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"Analysis" is really broad, can you specify? You can try Spivak and Apostol for the basics (Calculus) then Apostol's Mathematical Analysis for more advanced stuff. Rudin is probably a book you want to read after you know a little of everything of the others. For example, he gives a "crash course" in topology of the Euclidean space one wouldn't get anything off if hasn't already bumped into such ideas. – Pedro TamaroffAug 24 '13 at 3:46 What level of rigor are you interested in? Introductory real analysis or advanced (similar to the level of Rudin)? – Cameron WilliamsAug 24 '13 at 3:49 If you want an interesting alternative that goes deep into why things work out as they do in real analysis, then you can have a look at analysis textbooks (apart from the books already mentioned in the comments) such as This set of free lecture notes by Fields Medal winner Vaughan Jones are excellent. In that they are virtually verbatim, you get the full presentation as if he was speaking directly to you rather than a summary.They are very accessible, and assume no prior knowledge. They build from the beginning adding insight along the way. As one of the great mathematicians, he uses his insight in presenting his own treatment of the material and makes his train of thought very clear. For additional consideration: Pugh's "Real Mathematical Analysis" (as mentioned above) is also excellent, likewise with examples and pictures which are quit beneficial. Here is a short review from Promys: An absolutely fantastic introduction to Analysis, it has excellent exposition and is full of great examples and over 500 (good) exercises. A counterpart to Rudin, Pugh always builds up machinery first and uses it to provide very clear proofs that grant a good sense of "why" something is true. Judging by page count and the amount of material it covers, it seems that it must be as concise as Rudin, yet it reads very easily.
This course is not open to students who have successfully completed MATH 121 or higher. Minimum grade required to successfully complete this course is a C. This course is designed specifically for those students who need to develop a proficiency in algebraic skills that are essential for subsequent Math courses. Topics include: operations with signed numbers, solving equations and inequalities, the arithmetic of polynomials, factoring polynomials, rational functions, graphing exponents, and radicals.
Wolfram Calculus Course Assistant iPhone Screenshots iPad Screenshots - Plot basic, parametric, or polar plots of the function(s) of your choice. - Determine the limit of a function as it approaches a specific value. - Differentiate any function or implicit function. - Find the critical points and inflection points of a function. - Identify the local and absolute extrema of a function. - Integrate a function, with or without limits. - Sum a function given a lower and upper bound. - Find the closed form of a sequence or generate terms for a specific sequence. The Wolfram Calculus Course Assistant is powered by the Wolfram\|Alpha computational knowledge engine and is created by Wolfram Research, makers of Mathematica---the world's leading software system for mathematical research and education. The Wolfram Calculus Course Assistant draws on the computational power of Wolfram\|Alpha's supercomputers over 2G, 3G, or WiFi connection
Sample Worksheet: Algebraic Shortcuts for the SAT, GRE, GMAT Most students taking the SAT, GRE, or GMAT know their algebra fairly well, but many find they can't complete all the problems in the allowed time. Why? It's NOT because those students are just naturally slow: it's because they're doing more work than they need to! It's not their speed but their very approach --- the very way they conceive of the process of problem-solving --- that's flawed. To ace the math sections of standardized tests, you have to learn how to attack problems in new ways so that you get the right answers by doing as little work as possible! (Part of the reason so many students don't already know how to do this is that it's not taught well throughout middle and high school math classes. Learning how to think quickly and deeply often requires UNLEARNING habits your math teachers instilled in you in school!) To see if you're up to par, try the following problems, which test your ability to make deep algebraic connections that will save you time. If your algebraic skills are what they really should be, you should be able to do all the problems in TWENTY SECONDS OR LESS! If you can't, send me an email and start working with me today! EXERCISE SET: ALGEBRAIC SHORTCUTS Suppose 2x+7=19. Find the value of each of the following expressions WITHOUT solving for x!
More About This Textbook Overview Elementary Technical Mathematics Tenth Edition was written to help students with minimal math background prepare for technical, trade, allied health, or Tech Prep programs. The authors have included countless examples and applications surrounding such fields as industrial and construction trades, electronics, agriculture, allied health, CAD/drafting, HVAC, welding, auto diesel mechanic, aviation, natural resources, and others. This edition covers basic arithmetic including the metric system and measurement, algebra, geometry, trigonometry, and statistics, all as they are related to technical and trade fields. The goal of this text is to engage students and provide them with the math background they need to succeed in future courses and careers. From the Publisher "I was pleased with the exercises overall. They correspond well to the sections covered, and the balance is good." "Good graphics, good examples, good practical applications of geometry and trigonometry." "I have always been impressed with [Ewen and Nelson's] writing style. It parallels very much how I teach the course, trying to be as short and as straight to the point as possible." "My instruction time is filled with problem solving, and [the authors'] text is an extremely good fit to that teaching style." "The three greatest strengths of this text are its simple, clear plan of presenting a concept, detailing several examples, and offering many additional exercises; its many application problems from a variety of technical fields; and its chapter design with reviews, tests, and the laminated sheet of conversions." Related Subjects Meet the Author Dale Ewen, Executive Vice President of Parkland College, Illinois, (1999-present), graduated from the University of Illinois with a B.S. in 1963 and an M. Ed. in 1966. He has been the recipient of several AMATYC (American Mathematical Association of Two-Year Colleges) awards and served as the organization's President (1989-91). Dale continues to write a number of technical mathematic textbooks. C. Robert Nelson, retired mathematics teacher, taught high school math for 33 years. He earned his Associate's degree at Norfolk Junior College and his Bachelor's degree from Midland College. He later received his Master's degree from
Matrices (the plural of matrix) are a convenient way of organizing linear functions and systems of equations. Before you can move on to the higher-math applications of matrices, you have to master the basic methods of solving matrices. Your first introduction to solving matrices will probably be using them to solve systems of equations, using basic algebraic operations. Ad Steps "Reduced row form" means that any numbers may be in the rightmost column, but the rest of the entries in any given row consist of a single "1" entry accompanied by as many zeroes as necessary to fill the rest of the spaces. In reduced row form, order the rows so that the "1" entries like up in a rightward, downward diagonal line. So the first line of the matrix might be "1 0 0 24," the second line "0 1 0 46," and the third line "0 0 1 5." Ad 2 Switch any 2 rows in the matrix to make performing the other operations easier, or to arrange the "1" entries properly in reduced row form. This doesn't affect the overall value of the matrix. You must swap the 2 lines completely, with no intermingling of the numbers for each row. So for example if you had a matrix with entries "3 12 2" in the first row and "4 6 3" in the second row, you could swap "4 6 3" to be the first row and "3 12 2" to be the second row. But you couldn't swap just 1 or 2 of the elements from each row. Method 1 of 2: Row Addition and Subtraction 1 Combine the elements of any 2 matrix rows by adding and subtracting them. This creates a third row (the result), which you then substitute for 1 of the original 2 rows. Add and subtract each element individually, working your way across the row. So if you were to add the rows "3 12 2" and "4 6 3," the resulting new row would be "7 18 5." The results row must replace 1 of the rows you just used to create it; you cannot arbitrarily add a new row to the matrix and keep the other rows unchanged. Method 2 of 2: Scalar Matrix Multiplication 1 Multiply every element of a given row by the same scalar. As long as you multiply each element in the row by the same scalar, you don't actually change the value of the matrix. But scalar multiplication can make performing the other matrix row operations easier. For example, if you have the rows "2 5 3" and "-1 2 9," multiplying the second row by 2 is the perfect setup for then adding the resulting rows together. The scalar multiplication gives you "-2 4 18," which when added to the first row yields "0 9 21." If you then scalar multiply the resulting row by 9, you have "0 1 (21/9)", and this row is prepared for reduced row form
