation and scalar multiplication operation. Scalar product is nothing but defined as the multiplication of two vectors to produce a scalar. One more Point to be discussed in scalar math is that the vector space with the scalar product is known as an inner product space. We should know that the real part component of a quaternion is also known as its scalar part. The term scalar we use is sometimes used also in context with a vector or matrix or a compound when reduced to a single component. For instance, when we calculate the matrix product like 1 x n matrix and an n x 1 matrix, then it is generally called as a 1 x 1 matrix and it is usually known as a scalar. Topics Covered in Scalar Scalar definition is not a new term for all of us; we have seen it when we talk about vectors. Definition of Scalar is studied in linear Algebra. We can define scalar by using the operation called Scalar Multiplication, where vectors in vector space are being multiplied by a real number so as to get another vector. As you have seen above that how we have given the definit...Read More Scalar multiplication is study under Scalar Math, where the word scalar is what which scales vectors. Scalar multiplication definition is different from scalar product definition which is nothing but an inner product between two vectors. Scalar multiple is studied under the topic linear Algebra and if we talk about the simple definition, then it can be defined as ...Read More Function in general, is defined as any action or event performed by any person for which it is suited. In mathematical term, a function is defined as the relation of any variable with the other such that for each value of one variable, there exists a value for which second variable is also defined. It can also be defined as a Set, for which there exists a unique val...Read More In mathematics, scalar field is termed as a function, which gives us a single value of some variable for each and every Point in space. Scalar term can be composed of a mathematical term or a physical quantity. Scalar field should always be independent of coordinates which means that any two persons watching the objects will agree on same points of Scalar field in space. Te...Read More Slope or gradient refers to variation in space of a quantity. Gradient of any quantity reflects the steepness and direction of a line. The gradient of a Scalar function or field is a vector quantity that shows the direction of maximum rate of increase of that Scalar Field and magnitude will be equals to rate of increase. Assume that there is a Scalar Funct...Read More Function can be defined as a relation between inputs and outputs. A function normally relates each input exactly with one output. Let's take an example to define function properly in which 'x' is used as input and 'y' is used as output and suppose that relation between input 'x' and output 'y' is defined by rule 'y' = f(x). Above rule says that output 'y' is ...Read More
Algebra 1 Teachers This is a website created for Algebra Teachers that are adopting Common Core Math! Lesson Plans Take a look around the site! You will find unique algebra lesson plans for every skill. In week 2 you can find a great algebra lesson to help students write equations for functions and actually understand them complete with applets. In week 12, students will be motivated to learn algebra when they take a look at the relationship between their favorite movies and profit. For current thoughts and ideas on everything from lesson plans and updates to how it is going in my room, please take a look at my blog. Assessments Assessments are an area where we seem to all be watching and waiting. Please feel free to sign up for the newsletter to receive my assessments. I am in the process of switching them over to a dropbox so that everybody can access them. This will be ready soon. Performance Tasks No one seems to know for sure what they new performance tasks will look like, but offering our students lots of opportunities to learn and grow with some examples will be a great start. You can find some that I have created and examples from other places around the web on the blog. This is a great place to start! Common Core Although this website is using the Common Core State Standards for math as a beginning point, you will find great lessons for algebra regardless of your curriculum. As you browse, I hope you find what you are looking for! Algebra 1 Teachers is a tool that will help with Algebra 1 scope and sequence using the new Common Core State Standards. Lesson plans, assessments, activities, organization, and even tips on keeping your sanity will be addressed on this website and in my newsletter. While there is controversy surrounding the Common Core State Standards, this site is not an endorsement or a place for that discussion. Algebra is the gate keeper for student success and we must do an outstanding job for the kids future and ours as well. Most of us do want to retire someday :) Implementation As we move into implementation of the Common Core Standards we are seeing an amazing shift in what students must be able to accomplish at the end of Algebra 1. Solving linear equations is no longer taught at the Algebra 1 level, but instead at the middle school level. This is wonderful if they retain the information, but what do we do as the middle school is still shifting to the Common Core? I believe that there are some very definable and measurable ways that we can close the gap between what they are supposed to know and what they do know. Scope and Sequence The math department in my school will be using the Mathematics Common Core Toolbox scope and sequence for Algebra 1 next year. We all understand that this is a working document, and that there will need to be changes due to our population and the rate of implementation of the Math Common Core to the grades under us. We will be starting with the necessities and as holes no longer need to be filled and concepts no longer have to be retaught, we will be adding to the list of covered material and Quadrant D type lesson plans. Please sign up for the newsletter to receive assessments. It is my small attempt to keep them out of the hands of the kids :)
Mr. V's Math and Science Moodle Available courses I.B. mathematics course caters for students with varied backgrounds and abilities. More specifically, it is designed to build confidence and encourage an appreciation of mathematics in students who do not anticipate a need for mathematics in their future studies. Students taking this course need to be already equipped with fundamental skills and a rudimentary knowledge of basic processes. The course concentrates on mathematics that can be applied to contexts related as far as possible to other subjects being studied, to common real-world occurrences and to topics that relate to home, work and leisure situations. The course includes project work, a feature unique within this group of courses: students must produce a project, a piece of written work based on personal research, guided and supervised by the teacher. The project provides an opportunity for students to carry out a mathematical investigation in the context of another course being studied, a hobby or interest of their choice using skills learned before and during the course. This process allows students to ask their own questions about mathematics and to take responsibility for a part of their own course of studies in mathematics. analyze, qualitatively and quantitatively, data related to a variety of physics concepts and principles. Students will also consider the impact of technological applications of physics on society and the environment.
