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Our Beautiful Swat Meta Tags Because it involves lots of algebraic and trigonometric computations, Calculus is one of the most difficult branches of Math. If they could, students would have liked to avoid this subject altogether. Calculus, however, is often unavoidable. If you are about to take Calculus, you must understand that the best thing to do is to prepare yourself for the subject. Below are some tips. Stay focused. Focus is very important in learning Calculus. Without which, it is nearly impossible to master the subject. Sometimes, however, focusing is a very challenging to do, whether you are in class or doing your homework alone in your room. If you are having difficulty with focusing, try doing some exercises until you can keep your mind on the subject without wandering after every few seconds. Never skip a class. Yes, attendance is of utmost importance. A new lesson is introduced each day, which is usually connected to the previous and future lessons. Remember, Calculus lessons are intertwined which is why missing just one class will get you so far behind. If you need to skip a class, make sure to make up by borrowing notes from a classmate or asking someone to fill you in on the lesson. Do not go to class without studying the previous lesson; otherwise, you won't fully understand the present. Practice a lot. You can't master the concepts behind Calculus without practicing them over and over. Remember, practice establishes familiarity, and familiarity leads to mastery. Practicing shouldn't only be done in class but should also extend outside of the school. It will be best if you spend at least two hours of self-studying and work on different problems everyday. Take this time to spot and strengthen your weak points so that you can perform better in class and during exams. Join a study group. Better yet, build one on yourself. Meet with some of your classmates who share the same goal to do well in Calculus. It doesn't have to be a big group. You can meet with two to three people on a regular basis to review what you have learned from school. You can do some solving exercises or study for an exam. Meeting with a study group gives you an opportunity to learn without being exposed to the innate pressure of a classroom. Make notes. Have a big notebook where you will write all the techniques, tips, and strategies your teacher will give you. Make sure to review the notes when you get home and apply them to the problems you are solving on your own. Have supplementary references and resources. Your textbooks will bring you far along, especially if you study them diligently. But if you find that your textbooks are not enough, then by all means get additional resources. Ask your teacher for recommendations and try to look Calculus materials in your library. You can also search the Internet. Study very well. Unless you have some kind of a super power, you will never get through Calculus without studying long and hard. Take advantage of all the assistance that you can get from your teacher, classmates, books, and other resource materials. And, make sure to have a structured study schedule.
Derive 6.1 description Derive 6 is a powerful system for doing symbolic and numeric mathematics on your personal computer. It processes algebraic variables, expressions, equations, functions, vectors, matrices and Boolean expressions like a scientific calculator processes numbers. Problems in the fields of arithmetic, algebra, trigonometry, calculus, linear algebra, and propositional calculus can be solved with the click of the mouse. Make plots of mathematical expressions in two and three dimensions using various coordinate systems. By its seamless integration of numeric, algebraic and graphic capabilities, Derive makes an excellent tool for learning, teaching and doing mathematics. If you are familiar with Derive 5, you will find Derive 6 an (upward-compatible) extension. Here is a list of the major new features: display the steps in the simplification of an expression along with the transformation rules applied send and receive math worksheets to and from the TI-89, TI-92+, Voyage 200 TI CAS handhelds animate parameterized expression plots with slider bars automatically label plots showing the expression being plotted rotate 3D plots using the mouse easily navigate around the on-line help using the table of contents customize menus, toolbars, and shortcut keys profit from numerous other improvements, including fully scaleable Derive Unicode font support for Unicode characters and html link hot spots in text objects state variables saved in DfW files optional multi-line editing parentheses matching on the edit line controllable display of 3D mesh lines and data-point sizes
Online Math Center Mission Statement The mission of Whatcom Community College's Online Math Center is to provide free access to a wide range of resources related to mathematics, its application, technology, and mathematics education. Design Tied to Mission To this end, the Online Math Center has been designed around two main themes, Teaching and Learning Math, as well as the ancillary themes of Math Resources, Calculators, and Math Events. Learning Math Under Learning Math, there is an on "growing" set of topics. There are links to tutorial sites on the Web as well as on campus. Users have access to Web help pages and may find information about Math Placement and Math Classes, scholarships and other forms of financial aid. Teaching Math Here you will find applications to math from A to Z. Use LiveMath resources to visualize vectors, imaginary roots, three dimensional surfaces. The Math Calendar can locate the birthdays of mathematicians for any day of the year as well as provide information about many different calendars. Teaching Resources from prepared lesson plans to graph paper, and Real Data that can be used for mathematical modeling are also found under Teaching Math. To locate a WCC Math faculty member or find a text publisher, use the links provided under this section. Math Resources Found under Math Resources are Math Software Reviews, ERIC Resources, as well as The Online Math Center Library with links to math oriented web libraries, references, and journals. To locate professional mathematics organizations online, visit our Organizations page. To visit the homepage or math department homepage of many community colleges and four year universities try our Colleges page. Calculators Information about the specifications and operation of Casio, Texas Instrument, and Hewlett Packard graphing calculators and data gathering devices may be found on the Calculator page. There are links to tutorials and to sites from which programs may be downloaded to specific models of graphing calculators. Math Events For mathematical puzzles and contests, current research, and professional meetings, visit the Math Events page. The creation of the Online Math Center was funded through the U. S. Department of Education Title III Grant PO31A980143.
books.google.co.uk - This comprehensive three-part treatment begins with a consideration of the simplest geometric manifolds - line-segment, area, and volume as relative magnitudes; the Grassmann determinant principle for the plane and the Grassmann principle for space; classification of the elementary configurations of... mathematics from an advanced standpoint.
Elementary Statistics: A Step by Step Approach "Elementary Statistics: A Step by Step Approach" is for general beginning statistics courses with a basic algebra prerequisite. The book is non ...Show synopsis"Elementary Statistics: A Step by Step Approach" Minitab, and the TI-83 Plus and TI 84-Plus graphing calculators, computing technologies commonly used in such courses Elementary Statistics: A Step by Step Approach Easy to follow book. Very well prepared for an individual not knowledgeable in using Excel for statistics. I love the step by step Procedure Tables that show the process and the numerous
MATH 127: Precalculus IISolve problems using the distance formula and the pythagorean theorem. Compute trigonometric functions of special angles and use them to solve for the unknown part(s) of right triangles. Use the Laws of Sines and Cosines to solve for the unknown parts of triangles. Compute vector sums and differences. Solve trigonometric identities and equations. Graph trigonometric functions. Compute the values of inverse trigonometric functions. Graph equations and functions in polar coordinates. Use DeMoivre's theorem to find the powers and roots of complex numbers. III: Course Linkage Linkage of course to educational program mission and at least one educational program outcome. General Education Mission: This course addresses the fourth bullet under goal one of the college's mission to, "Provide instruction that contributes to a student's abilities to think critically and solve problems; to reason mathematically and apply computational skills." Math 127 satisfies the General Education Requirement for any degree or certificate program and addresses the following learning objectives of the General Education Requirement by ensuring that successful students: Are able to apply appropriate college-level mathematical skills to real life applications
Do the Math: Secrets, Lies, and Algebra Tess loves math because it's the one subject she can trust—there's always just one right answer, and it never changes. But then she starts algebra and is introduced to those pesky and mysterious variables, which seem to be everywhere in eighth grade. When even your friends and parents can be variables, how in the world do you find out the right answers to the really important questions, like what to do about a boy you like or whom to tell when someone's done something really bad? Will Tess's life ever stop changing long enough for her to figure it all out? Do the Math #2: The Writing on the Wall...
ELEMENTARY STATISTICS: A BRIEF VERSION is for introductory statistics courses with a basic algebra prerequisite. The book is non-theoretical, explaining concepts intuitively and teaching problem solving through worked examples and step-by-step instructions. In recent editions, Al Bluman has placed more emphasis on conceptual understanding and understanding results, along with increased focus on Excel, MINITAB, and the TI-83 Plus and TI-84 Plus graphing calculators; computing technologies commonly used in such courses. The 6th edition of Bluman, Elementary Statistics: A Brief Version provides a significant leap forward in terms of online course management with McGraw-Hill's homework platform, Connect Statistics – Hosted by ALEKS. Statistic instructors served as digital contributors to choose the problems that will be available, authoring each algorithm and providing stepped out solutions that go into great detail and are focused on areas where students commonly make mistakes. From there, the ALEKS Corporation reviewed each algorithm to ensure accuracy. The result is an online homework platform that provides superior content and feedback, allowing students to effectively learn the material being taught. show more show less List price: $151.00 Edition: 6th 2013 Publisher: McGraw-Hill Higher Education Binding: Trade Paper Pages: N/A Size: 8.75" wide x 10.75
Preface Modern computing tools like MAPLE (a symbolic computation package) and MATLAB® (a numeric and symbolic computation and visualization program) make it possible to use the techniques of scientific computing to solve realistic nontrivial problems in a classroom setting. These problems have been traditionally avoided, since the amount of work required to obtain a solution exceeded the classroom time available and the capabilities of the students. Therefore, simplified and linearized models ... [weiter lesen] Walter Gander Jiří Hřebíček Solving Problems in Scientific Computing Maple and MATLAB® From the reviews of previous editions: "... An excellent reference on undergraduate mathematical computing." American Mathematical Monthly "... manuals for such systems (Maple and MATLAB®) tend to use trivial examples, making it difficult for new users of such systems to quickly apply their power to real problems. The authors have written a good book to address this need... the book is worth b... [weiter lesen]
Number of places Schedule Part of programme Learning outcomes The overall goal is to give basic knowledge in Discrete mathematics, in particular a good knowledge in elementary combinatorics, knowledge of some abstract algebraic structure and the use of it, and knowledge of some selected topics in graph theory. After the course it is expected that the student will have achieved a better ability for treating and applying mathematics in general.
Calculators as an Aid to Problem Solving A common complaint among teachers is that students have great difficulty with computation and, what is worse, they are very weak in problem solving. Unfortunately this complaint is a self-perpetuating ill. Students who cannot succeed with arithmetic computation are constantly told to drill these skills and are rarely allowed to practice any problem-solving skills. Those who do go on to working on some elementary problems often do not get near an answer because of computational deficiencies. Their only exposure to problem solving is one of frustration, and they rarely realize success because of computational obstacles. Here the calculator can be of significant assistance. Selective use of the calculator to bypass potential computational barriers will allow students to concentrate on problem-solving skills without fear of meeting frustration previously caused by their computational deficiencies. Such activities should be carefully designed and monitored to be effective. After realizing success in problem solving, students should then be intrinsically motivated to conquer their computational deficiencies. Although continuously nurtured on typical textbook problems, students usually find them boring and unrealistic. Traditionally, textbook authors design the problems in a way that will make the arithmetic computations as simple as possible so as not to detract from the problem. Real-life situations frequently are quite different. The numbers used are generally not simple. With the aid of a calculator, a teacher can provide realistic situations for problem solving and not worry about computational distractions. A uniform-motion problem, for example, can involve fractional quantities and yield an answer that is not an integer and still cause no displeasure for the student who has a calculator available. Furthermore, students using a calculator can be encouraged to create problems based on their own experiences (e.g., calculating their average speed walking to school). New vistas are opened up when a calculator is used to assist in problem solving bypassing arithmetic. Problems in advanced secondary school mathematics courses can often involve extensive calculations. Not many years ago the slide rule or logarithms were used to solve such problems. Even Napier's rods and the abacus played a role at one point in the history of people's attempts to be free of the burden of onerous manual calculations. The abacus is still used in some parts of the less technologically advanced world. Today, the logical method of computation at this level is the calculator. A scientific calculator (i.e., one that, among other features, includes trigonometric functions) and a graphing calculator are very useful aids to instruction, but by no means replace instruction.
The main goal of the calculus course is to explain the basic principles and methods of higher mathematics that are necessary for the study of computer science. The practical aspects of applications of these methods and their use in solving concrete problems (including the application of contemporary mathematical software in the laboratories) are emphasized. Description: The limit and the continuity of a function. The derivative. Partial derivatives. Basic differentiation rules. The chain rule. The elementary functions. Applications of derivatives. Extrema for functions (of one and of several variables). Indefinite integral. Techniques of integration. The Riemann (definite)integral. Multiple integrals. Applications of integrals. Infinite sequences and infinite series. Taylor polynomials. Fourier series. Learning outcomes and competences: The ability of orientation in the basic problems of higher mathematics and the ability to apply the basic methods. Solving problems in the areas cited in the annotation above by using basic rules. Solving these problems by using modern mathematical software. Syllabus of lectures: Limit and continuity of a function of one and of several variables. Derivative of a function. Partial derivative. Derivative rules. Derivative of composite function. Differential of functions of one and several variables. Mean value theorem. L'Hospital's rule. Behaviour of continuous and differentiable function. Extrema of function of one and several variables, implicit functions (informatively).
Middle Years Program. All examples and exercises take an international viewpoint, giving students an opportunity to learn Mathematics with a global perspective. The content is appropriate for international curricula and will meet the needs of all middle school students studying Mathematics. This is the first book in the five book International Mathematics for the Middle Years series. Each full-colour student book in the series comes with an interactive student CD and includes access to online resources for both teachers and students. Table of contents Beginnings in Number Working Mathematically: Applying Strategies Number: Its Order and Structure Decimals Directed Numbers and the Number Plane Fractions, Percentages and Probability Calculators Patterns and Algebra Further Algebra Angles Shapes Measurement: Length and Time Area and Volume Using Geometrical Instruments Sets Features & benefits Well graded exercises have colour-coded questions to clearly identify the level of difficulty, allowing flexibility within the classroom. Worked examples are used extensively throughout the book and are easy for students to identify. Investigations encourage students to seek knowledge and develop research skills Assessment Grids ease the task of assessment for the teacher and provide students with guidelines for understanding the criteria required to succeed. ID Cards, Mathematical Terms and Reading Mathematics all assist in the development of mathematical literacy. Interactive student CD - free with every coursebook An electronic version of the book with links to Worksheets, Technology Applications and further enrichment and review exercises Author biography Pearson takes great pride in our authors. We source authors and contributors that are industry leading experts, with extensive experience of teaching and learning in their fields, from every state of Australia. We commission only the best authors who offer valuable insights and something unique to bring to the project. The authors of International Mathematics for the Middle Years include: Alan McSeveny Rob Conway Steve Wilkes Michael Smith International Consultant Michael Smith has extensive experience teaching mathematics in IB and international schools in Singapore, Sri Lanka, Vietnam, China and Australia. Target audience Suitable for students studying the International Baccalaureate Middle Years Program. The IB Middle Years Program is intended for students aged 11 to 16 years.
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Toolbar Click on the toolbar buttons to insert common math symbols and expressions into the Problem Editor. If the symbols do not appear, please activate JavaScript in your browser. Problem Editor Type your problem into MyAlgebra using this textbox. You can insert special math symbols and expressions using the MyAlgebra Toolbar, and/or manually enter in common expressions using the keyboard. A preview of the mathematically formatted problem appears underneath the textbox. Math Format The text that is entered into the Problem Editor textbox is formatted and displayed in the Math Format section, just as it appears in your math textbook. To view the problem in math format, click the Show button. If you click the Show button and the preview does not appear, please activate JavaScript in your browser. Topic Selector When entering a problem, the topics that can be used to solve your problem are automatically displayed in this dropdown list. When the problem has been entered in correctly, select the topic that most closely matches the topic you are looking for and click the Answer button. If no topics appear, it is possible that the problem has not been entered in correctly (in this situation, you can click the Answer button for more information), or JavaScript must be activated in your browser. Answer Button After a problem has been entered in and a topic has been selected, click the Answer button. If additional information is needed (such as which variable to solve for, etc.) you will be prompted after you click this button. If the input has not been entered in correctly and no topics are selected, clicking the Answer button will provide information on how to correct the input. 2. Examples You can generate various example problems by selecting a topic from the Example Problems window (image shown below). This window is located next to the Enter a Problem screen. 3. Keyboard Input Type How to Enter Numbers 0-9 Variables a-z Plus + Minus - Multiply * Divide/Fraction / Decimal Point . Parenthesis ( ) Brackets [ ] Absolute Value \| \| Exponent ^ Greater Than or Equal To >= Less Than or Equal To <= Square Root sqrt(?) Nth Root root:N:(?) Function f(x) Piecewise Function f(x)=piecewise[?_?] Matrix matrix[?,?,?_?,?,?_?,?,?] Pi Symbol [pi] Theta Symbol [theta] Union Symbol [union] Intersection Symbol [intersection] Base 10 Logarithm log(?) Base N Logarithm log[N](?) Natural Logarithm ln(?) 4. Frequently Asked Questions (FAQ) Q: How do I group multiple terms in the numerator and/or denominator of a fraction, under a radical, or in an exponent? A: Use parenthesis to group multiple terms. For instance, (x+1)/(x-2) will group x+1 in the numerator of the fraction and x-2 in the denominator of the fraction. The same technique can be used to group terms under a radical and in an exponent. Q: How do I enter fractional exponents? A: Use parenthesis to enter fractional exponents. For example, x^(1/2) will group 1/2 in the exponent. Q: How do I enter in [a certain type of problem]? A: Please use the Example Problems window to browse and generate example problems available in each subject.
Algebra Published by Facts on File ALGEBRA, Revised Edition describes the history of both strands of algebraic thought. This updated resource describes some of the earliest progress in algebra as well as some of the mathematicians in Mesopotamia, Egypt, China, and Greece who contributed to this early period. It goes on to explore the many breakthroughs in algebraic techniques as well as how letters were used to represent numbers. New material has been added to the chapter on "modern" algebra, a type of mathematical research that continues to occupy the attention of many mathematicians
This course is a continuation of Math 2030.03 with an emphasis on foundations and the theory of vector spaces and linear transformations. Additional topics include symmetric and orthogonal transformations, bilinear forms, inner product spaces, and various applications in mathematics, physics and computer science.
Student Solutions Manual for Intermediate Algebra for College Students Worksheets for Classroom and Lab Practice for Intermediate Algebra for College Students Summary This book provides a comprehensive coverage of intermediate algebra to help students prepare for precalculus as well as other advanced math. The material will also be useful in developing problem solving, critical thinking, and practical application skills. Real World Data and Visualization is integrated. Paying attention to how mathematics influences fine art and vice versa, the book features works from old masters as well as contemporary artists.
From time to time, not all images from hardcopy texts will be found in eBooks, due to copyright restrictions. We apologise for any inconvenience. Description THE ONLY MATHS RESOURCE INCORPORATING ALL STRANDS OF THE NEW NZ CURRICULUM Pearson Mathematics Level 4 Pearson Mathematics Level 4 is divided into two books, 4a and 4b. Students working at Level 4a have good additive strategies. Their knowledge of multiplication and division facts becomes fluent through the use of multiplicative strategies and developing proportional reasoning. Students' understanding of the properties of number operations is extended into algebraic equations. Geometry & Measurement, and Statistics provide contexts for using number operations and algebra. Statistical thinking is developed using multivariate data and a range of data displays, including the use of technology. Mathematics is used to solve problems. This series of books provides real context for students to extend and use their mathematical knowledge. Pearson Mathematics 4a Teachers' Guide The Teachers' Guide provides the tools to plan a mathematics programme to meet the needs of all students. The book is divided into units of work with curriculum links and learning outcomes for each chapter in a unit. Teacher guidance is provided on how to use the pages in the pupil book. There are assessment tasks and a record sheet for tracking individual students' progress are, as well as answers to all questions. Links to appropriate "Figure it Out" activities for each chapter are also included. Pearson Mathematics There is a very good philosophy behind the new Mathematics and Statistics curriculum. The aim of Pearson Mathematics is to bridge the gap between that document and classroom practice. The series emphasises real situations for using and applying mathematics. Two major features of these books are the mini projects and the challenges. Mini projects These are open-ended mathematical applications. Teachers need to be able to stand back and behave as facilitators rather than controllers. Children need to be allowed to make mistakes; trial and error is a recognised problem-solving strategy. Likewise the ability to communicate in mathematics is important and the mini projects allow for a variety of ways of communicating. They allow the children to apply their mathematical vocabulary, signs and symbols. Challenges These are an added motivation for generally, but by no means exclusively, the more able students. Teachers' Guides The Teacher's Guides are the centre of this series. They provide a framework and developmental structure to the teaching of mathematics. Each unit specifies particular Achievement Outcomes taken from the Mathematics and Statistics Curriculum. Each chapter has specific learning outcomes. They provide the teacher with some guidance on how to go about teaching specific objectives. The Guides may give suggestions on how to introduce a concept or provide ideas on how to extend or give further practice. A copy of each pupil's page is included in the Teachers' Guide as an aid to planning specific activities. Author biography Charlotte Wilkinson helps teachers develop exciting Maths programmes in their schools. She has an Honours degree specialising in the teaching of Primary Mathematics, combined with 20 years classroom experience, of which 7 years were at senior management level, followed by 4 years working with teachers on the Numeracy Project for the University of Waikato. She offers professional development and training in the teaching and learning of Primary Mathematics. Charlotte also designs and publishes Wilkie Way Numeracy Products.