Book Description: This text provides a solid foundation in the basic logical concepts for most of the subjects encountered in university mathematics, including basic college-level algebra and analysis. The first edition has been completely rewritten and expanded in response to a decade of teaching the subjects. This text is written for the students beginning "abstract pure mathematics" at university or college level. For the student beginning to study mathematics at this level there is a distinction between what she or he has done in the past and what lies ahead. What the student needs to acquire mastery of what is virtually an entirely new language -the language of mathematics- and to adopt an entirely new way of thinking
Geogebra Workshop Workshop run by Priscilla Allan To structure our learning, and to make learning visible, I have an "I can do" Checklist for you The GeoGebralessons in the laboratory guide focus on promoting the understand-ing of concepts and procedures. Figures 1 and 2 provide an example of a student ac-tivity sheet and accompanying GeoGebra sketch from the Using Geogebra for Online College Algebra & Trigonometry Courses 2 Geogebra is a free dynamic mathematics software and online program that many teachers ... Applying the use of Geogebra to create mathematics applets in these lessons opened my Activities with Geogebra in a preservice program Andreas Philippou and Costantinos Christou University of Cyprus Abstract The University of Cyprus is responsible for the preservice education of teachers of Geogebra, a useful tool for achieving school progress Adriana Bînzar ... lessons.This specific approach had lead to the school progress of my students . 1. Introduction The communicate way of teenagers evolves from one ... GeoGebra, lessons becoming more attractive for the audience. Also it should be mentioned that such lessons allow the presentation and explanation of a larger number of particular cases. By this article the authors intend to point out the importance of implementing GeoGebra in ... range of materials that could be useful to teachers in preparing GeoGebralessons. There are two GeoGebra institutes in Serbia and they offer different activities in order to increase GeoGebra use in classrooms". A teacher from seminar in Novi Sad: present lessons with GeoGebra. Our results suggest that the prospective teachers' perspectives on teaching and learning mathematics with technology were enriched as a result of their participation in course activities. Keywords: GeoGebra, ... First participants learned basic commands about GeoGebra. During lessons pre service teachers of mathematics used dynamic worksheets. Data were collected by participants' works and opinions on dynamic mathematics software. Your GeoGebra Unit circle shows the sine and cosine values on the left. There is a dotted line that completes the right triangle made from the angle theta and the point it terminates on the circle. Find the dotted line and notice how the triangle changes integrated GeoGebra to consolidate the derivative using the visual idea of zooming ... a topic and plan lessons collaboratively, subsequently observe these unfolding lessons in actual classrooms, and finally discuss their observations ... GeoGebra as e-Learning Resource for Teaching and Learning Statistical Concepts Dijana Capeska Bogatinoska1, Aleksandar Karadimce1, ... The probability and statistics lessons should provide to the students the ability to collect, organize and analyze numerical data, ... Use Geogebra's "Exterior Segments in Circles". (example on the left) Using explicit instruction, have students practice calculating the missing segment length. Repeat the exercise in Geogebra with several different measurements. GeoGebralessons. The analysis of the data revealed that focusing on the mathematical concept more than technology and using technology when it is really necessary were the basic criteria for effective technology based lesson. PSTs ... Integrating GeoGebra into IWB-equipped teaching environments: preliminary results ... lessons by participating teachers are currently being video-recorded and further interviews are to be conducted with teachers and students to better understand the GeoGebra in the Context of the IT Surrounding Environment and Curriculum, 2010 ... GeoGebra software in lessons. We agree a new level of competences, teacher trainer for GeoGebra which have expertise in pedagogy, psychology and didactic science. Classical geometry with GeoGebra ... In my lessons I use computer software for visualization, for the proving of geometric problems in the plane and in the space or for the demonstration of the application of geometry in practice. organize the work during lessons but also the use of GeoGebra together with other modern instructional equipments, e.g. other computer programs, SmartBoards, course management systems etc. The Institute will publish information and news of its work as well as GeoGebra worksheets in This unit is comprised of lessons in which students will be given various information and data to use to investigate different parent functions. ... Students can create a GeoGebra file to graph their equations from Calculus Animations with GeoGebraGeoGebra is a free, web-based software that does dynamic geometry and graphing. ... lessons, questioning strategies, and activities and watching clips of the lessons, I will lead the participants in a discussion about ways in which Effectiveness of Using Geogebra on Students' Understanding in Learning Circles Praveen SHADAAN[1] ... Such information is crucial in planning lessons for large classes and where learners are of varied abilities. The study ... through GeoGebra. All GeoGebralessons are integrated in eXe also. The response of students in learning geometry using this tool was incredible. The phobia for 5. doing geometry questions is no more there. It also helped in developing interest in the subject. Through ... Lessons using GeoGebra software in experimental groups were carried out for 8 hours, three times a week. The control group, on the other hand, attended tutorial session as usual using the tradi-tional approach. Post-tests were administered to both groups after All lessons are discussed in the context of a real world application. VIII. REFERENCE/RESOURCE MATERIALS: Graphing calculators will be required. Student Exploration Worksheets and Exit Slip Assessments will be needed for all three lessons. Computers to access GeoGebra would Effect of Students' Achievement in Fractions using GeoGebra Noorbaizura Thambi University of Malaya [email protected] Leong Kwan Eu University of Malaya [email protected] ... Mathematics is one of the subjects that is suitable to integrate technology during lessons. This Lessons for Geometry Perimeter, Area, Volume, Measurements in the English and SI (metric) Systems, Similar Triangles, Pythagorean Theorem, and Right Triangle Trigonometry ... the students how to use GeoGebra to make triangles and measure their angles. with GeoGebra Julie-Ann Edwards and Keith Jones review how geometry and algebra can be linked using a new free software package, ... a few resources for use in lessons and think it has great potential to be used in this environment. It supports the idea of pupils discovering certain Geogebra, a Tool for Mediating Knowledge in the Teaching and Learning of Transformation of Functions in Mathematics by RAZACK SHERIFF UDDIN ... algebra lessons with the DGS and thus, they were stimulated to participate in the lesson. They
The Knot Book An Elementary Introduction to the Mathematical Theory of Knots Colin C. Adams W. H. Freeman Available Formats Over a century old, knot theory is today one of the most active areas of modern mathematics. The study of knots has led to important applications in DNA research and the synthesis of new molecules, and has had a significant impact on statistical mechanics and quantum field theory. Colin Adams's The Knot Book is the first book to make cutting-edge research in knot theory accessible to a non-specialist audience. Starting with the simplest knots, Adams guides readers through increasingly more intricate twists and turns of knot theory, exploring problems and theorems mathematicians can now solve, as well as those that remain open. He also explores how knot theory is providing important insights in biology, chemistry, physics, and other fields. The new paperback edition has been updated to include the latest research results, and includes hundreds of illustrations of knots, as well as worked examples, exercises and problems. With a simple piece of string, an elementary mathematical background, and The Knot Book, anyone can start learning about some of the most advanced ideas in contemporary mathematics. Connect with the Author Sign Up for Author Updates Macmillan Newsletter Reviews Praise for The Knot Book "Adams is an expert in knot theory, and this shows in the clarity and accuracy of his writing, and in the rich store of examples and problems . . . We are going to see much more of knot theory and its applications, and this book is an excellent place to start." —Nature Reviews from Goodreads About the Author Colin C. Adams Colin Adams is Professor of Mathematics at Williams College. He is one of the world's leading researchers of knot theory and has published widely on this and other mathematical topics. He is the co-author of How to Ace Calculus and winner of the Mathematical Association of America Distinguished Teaching Award for 1998.