I have a solution for you and trust me it's even better than buying a new textbook. Try Algebra Buster, it covers a rather elaborate list of mathematical topics and is highly recommended. With it you can solve various types of questions and it'll also address all your enquiries as to how it came up with a particular solution. I tried it when I was having difficulty solving problems based on ration expretion work sheet`` and I really enjoyed using it.
Helps you understand the mathematical ideas used in computer animation, virtual reality, CAD, and other areas of computer graphics. This work also helps you to rediscover the mathematical techniques required to solve problems and design computer programs for computer graphic applications. more... Draws together a variety of geometric information that provides facts, examples and proofs for students, academics, researchers and professional practitioners. This book includes a summary hundreds of formulae used to solve 2D and 3D geometric problems; worked examples; proofs; a glossary of terms used in geometry; and more. more... Matrix transforms are ubiquitous within the world of computer graphics, where they have become an invaluable tool in a programmer's toolkit for solving everything from 2D image scaling to 3D rotation about an arbitrary axis. Virtually every software system and hardware graphics processor uses matrices to undertake operations such as scaling, translation,... more... The convergence of IT, telecommunications, and media is bringing about a revolution in the way information is collected, stored and accessed. There are 3 reasons why this is happening - reducing cost, increasing quality, and increasing bandwidth. This volume presents key aspects in this field in the areas of technology and information sciences. more...
Elementary Linear Algebra - 6th edition ISBN13:978-0618783762 ISBN10: 0618783768 This edition has also been released as: ISBN13: 978-0547004815 ISBN10: 0547004818 Summary: The cornerstone of Elementary Linear Algebra is the authors' clear, careful, and concise presentation of material--written so that students can fully understand how mathematics works. This program balances theory with examples, applications, and geometric intuition for a complete, step-by-step learning system.The Sixth Edition incorporates up-to-date coverage of Computer Algebra Systems (Maple/MATLAB/Mathematica); additional support is provided in a corresponding tec...show morehnology guide. Data and applications also reflect current statistics and examples to engage students and demonstrate the link between theory and practice. ...show less Hardcover Good 0618783768 Used, in good condition. Book only. May have interior marginalia or previous owner's name. $95.70 +$3.99 s/h Good Kansas Academics Lawrence, KS Good Hardcover; 6th edition; few if any interior marks; used stickers on spine and back cover; slight shelf wear to cover and corners. Overall, this book is still in great condition and looks barely...show more used. It could definitely be used again. ...show less $98.61 +$3.99 s/h New Premier Books BN Romulus, MI 0618783768 Brand New. Exact book as advertised. Delivery in 4-14 business days (not calendar days). We are not able to expedite delivery. $110.00 +$3.99 s/h New Cloud 9 Books FL West Palm Beach, FL Hardcover New 0618783768 New, Perfect Condition. Ships within 24 hours and all purchases are guaranteed or your money back. Brand New Title. We're a Power Distributor; Your satisfaction is our guarantee! $312.51 +$3.99 s/h New Extremely_Reliable Richmond, TX Buy with confidence. Excellent Customer Service & Return policy. $326.13 +$3.99 s/h New PROFESSIONAL & ACADEMIC BOOKSTORE Dundee, MI 0618783768
Algebra I is a mathematics class in which students will begin to learn more complex algebraic concepts. Topics in algebra I include solving equations, inequalities, and proportions, creating and assessing graphs, functions, and linear equations, and polynomials and factoring, among other concepts. Algebra II Algebra II is a mathematics class in which students build on concepts previously learned in algebra I. Topics in algebra II include matrices, quadratic equations and functions, polynomials and polynomial functions, basic trigonometric concepts, sequences and series, logarithmic functions, and probability and statistics. Calculus Calculus is a branch of mathematics that focuses on limits, functions, integrals, and derivatives. Calculus has applications in science, engineering, higher mathematics, and more. Differential Equations A course in differential equations involves the study of equations that represent real-world systems requiring multiple variables changing at different rates. Discrete Math Discrete math is the study of mathematical structures that are fundamentally discrete as opposed to continuous. It has been characterized as the branch of mathematics dealing with countable sets. Topics in discrete math include game theory, set theory, logic, probability, and number theory, among others. Geometry Geometry is the branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Topics in geometry include finding area, volume, and perimeter of a variety of shapes, properties of triangles, the Pythagorean Theorem, angles, and symmetry, among