Introduction What is Maple? Maple is a computer program for people doing mathematics. Using Maple to do your calculations should make the work more interesting, allow you to focus more on the concepts, and help you to avoid mistakes in calculation. How to use this tutorial This document is intended to get you started, and show you how to learn more. It is intended to be used while sitting at a terminal running Maple in a windowed environment, by entering the commands and thinking about the output. To use any software effectively, some knowledge of the computer's operating system is required. This document will assume that you are already familiar with the rudiments of windows -- things like point, click and drag, how to use menus, and the standard way to open and close files. Maple is essentially the same on Microsoft Windows, Macintosh, and the X windows system, but there are minor differences in their interface. This tutorial assumes that you are running Maple in one of the previously listed environments. If you are using a character-based terminal, for example in a telnet session, the Maple commands will be the same although the interface is different (no mouse, no menus, and typewriter graphics). In order to be more broadly understood, we don't include some things which require a lot of mathematical knowledge, for example linear algebra. Subject oriented guides are also available -see our By Subject page. We'll be using some standard conventions throughout this document. Example Explanation File -> Open Choose the file menu, and select Open. a := 5; Input to be typed at the Maple prompt. a := 5 Output from Maple. An important tip. Where to find Maple Maple is available for many different kinds of computers at Indiana University Bloomington. Finding your way around the window The Toolbar First of all, locate the toolbar at the top of the window. On Windows, it looks like this: Other operating systems have a similar toolbar. Every time you work with maple, you will use a "worksheet". The worksheet is the big, blank area in the middle of the screen. You may have more than one worksheet open at a time. The following toolbar buttons let you work with the worksheet. The first five buttons on the toolbar, in order, do the following: open a new, blank worksheet; open an existing worksheet; open a hyperlink; save the current worksheet; and print the current worksheet. The next three buttons are the standard cut, copy, and paste functions. The next two buttons let you "undo" and "redo" your last action. The next three buttons let you manage what "mode" Maple is currently in. The standard mode is represented by the capital Sigma button. This means that anything you type will be considered to be mathematical input. If you click the capital T, Maple switches to Text mode. Anything you type will be considered as text commentary, and Maple won't try to treat it as math. To switch back to math input mode, click the [> button. Notice that the prompt in the worksheet window changes to let you know what mode you are in. The next two buttons let you un-indent and indent lines in your worksheet. The next button has a stop sign on it. It is used as a "panic" button. If you start a computation and you would like to stop, click the stop sign. (Cntl-C will also do this.) The next three buttons control the amount of zoom. The next button displays non-printing characters in the worksheet. The next button expands the active worksheet to fill the available space. The last button clears all variables of their values. It is the same as typing the maple command restart; The Kernel The kernel is the part of Maple that does the actual calculation. The kernel is invisible, but you do need to know about it. You talk to the kernel by typing mathematical statements and commands at the Maple prompt. Here is an example. If you're using a graphics-enabled browser, you'll notice that input appears in red. Output from the kernel appears in blue, with variable names in italics. The Maple prompt looks like [>. The kernel will execute when you press the Enter key. The kernel decides what to execute by looking at the current execution group. An execution group is a set of input lines connected (along the left-hand margin) by a long, thin [. When you press Enter anywhere in the execution group, the entire group is executed. By default, each input line (along with its output) is an execution group unto itself. You can join execution groups together using the F4 key, or split them apart using the F3 key. Execution only occurs when you press the Enter key, or if you choose Edit->Execute->Worksheet. Execution does not occur when you open a worksheet. Worksheets The worksheet is the basic unit of work in Maple, like a document in a word processor. A worksheet stores every line of input and every line of output. To save your worksheet, choose File->Save As. To open a worksheet, choose File->Open. You may have more than one worksheet open at a time. However, they all share the same kernel. So any work you do in one worksheet is accessible from another open worksheet. This can lead to confusing results. Using the Help System Maple has an extremely in-depth help system. To access it, choose Help -> Topic Search. Enter the word you are looking for (e.g., matrix) and you should see a list of topics. Clicking on one will open a "help browser", a window that lets you wander through related topics. We suggest that you "surf" the help system - casually browse, looking at anything that seems interesting. That way you will have some idea of what is available to you in the future. If you know exactly what you need help on, you may also type (in Maple) ? simplify (for example) to get help on the Maple command "simplify". A very useful feature of the help system is the examples section. Use the Edit->Copy Examples menu command to copy the examples. Then switch to your worksheet (or open a fresh one) and use the Edit->Paste menu command. Now you can execute the examples, and experiment until you are comfortable with the commands. Maple Syntax and Built-in Data Capabilities Syntax As with any computer language, Maple has its own syntax. As a new user of Maple, you can save yourself a lot of head-scratching if you get to know these symbols. Enter the commands given or make up similar problems. Symbol Description Examples Sample Output ; End-of-line. Tells Maple to process the line and show the output. hello; hello : End-of-line. Tells Maple to process the line and hide the output. hello: := Assignment. Lets you assign values to variables. a := 3; a; a := 3 3 +, - Addition, subtraction. 1 + 3; 1 - 3; 4 -2 , / Multiplication, division 3412; 1236/3; 7/3; 1236 412 7/3 ^, sqrt Power, square root 2^3; sqrt(2); 2^(1/2); 8 evalf, . Floating-point (decimal) evaluation evalf(7/3); 7.0/3; 2.333333333 2.333333333 I,Pi Imaginary unit, Pi. 2 + 3I; (2I)^2; evalf(Pi); 2+3I -4 3.141592654 %, %% Recall the last output, recall the second-to-last output, etc. %; %%%; 3.141592654 -4 Some syntactical caveats: Maple is case sensitive. foo, Foo, and FOO are three different things. Maple requries you to show multiplication with the * character. Entering xy gives the product of x and y, but entering xy gives one variable with the name xy. To get the constant e use exp(1). Using the % operator can give confusing results. It always returns the last output from the Kernel, which may have nothing to do with where the cursor is (or which worksheet is active). If Maple doesn't recognize something, it will assume it is a variable. For example, typing i^2 will give you i2, while you may have wanted -1. You can move your cursor up to a previous line, press Enter, and the line will re-execute. When copying and pasting using a mouse, by sure to also highlight the execution group symbol ([). If you don't, the lines will be pasted in reverse order due to a bug. Spaces are optional. Greek letters may be entered by spelling their name. For example, alpha is always displayed as , and Gamma is displayed as (note upper-case). Built-in Data Capabilities Maple can handle arbitrary-precision floating point numbers. In other words, Maple can store as many digits for a number as you like, up to the physical limits of your computer's memory. To control this, use the Digits variable. sqrt(2.0); 1.414213562 Digits := 20: sqrt(2.0); 1.4142135623730950488 Maple sets Digits to be 10 by default. You can also temporarily get precision results by calling evalf with a second argument. evalf(sqrt(2), 15); 1.41421356237310 Large integers are handled automatically. Creating your own Mathematical Functions We have been working with expressions so far. Maple also supports the mathematical notion of a function. To define a function, you must specify a rule for going from one number to another. Consider the following commands: f := x^2; f := x2 This defines f to be an abbreviation for the expression x2. f := x -> x^2; f := x -> x2 This defines f to be a function, such that f(x) = x2. f(3); f(t); 9 t2 The function works as standard notation. A common mistake is to write f(x) := x^2;. This does not define a function. Instead, it makes the four characters on the left an abbreviation for the three characters on the right. Functions are often more useful than expressions. However, many Maple commands (for example, diff) expect an expression as input. If f := x -> x^2, then diff(f,x); doesn't work. However, diff(f(x),x); will work, since f(x) produces the expression x2. To convert an expression into a function, use the unapply command. p := x^3 + 1; p := x3 + 1 f := unapply(p, x); f(3); f := x -> x3 + 1 28 Using packages When you first load Maple, it knows how to execute several different functions. For example, we used the evalf and simplify functions without having to load them first. Maple comes with a huge number of other useful functions, bundled up in units known as packages. Maple has a modular design -- not all of its functions are loaded at startup. The more specialized capabilities must be explicitly loaded. For example, if you want to work with matrices and vectors, you would want to load the linalg package. with(linalg); The output from with is a list of the new commands that you now have access to. If you don't want to see the list (which can be rather long), use a colon as your end-of-line marker. with(linalg): Even if you use a colon, you may see warning messages. These usually indicate that a command has a new definition. In most cases, this should not be a concern. Some Maple functions are not in packages; instead, they are stored in the older library format. For example, to add the multivarate Taylor series function, mtaylor, use the command readlib(mtaylor); Go exploring among the packages. These are some of the most commonly used packages: student Includes commands for use in a classroom/homework setting. plots Tools for graphics, 3-d, animation, and visualization. linalg Matrices, vectors, and many linear algebra functions. detools Tools for working with ODEs and PDEs. To get a comprehensive list of available packages, choose Help->Introduction, then browse to Mathematics->Packages->Overview. Basic Plotting Maple can produce graphs very easily. Here are some examples, showcasing the basic capabilities. plot( x^2, x=-2..2); A basic plot. plot( x^2, x=-2..2, y=-10..10); A plot with vertical axis control. plot([x, x^2, x^3], x=-2..2); Plot multiple expressions by enclosing them in brackets. plot([sin(t),cos(t),t=0..3Pi/2]); Parametric plots include the plotting range in the brackets. plot3d(4-x^2-y^2, x=-3..3, y=-2..2); A basic 3-d plot. smartplot3d(x^2-y^2); Using smartplot to let maple set it's own scaling. You can control where plots are drawn by choosing Options->Plot Display->Inline or Window. Either way, if you select a plot with the mouse, you can use the toolbar to change the rendering style, axes, and lighting. To copy a plot to the clipboard (as a graphics file), right-click (or Option-Click for Mac users) on the plot and select Copy. Look into these commonly used plotting commands: textplot, textplot3d Draw text anywhere in a plot display Display several plots at once animate, animate3d Adds a dimension of time to your plot. plotoptions Various options, including line weight, color, sampling, etc. Further Reading For further guidance as a new user, try the tour. Choose Help->New User's Tour
More Algebra by Design Second Edition by Russell F. Jacobs Our earlier Algebra by Design contains topics of elementary algebra usually studied in the first semester of algebra. More Algebra by Design contains more advanced topics often taught in the second semester. The second edition, new in 2011, includes four new exercises on the slope/intercept form of a line and linear inequalities in the coordinate plane. Click here to download the table of contents in pdf format. Click here to download a sample activity in pdf format.
second semester of algebra 1 credit retrieval course covers these Washington state standards: linear functions, equations, and inequalities, quadratic functions and equations, data and distributions. Students begin with a diagnostic assessment on a Washington state standard within the Compass Learning program (CLO) and then based upon those results an individual learning plan is set up for the student. The student works the lessons needed and then demonstrates mastery of the skills in an assessment that must be passed before moving on to the next standard. Because high school students have unique needs and experiences, CompassLearning ensures that students know where they are while challenging them to grow. Odyssey High School Math focuses on foundational skills to support learners, emphasizes repetition and practice of key skills, reinforces study habits, including note-taking, to sharpen studentsí comprehension, and covers National Mathematics Advisory Panelís concepts for success in algebra.
COMPLETE MATH PRODUCTION PACKAGE --- DISCONTINUED. (Verified 02/2009) RETAINED IN DATABASE FOR REFERENCE. --- The Complete Math Production Package is a mathematical Braille translation program designed for use by individuals who are blind or have low vision. This package includes the Duxbury Braille Translator for Windows (see separate entry) and provides the additional capability of handling all types of equations from simple arithmetic to complex science and engineering notation....[More Information] MATHEMATIX --- DISCONTINUED. (Verified 3/2001) RETAINED IN DATABASE FOR REFERENCE. --- MathematiX is a software program that works with BEX (see entry) to enable printing or verbalizing of Nemeth Code mathematical braille data. If a speech synthesizer is used, literary text is spoken as words and mathematical material is spelled out sign for sign. MathematiX can also be used to prepare regular-print documents that include text and fractions, square roots, chemical symbols, and other technical material. Mat
Applied Mathematics A reader has identified this book as an undeveloped draft or outline. You can help to develop the work, or you can ask for assistance in the project room. Applied Mathematics is the branch of mathematics which deals with applications of mathematics to the real world problems, often from problems stemming from the fields of engineering or theoretical physics. It is differentiated from Pure Mathematics, which deals with more abstract problems. There is also something called Applicable Mathematics, which deals with real world problems which need the techniques and mindset usually used in Pure Mathematics. These distinctions do not really become apparent during school level mathematics.
Download Next: Describing Patterns Chapter 1: Algebraic Thinking Chapter Outline Loading Content Chapter Summary Description This chapter considers the basic principles surrounding algebra, including patterns, expressions, and equations. Additionally, students are introduced to the metric system and measurement as well as strategies for practical problem solving.
TEXTBOOK* Knot Theory Charles Livingston The author's book would be a good text for an undergraduate course in knot theory ... The topics in the book are nicely tied together...The topics and the exercises together can provide an opportunity for many undergraduates to get a real taste of what present day mathematics is like. — Mathematical Reviews This monograph by Charles Livingston is a most accessible introductory survey of serious, mathematical twentieth century knot theory...At a time when non-trivial topics are required for so many student projects, no school library with a mathematics section should be without this book. It is a thoroughly well written, well thought out account of a subject of current mathematical research which anyone of a mathematical orientation can enjoy. — Mathematical Gazette Knot Theory is a concise, comprehensive, and well-written introduction to the definitions, theorems, techniques, and problems of knot theory ... the expository sections of the text are quite well organized. — The Mathematics Teacher Knot Theory, a lively exposition of the mathematics of knotting, will appeal to a diverse audience from the undergraduate seeking experience outside the traditional range of studies to mathematicians wanting a leisurely introduction to the subject. Graduate students beginning a program of advanced study will find a worthwhile overview, and the reader will need no training beyond linear algebra to understand the mathematics presented. The interplay between topology and algebra, known as algebraic topology, arises early in the book, when tools from linear algebra and from basic group theory are introduced to study the properties of knots. Livingston guides you through a general survey of the topic showing how to use the techniques of linear algebra to address some sophisticated problems, including one of mathematics' most beautiful topics, symmetry. The book closes with a discussion of high-dimensional knot theory and a presentation of some of the recent advances in the subject — the Conway, Jones, and Kauffman polynomials. A supplementary section presents the fundamental group, which is a centerpiece of algebraic topology. A hardcover version of this book is available in the MAA Store. * As a textbook, Knot Theory does have DRM. Our DRM protected PDFs can be downloaded to three computers.
Mathematics is the means of looking at the patterns that make up our world, appreciating the intricate and beautiful ways in which they are constructed and realised. Numeracy is the means of making that knowledge useful. Mathematics contributes to the school curriculum by developing students' abilities to calculate, to reason logically, and to solve problems. It is also important in everyday living, in employment, and in public decision-making. The College curriculum enables pupils to build a secure framework of mathematical reasoning, which they can use and apply with confidence. The subject transcends cultural boundaries and its importance is universally recognised. Mathematics helps us to understand and change the World.
The fun and easy way® to understand the basic concepts and problems of pre-algebra Whether you're a student preparing to take algebra or a parent who needs a handy reference to help kids study, this easy-to-understand guide has the tools you need to get in gear. From exponents, square roots, and absolute value to fractions, decimals, and percentsThis third edition of Mathematica by Example is completely compatible with recent Mathematica versions. Highly readable and informative, this volume is geared toward the beginning Mathematica user, and focuses on the most often used features of this powerful tool. The book covers popular applications of mathematics within different areas including... more...