Numerical MethodsPresentation Transcript Numerical Methods Andrés Plata Grupo: O2 Numerical Methods Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations ) for the problems of continuous mathematics (as distinguished from discrete mathematics ). Numerical methods naturally finds applications in all fields of engineering and the physical sciences, but in the 21st century, the life sciences and even the arts have adopted elements of scientific computations. Ordinary differential equations appear in the movement of heavenly bodies (planets, stars and galaxies) ; optimization occurs in portfolio management; numerical linear algebra is important for data analysis; stochastic differential equations and Markov chains are essential in simulating living cells for medicine and biology. History The field of numerical methods predates the invention of modern computers by many centuries. Linear interpolation was already in use more than 2000 years ago. Many great mathematicians of the past were preoccupied by numerical analysis, as is obvious from the names of important algorithms like Newton's method, Lagrange interpolation polynomial , Gaussian elimination, or Euler's method. Areas of study The field of numerical methods is divided into different disciplines according to the problem that is to be solved. 1. Computing values of functions One of the simplest problems is the evaluation of a function at a given point. The most straightforward approach, of just plugging in the number in the formula is sometimes not very efficient. For polynomials, a better approach is using the Horner scheme, since it reduces the necessary number of multiplications and additions. Generally, it is important to estimate and control round-off errors arising from the use of floating point arithmetic. 2. Interpolation, extrapolation, and regression Interpolation solves the following problem: given the value of some unknown function at a number of points, what value does that function have at some other point between the given points? Extrapolation is very similar to interpolation, except that now we want to find the value of the unknown function at a point which is outside the given points. Regression is also similar, but it takes into account that the data is imprecise. Given some points, and a measurement of the value of some function at these points (with an error), we want to determine the unknown function. The least squares-method is one popular way to achieve this. 3. Solving equations and systems of equations Another fundamental problem is computing the solution of some given equation. Two cases are commonly distinguished, depending on whether the equation is linear or not. For instance, the equation 2x + 5 = 3 is linear while 2x2 + 5 = 3 is not. 4. Solving eigenvalue or singular value problems Several important problems can be phrased in terms of eigenvalue decompositions or singular value decompositions. For instance, the spectral image compression algorithm is based on the singular value decomposition. The corresponding tool in statistics is called principal component analysis. 5. Optimization Optimization problems ask for the point at which a given function is maximized (or minimized). Often, the point also has to satisfy some constraints. The field of optimization is further split in several subfields, depending on the form of the objective function and the constraint. For instance, linear programming deals with the case that both the objective function and the constraints are linear. A famous method in linear programming is the simplex method. The method of Lagrange multipliers can be used to reduce optimization problems with constraints to unconstrained optimization problems. 7. Evaluating integrals Numerical integration, in some instances also known as numerical quadrature, asks for the value of a definite integral. Popular methods use one of the Newton–Cotes formulas (like the midpoint rule or Simpson's rule) or Gaussian quadrature. These methods rely on a "divide and conquer" strategy, whereby an integral on a relatively large set is broken down into integrals on smaller sets. In higher dimensions, where these methods become prohibitively expensive in terms of computational effort, one may use Monte Carlo or quasi-Monte Carlo methods (seeMonte Carlo integration), or, in modestly large dimensions, the method of spars grids. 8. Differential equations Numerical analysis is also concerned with computing (in an approximate way) the solution of differential equations, both ordinary differential equations and partial differential equations. Partial differential equations are solved by first discretizing the equation, bringing it into a finite-dimensional subspace. This can be done by afinite element method, a finite difference method, or (particularly in engineering) a finite volume method. The theoretical justification of these methods often involves theorems from functional analysis. This reduces the problem to the solution of an algebraic equation.
Modify Your Results The theorems and principles of basic geometry are clearly presented in this workbook, along with examples and exercises for practice. Concepts are explained in an easy-to-understand fashion to help students grasp geometry and form a solid foundation for advanced learning in mathematics. Each page introduces a new concept, along with a puzzle or riddle which reveals a fun fact. Thought-provoking exercises encourage students to enjoy working the pages while gaining valuable practice in geometry
College Algebra Essentials -With CD - 3rd edition Summary: Chapter P. Prerequisites: Fundamental Concepts of Algebra.P.1 Algebraic Expressions, Mathematical Models, and Real Numbers1. Evaluate algebraic expressions.2. Use mathematical models.3. Find the intersection of two sets.4. Find the union of two sets.5. Recognize subsets of the real numbers.6. Use inequality symbols.7. Evaluate absolute value.8. Use absolute value to express distance.9. Identify properties of the real numbers.10. Simplify algebraic expressions.P.2 Exponents and Scient...show moreific Notation1. Use the product rule.2. Use the quotient rule.3. Use the zero-exponent rule.4. Use the negative-exponent rule.5. Use the power rule.6. Find the power of a product.7. Find the power of a quotient.8. Simplify exponential expressions.9. Use scientific notation.P.3 Radicals and Rational Exponents1. Evaluate square roots.2. Simplify expressions of the form ?a23. Use the product rule to simplify square roots.4. Use the quotient rule to simplify square roots.5. Add and subtract square roots.6. Rationalize denominators.7. Evaluate and perform operations with higher roots.8. Understand and use rational exponents.P.4 Polynomials1. Understand the vocabulary of polynomials.2. Add and subtract polynomials.3. Multiply polynomials.4. Use FOIL in polynomial multiplication.5. Use special products in polynomial multiplication.6. Perform operations with polynomials in several variables.Mid-Chapter Check PointP.5 Factoring Polynomials1. Factor out the greatest common factor of a polynomial.2. Factor by grouping.3. Factor trinomials.4. Factor the difference of squares.5. Factor perfect square trinomials.6. Factor the sum or difference of two cubes.7. Use a general strategy for factoring polynomials.8. Factor algebraic expressions containing fractional and negative exponents.P.6 Rational Expressions1. Specify numbers that must be excluded from the domain of rational expressions.2. Simplify rational expressions.3. Multiply rational expressions.4. Divide rational expressions.5. Add and subtract ...show less Bob Blitzer is a native of Manhattan and received a Bachelor of Arts degree with dual majors in mathematics and psychology (minor: English literature) from the City College of New York. His unusual combination of academic interests led him toward a Master of Arts in mathematics from the University of Miami and a doctorate in behavioral sciences from Nova University. Bob is most energized by teaching mathematics and has taught a variety of mathematics courses at Miami-Dade College for nearly 30 years. He has received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College, and was among the first group of recipients at Miami-Dade College for an endowed chair based on excellence in the classroom. Bob has written Intermediate Algebra for College Students, Introductory Algebra for College Students, Essentials of Intermediate Algebra for College Students, Introductory and Intermediate Algebra for College Students, Essentials of Introductory and Intermediate Algebra for College Students, Algebra for College Students, Thinking Mathematically, College Algebra, Algebra and Trigonometry, and Precalculus, all published by Pearson Prentice Hall. INSTRUCTOR EDITION.Identical to student edition.Black tape on cover. CD IS INCLUDED..SHIPS FAST!! SAME DAY OR W/N 24 HOURS.EXPEDITED SHIPPING AVAILABLE TOO2134.97 +$3.99 s/h LikeNew Nivea Books Lynnwood, WA Hardcover Fine 032157781744.97 +$3.99 s/h LikeNew New Earth Enterprises Germantown, WI No comments from the seller $49.00 +$3.99 s/h Acceptable AlphaBookWorks Alpharetta, GA 0321577849.94 +$3.99 s/h LikeNew Balkanika Online WA Woodinville, WA Hardcover Fine 0321577817