others. Pre-Algebra Pre-Algebra, as the name suggests, prepares students for algebra. Topics in pre-algebra include properties of operations, operations with integers, fractions, decimals, and negative numbers, solving basic algebraic expressions, roots, exponents, area, perimeter, and volume. Pre-Calculus Pre-Calculus, as the name suggests, prepares students for success in calculus. Topics in pre-calculus include exponential, rational, polynomial, and logarithmic functions and their properties, real and complex numbers, and limits, among others. Statistics Statistics is the science of the collection, organization, and interpretation of data. Statistics applies to a variety of fields including math, science, technology, and business, just to name a few. Statistics involves reading and interpreting tables and graphs, learning about qualifiers of data like mean, median, range, and mode, as well as more advanced topics and skills. Trigonometry Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and angles. Topics in trigonometry include the Pythagorean Theorem, the law of sines and cosines, trigonometric functions, right triangles, angles, graphs of trigonometric functions, and circles.
Math 8 Textbook Website: Applications and Connections (Course 3) (The Parent and Student Guide has worksheets that you can print out for each chapter. These one-page worksheets have a very brief, but clear explanation of each lesson and some examples for practice with answers at the bottom of the page.)
MathFast! MathFast! was designed with a single purpose in mind - to help you solve math problems correctly but quicker. The software is easy to use yet powerful.. Simplicity means you get real results that raise your confidence and build your math skills needed to finishs tests and homework in less time. Many tests given in school and when applying for a job must be completed in a certain amount of time. This is why the program prepares you by letting you practice the type of problems you are having trouble with but also let's you decide how much time you need to complete the problem type. As you get better you can allow less time to answer a question.
9781452230030 Buy New Textbook Not Yet Printed. Place an order and we will ship it as soon as it arrives. $30.23 6Get to the core of your students' understanding of math Your wait is over: finally, easy-to-implement diagnostic tools to help you quickly and reliably identify your students' understanding of Common Core math concepts, then determine next steps to accelerate instruction. Completely aligned with the Common Core mathematics standards, Cheryl Tobey and Emily Fagan's 20 formative assessment probes will enable you to: Determine each child's prior knowledge of basic math and numeracy Identify common student misconceptions before they become long-term problems Make sound instructional decisions, targeted at specific concepts and responsive to specific needs
02153 CIP Code This course has been verified by OSPI′s Career and Technical Education department as meeting all Washington State requirements for approved CTE courses. The course CIP code is: 270301. The CTE instructor vocational certification number for this course is V520300. Other Materials Description Building on the skills developed in the first two years of high school math, students will continue to improve their ability to reason mathematically by applying and extending their learning in this third year math course. This course will broaden their ability to model situations and solve problems. Students will formalize their understanding of two- and three-dimensional geometric figures. Triangles will continue to be a primary focus as we deepen the understanding of right triangles, special right triangles, applying the Pythagorean Theorem and applying the basic trigonometry ratios of sine, cosine and tangent. Students will also review and expand their understanding of transformations and uses of the coordinate plane. Students will develop an understanding of quadratics, functions and probability
Glossary Entries This abbreviation means "for example." When used in the Core, e.g. is not limited to the examples given. Edge A line segment where two faces of a three-dimensional figure meet. Elapsed Time The difference between two times. The amount of time that has passed. Ellipse A squished circle (put simply). If you took a regular circle and only changed the height or width, you would get an ellipse. Endpoint A point at either end of a line segment, arc, or the beginning point of a ray. Equal To A symbol that means two things have the same amount, size, number, or value. ( = ) Equation A mathematical sentence stating that two expressions are equal. Equidistant Having equal distances. Equilateral Having equal sides. Equilateral Triangle A triangle with all sides the same length. Equivalent Equal in value. Examples: 2.9 is equivalent to 2.90 (equivalent decimals), 1 yard is equivalent to 3 feetThe ratio of the value of one currency in relation to the value of another. Exchange Rate Table A table displaying the ratios of the values of several currencies in relation to each other. Expanded Form The expanded form of an algebraic expression is the equivalent expression without parentheses. For example, the expanded form of ( a + b )2 is a2 + 2ab + b2 . A way to write numbers that shows the place value of each digit. 