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Synopsis outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics. Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics?, Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts. Brought up to date with a new chapter by Ian Stewart, What is Mathematics?, Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved. Formal mathematics is like spelling and grammar--a matter of the correct application of local rules. Meaningful mathematics is like journalism--it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature--it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature--it opens a window onto the world of mathematics for anyone interested to view. Found In eBook Information ISBN: 97801997548
A First Course in Functional Analysis. Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts John Wiley and Sons Ltd, May 2008, Pages: 308 Requiring only a preliminary knowledge of elementary linear algebra and real analysis, A First Course in Functional Analysis provides an introduction to the basic principles and practical applications of functional analysis. Key concepts are illustrated in a straightforward manner, which facilitates a complete and fundamental understanding of the topic. This book is based on the author's own class-tested material and uses clear language to explain the major concepts of functional analysis, including Banach spaces, Hilbert spaces, topological vector spaces, as well as bounded linear functionals and operators. As opposed to simply presenting the proofs, the author outlines the logic behind the steps, demonstrates the development of arguments, and discusses how the concepts are connected to one another. Each chapter concludes with exercises ranging in difficulty, giving readers the opportunity to reinforce their comprehension of the discussed methods. An appendix provides a thorough introduction to measure and integration theory, and additional appendices address the background material on topics such as Zorn's lemma, the Stone-Weierstrass theorem, Tychonoff's theorem on product spaces, and the upper and lower limit points of sequences. References to various applications of functional analysis are also included throughout the book. A First Course in Functional Analysis is an ideal text for upper-undergraduate and graduate-level courses in pure and applied mathematics, statistics, and engineering. It also serves as a valuable reference for practitioners across various disciplines, including the physical sciences, economics, and finance, who would like to expand their knowledge of functional analysis. Preface. 1. Linear Spaces and Operators. 1.1 Introduction. 1.2 Linear Spaces. 1.3 Linear Operators. 1.4 Passage from Finite- to Infinite-Dimensional Spaces. Exercises. 2. Normed Linear Spaces: The Basics. 2.1 Metric Spaces. 2.2 Norms. 2.3 Space of Bounded Functions. 2.4 Bounded Linear Operators. 2.5 Completeness. 2.6 Comparison of Norms. 2.7 Quotient Spaces. 2.8 Finite-Dimensional Normed Linear Spaces. 2.9 Lp Spaces. 2.10 Direct Products and Sums. 2.11 Schauder Bases. 2.12 Fixed Points and Contraction Mappings. Exercises. 3. Major Banach Space Theorems. 3.1 Introduction. 3.2 Baire Category Theorem. 3.3 Open Mappings. 3.4 Bounded Inverses. 3.5 Closed Linear Operators. 3.6 Uniform Boundedness Principle. Exercises. 4. Hilbert Spaces. 4.1 Introduction. 4.2 Semi-Inner Products. 4.3 Nearest Points and Convexity. 4.4 Orthogonality. 4.5 Linear Functionals on Hilbert Spaces. 4.6 Linear Operators on Hilbert Spaces. 4.7 Order Relation on Self-Adjoint Operators. Exercises. 5. Hahn–Banach Theorem. 5.1 Introduction. 5.2 Basic Version of Hahn–Banach Theorem. 5.3 Complex Version of Hahn–Banach Theorem. 5.4 Application to Normed Linear Spaces. 5.5 Geometric Versions of Hahn–Banach Theorem. Exercises. 6. Duality. 6.1 Examples of Dual Spaces. 6.2 Adjoints. 6.3 Double Duals and Reflexivity. 6.4 Weak and Weak- Convergence. Exercises. 7. Topological Linear Spaces. 7.1 Review of General Topology. 7.2 Topologies on Linear Spaces. 7.3 Linear Functionals on Topological Linear Spaces. 7.4 Weak Topology. 7.5 Weak- Topology. 7.6 Extreme Points and Krein–Milman Theorem. 7.7 Operator Topologies. Exercises. 8. The Spectrum. 8.1 Introduction. 8.2 Banach Algebras. 8.3 General Properties of the Spectrum. 8.4 Numerical Range. 8.5 Spectrum of a Normal Operator. 8.6 Functions of Operators. 8.7 Brief Introduction to C-Algebras. Exercises. 9. Compact Operators. 9.1 Introduction and Basic Definitions. 9.2 Compactness Criteria in Metric Spaces. 9.3 New Compact Operators from Old. 9.4 Spectrum of a Compact Operator. 9.5 Compact Self-Adjoint Operators on Hilbert Spaces. 9.6 Invariant Subspaces. Exercises. 10. Application to Integral and Differential Equations. 10.1 Introduction. 10.2 Integral Operators. 10.3 Integral Equations. 10.4 Second-Order Linear Differential Equations. 10.5 Sturm–Liouville Problems. 10.6 First-Order Differential Equations. Exercises. 11. Spectral Theorem for Bounded, Self-Adjoint Operators. 11.1 Introduction and Motivation. 11.2 Spectral Decomposition. 11.3 Extension of Functional Calculus. 11.4 Multiplication Operators. Exercises. Appendix A Zorn's Lemma. Appendix B Stone–Weierstrass Theorem. B.1 Basic Theorem. B.2 Nonunital Algebras. B.3 Complex Algebras. Appendix C Extended Real Numbers and Limit Points of Sequences. C.1 Extended Reals. C.2 Limit Points of Sequences. Appendix D Measure and Integration. D.1 Introduction and Notation. D.2 Basic Properties of Measures 258 D.3 Properties of Measurable Functions. D.4 Integral of a Nonnegative Function. D.5 Integral of an Extended Real-Valued Function. D.6 Integral of a Complex-Valued Function. D.7 Construction of Lebesgue Measure on R. D.8 Completeness of Measures. D.9 Signed and Complex Measures. D.10 Radon–Nikodym Derivatives. D.11 Product Measures. D.12 Riesz Representation Theorem. Appendix E Tychonoff's Theorem. Symbols. References. Index. "Graduate and advanced undergraduate students in mathematics and physics will appreciate this book as a useful and stimulating contribution to the vast array of textbooks on the subject.." (Zentralblatt MATH, October 2010) "A First Course in Functional Analysis is an ideal text for upper-undergraduate and graduate-level courses in pure and applied mathematics, statistics, and engineering. It also serves as a valuable reference for practioners across various disciplines, including the physical sciences, economics, and finance, who would like to expand their knowledge of functional analysis." (Mathematical Reviews, 2009c) "It is written in a very open, nontelegraphic style, and takes care to explain topics as they come up. Recommended." (CHOICE Oct 2008) "This is an excellent text for reaching students of diverse backgrounds and majors, as well as scientists from other disciplines (physics, economics, finance, and engineering) who want an introduction to functional analysis." (MAA Reviews Oct 2008)
Math in the News: Algebra Double-click any word to see the explanation. Loading... Algebra is a branch of mathematics concerning the study of structure, relation and quantity. Together with geometry, analysis, combinatorics Al
The American Mathematics Competitions (AMC) seek to increase interest in mathematics and to develop problem solving abilities through a series of friendly mathematics competitions for junior (grades 8 and below) and senior (grades nine through twelve) high school students. This is Michigan's site for the AMC 8, the competition designed for grades 8 and below. On this site you will find results from the last AMC 8 in Michigan as well as registration information for the next offering of the competition. A cordial invitation is extended to your school to participate in the Seventeenth Annual AMC 8 to be held on Tuesday, November 22, 2001. A registration form for next year's examination is available at this site. We encourage you to register your school for next year's exam as soon as possible! The AMC 8 covers material normally associated with the middle school mathematics curriculum. In additional to seventh and eighth grade students, each year an increasing number of accelerated fifth and sixth grade students take part in the AMC 8. The subject matter includes (but is not limited to) such topics as: Estimation Reading and interpreting graphs Percent Spacial Visualization Graph Theory Everyday Applications The questions range in difficulty from easy to very difficult in order to appeal to a broad range of students. No problem requires the use of algebra. Even though calculators are allowed, no problem requires the use of a calculator. The AMC 8 is a 25-question, 40-minute multiple choice contest with no penalty for guessing. A student's score is the number of problems solved correctly. For general information on the American Mathematics Competitions, please visit the national AMC web site at For additional information specific to the AMC 8, please visit The American Mathematics Competitions are sponsored by the following national organizations: Major Contributors Mathematical Association of America The Akamai Foundation University of Nebraska, Lincoln Office of Naval Research Army Research Office The Microsoft Corporation Contributing Members Society of Actuaries Mu Alpha Theta National Council of Teachers of Mathematics Casuality Actuarial Society American Statistical Association American Mathematical Association of Two-Year-Colleges American Mathematical Society American Society of Pension Actuaries Consortium of Mathematics and its Applications Pi Mu Epsilon National Association of Mathematicians School Science and Mathematics Association Clay Mathematics Institute INFORMS The National Association of Secondary School Principals (NASSP) placed the AMC 8 on the NASSP National Advisory List of Contests and Activities for 2001-02. The Michigan AMC 8 is co-directed by Drs. Ricardo Alfaro and Kristina Hansen, both faculty members at the University of Michigan-Flint. Please feel free to contact either of them with any questions you may have about the exam.
Since I started university, almost every exam I've had in mathematics have ended up as failed mostly due to my lack of using proper "syntax" on paper, written by hand. Where can I learn the standard way of writing mathematics, beginning with the basics? Does this make sense? Is there a standard "uniform" syntax, or does it depend on locale - country from country? EDIT: With syntax I mean the way you write down your logic on paper - for instance, how you should put up a solution for display; what format to use, when to use deduction/implication arrows, how your answer should be represented etc. When to tell whether you are you allowed to skip mental steps and so on? How many mental steps you are allowed to skip really depends upon your level. The more basic your level, the more mental steps you should include. – Fredrik MeyerDec 6 '10 at 19:24 3 My basic rule of thumb as I convey to my students is: "If you have to stop and think about it before writing down the final answer, then you need to write down those mental steps." – Arturo MagidinDec 6 '10 at 19:28 4 Answers Learning to write mathematics properly is much like learning to write any language properly, only more so because such a premium is placed on logical organization and clarity. Mathematics, both the part that is written in words and the part that is written in symbols, is attempting to convey meaning. When you write and read symbols, think about what they say when you read them out loud. Every time you see the symbol $=$, remember that the symbol has a pronunciation when you read it, and it says "is equal to". So if you write things like $$2x = 4 = \frac{4}{2}=2,$$ (which I see far too often on exams) then you are saying "twice $x$ is equal to four, which is equal to four halves, which is equal to $2$", which of course is false and liable to cost you points, even though you probably don't actually think that $4$ and $\frac{4}{2}$ are equal. Remember, first and foremost, that every symbol has a meaning and a pronunciation. Unless you recognize that, you won't be able to get very far. So first you need to be clear on what you want to say, and then make sure that what you wrote actually conveys that meaning and not other meanings. If you can do that, even if it is with "plain English", you will have gotten over more than half the problem. That said, mathematics is also a technical language with a number of conventions and jargon. The very best thing you can do to become familiar with, and good at using those conventions, is to read a lot of mathematics, with an eye towards understanding what is written and how the language helps that understanding (just like doing a lot of reading is one of the best ways to improve one's spelling). A close second is to read books that are meant to help introduce you to proofs and logical arguments, usually with subtitles like "first course in advanced mathematics" or "introduction ot abstract/advanced mathematics". Find out what the "Intro to proofs" course is at your school, and look at the textbook they use. One important thing is not to simply try to mimic the language you see: that will result in the mathematical equivalent of saying "Buenos días. Yo quiero estación de tren ser, por favor" when trying to ask for directions to the train station ("Good morning. I want be train station, please.") You want to keep an eye on the meaning that the words are conveying, and how that particular choice of words (and even the order of the words) matters. Notice, for instance, that saying "For every $x$ there is a $y$" is not the same thing as saying "There is a $y$ such that for every $x$...", even though they may seem very similar when thought of in English. So: always think first about what you are trying to say and make sure you say that. Read what you've written, pronouncing every symbol to yourself to make sure you aren't saying that you "want to be train station". And read your books and professors' notes to see how the language works and become familiar with it. Added: It seems I rather badly misinterpret the true thrust of your question (despite the fact that you seem to have "accepted" my answer). In so far as what steps to add or what steps to skip, as has been pointed out, it depends on your level. I would not object to a student in my graduate abstract algebra class going from $x(x+1)(x+2)$ directly to $x^3+3x^2+2x$ (or even not writing out the computations before using it!) but I would definitely request a precalculus student to write out how he got to that final answer. If you have to stop and think carefully about what the answer is, then you should not skip the step and write it down. For a particular class, look at the textbook and which steps it works out explicitly and which steps it skips. Look at what steps your professor works out explicitly and which steps he skips. You'll want to not stray too far from them as far as skipping more steps (though of course you can always skip fewer steps if you are unsure about a calculation/argument). Lovely answer, and I believe what you say is true! I'll try and scour through my math books to see if I can find the hidden answer to the arts of mathematical representation. :) Thanks! – ZolomonDec 6 '10 at 19:58 2 IMHO, as far as "what steps to include", I think an even better rule of thumb is to imagine that you are explaining your solution to a classmate, maybe one who's on the slow side. If the classmate wouldn't see right away what you are doing, then you should explain it. – Nate EldredgeDec 7 '10 at 1:01 when you decide to write a book, please make sure to let me know :) – KerxPhiloApr 23 '11 at 8:12 Assuming you by "syntax" mean your way of reasoning, i.e. your "path" via logical connectives to the result, my best tip is to carefully read all proofs in your math book. Not only read through them, but understand them. You must be able to prove things correctly, i.e. using only valid deductions. They way they do it in your math book is not a "local" thing, but "global" (no pun!). As long as your reasoning is understandable by anyone else reading it, it should be fine. If you could be more spesific with what you mean by "syntax", I'm sure somebody could give a clearer answer. The level of allowed ellipsis depends very much of your reader. It is part of the style, not syntax. Some mathematicians like Laplace, are very boring to read because they spend so much time on tiny details. Some others are very difficult to follow because some of the most critical piece of reasoning are left as an exercise to the reader. A famous example was written by Fermat in 1637: «cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet» [I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.] It took 358 years to rebuilt the missing steps. In facts, almost every work of Fermat was first rejected by the mathematical community,... before he had a chance to work out and publish the details. It's worth noting here that Fermat's proof is still a mystery. Wiles' proof used contemporary ideas and techniques which Fermat did not know. In light of that, it seems very unlikely that Fermat had a valid proof. – Adam SaltzNov 30 '11 at 22:54
Certain contemporary mathematical problems are of particular interest to teachers and students because their origin lies in mathematics covered in the elementary school curriculum and their development can be traced through high school, college, and university level mathematics. This book is intended to provide a source for the mathematics (from beginning to advanced) needed to understand the emergence and evolution of five of these problems: The Four Numbers Problem, Rational Right Triangles, Lattice Point Geometry, Rational Approximation, and Dissection. Each chapter begins with the elementary geometry and number theory at the source of the problem, and proceeds (with the exception of the first problem) to a discussion of important results in current research. The introduction to each chapter summarizes the contents of its various sections, as well as the background required. The book is intended for students and teachers of mathematics from high school through graduate school. It should also be of interest to working mathematicians who are curious about mathematical results in fields other than their own. It can be used by teachers at all of the above mentioned levels for the enhancement of standard curriculum materials or extra-curricular projects. Readership High school students, undergraduate and graduate students, and teachers of all levels interested in mathematics. Reviews "I am a huge fan of this book! ... "Roots to Research" is very accessible, supported throughout with insightful examples and exercises that motivate both the ideas and the formal notation. I recommend this book to future and current math teachers, math majors, and working mathematicians who are interested in reading about cool math. ... the Sallys have done the mathematical community a service by writing a book that illustrates an approach that more of us should take when teaching upper-level undergraduate and graduate math courses." -- MAA Monthly "Many references are given but the book is largely self-contained. The authors have done a remarkable job of giving a seamless presentation of material at very different levels of difficulty. Teachers and students will appreciate this book both for the information it contains and as a model of expository writing." -- Mathematical Reviews "The book gives a very good introduction in how to solve mathematical problems and it is well suited as a basis for a beginner's seminar at universities."
Search Course Communities: Course Communities Lesson 13: Completing the Square Course Topic(s): Developmental Math \| Quadratics This lesson introduces completing the square as a means of expanding the set of quadratic equations that may be solved beyond the extraction of roots and factoring. Simpler cases are first presented and then towards the end of the lesson a procedure for completing the square of (ax^2 + bx + c = 0) is given.
Algebra 1/2 represents a culminatin of prealgebra mathematics, covering all topics normally taught in prealgebra, as well as additional topics from geometry and discrete mathematics. This program is recommended for seventh graders who plan to take first-year algebra in the eighth grade or for eighth-graders who plan to take first-year algebra in the ninth grade.
Practical Problems in Mathematics: For Welders, 5th Edition Practical Problems in Mathematics for Welders, 5E, takes the same straightforward and practical approach to mathematics that made previous editions so highly effective, and combines it with the latest procedures and practices in the welding industry. With this comprehensive, instructional book, readers will learn how to solve the types of math problems faced regularly by welders. Each unit begins with a review of the basic mathematical procedures used in standard operations and progresses to more advanced formulas. With real-world welding examples and clear, uncomplicated explanations, this book will provide readers with the mathematical tools needed to be successful in their welding careers
Buy Used Textbook Buy New Textbook eTextbook 180 day subscription $81.59 More New and Used from Private Sellers Starting at $92Elementary Linear Algebra : A Matrix Approach Summary Ideal as a reference or quick review of the fundamentals of linear algebra, this book offers amatrix-oriented approach--with more emphasis on Euclidean n-space, problem solving, and applications, and less emphasis on abstract vector spaces. It features a variety of applications, boxed statements of important results, and a large number of numbered and unnumbered examples.Matrices, Vectors, and Systems of Linear Equations. Matrices and Linear Transformations. Determinants. Subspaces and Their Properties. Eigenvalues, Eigenvectors, and Diagonalization. Orthogonality. Vector Spaces. Complex Numbers.A professional reference for computer scientists, statisticians, and some engineers.
Math for Welders is a combination text and workbook designed to help welding students learn and apply basic math skills. The basic concept behind each math operation is explained at the opening of the unit. Next, students are given clear instruction for performing the operation. Each unit includes a variety of weldingrelated practice problems to reinforce what the students have learned. The practice problems are identical to the types of problems the students will be required to solve in a welding shop. In addition to teaching basic math concepts, the problems give students a preview of the types of challenges they will face in a work environment. This helps the students develop solid troubleshooting skills that will serve them throughout their careers as weld
College Geometry A Problem-Solving Approach With Applications 9780131879690 ISBN: 0131879693 Edition: 2 Pub Date: 2007 Publisher: Prentice Hall Summary: For courses in Geometry or Geometry for Future Teachers. This popular book has four main goals: 1. to help students become better problem solvers, especially in solving common application problems involving geometry; 2. to help students learn many properties of geometric figures, to verify them using proofs, and to use them to solve applied problems; 3. to expose students to the axiomatic method of synthetic Euclidea...n geometry at an appropriate level of sophistication; and 4. to provide students with other methods for solving problems in geometry, namely using coordinate geometry and transformation geometry. Beginning with informal experiences, the book gradually moves toward more formal proofs, and includes special topics sections.[read more] Ships From:Wentzville, MOShipping:StandardComments: 0131879693 Student Edition. Missing up to 10 pages. Heavy wrinkling from liquid damage. Does not... [more] 013180131879693 Student Edition. Missing up to 10 pages. Heavy wrinkling from liquid damage. Does not affect the text. Heavy wear, wrinkling, creasing, Curling or tears on the cov [more] 01318
This informative hands-on training book explains Microprocessor Design using the Motorola MC68HC11Usually MC68HC12 with CD ROM Author Raj Shah Description This informative hands-on training book explains Microprocessor Design using the Motorola MC68HC12Digital Signal Processing Made Easy using TMS320 with CD ROM Author Dr. Ganeshan, Dr. Sudhakar Rao and Raj Shah Description This is a self-study workbook designed to introduce Digital Signal Processing design and its applications in a real-time environment. It offers the reader an in-depth knowledge of a complex subject in easy-to-understand language. It also provides step-by-step instructions with hands-on-training using several lab experiments. It uses TMS 320C5x DSP chips from Texas Instrument 8051/Philipps 80C552 includes CD ROM Author Raj Shah Description This informative hands-on training book explains Microprocessor Design using the 8051/80552Embedded Design Using PIC 16F877 includes CD ROM Author Raj Shah Description This informative hands-on training book explains Microprocessor Design using Microchip PIC. It explains in detail how the microprocessor works, including its architecture and its addressing modes. It also explains in easy-to-understand language the fundamentals of programming. This study guide uses EZ-MICRO TUTOR Board fromTroubleshooting Guide for Mathematics Author Vinaire Description The idea underlying the Math Club is to mobilize parents and students as a tutoring resource to complement the teaching efforts in schools. Members are encouraged to learn how to troubleshoot difficulties in math and become Math Club Tutors. Close attention and supervision from existing Math Club Tutors makes this possible. Individual programs are issued to new Math Club members to help them overcome their roadblocks in math.
Algebra I - Standards 15-25 Standards 1ALG.15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems. 1ALG.16.0 Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions. 1ALG.17.0 Students determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression. 1ALG.18.0 Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion. 1ALG.19.0 Students know the quadratic formula and are familiar with its proof by completing the square. 1ALG.20.0 Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations. 1ALG.21.0 Students graph quadratic functions and know that their roots are the x- intercepts. 1ALG.22.0 Students use the quadratic formula or factoring techniques or both to determine whether the graph of a quadratic function will intersect the x-axis in zero, one, or two points. 1ALG.23.0 Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity. 1ALG.24.0 Students use and know simple aspects of a logical argument. 1ALG.25.0 Students use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements.
You are here Linear Algebra (MIT) Course Description: This is a basic course on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.