Summary: This best-selling text balances solid mathematical coverage with a comprehensive overview of mathematical concepts as they relate to varied disciplines. The text provides an appreciation of mathematics, highlighting mathematical history, and applications of math to the arts and sciences. It is an ideal book for students who require a general overview of mathematics, especially those majoring in liberal arts, the social sciences, business, nursing and allied health fi...show moreelds. Let us introduce you to the practical, interesting, accessible, and powerful world of mathematics today-the world of A Survey of Mathematics with Applications, Expanded. ...show less25.53 +$3.99 s/h VeryGood Better World Books UK Dunfermline,34.96 +$3.99 s/h Acceptable AlphaBookWorks Alpharetta, GA 032150108
Infinite Algebra worksheets and tests with exactly the types of questions you want in just minutes. No more writing questions by hand, searching through old books and worksheets, or wading through a database of prewritten questions. Unlike other test generators, Infinite Algebra 2 actually creates the questions for you. You select the parameters for each question: the size of the numbers; types of numbers; the types of operations involved; and the number of steps. Our software chooses the variables and numbers for each question so the questions conform to the options you picked. Because the questions are written on-the-fly, you won't run out of suitable questions. You can create multiple versions of tests, vary the difficulty of questions, and change your assignments from year to year to adapt to your individual classes. Prepare your examples, class work, homework, and tests without ever running out of good material. Other features include: easily-controlled spacing, free-response and multiple-choice format, scale, merge, export, and a presentation mode to use while teaching (compatible with LCD projectors and other display systems). Invented by a math teacher, Infinite Algebra 2 covers all major Algebra 2 topics, from multi-step equations to trigonometric identities. All questions are completely customizable. Suitable for all levels from remedial to advanced. What's new in this version: New: Preference for notation for greatest integer function New: Added maximize/restore button to Presentation View Improved: Help files Improved: Scroll bars Improved: User interface Improved: When choices make a question too tall for a page, some choices are removed
1576854280 9781576854280 Math for Civil Service Tests:All civil service exams contain a mandatory math section. If you're like many candidates, you haven't taken math in years, and you might be nervous about putting your math skills to the test. Math for Civil Service Tests is an indispensable math workbook and resource guide that gives you the edge you need to ace the exam and beat the rest. The book provides two complete practice tests including full answer explanations, basic math instruction-including lessons on fractions, decimals, percentages, and measurement, practical math strategies and advice that break down and solve all math problems. There's also proven methods for setting up and solving word problems and a glossary of math terms to help you remember key concepts at test time. Plus, you'll get two study plans to meet your scheduling needs: a step-by-step 30-day plan and a concentrated 14-day plan! Back to top Rent Math for Civil Service Tests 1st edition today, or search our site for Jessika textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by LearningExpress, LLC.
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This book on symmetric geometric patterns of Islamic art has educational, aesthetic, cultural and practical purposes. Its central purpose is to bring to the attention of the world in general, and the people of Islamic culture in particular, the potential of the art for providing a unified experience of science and art in the context of mathematical... more... This book covers a wide range of topics, from orthogonal polynomials to wavelets. It contains several high-quality research papers by prominent experts exploring trends in function theory, orthogonal polynomials, Fourier series, approximation theory, theory of wavelets and applications. The book provides an up-to-date presentation of several important... more... Presents the results on positive trigonometric polynomials within a unitary framework; the theoretical results obtained partly from the general theory of real polynomials, partly from self-sustained developments. This book provides information on the theory of sum-of-squares trigonometric polynomials in two parts: theory and applications. more... DeMYSTiFieD is your solution for tricky subjects like trigonometry If you think a Cartesian coordinate is something from science fiction or a hyperbolic tangent is an extreme exaggeration, you need Trigonometry DeMYSTiFieD , Second Edition, to unravel this topic's fundamental concepts and theories at your own pace. This practical guide... more... Say goodbye to dry presentations, grueling formulas, and abstract theory that would put Einstein to sleep--now there's an easier way to master chemistry, biology, trigonometry, and geometry. McGraw-Hill's Demystified Series teaches complex subjects in a unique, easy-to-absorb manner and is designed for users without formal training, unlimited time,... more... Karl Gustafson is the creater of the theory of antieigenvalue analysis. Its applications spread through fields as diverse as numerical analysis, wavelets, statistics, quantum mechanics, and finance. Antieigenvalue analysis, with its operator trigonometry, is a unifying language which enables new and deeper geometrical understanding of essentially every... more... From the pyramids and the Parthenon to the Sydney Opera House and the Bilbao Guggenheim, this book takes readers on an eye-opening tour of the mathematics behind some of the world's most spectacular buildings. Beautifully illustrated, the book explores the milestones in elementary mathematics that enliven the understanding of these buildings and combines... more... The learn-by-doing way to master Trigonometry Why CliffsStudySolver Guides? Go with the name you know and trust Get the information you need--fast! Written by teachers and educational specialists Get the concise review materials and practice you need to learn Trigonometry, including: Explanations of All Elements and Principles * Angles and quadrants... more... CliffsQuickReview course guides cover the essentials of your toughest classes. Get a firm grip on core concepts and key material, and test your newfound knowledge with review questions. CliffsQuickReview Trigonometry provides you with all you need to know to understand the basic concepts of trigonometry ? whether you need a supplement to your textbook... more...
October 15th 2011, 02:57 AM e^(i*pi)In the UK calculus is taught at AS and A level; a non-compulsory level of education lasting 1 and 2 years respectively. October 18th 2011, 12:08 AM Devenoin the United States, calculus is sometimes taught in "high school" (4 years before college/university), sometimes taught as a first-year university course. the calculus taught in universities is usually more rigorous than that taught in high school. many calculus courses in the US are taught as AP (advanced placement) courses, meaning that universities will sometimes count them as college credit hours. there are two varieties, Calculus AB, and Calculus BC (BC is the "honors version, with more subjects covered). it sounds as if "your" calculus, comprises about 2/3rds of what Calculus AB normally covers (noticeably absent is any mention of integrals, and power series). Também sou de Portugal. I didn't really understand what you want. Do you want a book for calculus at first year of university of an engineering school? Calculus by Apostol is good. It's both rigorous enough and easy. If you want please send me a private message and we will discuss it in Portuguese.