263 = 200 + 60 + 3 or 263 is 2 hundreds, 60 tens, and 3 ones. The degree of probability of an occurrence based on probability, what would be expected to happen. Expected Value An average value found by multiplying the value of each possible outcome by its probability, then summing all the products. Experiment An action or process carried out under controlled conditions in order to discover an unknown effect or law, to test or establish a hypothesis, or to illustrate a known law. Experimental Probability Probability based on experimental data; the ratio of the total number of times the favorable outcomes happens to the total number of times the experiment is done found by repeating the experiment several times, given by the formula P(E)=Number of successful outcomes / total number of outcomes. Explain (See justify) Explore To look for patterns or relationships between elements within a given setting. Exponent A number that represents the power. How many times you multiply a number by itself. An exponent may be any real number. Example: For 215, 15 is the exponent, 2 is the base, and 215 is a power of 2. Exponential Form A number written using exponents (e.g., 32=25). Exponential Function A function used to study growth and decay. It has the form y = abx + c with a positive. "b" is not equal to 1. Exponential Notation A symbolic way of showing how many times a number or variable is used as a factor. In the notation 53, the exponent 3 shows that 5 is a factor used three times; that is 53 = 5 x 5 x 5 =125.
Course:UCSC Math 111B From SlugmathWiki Group theory including the Sylow theorem, the structure of abelian groups, permutation groups. Introduction to rings and fields including polynomial rings, factorization, the classical geometric constructions, and Galois theory.
In this Newsletter 1. Happy New Year and Information 2. Real life Math 3. Math tip - Radicals 4. New in IntMath - Integrator, from Mathematica 5. From the math blog 6. Final thought - Your goals for 2009... 6. Equations With Radicals It is important in this section to check your solutions in the original equation, as the process that we use to solve these often produces solutions which actually don't work when subsituted back into the original equation. (In fact, it is always good to check solutions for equations - you learn so much more about why things work the way they do. ^_^)
Culinary Math 3rd Edition with Culinary Artistry Set Math skills are an essential part of the day-to-day job functions of the professional chef. This book is designed to teach the culinary student or professional all the tools necessary to manage daily restaurant operations with maximum efficiency and profitability. Well-organized and easy-to-use, the book presents proven step-by-step methods for understanding food service math concepts and their practical applications in the kitchen. The authors begin with a review of math basics, including fractions, decimals, rounding, and percents, as well as an overview of customary U.S. and metric kitchen measurements. More advanced chapters include directions on conversions, calculating yield percents, determining edible portion costs, recipe costs, and beverage costs, purchasing, and converting recipe yields. Each chapter includes a clear set of outlined objectives, as well as practice problems to help readers develop their skills. Appendices include formulas, measurement equivalency charts, problem answers, and a blank food cost form. In addition, this revised edition will include input from prominent industry leaders, 35 all-new photographs, 150 new practice problems, and a companion website, all designed to help students apply basic math skills to the field of kitchen management.
Cliffs Quick Review Trigonometry * Prices displayed are in Australian Dollars and, where applicable, GST inclusive Description: Leading educators help you succeed When it comes to pinpointing the stuff you really need to know, nobody does it better than CliffsNotes. This fast, effective tutorial helps you master core trigonometer concepts -- from trigonometric functions and trigonometric identities to vectors, polar coordinates, and complex numbers -- and get the best possible grade. At CliffsNotes, we're dedicated to helping you do your best, no matter how challenging the subject. Our authors are veteran teachers and talented writers who know how to cut to the chase--and zero in on the essential information you need to succeed. Master the basics--fastComplete coverage of core conceptsAccessible, topic-by-topic organizationFree pocket guide for easy reference Details: Textual Format: Study Guide Depth (m): 0.013 Dewey: 516 Height (m): 0.203 Published Date: Sat 15 Sep 2001 Weight (g): 181
Your students may be able to correctly work math problems, but can they explain how they arrived at the solution? Step Up to Writing in Math is a powerful new resource for mathematics and content-area teachers looking for Assess individual proficiency in prealgebra and algebra. Algebra Readiness Assessment gives teachers the ability to design instruction that is appropriate for each student's learning needs. The perfect complement to Algebra...