Math Spring 2007 Section 1, TR 5:45-7:10pm Science 107 Professor: PHONE: Home Page: Andrew Diener 3213452 EMAIL ADDRESS: adiener@cbu.edu OFFICE: OFFICE HOURS: 103F Science 1pm-5pm MTWR. TEXT: Mathematics for Elementary Teachers, A Contemporary Approach, Seventh Edition, Gary L. Musser, William F. Burger and Blake E. Peterson, Wiley, 2006. COURSE CONTENT: (by catalog) This course includes concepts essential to mathematics for elementary school teaching candidates. Topics include: set theory, numbers and numeration, number theory, rational numbers and problem solving. This course does not meet the general education requirement in mathematics. Prerequisite: MATH 100 or equivalent. CALCULATOR: You must have access to the TI-83+ or TI-84+ graphing calculator on assignments and for part of each test. Tests may be in two parts, one with calculator and one without. HOMEWORK: A list of suggested homework problems will be given for each section covered. I do expect that you will attempt all homework problems. I will grade some, though not all, of these problems. We will spend some class time in groups working on these problems. Any homework must be turned in using the proper format and on time. NO late (or incorrectly formatted) homework will be accepted. Homework will account for 15% of your final grade. (100 pts) QUIZZES: There be will quizzes every week. These quizzes will be very short (approx. 10-15 min.) and will come almost directly from the homework. Each quiz will be worth 10 points and I will count 10 of them. Since I plan to give many of these quizzes (at least 12, hopefully 13) I will drop the extra ones. This does mean that quizzes cannot be made up. Quizzes will count for 15% of your final grade. TESTS: There will be three in-class exams, each exam worth 100 points, and a comprehensive final exam worth 150 points. I will not curve your test grades. If you miss a test for any reason, you need to notify me no later than the day after the test to set up a time for a make-up. PROJECTS: I strongly encourage students to work together when studying mathematics (except on exams!) and to further this goal there will be several 3 Math 105 December 12, 2006 Name You must show all your work. Partial credit will be given. 1. The following table shows the amounts spent on reducing sizes of rst-grade through thirdgrade public school classes in a certain state. Year 1988 199 EXAM 3 Math 105 April 11, 2008 Name You must show all your work. Partial credit will be given. 1. A laptop computer currently costs $787. The price of the laptop is expected to decrease by 2.9% per year. Find a mathematical model for the price of the EXAM 1 Math 105 November 2, 2006 Name You must show all your work. Partial credit will be given. 1. Calculate the value of H(t) = -16t 2 + 120 at t = 2, where H(t) is the height of a cliff diver above the water t seconds after he jumped from a 120 fo QUIZ 3 Name 1. Find the slope and the x-intercept of the line 2x + 3y = 7.2. Do the row operations needed to put the following matrix into nal form and then write down the solutions (if any exist) to the system represented by the matrix. 1 0 0 2 iContents iChapter 1Keeping It In The Ballpark1.1 Studying PhysicsHow do you study for physics? Do you read your physics book the same way your read a book for literature class? Although physics and English literature are both intellectual di Heinrich Rudolf Hertz(Redirected from Heinrich Hertz) Heinrich Rudolf Hertz (February 22, 1857 - January 1, 1894), was the German physicist for whom the hertz, the SI unit of frequency, is named. In 1888, he was the first to demonstrate the existenc MIDTERM EXAM IISolutions Math 21D Temple-F06 Write solutions on the paper provided. Put your name on this exam sheet, and staple it to the front of your finished exam. Do Not Write On This Exam Sheet. Problem 1. (20pts) (a)Calculate the gradient f (x MIDTERM EXAM IMath 21D Temple-F06 Write solutions on the paper provided. Put your name on this exam sheet, and staple it to the front of your finished exam. Do Not Write On This Exam Sheet.Problem 1. (15pts) Evaluate R x2y dA where R is the region
Loci: Resources Images of F by Steve Phelps (Madeira High School) Applet Description This interactive Geogebra applet allows exploration of a linear transformation in terms of images of a closed figure that happens to be in the shape of the letter F initially. The Geogebra interface allows dragging of points and vectors to make for versatile explorations of basic linear algebra ideas. Suggested activities and exercises using the tool are included on page 2 of this posting and as a separate pdf file for easy printing. Steve Phelps Madeira High School & GeoGebra Institute of OhioClick here or on the screen shot above to open the applet in a separate window. Investigations In the Images of F applet on page 1, the columns of the matrix are the elementary vectors e1 and e2. The blue figure is a pre-image initially in the shape of an F. The green figure is the image of the blue F under the transformation given by the matrix. To answer the questions below, you can drag the tips of the elementary vector to set up the appropriate matrices. You may also need to drag the vertices of the blue F as well. Warm Up: Set up the following matrices one at a time. Pay particular attention to the lattice points of F and to the lattice points of the image of F. 1. \left[ \begin{array}{cc} 2 & 3 \\ 0 & 1 \end{array} \right] 2. \left[ \begin{array}{cc} 1 & 0 \\ 3 & -1 \end{array} \right] 3. \left[ \begin{array}{cc} 1 & 2 \\ 3 & 1 \end{array} \right] 4. \left[ \begin{array}{cc} 2 & -1 \\ 2 & 1 \end{array} \right] 5. \left[ \begin{array}{cc} -2 & 1 \\ 2 & -1 \end{array} \right] 6. \left[ \begin{array}{cc} 1 & 2 \\ 3 & 4 \end{array} \right] Investigation 1: Drag the tips of the elementary vectors to set up the following matrices. Discuss the transformations and the resulting image of F under these matrix transformations. transformations with matrices of the form \left[ \begin{array}{cc} k & 0 \\ 0 & 1 \end{array} \right] transformations with matrices of the form \left[ \begin{array}{cc} 1 & 0 \\ 0 & k \end{array} \right] transformations with matrices of the form \left[ \begin{array}{cc} k & 0 \\ 0 & k \end{array} \right] transformations with matrices of the form \left[ \begin{array}{cc} 0 & k \\ k & 0 \end{array} \right] transformations with matrices of the form \left[ \begin{array}{cc} 1 & 0 \\ k & 1 \end{array} \right] transformations with matrices of the form \left[ \begin{array}{cc} 1 & k \\ 0 & 1 \end{array} \right] Investigation 2: Drag the tips of the elementary vectors to set up matrices that will perform the following transformations. Pay attention to the orientation of the vectors. Reflection over the x – axis Reflection over the y – axis 90-degree clockwise rotation around the origin Half-turn around the origin 90-degree counterclockwise rotation around the origin Reflection over the line y = x Reflection over the line y = -x Copyright 2013. All rights reserved. The Mathematical Association of America.
Introduction to or two-semester junior or senior level courses in Advanced Calculus, Analysis I, or Real Analysis.This text prepares students for future courses that use analytic ideas, such as real and complex analysis, partial and ordinary differential equations, numerical analysis, fluid mechanics, and differential geometry. This book is designed to challenge advanced students while encouraging and helping weaker students. Offering readability, practicality and flexibility, Wade presents fundamental theorems and ideas from a practical viewpoint, sh... MOREowing students the motivation behind the mathematics and enabling them to construct their own proofs. vickersa 11.9999 Normal 0 false false false This text prepares readers for fluency with analytic ideas, such as real and complex analysis, partial and ordinary differential equations, numerical analysis, fluid mechanics, and differential geometry. This book is designed to challenge advanced readers while encouraging and helping readers with weaker skills. Offering readability, practicality and flexibility, Wade presents fundamental theorems and ideas from a practical viewpoint, showing readers the motivation behind the mathematics and enabling them to construct their own proofs. ONE-DIMENSIONAL THEORY; The Real Number System; Sequences inR; Continuity onR; Differentiability onR;Integrability onR;Infinite Series of Real Numbers; Infinite Series of Functions; MULTIDIMENSIONAL THEORY; Euclidean Spaces; Convergence inR n ;Metric Spaces; Differentiability onR n ;Integration onR n ;Fundamental Theorems of Vector Calculus; Fourier Series For all readers interested in analysis. William Wade received his PhD in harmonic analysis from the University of California—Riverside. He has been a professor of the Department of Mathematics at the University of Tennessee for more than forty years. During that time, he has received multiple awards including two Fulbright Scholarships, the Chancellor's Award for Research and Creative Achievements, the Dean's Award for Extraordinary Service, and the National Alumni Association Outstanding Teaching Award. Wade's research interests include problems of uniqueness, growth and dyadic harmonic analysis, on which he has published numerous papers, two books and given multiple presentations on three continents. His current publication, An Introduction to Analysis,is now in its fourth edition. In his spare time, Wade loves to travel and take photographs to document his trips. He is also musically inclined, and enjoys playing classical music, mainly baroque on the trumpet, recorder, and piano.
For briefer traditional courses in elementary differential equations that science, engineering, and mathematics students take following calculus. This accessible, attractive, and interesting text teaches students to first solve those differential equations that have the most frequent and interesting applications. This motivates students and illustrates the standard elementary techniques of solution of differential equations. Precise and clear-cut statements of fundamental existence and uniqueness theorems allow understanding of their role in this subject. The first few sections of most chapters introduce the principle ideas of each topic, with remaining sections devoted to extensions and applications, giving instructors a wide range of choices regarding breadth and depth of coverage. A strong numerical approach emphasizes that the effective and reliable use of numerical methods often requires preliminary analysis using standard elementary techniques [via] This accessible, attractive, and interesting analysis using standard elementary techniques. The first few sections of most chapters introduce the principle ideas of each topic, with remaining sections devoted to extensions and applications. Topics covered include first-order differential equations, linear equations of higher order, power series methods, laplace transform methods, linear systems of differential equations, numerical methods, nonlinear systems and phenomena, fourier series methods, and eigenvalues and boundary value problems. For those involved in the fields of science, engineering, and mathematics [via] More editions of Elementary Differential Equations With Boundary Value Problems:
fromMath in Society is a free, open textbook. This book is a survey of mathematical topics, most non-algebraic, appropriate for a college-level topics course for liberal arts majors. The text is designed so that most chapters are independent, allowing the instructor to choose a selection of topics to be covered. Emphasis is placed on the applicability of the mathematics. Material for each topic is covered in the main text, with additional depth available through exploration exercises appropriate for in-class, group, or individual investigation. This book is appropriate for Math 107 (Washington State Community Colleges common course number). The purpose of this course is to expose you to the wider world of mathematical thinking. There are two reasons for this. First, for you to understand the power of quantitative thinking and the power of numbers in solving and dealing with real world scenarios. Secondly, for you to understand that there is more to mathematics then expressions and equations. The core course is a complete, ready to run, fully online course, featuring 9 topics: Problem solving, voting theory, graph theory, growth models, consumer finance, collecting data, describing data, probability, and historical counting. Additional optional topics are provided. The course materials can easily be used with a face-to-face course. This tool allows the individual or the classroom to explore several representations of fractions. After selecting numerator and denominator, any number from 1 to 100, learners see the fraction itself, a visual model, as well as decimal and percent equivalents. They can choose the model to be a circle, a rectangle, or a set model.
YourTeacher has aligned our lessons to over 160 textbooks in middle school, high school, community college and college. By simply entering the page number you are working on, YourTeacher will return the exact lesson covering that page of your textbook! Our textbook search tool is particularly helpful for math homework help, where students often get stuck and need background instruction in order to move forward. Need Online Math Help? Grade Reporting and Progress Tracking YourTeacher provides individualized grade reporting and progress tracking to ensure that parents, administrators and students know if the material is being mastered and how much the content is being utilized. Grade Reporting Each lesson contains a multiple-choice self-test to prove mastery. Unlike other programs, YourTeacher's self-tests can be taken multiple times with new problems each time. This allows students to continue to take self-tests until mastery has been proven. The results of the self-tests are recorded in the grade management system. The grades are a simple way for parents, administrators, and students to ensure that students are receiving the online math help they need and as a way to identify areas of weakness. Final grades for entire courses are also available online. Progress Tracking In addition to our grade reporting system, YourTeacher keeps track of student progress by monitoring usage. Parents, administrators, and students are able to see the number of lessons completed, the number of incomplete self-tests, total logins, and the last login. These basic metrics ensure that student usage can be easily tracked. YourTeacher uses the results of self-tests to automatically recommend background lessons based on areas of weakness. As an example, if a student scored below an 80% on a lesson such as Comparing Proper Fractions (Pre-Algebra), our system would automatically recommend the background lessons required to master this lesson. In this example, our system would automatically recommend the following lessons: Comparing Numbers, Multiples and Least Common Multiples, Equivalent Fractions, and Introduction to Fractions. When these background lessons are presented, students can also quickly see which of these lessons they have already mastered and which they need to work on. After completing the background lessons, the student then can re-take the self-test for Comparing Proper Fractions. Because the self-test is different each time, students will have to prove true mastery. If they score an 80% or above, the lesson is automatically removed from the recommendation list (note that if a student scores less than an 80% on one of the background lessons, then the system will continue to recommend lessons going backward until the student 'bottoms out'). This adaptive recommendation system ensures that no matter where a student starts, they can get the individualized online math help they need to succeed. REVIEWS OF MATH HELP FROM YOURTEACHER gets math help And you cannot beat the excellent price. This program works and is such a blessing. Thank you very, very much for this program." Luise "I was desperately seeking math help. I am working on an Associates Degree at a local community college. Pre-Algebra and Introductory Algebra were required classes for me. I was completely lost because I have absolutely no Algebra background. I was really struggling in my class. Then I found YourTeacher. The lessons were a tremendous help. I ended up making an A in the class and passed the exit test. Thank you for your help." Catherine "Since I was strapped for cash for a personal tutor, I decided to purchase the online subscription to help me pass the ASVAB. I brought my failing score up 20 points because of this web site. I could not have enlisted into the military without math help from this web site. Hats off to YourTeacher...I AM IN THE ARMY NOW." Kisha "First, let me say that YourTeacher was a godsend! I am finally pursuing my goal of obtaining a nursing degree. As you know, the very first step in returning to school is the ACCUPLACER test. Since I have been out of school for so long, I was very apprehensive about the math portion. What a fabulous way to get math help I had long forgotten! I took the ACCUPLACER, and scored well above the minimum on all sections, including math. Without YourTeacher, I'm certain I would have failed the math portion miserably....and would have then been discouraged in my attempts to return to school. I can't say enough about how helpful it was...It's definitely WELL WORTH the subscription fee." Tanya
Problems in Mathematics Aims This course aims to allow students to engage with some of the important problems which have shaped mathematics. Problems will be put in their historical context and will be used to illustrate the development of different areas of mathematics. You will have the opportunity to tackle more open-ended work and make links between the many branches of mathematics that have been studied on the degree programme. Teaching and Assessment This module is entirely coursework based; split into 40% for problem sheets and 60% for essays. Over the course of the year there will be several evenings of lectures. Each evening will concentrate on one topic (the choice of topics will vary each year). At the end of each lecture evening, students will be given a problem sheet to complete. This will consist of several short compulsory questions to be submitted within 4 weeks of the lecture. Each problem sheet will count 10% towards the final mark for the module, and students will complete four problem sheets. In addition, at the end of each lecture students will be given a short list of suggestions for essays with each topic. Over the course of the year students must choose any two of these questions to complete; each essay should be roughly 2,500 words and no more than 4,000 words. Optionally a student may, with permission, choose to write ONE essay of the two on a mathematical subject of their own choosing. If a student wishes to do this, he or she must obtain the permission of a member of School to supervise this project, and submit an abstract which must be approved by the essay supervisor before the end of the Spring Term. Each essay counts 30% giving a total of 60%. Syllabus A selection of typical topics is given below but will vary from year to year to keep current. Each topic would be the subject of one evening of lectures.
Fostering Algebraic Thinking Mark Driscoll's Fostering Algebraic Thinking School-Based Seminar expands on his popular book and professional-learning toolkits, leading participants to in-depth knowledge of the key ideas underpinning algebraic thinking. Teachers will explore algebraic thinking from two powerful perspectives. First they solve open-ended problems and observe their own algebraic habits of mind. Then they analyze student work to see how kids approached the problem. Ultimately they will discover commonalities and find out how knowledge of both approaches can inform instruction. During this seminar teachers will deepen their understanding of algebraic thinking through hands-on investigation and discussions and analysis of student work. In addition, they will learn structured approaches for analyzing student work that distinguish between evidence and interpretation, and reflect on ways to elicit productive algebraic thinking from students
A big advantage of numerical mathematics is that a numerical solution can be obtained for problems, where an analytical solution does not exist. An additional advantage is, that a numerical method only uses evaluation of standard functions and the operations: addition, subtraction, multiplication and division. Because these are just the operations a computer can perform, numerical mathematics and computers form a perfect combination. An analytical method gives the solution as a mathematical formula, which is an advantage. From this we can gain insight in the behavior and the properties of the solution, and with a numerical solution (that gives the function as a table) this is not the case. On the other hand some form of visualization may be used to gain insight in the behavior of the solution. To draw a graph of a function with a numerical method is usually a more useful tool than to evaluate the analytical solution at a great number of points. In this book we discuss several numerical methods for solving ordinary differential equations. We emphasize those aspects that play an important role in practical problems. In this introductory text we confine ourselves to ordinary differential equations with the exception of the last chapter in which we discuss the heat equation, a parabolic partial differential equation. The techniques discussed in the introductory chapters, for e.g. interpolation, numerical quadrature and the solution of nonlinear equations, may also be used outside the context of differential equations. They have been included to make the book self contained as far as the numerical aspects are concerned.
Mathematics in DPS Mathematics is the science of patterns and relationships. It is the language and logic of our technological world. We live in a mathematical world. Whenever we decide on a purchase, choose a cell phone plan, making or giving change, calculating the numbers of days until a holiday or birthday or use a spreadsheet, we rely on mathematical understanding. The World Wide Web, CD-ROMs and other media disseminate vast quantities of quantitative information. The level of mathematical thinking and problem solving needed in the workplace has increased dramatically. In such a world, those who understand and can do mathematics will have opportunities that others do not. Detroit Public Schools are committed to keeping all options open to our students. The mission of the Office of Mathematics Education is to empower students mathematically through their ability to explore, make conjectures, reason logically and use a variety of mathematical methods effectively to solve problems. Our goals go beyond just learning the basics. Learning the basics is important; however students who memorize facts or procedures without understanding often are not sure when or how to use what they know. In contrast, conceptual understanding enables our students to deal with novel problems and settings as well as solving problems that they have not encountered. Goals Students will acquire mathematical skills, including the ability to perform routine computation and symbolic manipulation. Students will develop an understanding of mathematical concepts and will be able to apply it to new situations. Students will become mathematical problem solvers. Students will learn to value mathematics and the quantitative nature of our world. Curriculum Detroit Public Schools offers a rigorous, high quality and relevant curriculum aligned to Michigan standards. Our students begin their preparation in kindergarten getting ready for college and careers in mathematics. The College and Career Readiness Mathematics standards have been adopted from the Common Core State Standards for Mathematics. Our schools have many opportunities for students to work at their own levels as well as advance to accelerated courses throughout the grades. We take great pride in offering individualized intervention in order to close gaps in students' prior knowledge. Technology is an essential tool for learning and modeling mathematics i.e., calculators, netbooks, SmartBoard™, and other handheld devices. The secondary mathematics course offerings include the following: Pre-Algebra (Grades 6 and 7 only) Algebra 1 (Grades 8 and 9) Geometry Algebra 2 Probability and Statistics Advanced Placement Statistics Pre-calculus Calculus Advanced Placement Calculus Discrete Mathematics High school graduation requirements include the completion of four years of secondary mathematics beginning with Algebra 1. Curriculum by Grade Level Student Programs DPS leagues have consistently brought home trophies from several tournament classifications. Chess is a game of imagination and strategy, one that provides rules, order and opportunities for intellectual growth. Chess teaches a skill that can be applied to other aspects of life. For example, it teaches one to plan carefully in advance, to visualize various situations before making a move, and the importance of patience. How many of us have acted without thinking and then wished we could take back our actions? Well, the game of chess will quickly teach a child to analyze before acting. Studies support the assertion that chess improves a person's organizational and analytical skills. Chess involves an infinite number of calculations, anything from counting the number of attackers and defenders in the event of a simple exchange to calculating lengthy continuations. Academic Games™ is a series of games designed to test a student's knowledge in several different subject areas. Students compete in games that cover math, English, social studies, & logic. The primary purpose of Academic Games is to make learning fun for students. All too often it seems, students turn off to math, English, or social studies because the students are bored or not challenged by the material. Academic Games helps to alleviate that problem by challenging students to pursue their own education in these subjects in order to succeed in the competition. Project SEED instruction combines a non-lecture, questioning method with techniques designed to encourage constant verbal and nonverbal feedback, promote student participation, and improve focus. The Project SEED method makes the class the arbiters of knowledge giving them a sense of ownership of the material.
Matlab: Linear Algebra Linear algebra is about the solution of simultaneous linear equations, linear eigensystems etc., and is based on numerical matrices. This course starts by covering Matlab's basic matrix facilities, fairly quickly, for people who are not experts with them. It then covers the basics of linear algebra using real and complex matrices. It is intended for people who can use Matlab, but need to know what it can do with matrices and linear algebra. Prerequisite Matrix arithmetic and how matrices are used in linear algebra (e.g. the solution of linear equations) is no longer taught in the ordinary mathematics A-level, but only Further Pure mathematics. If you do not know this, you MUST learn it first. For further information, see Matrix Prerequisites.
Recommended Mathematics Software Although many things such as emotion and thought may be difficult to measure, some things are much easier to quantitize. Measurement Converter aids in converting one measurement to another similar measurement. Why people care so much about measurements and conversions still remain a mystery to one such as myself. Do you think your kids may benefit from more math practice? If so, here's a simple program that will help! Works on most Palm PDAs.So easy to use, no instructions needed.Automatically adjusts to your way of learning to make it more efficient and fun. Multiplication Practice (Numbers 1 to 12). Division Practice (Numbers 1 to 144),andMoreAll Mathematics Software Downloads R is a language and environment for statistical computing and graphics. R st... Math-o-mir is an Equation Editor. However it is not centered over one single equation but you can write your mathematical text over several pages. Inside your mathematical document, you can copy equations and expressions easily by mouse click. You can also make simple drawings or sketches. Symbolic calculator and function plotter are included. Scilab was designed to be a scientific software package for numerical computations providing a powerful open computing environment for engineering and scientific applications. Scilab is an open source software. Since 1994 it has been distributed freely along with the source code via the Internet. It is currently used in educational and industri... With this free Organic Chemistry Analysis and Visualisation Tool you can write chemical formulas and let the computer calculate the threedimensional structure of the molecule, compute atomic properties and export your results as image or video files. The 3D-view uses a state-of-the-art shader-enabled realtime renderer to generate high-quality i... DX Central is a desktop application for those interested in observing the earths sun or its effect on radio propagation. This small application provides images of the sun and vital, timely information about solar activity in a way that is concise and easy to use. Current solar Images are included. For sun watchers and SWL/DX. Information displa... yoshinoGRAPH is a scientific graph software for data analysis and presentation. You can make 2D and 3D graphs quickly from data files in text format. This software is tiny but includes many basic functions to analyze/edit data as well as rather advanced ones. Features: easy to make sientific graphs for presentation and publication plot ... Earth Alerts is a Windows-based application that provides alert notifications and information on all weather, earthquake, and volcano related events. These events are tracked anywhere within the United States, Guam, Puerto Rico, and the U.S. Virgin Islands. Weather, earthquakes, and volcanos...the kind of stuff our planet dishes out to arouse h...