VIII. Mathematics, Grade 8 Grade 8 Mathematics Test The spring 2004 Grade 8 MCAS Mathematics Test was based on learning standards in the Massachusetts Mathematics Curriculum Framework (2000). The Framework identifies the five major content strands listed below. I Number Sense and Operations I Patterns, Relations, and Algebra I Geometry I Measurement I Data Analysis, Statistics, and Probability The grade 7–8 learning standards for each of these strands appear on pages 62–66 of the Mathematics Curriculum Framework, which is available on the Department website at In Test Item Analysis Reports and on the Subject Area Subscore pages of the MCAS School Reports and District Reports, Mathematics test results are reported under five MCAS reporting categories, which are identical to the five Mathematics Curriculum Framework content strands listed above. Test Sessions and Content Overview The grade 8 Mathematics Test contained two separate test sessions. Each session included multiple-choice and open-response questions. Session 1 also included short- answer questions. Common test items are shown on the following pages as they appeared in test booklets. Reference Materials and Tools During testing, each student taking the Grade 8 Test was provided with a Grade 8 Mathematics Reference Sheet and a plastic ruler. A copy of the reference sheet follows the final question in this chapter. While answering questions during Session 2, each student had sole access to a calculator with at least four functions and a square root key. Calculator use was not allowed during Session 1. No other reference tools or materials were allowed, with the exception of bilingual word-to-word dictionaries used by limited English proficient students. Cross-Reference Information The table at the conclusion of this chapter indicates each item's reporting category and the Framework learning standard it assesses. The correct answers for multiple-choice and short-answer questions are also displayed in the table. 179 HOW TO ANSWER OPEN-RESPONSE QUESTIONS Be sure to • read all parts of each question carefully. • make each response as clear, complete, and accurate as you can. • check your answers. Mathematics SESSION 1 You may use your reference sheet and MCAS ruler during this session. You may not use a calculator during this session. DIRECTIONS This session contains fifteen multiple-choice questions, five short-answer questions, and two open-response questions. Mark your answers to these questions in the spaces provided in your Student Answer Booklet. 2097384 C 2097265 C Art Code 2097265.AR1 1 What is the value of the expression below 2 The circles below represent the gears when x 12 and y 12? of a bicycle. The diameter of Gear A (x y)(x y) is 30 centimeters. The ratio of the diameter of Gear A to the diameter A. 288 of Gear B is 3:1. B. 144 C. 12 D. 0 * 30 cm Gear A Gear B What is the circumference, in centimeters, of Gear B? A. 5π cm B. 10π cm * C. 15π cm D. 30π cm 181 Mathematics Session 1 3005201 C 3009711 C 3 Which of the following is equivalent to 4 The owner of a car dealership noticed a the equation below? pattern in the weekly car sales, as shown n in the table below. 30 6 Weekly Car Sales A. n 30 6 * Week (w) Number of Cars Sold (s) B. 6 30 n 1 12 2 18 30 C. n 3 24 6 4 30 30 D. 6 n For weeks 1 through 4, which of the following equations could represent the pattern of s cars sold during week w? A. s 6w B. s 12w C. s 6(w 6) D. s 6(w 1) * 182 Mathematics Session 1 3005253 C Art Code 3005253.AR1 5 A part of the real number line is shown below. Q R S T Which letter best represents the location of 250? 0 5 10 15 20 25 A. Q B. R * C. S D. T 2024112 C 6 What value of a makes the equation below true? 12 ( 3a) 0 A. 5 B. 4 C. 4* D. 5 183 Mathematics Session 1 Questions 7 and 8 are short-answer questions. Write your answers to these questions in the boxes provided in your Student Answer Booklet. Do not write your answers in this test booklet. You may do your figuring in the test booklet. 3011635 C 7 Acme Doll Company makes the Super Hero Doll that sells for $10. The table below shows that the profit the company earns is based proportionally on the number of dolls sold. Super Hero Doll Profits Sales Profits (number of dolls) 1,000 $50 1,500 $75 3,000 $150 4,500 $225 What is the profit for sales of 15,000 Super Hero Dolls? 3011634 C 8 Compute: 1 1 3 12 184 Mathematics Session 1 Question 9 9 in the space provided in your Student Answer Booklet. 3009941 C Art Code 3009941.AR1 9 Last weekend, Lauren helped organize some students to participate in a fundraiser for charity. The students had a choice of working one shift at the information booth in town or one shift at the school headquarters. Students could also choose to work 2 shifts, one in town and one at school. After the fundraiser, Lauren prepared a report for the school board. In her report, she drew the Venn diagram below to show where the students worked. Students Working at the Fundraiser 37 6 12 Town Booth School Headquarters a. Based on the Venn diagram, how many students worked shifts at the Town Booth? b. Based on the Venn diagram, how many students participated in the fundraiser? c. Lauren could have drawn a bar graph to represent the same information as the Venn diagram. In your Student Answer Booklet, create a bar graph that contains the same information as the Venn diagram. 185 Mathematics Session 1 Mark your answers to multiple-choice questions 10 through 18 in the spaces provided in your Student Answer Booklet. Do not write your answers in this test booklet. You may do your figuring in the test booklet. 3005137 C 10 Erin determined the masses of some samples for her science project. The mass of each sample is listed below. Sample Mass (grams) 1 17 2 16.7 3 17.6 4 16.67 Which of the following correctly lists the samples in order from the least mass to the greatest mass? A. 1, 2, 3, 4 B. 2, 3, 4, 1 C. 2, 4, 1, 3 D. 4, 2, 1, 3 * 186 Mathematics Session 1 3009714 C Art Code 3009714.AR1, .AR2, .AR3, .AR4, .AR5 11 Stephanie conducted a survey to determine the number of siblings that each of her classmates has. The data appears in the table below. Number of Classmates Having That Siblings Number of Siblings 0 1 2 3 Which of the following circle graphs best represents the data in the table? A. C. * Comparison of Classmates Comparison of Classmates By Number of Siblings By Number of Siblings 3 0 3 0 2 1 2 1 B. D. Comparison of Classmates Comparison of Classmates By Number of Siblings By Number of Siblings 0 3 0 3 1 2 1 2 187 Mathematics Session 1 3005233 C 3005214 C 12 What is the prime factorization of 300? 