Based on the approach "thinking mathematically", includes statistics, algebra, metric measurement, geometry, probability, customary measurement, ratio. Early high school level. A Survey of Modern Algebra Editorial review A new edition of the classic undergraduate text introducing abstract algebra using concrete examples. The authors ground their explanations with computational and theoretical exercises to develop the student's "power to think for himself, Reviewed by "felly", (Reston, Virginia United States) ything make sense? Reviewed by a reader per understanding of algebra, this book should serve as an excellent introduction. Reviewed by Andrew Young "ayoung8511", (Manhattan, KS) Modern algebra is an extraordinary topic and Birkhoff and MacLane do a superb job of exploring it. However, as is often the case with mathematical texts, the material can be somewhat dry. College algebra Reviewed by a reader, (Manila, Philippines) This book is of great value, it is one of the best calculus book I have ever encountered. Mr. Leithold really explains the lessons step-by-step by truly applying the "learn by example"method in teaching. Many examples are given ranging fr Queuing Theory: A Linear Algebraic Approach Reviewed by a reader This book is an excellent introduction to queueing analysis using matrix analytic techiques. The book is very readable and the author provides numerous examples to illustrate crucial points. Analysis of the M/M/1, M/G/1, GI/M/1, M/G/C, an College Algebra With Review (Precalculus Series) Editorial review A user-friendly and accessible treatment of college algebra. Linear Algebra: An Introduction to the Theory and Use of Vectors and Matrices [FACSIMILE] Editorial review y uses of linear algebra with the traditional theory of vector spaces and linear transformations, providing math majors with a broader view of linear algebra. Reviewed by a reader Good book for cramming for the linear algabra final at college. it will save you! College Algebra: A View of the World Around Us Editorial review This text places mathematics into a real-world setting. Concepts are developed through the "Rule of Four"--Numeric, Analytic, Graphic, and Verbal. Graphing utilities are integrated as a tool while the focus is on the mathematics. --This t Matrix Algebra Editorial review Emphasizing matrix manipulation, this book covers concepts in a clear manner with a computational orientation. Geometric phenomena are illustrated with the use of figures. Volume 2 of the "Carpenters and Builders Library" contains very valuable solutions to any math problem you will encounter in carpentry. Covers stress, strain, wind loads on roofs, geometry, Essentials of Math with Business Applications, Student Edition Editorial review This 8-12 week course, organized into 60 distinct Skillbuilders, is targeted toward students with lower-level math skills and can be used with individuals or groups. Students gain real-world math skills by working business problems and ap
1. Use of calculators and calculators with Computer Algebra System are up to the discretion of each instructor. 2. Items with ** are optional. 3. Chapter 3 (Graphs and Functions) and Chapter 5 (Polynomials and Factoring) should be a review; so go over them quickly. 4. Be sure to cover 'Equations in the Quadratic Form' found in Examples 4 and 5 of Section 8.1. 5. Stress word problems. 6. Section 6.5 will be covered in Math 22. 7. The Final Exam must consist of questions that cover the fol lowing topics . Chapter 3 The distance formula Graphing an equation by hand Finding x- and y- intercepts of the graph of an equation Finding the slope of a line Evaluating functions Graphing a function Finding the domain and range of a function
Important Books For IIT JEE R.D Sharma is very famous among IIT-JEE aspirants.Every the one of the best books in Mathematics for beginners. It includes the exercises covering the entire syllabus of Mathematics pertaining to IIT JEE, AIEEE and other state level engineering examination preparation. Although all the topics are covered very well but the topics of Algebra have an edge over others. Permutations and Combinations, Probability, Quadratic equations and Determinants are worth mentioning. It's a one stop book for beginners. It includes illustrative solved examples which help in explaining the concepts better. Room for improvements (Why should I keep away from this book?) Though the book has a good collection of problems but it cannot be said to be self sufficient for the whole syllabus of Mathematics. An aspirant should also practice from other standard sources too. A good book for beginners not only for competitive examinations but also from 10+2 examination perspective. User Reviews: * for topers Posted On:May 27, 2012 08:11 PM Review By prem it is good book my mark in mathes iit jee 12 is 112 * 4 Posted On:Nov 16, 2011 10:33 PM Review By Caelii Absolutely first rate and copper-bottomed, gnetleemn! * Thopulaki thopu(topper than toppers) Posted On:Sep 30, 2011 02:14 AM Review By A Hemanth Kumar The thing is if u r not good at ALGEBRA,just do one thing GO FOR IT * Wide range of problems Posted On:Sep 15, 2011 07:41 AM Review By Abdul Wajid Excellent book for those who are IIT-JEE aspirants and covers the entire syllabus with wide range of problems. * BOOK Posted On:Jul 26, 2011 08:31 AM Review By RAJIV KHANNA SIR, i have objective mathematics for IIT and aieee of rd sharma. Is there any other book of rd sharma for the preparation of IIT?BECAUSE I HAVE HEARD ANOTHER BOOK OF RD SHARMA NAMED AS OBJECTIVE APPROACH TOO IIT JEE. * rd sharma Posted On:Jul 20, 2009 02:41 AM Review By purav it is a very great book and it gives a complete knowledgeRevise this book for IIT-JEE Posted On:Mar 17, 2009 08:20 AM Review By Anand Shankar As all of you must have already finished this book,therefore the only thing required for IIT-JEE is to revise it thouroughly.