Online Interactive Modules for Teaching Computer Science This site was developed by the Center for Innovation in Learning at Virginia Tech. It contains eight web-based learning modules similar to chapters in a text book: Algorithms, Artificial Intelligence, Data Structures, Machine Architecture, Number Systems, Operating Systems, Programming Languages, and Software Engineering. Each module consists of a set of lessons that should be worked through in order. Many lessons contain animations, tutorials, Java applets, and other activites that supplement the material. Every lesson contains a set of review questions (click on the icon of the "notepad") for which you can obtain answers. In the upper right hand corner click on the pull down screen "Jump to Module",to proceed to the module you are interested in exploring. To view all features, you may be required to download plug-ins or helper applications. courses.cs.vt.edu/~csonline/index.html Discrete Math Flash Exercises Contains some useful Flash tutorials to illustrate concepts in discrete math. To view all features, you may be required to download plug-ins or helper applications. Unification of System of Linear Equations, Matrix Inversion, and Linear Programming Part of the University of Baltimore's website, this article discusses the connections among linear systems of equations, matrix inversion, and linear programming and how problems in each may be solved by way of the other. Additional links give access to computer package-solvers to model and solve a problem. The site links to a collection of JavaScript E-labs Learning Objects for decision making. home.ubalt.edu/ntsbarsh/opre640a/partXII.htm Non-Interactive Tutorials Eric Weisstein's World of Mathematics - Discrete Mathematics This site is a comprehensive, non-interactive mathematics encyclopedia covering discrete mathematics. It features a search option to find specific math concepts. mathworld.wolfram.com/topics/DiscreteMathematics.html
This six-page chart covers: Basic accounting concepts and objectives Transaction basics Balance sheets and statements of income, cash flows, and changes in owner's equity SparkChartsTM-created by Harvard students for students everywhere- This four-page chart reviews:Polynomial basicsFactoring polynomialsQuadratic equations in one variableDivision of polynomialsInequalities in two variablesGraphing absolute valueLogarithms definition and lawsSequences and seriesFactorials, combinations, permutations, and Pascal's triangleProbabilityComplex numbersConic sections types and table [via]Smart Novels are compelling, full-length novels with edgy and mature themes that will appeal to teens. Each book showcases more than 1,000 vocabulary words frequently included on the SAT. Brief definitions appear on the same page so that readers can quickly access and digest the meanings as they read alongThis four-page chart summarizes the Constitution, the Bill of Rights, and amendments 11 to 27 in modern-day English. The original text of the preamble and Bill of Rights are also included. Cross-references and notes are provided where relevant. SparkChartsTMcreated by Harvard students for students
Student feedback With WIRIS quizzes, you can insert mathematical content in the wording of the question and perform some verifications on the answer, as well as inserting mathematical content in the feedback provided to the student. In the following example, we will simply return a text string, but this string will be sensitive to the answer given by the student. The question posed is a Multiple choice, and the student will be requested to report the degree of a random polynomial. The possible answers will be the degree, the coefficient of the highest degree term and the constant term. System answer will depend on the student's answer. This is the appearance of the question posed to the student and the feedback presented when s/he inserts a wrong answer: If you wish to obtain this behaviour from WIRIS quizzes, start as usual by creating the appropriate type of question, in this case Multiple choice, and inserting the name and the wording of the question. p variable will contain the random polynomial that we will define here following. In order to act on the student's answers, we must foresee them; so we will insert in the system all the options as we would do in a common Multiple choice exercise. g variable will contain the polynomial degree, i. e., the correct answer. In the other possible answers, we simply link the false option presented in this exercise with the feedback desired, that is, the sentence "You chose the coefficient of the highest degree term of the polynomial." Please note that the editor offers WIRIS editor and WIRIS cas icons and, thus, as we inserted plain text, we can also insert the values or graphics wished. In this case, we are not doing so in order to avoid complexity, but you can check the Algorithm field and Graphic content for more information. Given that all text fields are treated uniformly by WIRIS quizzes, inserting any value or graph in the feedback is similar to inserting it in the wording. With the aim of presenting the complete solution of the exercise, we will show a possible feedback for the third answer (also false, consequently). And, finally, a possible way of defining a random polynomial. Since compact writing took priority at the expense of readability of the proposal, we will describe it in detail to make it more understandable: The first line defines an f function that generates, at each call, a monomial with random coefficient between -10 and 10, with random degree as well, oscillating between 0 (constant term) and 5. The second line defines g as the degree of the p polynomial, still undefined, but that we will define shortly. The third line defines c as the coefficient of the highest degree term of the future p polynomial. The fourth line defines i as the constant term of the p polynomial. Please note that defining these elements in advance is required because we will use them in the interruption condition of the repeat-until command displayed here following. Lines 5 to 7 form the mentioned repeat-until command, that will define the p polynomial as the sum of five monomials using the f function, and it will verify afterwards whether degree, coefficient of highest degree term and linear term of the polynomial are different from each other, since we will provide them as options for the student and no repetition is desired. If there was a repetition, the repeat section will run again, generating another p polynomial, and so on indefinitely until we find a polynomial that matches all conditions required. Out of the yellow box, that is, out of the library, we can see a random example of the run of our program, with the corresponding values of c (highest degree coefficient), g (degree) and i (constant term).
Rent Textbook Used Textbook eTextbook New Textbook We're Sorry Sold Out Related Products A Graphical Approach to Precalculus Precalculus Precalculus Precalculus Precalculus Precalculus Plus NEW MyMathLab -- Access Card Package Summary This book, intended for a graphing calculator optional precalculus course, offers students the content and tools they will need to successfully master precalculus concepts. The authors have addressed the needs of students who will continue their study of mathematics, as well as those who are taking precalculus as their final mathematics course. Emphasis is placed on exploring mathematical concepts by using real data, current applications and optional technology.
Students narrow their choice of college by following a process used to determine locations of airports, power plants, and medical facilities. Multi-Attribute Utility Theory is a structured methodology that handles tradeoffs among multiple and often competing objectives. Students identify key variables, create measures of the variables, collect data on the measures, scale the data, estimate weights for the variables, and compute a weighted sum. Activity sheets guide students step by step through the process. Also included are extension activities, homework problems, complete solutions to activities and problems, and a video discussing the value of the mathematical ideas. Teacher materials are available only through Key Curriculum Press, but the essence of the lesson is incorporated in the student activity sheets. (sw/js4 Model with mathematics. High School - Number and Quantity Quantities Reason quantitatively and use units to solve problems. HSN-Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. HSN-Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. Ohio Mathematics Academic Content Standards (2001) Number, Number Sense and Operations Standard Benchmarks (11–12) D. Demonstrate fluency in operations with real numbers, vectors and matrices, using mental computation or paper and pencil calculations for simple cases and technology for more complicated cases. Grade Level Indicators (Grade 11) 9. Use vector addition and scalar multiplication to solve problems. Measurement Standard Benchmarks (11–12) B. Apply various measurement scales to describe phenomena and solve problems. Data Analysis and Probability Standard Benchmarks (11–12) A. Create and analyze tabular and graphical displays of data using appropriate tools, including spreadsheets and graphing calculators. D. Connect statistical techniques to applications in workplace and consumer situations. Transform bivariate data so it can be modeled by a function; e.g., use logarithms to allow nonlinear relationship to be modeled by linear function. Mathematical Processes Standard Benchmarks (11–12) C. Assess the adequacy and reliability of information available to solve a problem. J. Apply mathematical modeling to workplace and consumer situations, including problem formulation, identification of a mathematical model, interpretation of solution within the model, and validation to original problem situation. Principles and Standards for School Mathematics Number and Operations Standard Compute fluently and make reasonable estimates Expectations (9–12) develop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases. Measurement Standard Understand measurable attributes of objects and the units, systems, and processes of measurement Expectations (9–12) make decisions about units and scales that are appropriate for problem situations involving measurement. Data Analysis and Probability Standard Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them Expectations (9–12) understand the meaning of measurement data and categorical data, of univariate and bivariate data, and of the term variable;
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Description of The Physics Tutor�� (English) [DVD] Physics Is Frequently One Of The Hardest Subjects For Students To Tackle Because It Is A Combination Of Two Of The Toughest Subjects For Most Students: Math And Word Problems. If You Understand The Math But Don'T Do Well In Word Problems Or You Understand Word Problems But Have No Idea Where To Begin With The Math, You'Ll Have Trouble With Physics. The Physics Tutor Series Is A Complete Physics Course For The Beginning Physics Student And A Great Refresher Course For Continuing Students. The Entire Course Is A 24 Lesson Series Covering All Of The Core Topics In Detail. What Sets This Series Apart From Other Physics Teaching Tools Is That The Concepts Are Taught Entirely Thought Step-By-Step Example Problems O Increasing Difficulty. It Works By Introducing Each New Concept In An Easy To Understand Way And Using Example Problems That Are Worked Out Step-By-Step And Line By Line To Completion. If A Student Has A Problem With Coursework Or Homework, Simply Find A Similar Problem Fully Worked On In The Series And Review For The Steps Needed To Solve The Problem. Students Will Immediately Improve Their Problem-Solving Skills Which Will Help With Homework And Exams And Will Have A Reference For Many Of The Commonly Asked Problems In Physics
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Sample chapters for download About the book This aim of this Guide is to help students prepare for the Mathematics HL final examinations. The Guide has three distinct sections: the first part covers all seven topics in the course. Each topic begins with a succinct summary of important concepts followed by a set of 'skill builder' questions. The number of 'skill builder' questions has been increased in this second edition. the second part comprises fifteen 'exam practice' sets, with about 26 questions in each. In this second edition, each exam practice set is categorised as 'calculator' or 'no calculator' in response to the introduction of a calculator-free examination paper. the third part provides the fully worked solutions to all the skill builder questions and examination practice sets, altogether a total of almost 700 questions. Good examination techniques come from good examination preparation and practice – and we hope this Guide will help you succeed.
MAA Review [Reviewed by William J. Satzer, on 12/29/2008] Lectures on Surfaces: (Almost) Everything You Wanted to Know about Them does a masterful job of introducing the study of surfaces to advanced undergraduates. Although there are many attractive volumes in the AMS Student Mathematical Library series, this is the first one I've seen that would really have captured my interest as an undergraduate. One of the reasons why this text works so well (I think) is that the authors are not experts in the area. They take extra care to elaborate or explain things that an expert would not, and then anticipate those places where a newcomer might get stuck. Nonetheless, their scope is ambitious and ranges all the way from triangulation and classification of surfaces to Riemann surfaces, Riemannian geometry on surfaces, and the Gauss-Bonnet theorem. The Euler characteristic in its many guises is ubiquitous. The book is divided into five chapters consisting of thirty-six lectures. Since this work developed from the MASS (Mathematics Advanced Study Semesters) program at Penn State, the lecture subdivision is a natural consequence of how material was divided for presentation in the classroom. The authors assume that students' background includes the usual calculus sequence, basic linear algebra, rudimentary differential equations, and a bit of real analysis. As important as the prerequisites is an appetite for learning new mathematics at a pretty brisk pace. The authors begin with basic examples of surfaces and describe various ways of representing surfaces: by an equation, by planar model and quotient space, by local coordinates, or parametrically. The second chapter focuses on the combinatorial structure and topological characterization of surfaces. This includes classification of compact surfaces, with a proof for the orientable case. The authors introduce triangulations and the Euler characteristic of a triangulation; then they go on to define homology groups and Betti numbers and so provide a second interpretation of the Euler characteristic. The third and fourth chapters take up differentiable structures and vector fields on surfaces, Riemann surfaces, and then Riemann metrics. This brings us to geodesics, curvature, the hyperbolic plane, and the Gauss-Bonnet theorem. The final chapter comes back to topology and smooth structures for a discussion of degree and index of vector fields. It is amazing how much mathematics is naturally associated with the study of surfaces, and how the pieces fit together so remarkably. The authors succeed in pulling in many topics while keeping their story coherent and compelling. This book would work well as the text for a capstone course or independent reading. However, there are relatively few exercises, so an instructor would probably need to develop supplementary problem sets for classroom use
Elementary Differential Equations, CourseSmart eTextbook, 6th Edition Description For briefer traditional courses in elementary differential equations that science, engineering, and mathematics students take following calculus. The Sixth Edition of this widely adopted book remains the same classic differential equations text it's always been, but has been polished and sharpened to serve both instructors and students even more effectively.Edwards and Penney teach students to first solve those differential equations that have the most frequent and interesting applications. Precise and clear-cut statements of fundamental existence and uniqueness theorems allow understanding of their role in this subject. A strong numerical approach emphasizes that the effective and reliable use of numerical methods often requires preliminary analysis using standard elementary techniques. CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book. Table of Contents C O N T E N T S Preface vii CHAPTER 1 First-Order Differential Equations 1 1.1 Differential Equations and Mathematical Models 1 1.2 Integrals as General and Particular Solutions 10 1.3 Slope Fields and Solution Curves 19 1.4 Separable Equations and Applications 32 1.5 Linear First-Order Equations 46 1.6 Substitution Methods and Exact Equations 59 1.7 Population Models 74 1.8 Acceleration-Velocity Models 85 CHAPTER 2 Linear Equations of Higher Order 100 2.1 Introduction: Second-Order Linear Equations 100 2.2 General Solutions of Linear Equations 113 2.3 Homogeneous Equations with Constant Coefficients 124 2.4 Mechanical Vibrations 135 2.5 Nonhomogeneous Equations and Undetermined Coefficients 148 2.6 Forced Oscillations and Resonance 162 2.7 Electrical Circuits 173 2.8 Endpoint Problems and Eigenvalues 180 CHAPTER 3 Power Series Methods 194 3.1 Introduction and Review of Power Series 194 3.2 Series Solutions Near Ordinary Points 207 3.3 Regular Singular Points 218 3.4 Method of Frobenius: The Exceptional Cases 233 3.5 Bessel's Equation 248 3.6 Applications of Bessel Functions 257 v vi Contents CHAPTER 4 Laplace Transform Methods 266 4.1 Laplace Transforms and Inverse Transforms 266 4.2 Transformation of Initial Value Problems 277 4.3 Translation and Partial Fractions 289 4.4 Derivatives, Integrals, and Products of Transforms 297 4.5 Periodic and Piecewise Continuous Input Functions 304 4.6 Impulses and Delta Functions 316 CHAPTER 5 Linear Systems of Differential Equations 326 5.1 First-Order Systems and Applications 326 5.2 The Method of Elimination 338 5.3 Matrices and Linear Systems 347 5.4 The Eigenvalue Method for Homogeneous Systems 366 5.5 Second-Order Systems and Mechanical Applications 381 5.6 Multiple Eigenvalue Solutions 393 5.7 Matrix Exponentials and Linear Systems 407 5.8 Nonhomogeneous Linear Systems 420 CHAPTER 6 Numerical Methods 430 6.1 Numerical Approximation: Euler's Method 430 6.2 A Closer Look at the Euler Method 442 6.3 The Runge-Kutta Method 453 6.4 Numerical Methods for Systems 464 CHAPTER 7 Nonlinear Systems and Phenomena 480 7.1 Equilibrium Solutions and Stability 480 7.2 Stability and the Phase Plane 488 7.3 Linear and Almost Linear Systems 500 7.4 Ecological Models: Predators and Competitors 513 7.5 Nonlinear Mechanical Systems 526 7.6 Chaos in Dynamical Systems 542 References for Further Study 555 Appendix: Existence and Uniqueness of Solutions 559 Answers to Selected Problems 573 Index I-1
For those of you who are new on campus, welcome to the University and to college life! You have a straight A average so far at the University of Illinois, and I will try to help you keep it that way. For the rest of you, welcome back! You can succeed in calculus, even though it is harder than the math courses you have had in high school. It might be twice as hard! Here is what you have to do. Read, study, and think about the book. Attend the lectures on Monday, Wednesday, and Friday. Attend the discussion sessions on Tuesday and Thursday, during which quizzes are given.. Do the homework regularly. Form a study group -- meet weekly, prepare a homework assignment, and then discuss your solutions in the group. (Discussing the solutions is fine, but don't copy them -- you are expected to write up your own homework.) Get help from the discussion leaders for problems you can't do. Use the newsgroup to get help. Identify the things you don't understand and get help on them. Don't let your work for this course slide for even a week. You should study the book carefully and learn from it outside of class. It is well written and will reward close study. Plan on allotting at least an hour per day for this, starting from the first day. We love to answer questions about the material in the book, so if there is a sentence or paragraph that doesn't make sense to you, let us know (hopefully, using the news group) so we can help you out. The main thing is to start today! At the pace things happen in college, you don't want to procrastinate for even a week. Goal of the course: The chief difference between calculus and high school geometry is that we take the passage of time into account and use it as a tool. For example, we might try to measure the volume of a sphere by letting its radius shrink to zero and recording the rate at which the volume dissipates. The fundamental laws of physics that govern the world tend to be expressed as differential equations. These equations encapsulate information about how each little bit of matter interacts with each other little bit. One of the applications of calculus is to pass from the fundamental laws to explicit formulas for the global behavior of particular systems. In this course we take the first step toward understanding the role mathematics has to play in coordinating the basic laws of nature by learning about differentiation and integration of functions. Textbook: The textbook is "Calculus: Early Transcendentals", by Stewart, Fourth Edition. It's available in the book stores. Lectures: Lectures take place on Monday, Wednesday, and Friday at 1PM in 314 Altgeld Hall. In the lectures we will present to you the basic concepts and tools which you will need for learning the material and attacking the problems. Discussion leaders: Discussion sections take place on Tuesday and Thursday at 1 (the R sections) or 2 PM (the S sections). They have a maximum enrollment of 35, so this is the place where you can get practical help in executing the algorithms explained in lecture, and you can get answers to your questions about the material in the book or homework. Prepare for discussion by reading the material, reviewing your notes from lecture, and doing the homework. The discussion leaders will have office hours, mark your homework, grade your quizzes, and spend time looking at the news group to answer questions that appear there. You are welcome to go to the office hours of any of the discussion leaders. The professor, teaching assistants, and other students will be able to see the newsgroup, and we will monitor the news group and try to answer your questions promptly. If you are using a browser as a newsreader, you will want to tell it who you are, so the messages you post will be identified. For example, in Netscape, select "Preferences" from the "Edit" menu, and then under "Mail & Newsgroups" select "Identity". Don't be embarrassed about not knowing the answer to a problem. Just post your question and get the help you need to succeed! Learn how to post articles to the news group. There are two ways, depending on whether you want to follow up on a topic in a message previously posted, or to initiate a new topic of discussion. If your followups are posted as such, it makes it a lot easier for readers of the news group to follow the various threads of discussion. Here is a primitive but serviceable way to include mathematical formulas in email messages and articles in the news group. Use a caret (^) to indicate exponentiation, an underscore (_) to indicate a subscript, and an asterisk () to indicate multiplication. Thus "x^2" would mean "x squared", "x_3" would mean "x sub 3", and "xy" would mean "x times y". Never use "x" as a "times" sign. Some formulas can often be rendered in a 2-dimensional form that looks like this: 2 2 (x + 2) = x + 4 x + 4 dy 2 -- = 2x if y = x dx If you try that, remember to tell the browser to use a fixed-width font in that region. Some of you may also wish to experiment with methods for including graphical images. Let's talk about some more detailed ways to access newsgroups from sites around campus. Here's the procedure on PC's. Open up Internet Explorer by clicking on the icon with an e in it in the taskbar, lower left part of the screen. Then enter in the Address box, getting to my home page. Then click on the link for math 120, then click on the link for the newsgroup. At this point, internet explorer will start up netscape for you, and the newsgroup will be visible. If you want to start up netscape directly, instead of Internet Explorer, click on the "Start" icon in the lower left corner, click on "Network Services" in the menu, and then click on "Netscape 4.77" in that menu. Here's the procedure for accessing newsgroups from a Macintosh in the computer labs. Locate the folder MAC_APPS in the upper right hand corner of the screen and double click on it to open it. Inside it you will see a folder called "Network Services": open it the same way. Inside that you will see an icon for "Netscape Communicator", a program. Open it the same way. Enter into the Location box to get to my home page. Click on the link for Math 120 this semester. Click on the link for the newsgroup. Here is the procedure for getting Outlook Express to look at newsgroups. Go to to "Tools" then "Accounts" then hit the "Add -> News" button. After that, fill in the correct news server name, and it will walk you through everything else. Then, once the group is shown on the left side, you click on it, and hit the "subscribe" button, and pick the ones you want to subscribe to. Email: My email address is drg@uiuc.edu. Send me some introductory email telling me about yourself, once you get the hang of the email system here. I always reply to email. If you have a question about a homework problem, I prefer it to be posted to the news group so my teaching assistants can answer it, and so the other students can benefit from the answer. It is important to do the homework so you can learn the material and do well on the exams, which will draw material substantially from the homework. Homework is collected every Tuesday and Thursday at the beginning of the discussion period, and is marked by your discussion leader. It may happen that more solutions are submitted than can be marked in the time allotted, in which case we will mark just some of them. One thing I especially like about the book is the sections called "Applications Plus" and "Problems Plus". The problems in these sections demand extra creativity and extra time spent thinking about it. Please don't get discouraged when you encounter a problem like this and you don't know the method for solving it immediately. We'll discuss problem solving techniques in class that ought to apply to this type of problem. Tricky problems: Some students complain that math courses contain tricky problems put there just to weed out the weaker students, and not for any useful pedagogical purpose. This is not true. Doing homework problems is a lot like lifting weights - you have to do it a lot to get strong. We want you to be strong at solving problems and thinking about mathematics. Mathematical theory: Some students complain that there is too much emphasis on theory in math courses, and that math professors spend too much time explaining the ideas and not enough time teaching how to execute the algorithms. If it were possible for you to live in this world and be successful at your chosen career by following a simple algorithm we would teach you that algorithm. Life today demands a broad set of adaptible skills, and a solid intellectual understanding of science and mathematics is one of them. Think about those algorithms - do you want to spend all of your time studying to do something that computers can already do so well? Will that skill be valuable to your future employer? In real life, the problems aren't like homework problems. For example, suppose the problem you confront is to design a way of encoding sound on a CD to render it more resistant to scratches. Are you going to find the answer to that in a textbook? Or will you have developed ways of thinking about problems that will allow you to invent something new and better than what came before? Quizzes: There will be frequent quizzes administered in the discussion sections. Exams: Here is the University's academic calendar. There will be three 1 hour exams in class and a 3 hour final exam, on the following dates.