14 Which graph below best represents y 3x 4 ? A. 3 102 B. 2 52 6 y A. C. 22 3 25 4 3 D. 22 3 52 * 2 1 2097417 C -4 -3 -2 -1 0 1 2 3 4 x - -1 13 What is the minimum number of -2 congruent, equilateral triangles needed to -3 construct a three-dimensional figure if no -4 other shapes are used? A. 3 y B. 4 * B. 4 C. 6 3 2 D. 8 1 -4 -3 -2 -1 0 1 2 3 4 x -1 -2 -3 -4 y C. 4 3 2 1 -4 -3 -2 -1 0 1 2 3 4 x -1 -2 -3 -4 y * D. 4 3 2 1 -4 -3 - 2 -1 0 1 2 3 4 x -1 -2 -3 -4 188 Mathematics Session 1 3005172 C Art Code 3005172.AR1 3005212 C 15 At 4:00 P.M. on a sunny day, a stick 16 The president of the science club brought 2 feet tall casts a shadow 5 feet long. 134 cans of juice on a field trip. Each At the same time, a tree nearby casts person on the trip received 3 cans of a shadow 55 feet long. juice, and there were 20 extra cans. Which equation could be used to find n, the number of people who went on the 2 feet field trip? 5 feet n A. 134 20 3 n B. 134 20 3 C. 134 3n 20 D. 134 3n 20 * 55 feet What is the height, in feet, of the tree? A. 137.5 feet B. 27.5 feet C. 22 feet * D. 10 feet 189 Mathematics Session 1 3005206 C Art Code 3005206.AR1 17 A comparison of the median wage for a business employee in three cities is shown below. Median Wages Per Year $ 50,000 $ 40,000 $ 30,000 Wage $ 20,000 $ 10,000 $0 City 1 City 2 City 3 City Which of the following is closest to the difference between the median wage in City 2 and the median wage in City 1? A. $4,000 * B. $8,000 C. $12,000 D. $64,000 2097412 C 18 If 7x 3 17, what is the value of 7x 3? A. 14 B. 11 * C. 0 D. 3 190 Mathematics Session 1 Question 19 is a short-answer question. Write your answer to this question in the box provided in your Student Answer Booklet. Do not write your answer in this test booklet. You may do your figuring in the test booklet. 3011615 C Art Code 3011615.AR1 19 Sam's Pizza offers the luncheon special shown in the advertisement below. How many combinations of one entrée, one salad, and one drink are possible for the luncheon special? 191 Mathematics Session 1 Questions 20 and 21 are short-answer questions. Write your answers to these questions in the boxes provided in your Student Answer Booklet. Do not write your answers in this test booklet. You may do your figuring in the test booklet. 2097413 C Art Code 2097413.AR1 20 The stem-and-leaf plot below shows the ages of the people who bought skateboards at a store during a sale. Ages of People Stem Leaf 1 134556668 2 0178 3 9 4 36 5 6 55 7 1 Key 6 \| 2 represents 62 What is the range of ages of people who bought skateboards during the sale? 3011572 C Art Code 3011572.AR1 21 Triangle ABC is shown below. Points B, C, and D are collinear. A 50 110 B C D What is the degree measure of B? 192 Mathematics Session 1 Question 22 22 in the space provided in your Student Answer Booklet. 3005219 C Art Code 3005219.AR1 22 Alex made a table of values based upon the rules of a new operation. The table has 7 columns and 6 rows as shown below. Columns 1 2 3 4 5 6 7 1 –1 –3 –5 –7 –9 –11 2 0 –2 –4 –6 –8 Rows 3 7 5 3 1 –1 –3 4 14 12 10 8 6 4 5 23 21 19 17 15 13 6 a. Each row of the table contains a pattern of numbers where each number is 2 less than the previous number in the row. Based on the pattern, what number belongs in column 1 and row 2 of the table? b. Based on the pattern, what numbers belong in rows 1 through 5 in column 7 of the table? c. Describe, in your own words, a rule that fits the pattern of numbers going down each column. Next, use the rule to determine the 7 numbers that belong in row 6 of the table. 193 Mathematics SESSION 2 You may use your reference sheet and MCAS ruler during this session. You may use a calculator during this session. DIRECTIONS This session contains fourteen multiple-choice questions and three open-response questions. Mark your answers to these questions in the spaces provided in your Student Answer Booklet. 3009724 C 3005226 C Art Code 3005226.AR1 23 Orlando and Carol each started an exercise 24 The circle graph below shows the program that included riding a bike. percentages of people who brought The table below shows the number of each type of baked good to sell at a miles each traveled for 5 weeks of recent bake sale. the program. Percentage of People Bringing Baked Goods Weekly Miles Traveled Week Orlando Carol Other Cookies 1 8 5 14% 20% 2 8.5 6 3 9 7 4 9.5 8 5 10 9 Brownies 6 20% Pies 7 16% 8 If both Orlando and Carol continue to increase the number of miles traveled Cakes each week at the constant rates shown 30% in the table, which of the following is a true statement about week 8? If 15 people brought cakes to sell, what is the total number of people who brought A. Carol will travel more miles baked goods to sell at the bake sale? than Orlando. * A. 45 B. Orlando and Carol will travel the same number of miles. B. 50 * C. Carol will travel a total of 13 miles. C. 70 D. Orlando and Carol will travel a D. 75 total of 20 miles. 194 Mathematics Session 2 3009734 C Art Code 3009734.AR1 2097322 C 25 The figure below shows a circle inscribed 26 Pittsfield and Provincetown are in a square. approximately 258,000 meters apart. Which of the following shows this number in scientific notation? A. 258 103 3 B. 258 10 C. 2.58 105 * 5 D. 2.58 10 2024167 C 27 An object is dropped from a small plane 7 cm flying at a height of 1000 feet above the ground. As the object falls, d, its distance above the ground after t seconds, is given Which of the following is closest to the by the formula below. area of the circle? A. 22 cm2 d 16t 2 1000 B. 38 cm2 * How far above the ground is the object when it has fallen for 4 seconds? C. 49 cm2 A. 984 feet D. 154 cm2 B. 936 feet C. 872 feet D. 744 feet * 195 Mathematics Session 2 Questions 28 and 29 are open-response questions 28 in the space provided in your Student Answer Booklet. 3005204 C Art Code 3005204.AR1 28 Colin plans to order three types of skateboard parts. He plans to order a total of ten parts. He can order online (over the Internet) from Tony's Skateboard Shop, or he can order from a local store. Colin's online order from Tony's Skateboard Shop is shown in the order form below. Tony's Skateboard Shop Order Form Type of Part Price per Unit Units Ordered Cost Truck $8.95 2 Wheel $6.95 4 Package of Bearings $2.45 4 Subtotal Online Discount –$2.00 Subtotal After Discount Sales Tax (5% of the Subtotal After Discount) Total Payment Due Use the order form above to answer parts a, b, and c. a. The Subtotal amount is the total cost of all ten parts before any discount or tax. What is the Subtotal amount for the ten parts that Colin plans to order? Show your work or explain your answer. b. By ordering online from Tony's Skateboard Shop, Colin is entitled to an Online Discount of $2.00 off the Subtotal amount. Sales Tax of 5% is added to the Subtotal After Discount. What is the Total Payment Due if Colin orders online from Tony's Skateboard Shop? Show your work or explain your answer. c. Colin learns that the local store can provide the same ten parts, each one at the same Price per Unit that Tony's Skateboard Shop charges, but the local store will give Colin a 20% discount on the Subtotal amount. After this discount, Colin will still need to pay sales tax of 5%. If Colin orders from the local store, how much less will Colin pay for the skateboard parts than if he ordered the same parts online from Tony's Skateboard Shop? 196 Mathematics Session 2 Write your answer to question 29 in the space provided in your Student Answer Booklet. 3011686 C Art Code 3011686.AR1 29 Arsenio was studying signal flags in his sailing class. On grid paper, he made a drawing of the flag that means a boat is disabled, as shown below. The flag is a large, white square that contains a smaller, red square (shown shaded in the drawing). Arsenio's Drawing Disabled Boat Flag Key: represents 1 square unit a. What is the area, in square units, of the large square in Arsenio's drawing of the flag? Show your work or explain how you got your answer. b. What is the total area, in square units, of the 4 unshaded interior parts of Arsenio's drawing of the flag? Show your work or explain how you got your answer. c. What is the perimeter, in units, of the smaller square in Arsenio's drawing of the flag? Show your work or explain how you got your answer. 