An intermediate treatment of the theory and application of numerical methods, much of this material has been presented at the University of Michigan in a course for senior and graduate engineering students. The main feature of this volume is that the various numerical methods are not only discussed in the text, but are also illustrated by completely documented computer programs. Many of these programs relate to problems in engineering and applied mathematics. The reader should gain an appreciation of what to expect during the implementation of particular numerical techniques on a digital computer. Cloth/Paper C Reviews U.S. Dollars $87.50 You may copy this unique Krieger Book Number into the Quote and Information Form, for quick processing, if you're interested in this book
This course is designed to continue students' math education in preparation for post-high school study. The topics covered will be investigated through projects, readings and reporting, as well as traditional mathematics approaches. To maximize learning by increasing motivation and expectations, and by ensuring that students perform at their level of potential.
Chapter 10 Factorisation Techniques Knowledge of factorisation enables us to learn advanced mathematics and solve problems which occur in science, business, computer programming and engineering. In this chapter, we will consider the highest common factor, the difference of two squares, factors of quadratic trinomials over Q, use of perfect squares, factorisation of four terms and factors of quadratic trinomials over R.
Beginning Algebra - 2nd edition ISBN13:978-0073312675 ISBN10: 0073312673 This edition has also been released as: ISBN13: 978-0073028712 ISBN10: 0073028711 Summary: New Features NEW! Problem Recognition Exercises Developmental math students are sometimes conditioned into algorithmic thinking to the point where they want to automatically apply various algorithms to solve problems, whether it is meaningful or not. These exercises were built to decondition students from falling into that trap. Carefully crafted by the authors, the exercises focus on the situations where...show more students most often get "mixed-up." Working the Problem Recognition Exercises, students become conditioned to Stop, Think, and Recall what method is most appropriate to solve each problem in the set. NEW! Skill Practice exercises follow immediately after the examples in the text. Answers are provided so students can check their work. By utilizing these exercises, students can test their understanding of the various problem-solving techniques given in the examples. NEW! The section-ending Practice Exercises are newly revised, with even more core exercises appearing per exercise set. Many of the exercises are grouped by section objective, so students can refer back to content within the section if they need some assistance in completing homework. Review Problems appear at the beginning of most Practice Exercise Sets to help students improve their study habits and to improve their long-term retention of concepts previously introduced. NEW! Mixed Exercises are found in many of the Practice Exercise sets. The Mixed Exercises contain no references to objectives. In this way, students are expected to work independently without prompting --which is representative of how they would work through a test or exam. NEW! Study Skills Exercises appear at the beginning of the Practice Exercises, where appropriate. They are designed to help students learn techniques to improve their study habits including exam preparation, note taking, and time management. NEW! The Chapter Openers now include a variety of puzzles that may be used to motivate lecture. Each puzzle is based on key vocabulary terms or concepts that are introduced in the chapterAcceptable Hungry Bookworm ca Los Angeles, CA 2006 Hardcover
This class is designed for students who have successfully completed intermediate algebra. This course will attempt to make mathematics enjoyable, practical, understandable, and informative using a variety of real-life applications. Topics include: linear, quadratic, exponential, and logarithmic models, geometry, tessellations, fractals, logic, interest, annuities, loans, probability, and statistics. The class will satisfy the quantitative skills requirement for the AA degree. Prerequisite: grade of 2.0 or better in MATH 095, MATH 098, or COMPASS test placement.