Everything in math can be represented as a function. Whether it is the surface area of a cylinder, its volume, or area of a square, it can be all represented by Calculus. It is safe to say that everything you learn up to Algebra 2 is leading up to Calculus. Invented by Sir Isaac Newton and William Gottfried Leibniz Calculus is the math of change. Consider any function that's quadratic, or more than 2nd degree, the function could be an inverse function, it could be logarithmic function, what ever. If the function is curved, mathematicians are faced with the challenge of finding the derivative of a function – in simple terms its slope, which shows the rate of change of that function and the area under the curve of that function – simply the anti-derivative found through integration. The whole meat of calculus lies in the limit process. The limit process sets the ground rules for finding the area and the slope of any function. The limit process is the making of a calculus. The limit of anything that is changing can be found if you get smaller and smaller to infinity and find the function. This is where the limit process comes in. You can get complex with the applications of calculus in Engineering courses, or Physics courses. These are places where you extensively apply the theory of Calculus. It is advisable that few years of Calculus be taken before getting into these courses, simply because it takes a lot of getting used to Calculus before you can be successful at the courses. It will also be an amazing observation that most of the concepts of physics and other math-based sciences are developed by the same people who invented Calculus, or worked with it a lot. A few popular names such as Sir Isaac Newton – invented basics of physics and Newton' Laws; and Albert Einstein – theory of relativity and other major cosmological research – come to mind. Now-a-days Calculus is applied in all types of Engineering and Computer Science and all fields requiring design. It is easy to use if you are well versed in Algebra and all the basic Mathematics from K-12, or up to Algebra 2. In a nut-shell, Calculus makes life simple at the expense of extensive Algebra!
GRADES 1-2 Being able to calculate accurately isn't enough to prepare students to successfully solve complex problems both inside and outside of the mathematics classroom. This new series builds students' confidence in their ability.. GRADES 3-4 Being able to calculate accurately isn't enough to prepare students to successfully solve complex problems both inside and outside of the mathematics classroom. This new series builds students' confidence in their ability.. GRADES 5-6 Being able to calculate accurately isn't enough to prepare students to successfully solve complex problems both inside and outside of the mathematics classroom. This new series builds students' confidence in their ability.. GRADES 6-8 Explore and apply algebraic thinking and data analysis in the context of engineering design and adventure. The books will guide students through simulations of climbing Mt. Everest, being stranded on an island in the South Pacific, a.. GRADE 6-8 Explore and apply algebraic thinking and data analysis in the context of engineering design and adventure. The book will guide students through a simulation of climbing Mt. Everest. Includes 3 design challenges, each lasting about 3 w.. GRADE 6-8 Explore and apply algebraic thinking and data analysis in the context of engineering design and adventure. The book will guide students through a simulation of being stranded on an island in the South Pacific. Includes 3 design chall.. GRADE 6-8 Explore and apply algebraic thinking and data analysis in the context of engineering design and adventure. The book will guide students through a simulation of navigating a mission in the Amazon. Includes 3 design challenges, each las.. Five investigation units give middle school teachers opportunities to explore mathematics skills and concepts in familiar contexts that make sense. These 4- to 8-week integrated units encourage sustained work that involves students in high-l.. A wealth of reproducible lists and other teaching aids, this highly-practical book offers specific information on over 275 topics. Every list is updated, and the book includes new information incorporating advanced topics such as fractals, discrete .. Prices listed are U.S. Domestic prices only and apply to orders shipped within the United States. Orders from outside the United States may be charged additional distributor, customs, and shipping charges.
A set of complex problems in real analysis are solved in detail A subset X of R2 or R3 is convex if whenever x and y are in X the segment connecting them is also in X. Using this definition, a series of problems are presented and solved. Organized by chapter, they are Chapter 1) Problems in which convexity is used either by analogy or for subsidiary arguments ) The intersection of connected open sets ) Approximations to homomorphisms of R2 onto itself ) On the projection of a plane set of finite linear measure Chapter 2) Problems which can be reduced to problems on convex sets ) Covering a three-dimensional set with sets of smaller diameter Chapter 4) Problems concerned with the structure of subclasses of the class of convex sets ) The asymmetry of curves of constant width ) Sets of constant width contained in a set of given minimal width ) Extremal properties of triangles circumscribing plane convex sets ) On the closest packing by equilateral triangles Each of the problems is dealt with in detail with theorems followed by proofs. A remark summarizing the problem occurs after every problem is resolved. In terms of difficulty, some real analysis background is necessary to understand the work. Charlie Ashbacher is a compulsive reader and writer about many subjects. His prime areas of expertise are in mathematics and computers where he has taught every course in the mathematics and computer … more Wiki This text for advanced undergraduates and graduate students examines problems concerning convex sets in real Euclidean spaces of 2 or 3 dimensions. It illustrates the different ways in which convexity can enter into the formulation as the solution to different problems in these spaces. 1957 edition.
Graph Theory is a subject on the cutting edge of mathematics and has applications to such diverse subject areas as operations research, economics, chemistry, sociology, computer science, and genetics. This course will provide a thorough introduction to graph theory. Topics to be covered include: paths, cycles, trees, planar graphs, graph colorings, digraphs and applications to optimization problems.
Resources I've been asked which text book I use. I chose AQAGCSE Mathematics for Higher Sets (grades D to A) published by Longman (ISBN 978−1−408232−78−1). Please take care to make sure you get the right book for you. I chose the higher sets book as I hope that my children will get at least a grade C and hopefully grade A. It maybe appropriate to study Middle Sets ( grades E to B) or Foundation (Grades G to C). Make sure you understand what's required or necessary for your circumstances. I chose this book just by looking at Amazon reviews and popularity. However, I've found it clear, colourful and easy to follow. Please note that all these links are for the new Maths GCSE syllabus (2010) and are for the linear course. Here's link to Amazon for the Higher sets book (Grades D to A):- Here's link to Middle sets book (Grades E to B):- Finally here's link to Foundation sets book (Grades G to C):- (Please note these are referral links, so I may earn a small commission if you buy after clicking these links) I will be building up this list of resources as I come across them during my maths challenge. I will be concentrating on free, not for profit resources. Please let me know about any resources that I should list (I'm sure there are hundreds). 1. Teaching AQAGCSE maths — This is really aimed at teachers but I've found it useful. Particularly impressed by their Sherlock Holmes episodes (would be great if all Maths lessons could be like this!). Specimen Papers These are links to specimen papers for the AQA's new GCSE syllabus (2010)- first sitting June 2012:- I've been asked which text book I use. I chose AQA GCSE Mathematics for Higher Sets (grades D to A*) published by Longman (ISBN 978-1-408232-78-1). Please take care to make sure you get the right book for you. I chose the higher sets book as I hope that my children will get at least a grade C and hopefully grade A. It maybe appropriate to study Mid
11C Scientific RPN Calculator 1. 11C Scientific RPN Calculator 1.0 is a product including all the features of the real one. Over 120 built-in functions including :Hyperbolic and Inverse hyperbolic Trig functions.Probability permutations and combinations.Factorial, absolute,... Minimum system requirements: Windows...
Description Mathematics for Physical Chemistry, Third Edition , is the ideal text for students and physical chemists who want to sharpen their mathematics skills. It can help prepare the reader for an undergraduate course, serve as a supplementary text for use during a course, or serve as a reference for graduate students and practicing chemists. The text concentrates on applications instead of theory, and, although the emphasis is on physical chemistry, it can also be useful in general chemistry courses. The Third Edition includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The first ten chapters are constructed around a sequence of mathematical topics, with a gradual progression into more advanced material. The final chapter discusses mathematical topics needed in the analysis of experimental data. Numerous examples and problems interspersed throughout the presentations Each extensive chapter contains a preview, objectives, and summary Includes topics not found in similar books, such as a review of general algebra and an introduction to group theory Provides chemistry specific instruction without the distraction of abstract concepts or theoretical issues in pure mathematics Recommendations: Save 4.89% Save 27.62% Save 26.7% Save 7.13% Save 23.58% Save 5.03% Save 6
Algebra II Algebra II is typicality an upper math class taught to juniors. Out of any other class offered to highschool students it is a leading indicator of college and work success according to a study reported by the Washington Post. Most students take algebra I and geometry before algebra II, however some advanced students may be encouraged to take it their freshmen year after taking algebra I in 8th grade. The class has significant focus on higher level operations in algebra including radical, logarithmic, and exponential functions. Modeling and application is particularly important. Looking to compare unit and pacing guides? We have a small collection of planning resources from unit plans to full semester course plans. Take what you need, all we ask is that you upload any great planning guides you have.
Browse Bestsellers The Eighth Edition of this highly dependable book retains its best features–accuracy, precision, depth, and abundant exercise sets–while substantially updating its content and pedagogy.Now in its third edition, Mathematical Concepts in the Physical Sciences provides a comprehensive introduction to the areas of mathematical physics. It combines all the essential math concepts intoDesigned for students in various disciplines of engineering, science, mathematics, management and business, this effective study tool includes hundreds of problems with step-by-step solutions and ... > read more Eminently suited to classroom use as well as individual study, Roger Myerson's introductory text provides a clear and thorough examination of the models, solution concepts, results, and ... > read more "Amoeba" Don't ever tease a wee amoeba By calling him a her amoeba. And don't call her a him amoeba. Or never he a she amoeba. 'Cause whether his or hers amoeba, They too feel like you and meba. ... > read more Focusing on helping students to develop both the conceptual understanding and the analytical skills necessary to experience success in mathematics, we present each mathematical topic in this text ... > read more
Mathematics Frequently Asked Questions Studying mathematics at university is very different to high school. To ensure that you are appropriately prepared, you should choose your HSC subjects carefully and check the assumed knowledge required for your chosen program. What level of maths should I take for my HSC if want to study Mathematics at university? We suggest that you take the highest level of mathematics that you can at school. While there are no prerequisites for the BMath, the assumed knowledge requirement is currently HSC Mathematics Extension 1 with results in Band 4, or the equivalent in your state or country. You will fmd it difficult to undertake the advanced first-year mathematics courses MATH1210 and MATH1220 if you do not have this assumed knowledge. What if I don't have the assumed knowledge, or if HSC Mathematics Extension 1 was not available at my school? You can still enrol in the BMath if you have not met the assumed knowledge criteria. The flexible structure of the degree includes an alternative program, which allows you to take the foundational mathematics courses MATH1110 and MATH1120 in first year. Combined with the second-year course MATH2340, this structure provides an alternative pathway to more advanced topics in mathematics. Are there any other HSC subjects I should take? If you have a clear idea of what you want to do in the future, then you should make appropriate choices of subjects at school. For example, if you know that you are interested in studying Engineering as a combined degree with Mathematics, taking science subjects such as Physics and Chemistry will help you meet the assumed knowledge for that discipline. If you are not sure what you want to do in the future, then you should study a broad base of enabling subjects such as Physics and English. Remember that the BMath gives you a wide choice of electives and can prepare you for diverse career paths, so you can explore your areas of interest at university as well as high school.
Modern Geometry / With Cd - 02 edition Summary: Modern Geometry was written to provide undergraduate and graduate level mathematics education students with an introduction to both Euclidean and non-Euclidean geometries, appropriate to their needs as future junior and senior high school mathematics teachers. Modern Geometryprovides a systematic survey of Euclidean, hyperbolic, transformation, fractal, and projective geometries. This approach is consistent with the recommendations of the National Council of Teachers...show more of Mathematics (NCTM), the International Society for Technology in Education (ISTE), and other professional organizations active in the preparation and continuing professional development of K-12 mathematics teachers. ...show less The Concept of Parallelism. Points, Lines, and Curves in Poincare's Disc Model. Polygons in Hyperbolic Space. Congruence in Hyperbolic Space. 4. TRANSFORMATION GEOMETRY. An Analytic Model of the Euclidean Plane. Representing Linear Transformations in 2-space with Matrices. The Direct Isometries: Translations and Rotations. Indirect Isometries: Reflections. Composition and Analysis of Transformations. Other Linear Transformations. 5. FRACTAL GEOMETRY. Introduction to Self-similarity. Fractal Dimension. Iterated Function Systems. From Order to Chaos. The Mandelbrot Set87.3288.6796.50 +$3.99 s/h VeryGood
Just the critical concepts you need for cramming, homework help, and reference Whether you're cramming, you're studying new material, or you just need a refresher, this compact guide gives you a concise, easy-to-follow review of the most important concepts covered in a typical Algebra I course. Free of review and ramp-up materials, it lets you skip right to the parts where you need the most help. It's that easy! Set the scene — get the lowdown on everything you'll encounter in algebra, from words andsymbols to decimals and fractions Attention Guests! This article is made available free of charge, as a service to our users. Please login to access the full article, or register if you do not yet have a username and password.
NZ 'pilot' School : Who is this Aussie anyway? : Who is this Aussie anyway? I'm not a salesman I currently teach at a large co-educational, independent, metropolitan school in Melbourne. My school currently use TI89's but are up-dating soon to . . . Who do we have here today? : Who do we have here today? RED – What is this 'CAS' you speak of. AMBER – I know what it is but I haven't really used it in the classroom GREEN - I use CAS with my classes already What is CAS? : What is CAS? Computer Algebra System A CAS has the ability to perform symbolic manipulations in much the same way as we might do ourselves with pen and paper. For example, expand and factorise algebraic expressions. CAS has also powerful numerical computational capabilities and the ability to represent and analyse mathematical problems graphically and in spreadsheets. But CAS can also be used as a learning tool Why do I think that CAS is good for 14 – 16 year olds? : Why do I think that CAS is good for 14 – 16 year olds? For learning rules from pattern recognition. For scaffolding of Algebra. For multiple representations and making connections between them. Can use parameters to explore graphs or equations to find generalised solutions to big questions. And all on the one portable piece of plastic 1. For learning rules from pattern recognition : 1. For learning rules from pattern recognition How would you normally teach Solving quadratic equations The 'Null factor law' 2.For scaffolding of Algebra. : 2. For scaffolding of Algebra. : 2. For scaffolding of Algebra. Training wheels for solving equations Allows a 'safe environment' for students to make mistakes and learn from the effects. Undo the mistake and try something else. Particularly good for weaker students. Demonstrates that there isn't just one algorithm to solve something. How many ways can you solve it? Can work backwards to generate own questions. 3. Multiple representations and making connections. : 3. Multiple representations and making connections. How do you currently teach Simultaneous Equations? Substitution? Elimination? Graphically? 3. Simultaneous Equations – what we did with year 10 : 3. Simultaneous Equations – what we did with year 10 Tell me a story Worded problems Table of values Graphically Home screen Substitution and elimination by CAS Saved 'by hand' techniques for extension and until year 11. 3. Tell me a story : 3. Tell me a story A picture is worth a thousand words In small groups, students were given a theme and asked to decide what was happening in the graph and then present their story to the rest of the class. Themes included: Cyclists, Cars, Planes, Bushwalkers, Mobile phones, Filling a beaker, Taxi fare, movies, goal scoring, Chinese characters 3. Tell me a story : 3. Tell me a story Hints Decide what each of the axes represent What is happening At the start Before the lines cross When the lines cross After the lines cross Slide 17: E.g. Two groups went to the movies. The first group included 5 adults and 5 kids and paid a total of $115. The second group included 2 adults and 7 kids and paid a total of $107. If ticket prices were the same for each group, find the cost of each type of ticket. Examine the following screen from a CAS calculator, which has been used to find a solution to the simultaneous equations x + y = 5 and 3x + 2y = 11. : Examine the following screen from a CAS calculator, which has been used to find a solution to the simultaneous equations x + y = 5 and 3x + 2y = 11. Explain how the CAS has been used to find a solution Use this method to check the solutions you obtained earlier 3. Multiple representations and making connections. : 3. Multiple representations and making connections. Next generation CAS Nothing new CAS Sketch-pad add on 4. Can use parameters to explore graphs or equations. : What happens to the volume of a sphere if the radius is doubled? Beyond most kids algebra, but raises questions so we can then explore why. 4. Can use parameters to explore graphs or equations. Belt around the Earth : Belt around the Earth Consider a belt that is placed to fit around the equator of the earth. If 6m is then added to the belt circumference, can you: A slip a piece of paper under it? B slide your hand under it? C crawl under it? D walk under it? CAS as a learning tool : CAS as a learning tool Represents a move away from algorithms, providing opportunities to develop thinking and a deeper understanding. Moving away from compartmentalised Mathematics Instead of skill, skill, skill, application Now start with a 'real-life' problem as a hook and learn the skills because we need them Also represents a move to less 'contrived' Mathematics Provides Motivation CAS the 'black box' : CAS the 'black box' Great way to get answers Great way to Generate Questions But won't it mean my student will lose their algebra skills? : But won't it mean my student will lose their algebra skills? Yes CAS gives the Answer Want to know why? Must do by hand Still need algebra skills, in fact more of them to interpret CAS output as it doesn't always come up as expected. (e.g. transposing some formulae) Issues : Issues Cost Theft Class sets Syntax – Can be a pain to start with i-pods and mobiles are here to stay Qualified staff - Some staff prefer the algorithmic approach Assessment Assessment : Assessment : Assessment Don't ask traditional type questions Assessment of students understanding of mathematical concepts Not assessing how well students have memorised algorithms Benefits : Benefits Top of the tree analogy (Tony McRae) We can see the destination, where we are headed. Allows you to quickly see where you are going. F1 race car analogy (Tony McRae) Safety car holds back all the cars. Ear piece, can give instruction but let your better students fly ahead at their own pace. First golf game analogy (Peter Fox) Driving range first to get skills? Or . . . Play the game first, then want to learn skills .