197 Mathematics Session 2 Mark your answers to multiple-choice questions 30 through 38 in the spaces provided in your Student Answer Booklet. Do not write your answers in this test booklet. You may do your figuring in the test booklet. 3005218 C Art Code 3005218.AR1 30 Two rectangles, ABCD and WXYZ, are shown below. The measure of each side of WXYZ is 5 times the measure of each corresponding side of ABCD. A B D C W X Z Y Which statement is true of the areas of these two rectangles? A. The area of WXYZ is 5 times the area of ABCD. B. The area of WXYZ is 10 times the area of ABCD. C. The area of WXYZ is 20 times the area of ABCD. D. The area of WXYZ is 25 times the area of ABCD. * 198 Mathematics Session 2 3005195 C 2097404 C Art Code 2097404.AR1, AR2, AR3, AR4 1 31 A sugar cookie recipe calls for 3 2 cups of 32 Which of the following shows the graph of a line with positive slope? sugar to make 6 dozen cookies. Based on the recipe, how many cups of sugar must A. y * 6 be used to make 20 dozen sugar cookies? 4 2 1 A. 9 2 cups x -6 -4 -2 0 2 4 6 2 -2 B. 11 3 cups * -4 C. 61 cups -6 D. 70 cups B. y 6 4 2 0 x -6 -4 -2 2 4 6 -2 -4 -6 C. y 6 4 2 0 x -6 -4 -2 2 4 6 -2 -4 -6 D. y 6 4 2 0 x -6 -4 -2 2 4 6 -2 -4 -6 199 Mathematics Session 2 3005187 C 3005237 C 33 In a citywide survey, bicycle owners were 34 A group of 36 people from the Nantucket asked how many bicycles they owned, and Recreation Center plans to purchase tickets whether any had been stolen during the for a cruise to Bermuda. The standard fare previous year. The results indicated that for an individual ticket is shown below. people in the city owned 9017 bicycles and, of these, 450 had been stolen. Based on this information, which conclusion is Cruise Price most reasonable? Standard Fare A. No bicycle owners will have their Individual Ticket Price $1200 bicycles stolen this year. B. All bicycle owners will have their The group is informed that, because bicycles stolen this year. of the size of the group, the standard fare will be reduced by 30%. C. The probability that any one bicycle 1 With the discount of 30%, how much does will be stolen is about 5 . each member of the Nantucket Recreation Center have to pay for a cruise ticket? D. The probability that any one bicycle A. $360 1 will be stolen is about 20. * B. $432 C. $768 D. $840 * 3005259 C 35 Which of the following is equivalent to the expression below? (4)( x)( y) A. 4xy * B. 4xy C. ( 4)(x)(y) D. ( 4)( x)( y) 200 Mathematics Session 2 2097366 C 3 36 Mr. Lowery has 8 4 pounds of ground beef that he will use to make hamburgers for a picnic. What is the maximum number of quarter-pound hamburgers he can make? A. 9 B. 17 C. 35 * D. 36 3009722 C Art Code 3009722.AR1 37 An artist creates a design by drawing circles in steps, as shown below. Step 1 Step 2 Step 3 The table below shows a pattern of the total number of circles formed at each step. Pattern of Circles Step 1 2 3 4 5 Total Number of 1 4 13 Circles If the pattern shown in the table continues, what will be the total number of circles formed at step 5? A. 52 B. 117 C. 121 * D. 283 201 Mathematics Session 2 2097268 C 38 The chart below shows basketball shots attempted and made by four players on a team. Basketball Shots Name Shots Attempted Shots Made Kenzo 10 6 Chris 12 7 Kyle 5 4 Ramon 12 3 Which of the following lists the players in order from the highest to the lowest percentage of shots made out of shots attempted? A. Kyle, Kenzo, Chris, Ramon * B. Chris, Kenzo, Kyle, Ramon C. Chris, Kyle, Kenzo, Ramon D. Kyle, Chris, Kenzo, Ramon 202 Mathematics Session 2 Question 39 is an open-response question 39 in the space provided in your Student Answer Booklet. 2097375 C Art Code 2097375.AR1 39 The figure below shows an aquarium that is shaped like a rectangular prism. 18 in. 24 in. 12 in. a. What is the volume, in cubic inches, of the aquarium? b. One gallon is equal to 231 cubic inches. How many gallons of water will the aquarium hold? c. If 10 gallons of water were poured into the empty aquarium, what would be the depth, in inches, of the water? Show your work or explain how you got your answer. 203 Massachusetts Comprehensive Assessment System Grade 8 Mathematics Reference Sheet PERIMETER FORMULAS AREA FORMULAS square..............P = 4s square..............A = s 2 rectangle .........P = 2b + 2h rectangle..........A = bh triangle............P = a + b + c OR A = lw 1 triangle ............A = 2 bh CIRCLE FORMULAS circle ...............A = r2 circle ...............C = 2 r 1 trapezoid .........A = 2 h(b1 b2) OR C = d A= r2 VOLUME FORMULAS rectangular prism .........V = Bh (B = area of base) PYTHAGOREAN THEOREM 1 cone..............................V = 3pr2h cylinder ........................V = r2h a c cube..............................V = s3 b (s = length of an edge) 2 2 a + b = c2 CONVERSIONS 1 mile = 5280 feet 1 square mile = 640 acres 204 Grade 8 Mathematics Spring 2004 Released Items: Reporting Categories, Standards, and Correct Answers Correct Answer Item No. Page No. Reporting Category Standard (MC/SA)* 1 181 Patterns, Relations, and Algebra 8.P.2 D 2 181 Geometry 8.G.2 B 3 182 Number Sense and Operations 8.N.9 A 4 182 Patterns, Relations, and Algebra 8.P.9 D 5 183 Number Sense and Operations 8.N.2 B 6 183 Number Sense and Operations 8.N.8 C 7 184 Patterns, Relations, and Algebra 8.P.1 $750 1 8 184 Number Sense and Operations 8.N.10 2 9 185 Data Analysis, Statistics, and Probability 8.D.2 10 186 Number Sense and Operations 8.N.1 D 11 187 Data Analysis, Statistics, and Probability 8.D.2 C 12 188 Number Sense and Operations 8.N.5 D 13 188 Geometry 8.G.7 B 14 188 Patterns, Relations, and Algebra 8.P.6 D 15 189 Measurement 8.M.4 C 16 189 Patterns, Relations, and Algebra 8.P.4 D 17 190 Data Analysis, Statistics, and Probability 8.D.2 A 18 190 Patterns, Relations, and Algebra 8.P.7 B 19 191 Data Analysis, Statistics, and Probability 8.D.4 18 20 192 Data Analysis, Statistics, and Probability 8.D.3 60, or 11 to 71 21 192 Geometry 8.G.1 60° 22 193 Patterns, Relations, and Algebra 8.P.1 23 194 Patterns, Relations, and Algebra 8.P.10 A 24 194 Data Analysis, Statistics, and Probability 8.D.2 B 25 195 Measurement 8.M.3 B 26 195 Number Sense and Operations 8.N.4 C 27 195 Measurement 8.M.5 D 28 196 Number Sense and Operations 8.N.12 29 197 Measurement 8.M.3 30 198 Patterns, Relations, and Algebra 8.P.8 D 31 199 Number Sense and Operations 8.N.3 B 32 199 Patterns, Relations, and Algebra 8.P.5 A 33 200 Data Analysis, Statistics, and Probability 8.D.4 D 34 200 Number Sense and Operations 8.N.10 D 35 200 Patterns, Relations, and Algebra 8.P.3 A 36 201 Number Sense and Operations 8.N.12 C 37 201 Patterns, Relations, and Algebra 8.P.1 C 38 202 Number Sense and Operations 8.N.1 A 39 203 Measurement 8.M.3 * Answers are provided here for multiple-choice and short-answer items only. Sample responses and scoring guidelines for open-response items, which are indicated by shaded cells, will be posted to the Department's website later this year.