Many faculty ask their students to watch the "Hands on Start to Mathematica" screencast during the first week of class, to get them familiar with the basics of using Mathematica. For those of you who are using Mathematica 8, you'll be interested to know that an updated version of this screencast is now available: ... dsonstart/ This tutorial screencast is a great resource for new users because it encourages viewers to follow along in Mathematica 8 as they learn the basics to create their first notebook, calculations, visualizations, and interactive examples. Each topic is broken out into its own section, and the new video player allows you to easily jump between each of the eight sections. This multi-part screencast replaces the previous "Hands on Start to Mathematica--Part 1" and "Hands on Start to Mathematica--Part 2". If you or your students are still using Mathematica 7, you can access the previous screencasts through the following links: Plans are in the works to make the "Hands on Start to Mathematica" screencast available in other languages besides English, and I'll keep you all posted on the progress. In the meanwhile, I'd be interested in your feedback on the new version, so please let us know what you think.
Softpedia Editor's Review for Microsoft Mathematics Learn to solve equations step-by-step Microsoft Mathematics is a software designed to help you learn equations in a user-friendly environment. The interface of the program is clean and intuitive. In the "Worksheet" area you can type an expression on the lower part of the screen and press the "Enter" button to process it. Results are instantly displayed above this area. For each equation you can edit the entry or view keyboard equivalents. Furthermore, you can plot an equation or function in the "Graphing" tab (2D or 3D, Cartesian or Polar), as well as insert a data set, parametric functions and inequalities. On the left side of the screen, you can use the calculator pad to input shortcuts for complex numbers, calculus (e.g. partial derivatives, indefinite integrals), statistics (e.g. geometric means, permutations), trigonometry, linear algebra (e.g. matrix insertions, transpositions) and standard elements (e.g. expand, slope, pi). Also, you can create a "favorite buttons" group. In addition, you can use the "Undo" and "Redo" buttons, as well as initiate a triangle solver, equation solver, unit converter, formulas and equations (e.g. geometry, physics, chemistry, laws of exponents, logarithm properties, constants). The program uses a pretty high amount of system resources and contains a comprehensive help file (also includes a glossary). We haven't encountered any kind of problems during our tests and we strongly recommend Microsoft Mathematics to teachers or students. Microsoft Mathematics description Here are some key features of "Microsoft Mathematics": · The Graphing Calculator, with extensive graphing and equation-solving capabilities. · Step-by-Step Math Solutions that guide students through problems in subjects from pre-algebra to calculus. · The Formulas and Equations Library, with more than 100 common math equations and formulas to help students identify and easily apply the right equation. · The Triangle Solver, a graphing tool that students can use to explore triangles, and understand the relationship between different components to solve sides, angles, values and formulas. · The Unit Conversion Tool lets students quickly and easily convert units of measure including length, area, volume, weight, temperature, pressure, energy, power, velocity and time. · New! 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.
Elementary Algebra 9780077224790 ISBN: 0077224795Elementary Algebra, 6e is part of the latest offerings in the successful Dugopolski series in mathematics. The author's goal is to explain mathematical concepts to students i [more] Elementary Algebra, 6e is part of the latest offerings in the successful Dugopolski series in mathematics. The author's goal is to explain mathematical concepts to students in a language they can understand. In this book, students and faculty will fi...
Course Goals: This course provides the student with a foundation in basic programming concepts in general, and in the MATLAB environment and syntax in particular. After completing this course, the student will be able to design, write, test and debug MATLAB programs to solve scientific and mathematical problems. Specific Objectives Upon successful completion of this course, the student should be able to: Textbook: Required software: The student must have MATLAB available, either the standard version, or purchase the student version from the Mathworks. How to register for this course: This course is offered by the Oceanography Department of the Naval Postgraduate School as a distance learning course. It is an instructor-led, web-based course, and is available to any DoD service member or Civilian. NPS follows a quarter system, with 11-week quarters. There will be weekly assignments and tutorials. The tuition must be paid by your command. For more information, please contact the instructor at aguest@nps.edu.