Elayn Martin-Gay's developmental math textbooks and video resources are motivated by her firm belief that every student can succeed. Martin-Gay's focus on the student shapes her clear, accessible writing, inspires her constant pedagogical innovations, and contributes to the popularity and effectiveness of her video resources. This revision of Martin-Gay's algebra series continues her focus on students and what they need to be successful. Description: This text presents methods of modern set theory as tools that can be usefully applied to other areas of mathematics. The author describes numerous applications in abstract geometry and real analysis and, in some cases, in topology and algebra. ... Description: Did you decide NOT to purchase the accompanying textbook at the beginning of the semester? Are you now wishing that you had a textbook? We have designed a product just for your situation more economical, more portable (thinner and ...
Numerical the intelligent application of approximation techniques to the type of problems that commonly occur in engineering and the physical sciences. Students learn why the numerical methods work, what type of errors to expect, and when an application might lead to difficulties. The authors also provide information about the availability of high-quality software for numerical approximation routines. The techniques are essentially the same as those covered in the authors' top-selling Numerical Analysis text, but in this text, full m... MOREathematical justifications are provided only if they are concise and add to the understanding of the methods. The emphasis is placed on describing each technique from an implementation standpoint, and on convincing the student that the method is reasonable both mathematically and computationally. This book emphasizes the intelligent application of approximation techniques to the type of problems that commonly occur in engineering and the physical sciences. Readers learn why the numerical methods work, what type of errors to expect, and when an application might lead to difficulties. The authors also provide information about the availability of high-quality software for numerical approximation routines. In this book, full mathematical justifications are provided only if they are concise and add to the understanding of the methods. The emphasis is placed on describing each technique from an implementation standpoint, and on convincing the reader that the method is reasonable both mathematically and computationally.
We've produced a scheme of work to help you extend and enrich the mathematical learning of Higher Tier students who are following the Edexcel Certificate in Mathematics or the International GCSE Mathematics A specifications. Through teaching the Edexcel GCE Core Mathematics 1 unit alongside the Higher Tier content, you will be able to prepare your Higher Tier students for the transition from Level 2 Mathematics to AS Mathematics and beyond. The scheme of work also enables you to extend several topic areas of the Mathematics Higher Tier content. It should be used together with the higher tier course planner in the Teacher's Guide produced for this qualification. You'll find the scheme of work in the documents list under 'Teacher support materials', alongside the Teacher's Guide.
In order to succeed in this system you must first understand it. We begin by examining some of the components of a mathematics course, and then looking at how they all fit together. The most prominent feature of large mathematics courses is the lecture. Lectures typically meet for an hour (actually, fifty minutes) on Mondays, Tuesdays and Wednesdays. In a thirteen week semester this adds up to a maximum of thirty-nine hours. University courses generally require that students learn in much greater depth and breadth than high school courses. Considering the volume of material to be covered in a semester, it is clear that these thirty-nine hours must be used extremely efficiently by both the instructor and the student. An instructor may sometimes use the lecture to point out interesting things not contained in the book, to give alternate explanations to those presented in the text or to unify the concepts as presented in the text. The next feature is the recitation section. These are one-hour meetings, generally on Thursday or Friday mornings, with a TA. The main purpose of these section meetings is to reinforce the material covered that week by focusing on additional examples, especially of the type assigned for homework. Mathematics is not a spectator sport; rather, it is a contact sport. The section meetings provide an interactive setting in smaller groups in which applications of mathematical concepts may be explored. The final major component of a course is the help available outside of class. The many options for assistance are discussed below. The student should take care to view all of the components of a course, including lectures, sections, examinations, homework, textbook and help availability as a collection of elements designed to help them in their continuing study of mathematics. All of these components are designed to fit together as a package to help the student understand the material from as many points of view as possible.
MathsHere are a few notes that are useful when working with algebraic expressions and functions. Remember you simplify an expression by collecting like terms You can also simplify expressions by using rules of indices (powers) [IMAGE] [IMAGE] [IMAGE] To expand negative areas. It covers understanding that areas below the x axis are negative, calculating areas under a curve, some or all of which may be under the x axis. Before attempting this chapter you must have prior [...] solving equations with algebraic fractions. It covers understanding how to solve equations involving fractions, working with denominators with either constants or linear factors. Before attempting this chapter you must have prior knowledge of expanding brackets and factorising [...]
Video Summary: This learning video introduces students to the world of Fractal Geometry through the use of difference equations. As a prerequisite to this lesson, students would need two years of high school algebra (comfort with single variable equations) and motivation to learn basic complex arithmetic. Ms. Zager has included a complete introductory tutorial on complex arithmetic with homework assignments downloadable here. Also downloadable are some supplemental challenge problems. Time required to complete the core lesson is approximately one hour, and materials needed include a blackboard/whiteboard as well as space for students to work in small groups. During the in-class portions of this interactive lesson, students will brainstorm on the outcome of the chaos game and practice calculating trajectories of difference equations
...Product Description: and examining in detail many relatively recent theorems. Several hundred theorems and corollaries are formulated and proved completely; numerous others remain unproved, to be used by students as exercises. The author makes liberal use of circular inversion, the theory of pole and polar, and many other modern and powerful geometrical tools throughout the book. In particular, the method of "directed angles" offers not only a powerful method of proof but also furnishes the shortest and most elegant form of statement for several common theorems. This accessible text requires no more extensive preparation than high school geometry and trigonometry
This instructor is phenomenal! I have listened to many of the sample lessons and in my opinion, her teaching skills are superior to any others. I am currently fulfilling a math requirement after a hiatus of 50 years and find her instructional method clear, concise, and extremely easy to understand. She is the epitome of what a teacher should be. This lesson was easy to follow. With my continuing troubles with the instructors voice aside, there were tons of examples that were easy to follow along with. After the first few I was pausing the video, working the problem, then checking as she explained it which was a good way to catch a few of the mistakes I was doing. Below are the descriptions for each of the lessons included in the series: Algebra: Operations With Radicals 160 This 75 minute basic algebra lesson deals with radicals (roots). You will learn how to simplify by adding, subtraction, multiplying and dividing radicals without the use of a calculator. You will learn: - definitions, perfect squares and cubes, radical, radicand, index, square and other roots, mixed radical, entire radical, like radicals - to simplify radicals - to change mixed radicals to entire radicals - to multiply & divide radicals - add & subtract radicals - to work with radicals and special products: difference of squares & perfect squares - identities - word problems involving rectangles and squares This lesson contains explanations of the concepts and 44 example questions with step by step solutions plus 5 interactive review questions with solutions. Lessons that will help you with the fundamentals of this lesson: - 100 All About Numbers ( - 105 Rules for Integers and Absolute Value ( - 125 Multiplication of Polynomials ( This lesson contains explanations of the concepts and 28 example questions with step by step solutions plus 6 interactive review questions with solutions. Lessons that will help you with the fundamentals of this lesson: - 100 All About Numbers ( - 105 Rules for Integers and Absolute Value ( - 115 The 5 Basic Exponent Laws ( - 160 Operations With Radicals ( Basic Algebra: Factoring Polynomials 170 This 82 minute basic algebra lesson explains what factoring is and teaches how to factor different types of polynomials using the three most common types of factoring: - common factoring (find the greatest common factor (GCF) - factoring trinomials in the form ax^2 + bx + c - factoring as a difference of squares, questions like 81x^2 – (y + w)^2 A factoring strategy is also outlined to help you with factoring. This lesson contains explanations of the concepts and 37 example questions with step by step solutions plus 5 interactive review questions with solutions. Lessons that will help you with the fundamentals of this lesson: - 105 Rules for Integers and Absolute Value ( - 110 Basic Algebra Part I ( - 120 Basic Algebra Part II ( - 125 Multiplication of Polynomials ( Coordinate Geom: Graphing Linear Relations 195 This 79 minute coordinate geometry lesson covers graphing linear relations (straight lines), x & y intercepts and lines perpendicular to a graph of an equation. After this lesson you will be able to: - find the slope and y intercept from an equation - write equations of lines given one point and the slope or given two points - understand relations (sets of ordered pairs) - graph linear relations using: a calculator, table of values, x and y intercepts, slope of a line and a point on the line - understand a missing variable - work with positive, negative, zero and undefined slope - understand slope intercept form y = mx + b and understand point slope form - recognize the standard form of a linear equation Sample question: Find the equation in standard form of the line passing through (4, -2) and perpendicular to the graph of 5x – y – 1 = 0 This lesson contains explanations of the concepts and 23 example questions with step by step solutions plus 7 interactive review questions with solutions. Lesson that will help you with the fundamentals of this lesson: - 190 Coordinate Plane, Distance and Midpoint Formulas ( Algebra: Solving Systems of Linear Equations 205 This 86 minute intermediate algebra lesson focuses on solving linear (first degree) equations. The equations in a system of two linear equations are studied together with both graphic and algebraic methods used for solution. This lesson will help you understand how to solve: - using the graphing method - algebraically using the substitution method, the the comparison method, and the addition or subtraction (elimination) method (e.g. solve for x and y in using 5x + 3y = -14 and 3x – 6y = -11) - a consistent and dependent system of two linear equations algebraically - a consistent and independent system of two linear equations - an inconsistent system of two linear equations - a system of linear equations in three variables This lesson contains explanations of the concepts and 19 example questions with step by step solutions plus 6 interactive review questions with solutions. Lesson that will help you with the fundamentals of this lesson: - 190 Coordinate Plane, Distance & Midpoint Formulas, Slope ( Algebra: The Quadratic Function 220 This 84 minute intermediate algebra lesson focuses on the quadratic function y= ax^2 + bx + c, a ≠ 0. This lesson will help you understand and learn to: - work with the quadratic function of the form y= ax^2 + bx + c, a ≠ 0 to draw parabolas - graph y = ax^2 with different values for a - graph y = ax^2 + c with different values for c - complete the square on the form y = ax^2 + bx + c to change to the form y = a(x-p)^2 +q in order to find the vertex, the equation of the axis of symmetry, the minimum or maximum value, the range of the function, and what happens when (p is positive? negative?) (q is positive? negative?) - solve minimum and maximum word problems - work with parabolas to determine if they are functions or not, if they are expanded vertically (stretch in the y direction), if they are compressed vertically (shrink in the y direction), and if they open upward or downward This lesson contains explanations of the concepts and 16 example questions with step by step solutions plus 6 interactive review questions with solutions. Lessons that will help you with the fundamentals of this lesson: - 170 Factoring Polynomials ( - 210 Relations & Functions (Domain, Range, Functional Notation, & Inverses of Functions) ( Algebra: Factoring Quadratic Equations 230 This 75 minute intermediate algebra lesson focuses on solving quadratic (2nd degree) equations. This lesson will help you understand and learn how to solve quadratic equations using different types of factoring: - common factor - factoring a difference of squares - factoring simple and complex trinomials and perfect square trinomials Also covered in this lesson are: - parabolas - x intercepts - roots (distinct, equal and non-real) - standard form and the zero product property - how to find a quadratic equation given its roots. This lesson contains explanations of the concepts and 41 example questions with step by step solutions plus 5 interactive review questions with solutions. Lessons that will help you with the fundamentals of this lesson include: - 125 Multiplication of Polynomials ( - 170 Factoring Polynomials ( Algebra: Using the Quadratic Formula 235 This lesson will help you understand how to find the values of a, b & c and solve equations using the quadratic formula when:: - answers are in the simplest form - answers must be simplified - there are no real roots - the quadratic equation can be factored - you use your calculator to express answers as decimals Sample question: Solve 2x^2 + x = -5 This lesson contains explanations of the concepts and 25 example questions with step by step solutions plus 6 interactive review questions with solutions. Lessons that will help you with the fundamentals of this lesson include: - 160 Operations with Radicals ( - 230 Solving Quadratic Equations by Factoring ( Algebra: Polynomial Functions Synth Div 260 This 81 minute advanced algebra lesson studies 3rd & 4th degree polynomial functions. The lesson begins with a review of long division of a polynomial by a binomial and then introduces synthetic division. You will learn how to: - define a polynomial function - find the remainder using the remainder theorem - evaluate polynomials - find a zero of a polynomial function using the factor theorem for example and factor completely and find the zeros of f(x) = x^3 + 4x^2 + x - 6 - factor 3rd & 4th degree polynomial functions - classify zeros as integral or rational and determine their multiplicities This lesson contains explanations of the concepts and 18 example questions with step by step solutions plus 6 interactive review questions with solutions. Lessons that will help you with the fundamentals of this lesson include: - 130 Long Division of a Polynomial by a Binomial ( - 170 Factoring Polynomials ( - 205 Solving Systems of Linear Equations ( Exponents & Logs: Graphing Functions 405 This 64 minute exponents & logarithms lesson studies the graphs of the exponential function and the inverse of the exponential function, which is the logarithm: This lesson will show you how to: - graph exponential functions and summarize the characteristics of the graphs - find the inverse of the exponential function - graph logarithmic functions and summarize the characteristics of the graphs - understand the x and y intercepts, an asymptote, domain & range, growth and decay functions, and the reflection property Sample question: Given the exponential function y = 2^x, write its inverse in exponential form On the same grid, draw the graphs of y = 2^x and its inverse x = 2^y. Show the line of reflection y = x This lesson contains explanations of the concepts and 13 example questions with step by step solutions plus 3 interactive review questions with solutions. Lesson that will help you with the fundamentals of this lesson: - 400 Solving Exponential Equations
Stamford, CT Precalculus equations that involve an unknown function and one or more of its derivatives. They are solved by determining the functions that satisfy the equations. They are very common in physics, engineering, economics, and many other sciences. for one year.
This course is designed for Pennsylvania students who will be taking the PSSA math assessment in the spring of their third grade year. This course will prepare students in the areas of Numbers and Operations, Algebraic concepts, Geometry, Measurement, Data Analysis and Probability; the specific areas assessed on the PSSA test. Not only will the students become familiar and comfortable with the overall application of the mathematical skills presented in this course, but they will also gain a deeper understanding of all mathematical concepts.
Quick Review Math Handbook hot words hot topics 9780078601262 ISBN: 0078601266 Pub Date: 2004 Publisher: McGraw-Hill Higher Education Summary: "Quick Review Math Handbook: Hot Words, Hot Topics" (available in English and Spanish) provides students and parents with a comprehensive reference of important mathematical terms and concepts to help them build their mathematics literacy. This handbook also includes short-instruction and practice of key standards for Middle School and High School success
I guess that's what TI is for, the boring maths stuff these days. The calc community handles the fun stuff, and trying to outmaneuvre TI's OS protection. Math gives you the ability to upgrade a qualitative understanding to a more precise and powerful quantitative point of view. And when someone bores you with details, that's not a characteristic of math, it's a problem with the presenters personality and we all know a few teachers who have that problem. Take the simple act of subtraction for example. Consider adding a negative instead?Edit: And math is not boring Yeah I didn't mean Maths is boring, but that the technical mathematical features they handle and add with blocking third-party programs, all official things and stuff
MATH 220.921: Mathematical Proof The main aim of the course is to learn how write clear and correct mathematical proofs. It provides the gateway to more advanced mathematics. A little more precisely (though this is provisional) we cover subjects from: 07/29/2020- There will be extra office hours on Friday 12--1 and 3--5 and Saturday 12--2. 07/29/2010- Solutions to Homework 8 posted. 07/23/2010- Solutions to Homework 7 posted. 07/22/2010- Homework 8 posted due on Thursday July 29th. 07/13/2010- Homework 7 posted due on Tuesday July 20th. 06/29/2010- Second Midterm will be on Thursday July 8th, with questions on Chapters 5, 6 and 9. 06/29/2020- Our next lecture on July 6th will be a problem solving session. 06/29/2010- Solutions to HW6 has been posted and there will be no homework for next week. 06/22/2010- Homework 6 and solutions to midterm1 and HW 5 have been posted. 06/02/2010- The first midterm is on chapters 1--5. 06/01/2010- There will be a problem solving session on Monday June 7th 10--12 in MATH100. 06/01/2010- There will be no lecture on Tuesday June 8th and first Midterm will be on Thursday June 10th. 05/28/2010- Homework 3 and solutions to HW 2 posted. 05/20/2010- Homework 2 posted due on Thursday May 27th. 05/13/2010- Homework 1 posted due on Thursday May 20th. 05/04/2010- Website Created. You must have either a score of 64% or higher in one of MATH 101, MATH 103, MATH 105, SCIE 001, or one of MATH 121, MATH 200, MATH 217, MATH 253, MATH 263. If you do not have these prerequisites then you must see your lecturer as soon as possible. Exams: There will be two Midterm Exams totally worth 40% of the term grade, tentatively on June 10th, and one on July 8th. There will be a final examination held either the evening of Friday July 30 or Saturday July 31. This exam will account for 50% of a student's final grade. The final exam will not generally be weighted higher for students who perform better on the final exam than they did during the term, although some allowance may be made for students who perform much better on the final exam than they did during the term. Homework Assignments: On this web-page you will find the sections from the text that you should be reading before to come to class. The instructor will try to observe this pre-determined schedule. It is important that you check regularly this course webpage. Homework assignments will be posted weekly on this course website, best 8 grades (out of 9 or 10 homworks in total) is counted as 10% of the term grade. Homework is the essential educational part of this course. You cannot expect to work problems on the exams if you have not worked lots of homework problems. Therefore, it is important that you spend an adequate time on homework regularly, each week. Late homework will not be accepted. You can work together on the homework, but you should always write up your own homework solutions in your own words.
What is Algebra??? An introduction to Algebra twelve slide presentation has been designed to introduce my 11th grade algebra students to get their minds thinking about what they have learned in their previous two years of mathematics study. There is a brief 10 minute video clip that gets the students hooked on the topic. I have included questions that accompany the video that I obtained from United Streaming. I used this lesson this morning with my 2 ALgebra 2 classes, and it went really well. Presentation (Powerpoint) File Be sure that you have an application to open this file type before downloading and/or purchasing. 169 Vanessa Moon a question. They will receive an automated email and will return to answer you as soon as possible. Please Login to ask your question. QUESTIONS AND ANSWERS: abaumer Hello, I purchased What is Algebra??? An introduction to Algebra 2 and downloaded the powerpoint. The video file Part_One_What_is_Algebra_.asf was not included. Would you e-mail it to me or send me the link? Thanks. August 9, 2010 Showing 1-1 of 1
This introduction to combinatorics, the foundation of the interaction between computer science and mathematics, is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics. The four-part treatment begins with a section on counting and listing that covers basic counting, functions, decision trees, and sieving methods. The following section addresses fundamental concepts in graph theory and a sampler of graph topics. The third part examines a variety of applications relevant to computer science and mathematics, including induction and recursion, sorting theory, and rooted plane trees. The final section, on generating functions, offers students a powerful tool for studying counting problems. Numerous exercises appear throughout the text, along with notes and references. The text concludes with solutions to odd-numbered exercises and to all appendix exercises. Revised version of the Redwood City, CaliforniaMatroid Theory by D. J. A. Welsh Text by a noted expert describes standard examples and investigation results, using elementary proofs to develop basic matroid properties before advancing to a more sophisticated treatment. Includes numerous exercises. 1976 edition. read more
Solving the Unknown with Algebra Pre-Algebra Skills: Using Formulas, Solving for Unknowns, and Manipulation of Equations Welcome to "Solving the Unknown with Algebra," a new math program aligned with NCTM standards and designed to help students practice pre-algebra skills including using formulas, solving for unknowns, and manipulating equations. Follow the adventures of Rick and Athena as they solve real-world questions through powerful mathematical thinking! Developed by The Actuarial Foundation with Scholastic, this program provides skill-building activities that use mathematics for real purposes, while motivating students to achieve success in the classroom and in real-world situations outside of school. Each of the three lessons below is accompanied by fun printables that include a lesson worksheet, bonus worksheet, and take-home activity. Lesson 3: Functions and Formulas/Square Roots In this lesson, students will understand what a square root is and that squares and square roots are inverse operations and can be used to manipulate equations as long as "whatever is done to one side of the equation is done to the other."