3 Mathematically speaking Mathematicians have rigorous ways of defining things like maps. As Wolfram MathWorld explains: A map is a way of associating unique objects to every element in a given set. So a map ƒ:A\|->B from A to B is a function ƒ such that for every a ∈ A, there is a unique object ƒ(a) ∈ B. What does that mean? Say you have a bunch of things — a set, in mathematical terms — and you want to put them someplace or refer to them in a more convenient way. Call that set A. You need to map (verb) each element, or object, in set A to some other element in another set, which we'll call B. And each object in A can only go one place. So, as Wolfram says, we need to associate unique elements in B with each element in A. Those of you who liked high school algebra may note that this is the same as the definition of a function. In fact, mathematically speaking, a map and a function are the same thing. For the rest of you, here's an example. A classroom example Consider the students in your class — a set of students. Each student needs a desk — a unique desk; one student can't sit at two desks, although in a pinch they could share — and so you could map (verb) students to desks by creating a seating chart. Your seating chart would be the map (noun). You didn't know that when you assigned seats you were writing a mathematical function, but there you go: Algebra in practice! That's a simple example. The original data set, your set of students, has just one variable, the student's identity or name; and the set of desks can simply be numbered. You might say it's one-dimensional. Figure 4-1. Mapping students to numbered desks. Student Desk Anastasia 11 Billy Bob 1 Candi 5 Dora 3 Elwin 8 Fiona 9 Grover 2 Hargrove 4 Ingrid 12 Josepha 6 Kaga 10 Lerlene 7 Of course, this is assuming you've numbered your seats — you've created a second map, by mapping the physical desks in your classroom to the whole numbers 1 to 12. If you actually want your students to be able to find their seats, though, you may want to do more than simply number them. You may want to map your list of students to the two-dimensional space of your classroom. (I say two-dimensional because I assume you don't have a mezzanine. If you do, hang on, we'll get to three dimensions later on.) For simplicity, let's say you have a simple rectangular arrangement of three rows of four desks each, numbered this way: Figure 4-2. Numbering your desks by rows and columns: or, mapping a two-dimensional space to a set of whole numbers.1 Then you can give students this map of their seating assignments, representing students by their first initials:2 Figure 4-4. Mapping students to physical desks. Now this is starting to look like what most people think of as a map, which is a two-dimensional representation of physical space. Actually "a representation of a space" is a pretty good way to define a map more generally. A space, mathematically speaking, doesn't have to be a physical space. It can be a coordinate space, which is the imaginary space defined by the axes of a graph. Remember Cartesian coordinates from high school algebra? Figure 4-5. Two-dimensional Cartesian coordinate space. Here you can see the "space" defined by the x and y axes. But of course we can map a physical space to coordinate space — that's what we do when we make a map of the world or of a geographical region. Those of you who enjoyed high school algebra may observe that if the desk number n is a function ƒ(r,c) where r=row and c=column, then n=4(r-1)+c. Pointing this out is of no real help in organizing your classroom, but it might be useful if you had a very complicated seating arrangement and needed to convince your principal that it was serious and important. [return] Note that in my hypothetical classroom, I have only one student per first initial. I recommend this in real life, as well. Students are often perfectly willing to change their names, and if you have more than twenty-six, you can use Greek or Russian names. (You may even be able to get away with calling this "globalizing your curriculum," but I don't recommend it.) [return]
I'm so glad I found this group!! Today I was helping my little brother with his math homework (a.k.a. I was doing it for him) and when we were done I was so disappointed. I wanted to do more! And I'm not being challenged enough in my math class at school :( (I'm in 8th grade, but I take 9th grade advanced math. It's still too easy! I think it's a problem with the teacher.) I learned slope-intercept first... and then they taught me point slope and I haven't really gone back to thinking of it as slope-intercept when I use that at the origin. I wonder if it's better to start with specific cases and then generalize or to learn the general method and then apply it in specific cases... Hi! I'm more of an applied math person myself and I like differential equations more than I like discrete (though number theory was fun). That said, analysis was one of my favorite classes last semester! I can access JSTOR, but only at work and I don't go back there until Monday. I'm really sorry. :¬( Feel free to contact me, though, if I can help in the future. (That goes for everyone, not just Lexie.)
Discovery Math Discovery Math is a two-semester course designed to cover the material traditionally taught in a seventh-grade classroom. The course introduces students to a wide range of mathematical topics. Students will use interactive media and content to develop an understanding of integers, number sense, fractions, decimals, ratios and percents, geometric figures, area, perimeter, scale, measurement, solving equations, working with functions, and introductory probability and statistics. Through discussion activities and writing exercises, students will learn to communicate mathematically by expressing ideas, analyzing situations, explaining procedures for correct computation, and describing results numerically and graphically. Discovery Math 1A In the first semester of Discovery Math, students will learn the basics of working with integers, decimals and fractions, algebraic thinking, and factors and fractions. Scope and Sequence Discovery Math 1B The second semester of Discovery Math covers ratios, proportion and percent, geometry figures and measurement, equations and functions, and probability and statistics. Scope and Sequence
Aldie Algebra Equatio... ...Chemistry is a building block subject where previously covered topics combine in more complex ways as newer subjects are introduced, so clear understanding of earlier concepts is essential to ongoing success. Geometry is the branch of mathematics that studies figures, objects, and their relation...

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