Graphing Author: ISBN-13: 9780768202373 ISBN: 076820237X Publisher: Schaffer Publications, Frank Summary: Help students succeed in math! Math Minders provide students with the self-confidence they need to succeed in math. Students learn one step at a time, reviewing skills learned in earlier grades, then moving to skills appropriate for their grade level. They progress gradually, giving them the constant feeling of success! Vocabulary is kept at a level appropriate for each grade level to help ensure success. Fun and sim...ple formats help maintain a high level of student interest. Perfect for home or school, or to reinforce any existing math program.[read more] A copy that has been read, but remains in excellent condition. Pages are intact and are not marred by notes or highlighting. The spine remains undamaged. We make every effort [more] A copy that has been read, but remains in excellent condition. Pages are intact and are not marred by notes or highlighting. The spine remains undamaged. We make every effort to identify defects, but as we're only human, we do occasionally miss one. If you get a problem item be sure to contact us
Jeremy Ross Copyright 2008 by Sharp Electronics Corporation. All rights reserved. This publication may not be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise without written permission. Sharp is a registered trademark of Sharp Corporation. Table of Contents Calculator Layout Special Functions Examples Using the Sharp EL-W535B Calculator TEACHING ACTIVITIES FOR THE CLASSROOM BASIC ARITHMETIC Calculator Activity Practice Activity FRACTIONS Calculator Activity Practice Activity POWERS AND ROOTS Calculator Activity Practice Activity PARENTHESES AND EDITING Calculator Activity Practice Activity ANGLE CONVERSIONS Calculator Activity Practice Activity TRIGONOMETRIC FUNCTIONS Calculator Activity Practice Activity INVERSE TRIGONOMETRIC FUNCTIONS Calculator Activity Practice Activity COORDINATE CONVERSIONS Calculator Activity Practice Activity LOGARITHMS Calculator Activity Practice Activity INVERSE LOGARITHMS Calculator Activity Practice Activity BASE CONVERSIONS Practice Activity Practice Activity RANDOM NUMBERS, DIE, COINS, AND INTEGERS Calculator Activity Practice Activity PROBABILITY Calculator Activity Practice Activity 34 1 VARIABLE STATISTICS Calculator Activity Practice Activity 2 VARIABLE STATISTICS & LINEAR REGRESSION Calculator Activity Practice Activity ANSWERS Special Functions of the Sharp EL-W535B Calculator Modes. This calculator has three modes. NORMAL, STAT, and DRILL mode. To access these modes press STAT, and for DRILL. followed by for NORMAL, for Degrees. The EL-W535B can be set to degrees, radians, or grads. Press and enter and for grads. for DRG. Then press for degrees, for radians, Display. There are five display notation systems. To set the number of decimals places press for FSE. For fixed decimal type and then choose your TAB or decimal setting. To set the calculator for scientific notation press. Now enter the number of significant figures. To set the calculator for engineering notation press and then enter the desired TAB setting. To set the floating-point number system in scientific notation press either or to choose NORM1 or NORM2. To choose WriteView, which displays formulas and equations just like textbooks, press. For Line Editor press followed by. Then press. If in and then followed by . Then press Line Editor you can choose an entry mode by pressing for insert and for overwrite. and the function key,. , Hyperbolic Functions. Press Enter the angle. Then press Trigonometric Functions. Press the trigonometric function key,. Enter the angle. Then press Inverse Hyperbolic Functions. Press trigonometric function key. , ,. followed by . Then press. . Enter the number. Then press. Enter the number. Then press Base Logarithms. If in WriteView mode press press and enter the number. Then press. Enter the base. Then press. Higher roots. Enter the index. Press radicand. Then press Cube roots. Press. followed by . Enter the base. Then. If in Line Editor press. Enter the number. Then Press . Enter the . Enter the radicand. Then press followed by Reciprocals. Enter the number. Press. Antilogarithms. Press Exponentials. Press. . Enter the exponent. Then press followed by . Enter the exponent. Then press Cubes. Enter the number to be cubed. Press Scientific Notation. Enter the number. Press press. . Enter the. Memory. The calculator has 9 memories. Memory calculations can be performed in NORMAL and STAT modes. Enter the value to be stored. Press. Press the location you wish to store the value A-F, M, X, or Y. Recall Memory. Press or Y. Press the location you wish to access A-F, M, X, Last Answer Recall. Perform a calculation. Press the operation key. The last answer will be recalled. Enter the number. Then press. Definable Memories. You can store functions or operations in definable memories (D1-D4). Press function , , ,. Press the location you wish to store your. Press the operation you want to store. Change. You can change your answer from decimals to mixed numbers to fractions by pressing. Also, you can change your answer from decimals or fractions to answer containing the pi symbol or square root symbol by pressing. Random. You can generate random numbers, dice, coin flips, or integers. Press. Press for random numbers between 0 and 1. Press for random coin flips where 0 is for random dice rolls from 1 to 6. Press heads and 1 is tails. Press for random integers between 0 and 99. P<->R Conversion. To convert to polar coordinates enter your x-coordinate first. Then press. Then enter the y-coordinate. Press. To convert to rectangular coordinates enter your r-value. Press theta. Press. followed by . Enter . Enter the number. Enter the expression. Press. Binary. To convert from one of the supported base systems into binary enter the number. Then press. Hexadecimal. To convert from one of the supported base systems into hexadecimal enter the number. Then press. Octadecimal. To convert from one of the supported base systems into octadecimal enter the number. Then press. Decimal. To convert from one of the supported base systems into decimal enter the number. Then press. Pentadecimal. To convert from one of the supported base systems into pentadecimal enter the number. Then press. Examples: Please refer to the following examples and the keystrokes required to enter each problem. From these simple examples more complicated expressions can be easily entered. 153 33% log10 ln e sin 30 cos 1 0 tanh 78 3! 10C 5 6P1 Using the Sharp EL-W535B Calculator GETTING STARTED The National Council of Teachers of Mathematics and many other organizations with a commitment to the mathematics education of our youth have all given their support to the ongoing and appropriate use of calculators. In this document, convincing arguments for the ongoing use of calculators to enhance the mathematical capabilities of students at all grade levels are presented as well as a description of the features expected to be available on calculators. The EL-W535B uses WriteView technology and allows students to enter equations as they are seen in their textbooks. ACTIVITY AND PRACTICE SHEETS The fifteen calculator activities and practice sheets found in this book have been designed to be used with the Sharp EL-W535B calculator. The activities have been written and developed for students in grades nine through twelve. Some of the activities will be more appropriate for students in a particular grade, while others could be used at any grade level. Of course, the classroom teacher can and should make the decision as the appropriateness of each activity. Each activity page has an objective statement and some practice key strokes. The activity page does not attempt to teach mathematics. It only identifies the mathematics being used and demonstrates the calculator key strokes necessary to conduct a calculation. The practice page provides activities for the students to practice using the key strokes presented on the activity page. Answers to the activity and practice sheets are provided at the end of this booklet. TEACHING ACTIVITIES FOR THE CLASSROOM The Sharp EL-W535B was designed with you and your students in mind. The following activities have been written to provide the practice students need to succeed in mathematics, as they become familiar with the wonderful features of this exciting and powerful mathematical tool. Calculator Activity BASIC ARITHMETIC OBJECTIVE: To perform basic operations by developing a sequence of numbers. Performing a specified operation repeatedly can generate a sequence of numbers. For example, if you start with the number 4 and add 2 repeatedly you will generate the sequence 4,6,8,10 1. Add 13 to 54 twice: STEP 1: Enter 13 by pressing STEP 2: Add by pressing STEP 3: Enter 54 by pressing STEP 4: Find the first sum by pressing STEP 5: Add 13 again by pressing. 2. Subtract 9 from 32 once. STEP 1: Enter 32 by pressing STEP 2: Subtract by pressing STEP 3: Enter 9 by pressing. STEP 4: Find the difference by pressing 3. Multiply -2 by 5 three times. STEP 1: Enter 2 by pressing STEP 2: Multiply by pressing STEP 3: Enter 5 by pressing. followed by. STEP 4: Find the first product by pressing STEP 5: Multiply by 5 again by pressing STEP 6: Multiply by 5 a third time by pressing NAME ___________________________________________ DATE________________ BASIC ARITHMETIC Use your EL-W535B to develop a series of sequences. 1. Find the first seven numbers of the sequence starting with 3 where each additional term is found by adding 4. -3, ___, ___, ___, ___, ___, ___, 2. Find the first four numbers of the sequence starting with 2 where each additional term is found by adding 1. 2, ___, ___, ___, 3. Find the first five numbers of the sequence starting with 6 where each additional term is by adding 3. 6, ___, ___, ___, ___, 4. Find the first three numbers of the sequence starting with 144 where each additional term is found by dividing by 2. 144, ___, ___, 5. Find the first six terms of the sequence starting with 729 where each additional term is found by dividing by 3. 729, ___, ___, ___, ___, ___, 6. Find the first three terms of the sequence starting with 1 where each additional term is found by multiplying by 45. 1, ___, ___, 7. Find the first five terms of the sequence starting with 100 where each additional term is found by subtracting 10. 100, ___, ___, ___, ___, 8. Find the first four terms of the sequence starting with 1 where each additional term is found by adding 20. 1, ___, ___, ___, 4. Simplify 2 3 5. Simplify Calculator Activity PARENTHESES AND EDITING OBJECTIVE: To perform basic operations with parentheses by finding the volume of a sphere, by recalling the expressions, and editing them to perform a new calculation. The volume of a sphere is defined to be Volume radius of the sphere. r , where r is the 3 1. Given the radius is 2 find the volume of the sphere. . and then. 2 by pressing 2 to the third power by pressing STEP 5: Calculate the answer by pressing 2. Edit the previous equation and solve the volume of the sphere given the radius is 1. Then convert the answer to a decimal STEP 1: Recall the previous equation by pressing or. STEP 2: Move the cursor so it is to the immediate right of the third power. STEP 3: Delete the power, the parenthesis, the 2, and the square root by pressing five times. followed by. STEP 4: Enter the number 1 by pressing STEP 5: Raise 1 to the third power by pressing STEP 6: Calculate the answer by pressing STEP 7: Press to convert it to an improper fraction. Press one more time to convert it to a decimal. PARENTHESES AND EDITING Use your EL-W535B and the formula to find the volume of a sphere. Recall and edit previous equation to prevent typing the whole expression over and over again. Volume 1. Find the volume of the sphere whose radius is 6. ____________________________ 2. Find the volume of the sphere whose radius is 5. ____________________________ 3. Find the volume of the sphere whose radius is 9. ____________________________ 4. Find the volume of the sphere whose radius is 10. ____________________________ 5. Find the volume of the sphere whose diameter is 10. ____________________________ 6. Find the volume of a sphere whose diameter is 12. ____________________________ Calculator Activity ANGLE CONVERSIONS OBJECTIVE: To make angle conversions by finding the missing angle of a polygon. Angles can be expressed in degrees, radians and grads. Degrees can be expressed in either decimal degrees or degrees-minutes-seconds. Remember 180 = radians = 200 grads. The formula for the sum of the angles of an n-side polygon in degrees is 180(n-2). Before inputting an angle for conversion, press angular units. and then choose the appropriate 1. Convert 45 to radians and grads. STEP 1: Set the angular units to degrees by pressing STEP 2: Enter 45 by pressing STEP 3: Convert to radians by pressing STEP 4: Convert to grads by pressing. ANGLE CONVERSIONS The sum of the angles in degrees of an n-side polygon is 180(n-2). Remember 180 radians 200 grads. Before inputting an angle for conversion press and then choose the corresponding angular units. Use your EL-W535B to find the missing angle in the specified units. 1. A triangle has two angles, which are 45 and 60. Find the missing angle and express your answer in radians. _____________________ 2. A pentagon has four angles, which are 30, 30 , 60, and 100. Find the missing angle and express your answer in grads. _____________________ 3. A triangle has two angles, which are 100 grads and 20 grads. Find the missing angle and express your answer in radians. _____________________ 4. A hexagon has five angles, which are 1.5 radians,.3 radians,.4 radians,.5 radians, and radians. Find the missing angle and express your answer in degrees. _____________________ 5. A four-sided figure has three angles, which are 16.3, 22.1, and 45. Find the missing angle and express your answer in degrees-minutesseconds. _____________________ Calculator Activity TRIGONOMETRIC FUNCTIONS OBJECTIVE: To find the distance between points by using trigonometric functions. The law of sines and the law of cosines can help determine the sides and a b c . sin sin sin The law of cosines is as follows c 2 a 2 b 2 2ab cos . angles of triangles. The law of sines is as follows 1. Using the law of sines find the length of side a given 37, 53, b 4. STEP 1: Set the angular units to degrees by pressing STEP 2: Multiply 4 by sin(37) by pressing. STEP 3: Divide by sin(53) by pressing. 2. Using the law of cosines fine the length of c given a 5, b 12, radians. 2 STEP 1: Set the angular units to radians by pressing STEP 2: Add and by pressing STEP 3: Subtract 12 cos( ) by pressing 2 . STEP 4: Take the square root by pressing. Note: Tangent can be used in a similar manner as sine as cosine TRIGONOMETRIC FUNCTIONS Use your EL-W535B together with the law of sines and the law of cosines to find the distance of the missing side The law of sines is a b c . sin sin sin The law of cosines is c 2 a 2 b 2 2ab cos . 1. Given 30, 63, a 11 determine the length of side c. ___________________ 2. Given 16 grads, 69 grads, b 123 find the length of side a. ___________________ 3. Given a 30, b 40, 1.5 radians find the length of side c. ___________________ 4. Given a 15, c 30, 45 find the length of side b. 5. Given b 13, c 23, 100 grads find the length of side a using the law of sines. Calculator Activity INVERSE TRIGONOMETRIC FUNCTIONS OBJECTIVE: To perform operations with inverse trigonometric functions. 1. Find in degrees when tan 1 STEP 1: Set the angular units to degrees by pressing STEP 2: Enter tan 1 (1) by pressing STEP 3: Calculate the answer by pressing. 2. Find in degrees when cos 0 STEP 1: Set the angular units to degrees by pressing STEP 2: Enter cos 1 (1) by pressing STEP 3: Calculate the answer by pressing. 3. Find in radians when sin STEP 1: Set the angular units to radians by pressing STEP 2: Enter sin 1 ( 2 ) by pressing 2 INVERSE TRIGONMETRIC FUNCTIONS Use your EL-W535B and the law of sines and the law of cosines to find the missing angle. 1. Given a 2, b 7, 23 find in grads. ___________________ 2. Given a 34, c 21, 94 grads, find in radians. ___________________ 3. Given a 3, b 4, c 5 find in degrees. ___________________ 4. Given a 40, b 24, c 17 find in radians ___________________ 5. Given a 5, b 12, c 13 find in degrees. ___________________ Calculator Activity COORDINATE CONVERSIONS OBJECTIVE: To convert from polar coordinates to rectangular coordinates and vice versa. A point on a circle can be described with rectangular coordinates ( x, y ) or polar coordinates ( r , ) , where r is the radius of the circle and is the angle counterclockwise from the positive x-axis. ( r , ) 1. While in degrees convert the rectangular coordinates (1,1) to polar coordinates. STEP 1: Set the angular units to degrees by pressing STEP 2: Enter 1,1 by pressing. STEP 3: Convert to polar coordinates by pressing 2. While in radians convert the polar coordinates of ( ,60) to rectangular coordinates. STEP 1: Set the angular units to radians by pressing STEP 2: Enter ,60 by pressing. STEP 3: Convert to rectangular coordinates by pressing. COORDINATE CONVERSIONS A point on a circle can be described with rectangular coordinates ( x, y ) or polar coordinates ( r , ) , where r is the radius of the circle and is the angle counterclockwise for the positive x-axis. Before converting, press and then choose degrees, radians, or grads. Use your EL-W535B to find the corresponding point on the circle. 1. While in degrees convert the rectangular coordinates (2,2) to polar coordinates ( r , ). 6. Solve for z. z e 23 followed by either 1. Convert the binary number 10011001 to decimal. STEP 1: Set the calculator to binary by pressing STEP 2: Enter 10011001 by pressing. STEP 3: Convert to decimal by pressing. 2. Convert the hexadecimal number 16841601 to octadecimal. STEP 1: Set the calculator to hexadecimal by pressing STEP 2: Enter 16841601 by pressing. STEP 3: Convert to octadecimal by pressing. 3. Convert the decimal number 144169 to pentadecimal. STEP 1: Set the calculator to decimal by pressing STEP 2: Enter the number 144169 by pressing. STEP 3: Convert to pentadecimal by pressing. BASE CONVERSIONS Use your EL-W535B to convert to and from binary, decimal, hexadecimal, octadecimal, and pentadecimal base systems. Before converting make sure you are in the right base system by pressing followed by either , , , ,. 1. Convert the octadecimal number 161033 to pentadecimal. ____________________________ 2. Convert the hexadecimal number 123 to binary. 3. Perform the indicated operations in hexadecimal and then convert your answer to octadecimal. (12) 4. Perform the indicated operations in decimal and then convert your answer to binary. 5. Convert the binary number 10101010 to decimal, octadecimal, and pentadecimal. 2. How many different ways can you choose 1 from a group of 6? STEP 1: Enter the larger number, 6, by pressing STEP 2: Enter the combination symbol by pressing STEP 3: Enter the smaller number, 1, by pressing STEP 4: Calculate the answer by pressing. 3. Find the number of permutations of 4 things taken 2 at a time. STEP 1: Enter the larger number, 4, by pressing STEP 2: Enter the permutation symbol by pressing STEP 3: Enter the smaller number, 2, by pressing STEP 4: Calculate the answer by pressing. PROBABILITY Use your EL-W535B to find the following number of combinations and permutations and to evaluate factorials. 1. How many groups or 4 can be formed from a class of 10 where order does not matter? ____________________________ 2. How many groups of 4 can be formed from a class of 10 where order does matter? ____________________________ 3. How many sets of 3 officers can be formed from a group of 15 where order does not mater? ____________________________ 4. How many sets of 3 officers can be formed from a group of 15 where order does matter? ____________________________ 5. Evaluate 5! ____________________________ 6. What is 0! ? What is 1! ? Explain why the answer is so. ____________________________________________________ ____________________________________________________ ____________________________________________________ Calculator Activity 1 VARIABLE STATISTICS OBJECTIVE: To perform 1 variable statistics. 15 1. Analyze the set ,25,35,35, 50using 1 variable statistics. STEP 1: Set the calculator to single variable statistics by pressing. STEP 2: Enter 15 by pressing STEP 3: Enter 25 by pressing STEP 4: Enter 35 two times by pressing STEP 5: Enter 50 by pressing. STEP 6: To determine the mean of the sample press STEP 7: To determine the sample mean standard deviation press. STEP 8: To determine the population standard deviation press. STEP 9: To determine the number of samples press STEP 10: To determine the sum of the samples press STEP 11: To determine the sum of squares of samples press. 1 VARIABLE STATISTICS Use your EL-W535B to analyze the following sets using 1 variable statistics. 1. Analyze the set {1,1,2,2,2,3,3,3,3} STEP 1: Set the calculator to 2 variable statistics by pressing STEP 2: Enter 1,2 two times by pressing STEP 3: Enter 2,4 by pressing STEP 4: Enter 3,7 by pressing STEP 5: Enter 10,10 by pressing. STEP 6: To determine the mean of the sample press. STEP 7: To determine the sample mean standard deviation for x press. STEP 8: To determine the population standard deviation for x press STEP 9: To determine the number of samples for x press STEP 10: To determine the sum of the samples for x press STEP 11: To determine the sum of squares of samples for x press STEP 12: To determine the mean of the samples for y press. STEP 13: To determine the sample mean standard deviation for y press STEP 14: To determine the population standard deviation for y press. STEP 15: To determine the sum of the samples for y press STEP 16: To determine the sum of squares of samples for y press STEP 17: To determine a press STEP 18: To determine b press. NOTE: Other regressions can be done in a similar manner by just setting your EL-W535B to the proper STATS Mode. 2 VARIABLE STATISTICS & LINEAR REGRESSION Use your EL-W535B to analyze the following sets using 2 variable statistics and to perform a linear regression. 1. Analyze the set and run a linear regression. X Y 4 8

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