Overview This book is the first general introduction to stability of ordinary and functional differential equations by means of fixed point techniques. It contains an extensive collection of new and classical examples worked in detail and presented in an elementary manner. Most of this text relies on three principles: a complete metric space, the contraction mapping principle, and an elementary variation of parameters formula. The material is highly accessible to upper-level ... More About This Book Overview This book is the first general introduction to stability of ordinary and functional differential equations by means of fixed point techniques. It contains an extensive collection of new and classical examples worked in detail and presented in an elementary manner. Most of this text relies on three principles: a complete metric space, the contraction mapping principle, and an elementary variation of parameters formula. The material is highly accessible to upper-level undergraduate students in the mathematical sciences, as well as working biologists, chemists, economists, engineers, mathematicians, physicists, and other scientists using differential equations. It also introduces many research problems that promise to remain of ongoing
Synopses & Reviews Publisher Comments: From signed numbers to story problems — calculate equations with ease Practice before each set of problems, this workbook shows you how to work with fractions, exponents, factoring, linear and quadratic equations, inequalities, graphs, and more! 100s of problems! Hundreds of practice exercises and helpful explanations Explanations mirror teaching methods and classroom protocols Focused, modular content presented in step-by-step lessons Practice on hundreds of Algebra I problems Review key concepts and formulas Get complete answer explanations for all problems Synopsis: About the Author Mary Jane Sterling is the author of Algebra I For Dummies, 2nd Edition, Trigonometry For Dummies, Algebra II For Dummies, Math Word Problems For Dummies, Business Math For Dummies, and Linear Algebra For Dummies. She taught junior high and high school math for many years before beginning her current 30-years-and-counting tenure at Bradley University in Peoria, Illinois. Mary Jane especially enjoys working with future teachers and trying out new technology. "Synopsis" by Wiley,
... More About This Book their skills and succeed on this high-stakes exam! Fully aligned with California's core curriculum standards, our test prep provides up-to-date instruction and practice high school students need to improve their math abilities. The comprehensive review features student-friendly, easy-to-follow examples that reinforce the concepts tested on the CAHSEE math exam, including: Number Sense; Measurement and Geometry; Statistics, Data Analysis and Probability; Algebra and Functions; and Algebra I. Our tutorials and targeted drills increase comprehension while enhancing the student's math skills. Color icons and graphics throughout the book highlight important concepts and tasks. REA's test-taking tips and strategies give students the confidence they need so they can pass the exam and graduate. Authored by a math tutor with 20 years of experience, the book contains two full-length practice exams that allow students to test their knowledge and reinforce what they've learned. The interactive CD-ROM TestWare® includes two unique practice tests not found in the book – for a total of four exams! The tests on CD-ROM are given in a timed format with automatic, instant scoring. Each practice exam comes complete with detailed explanations of answers, allowing students to focus on areas in need of further study. This book is a must for any California student preparing for the CAHSEE math exam! Related Subjects Meet the Author Stephen Hearne is currently a Professor of Psychology at Skyline College in San Bruno, California where he teaches Quantitative Reasoning among other subjects. For the past twenty years, Stephen Hearne has worked as a mathematics tutor teaching students of all ages in math, algebra, statistics, and test preparation. He prides himself in being able to make the complex simple. Read an Excerpt Passing the CAHSEE-Math About This Book and TestWare® This book, along with our companion TestWare® software, provides you with an accurate and complete representation of the Mathematics section of the California High School Exit Examination* (CAHSEE). Inside, you will find reviews that are designed to provide you with the information and strategies needed to do well on the test. Four complete practice tests are provided: two printed in this book and two additional tests on the accompanying CD-ROM. All of the tests are based on the official CAHSEE. The practice tests contain every type of question that you may expect to appear on the CAHSEE Math. Following each test, you will find an answer key with detailed explanations designed to help you completely understand the test material. About the Test Who Takes the Test and What Is It Used For? Beginning with the class of 2006, every high school student who plans to graduate from a California public high school has been required to pass the California High School Exit Examination. The test consists of two parts: Mathematics and English-Language Arts. Students are first required to take the CAHSEE in grade 10. If you pass both the Mathematics and the English-Language Arts sections, you will not be required to retake the test. If you pass only one section, you must retake the other part in grades 11 and 12, until you pass. If you do not pass either part of the CAHSEE, you get the chance to retake both sections in grades 11 and 12, until you pass. When and Where Is the Test Given? Every public school district in California has to provide students with multiple opportunities to take the CAHSEE. Your high school may choose from a list of test dates for administering the CAHSEE that are designated by the State Superintendent of Public Instruction. Your school is also responsible for accommodating the test takers. The questions and scoring guides are provided by Educational Testing Service. The CAHSEE test is administered over two days. The English-Language Arts section is given on the first day, followed by the Mathematics portion the next day. The CAHSEE is an untimed test, so if you need until the end of the school day to finish, take the time. Is There a Registration Fee? No. Because all California public high school students are required to take and pass this test in order to receive a high school diploma, no fee is required. Special Test Arrangements Parents of special education students, students with disabilities, and students who are learning English should contact their local high school officials regarding possible waivers or special arrangements, such as the use of a calculator when they take the CAHSEE. In order to be considered for a waiver, students must be diagnosed with a physical or learning disability or be in the process of learning the English language. Additional Information and Support Additional resources to help you prepare to take the CAHSEE include the official State of California CAHSEE website at How to Use This Book and TestWare® What Do I Study First? Learn about the format and content of the CAHSEE Mathematics exam by reading the introductory section of this book. Pay particular attention to our test-taking strategies. Then read and study the review sections of this book found in Parts 1 through 5. Take the practice tests found in this book and on the two practice tests found on the accompanying TestWare® CD-ROM to become familiar with the format and procedures involved with taking the actual CAHSEE. To best utilize your study time, follow our CAHSEE Independent Study Schedule located in the front of this book. When Should I Start Studying? It is never too early to start studying for the CAHSEE the exam content. Format of the CAHSEE Math The Mathematics portion of the CAHSEE is designed to test the following skills: • Statistics, Data Analysis, and Probability: These questions deal with statistical measurements, data samples of a population, theoretical and experimental probabilities, and data sets with one or more variables. • Number Sense: These questions deal with properties of rational numbers and fractions, exponents, powers, and roots. • Measurement and Geometry: These questions deal with units of measure, ratio conversion, changes of scales, the Pythagorean theorem, and computing perimeter, area, and volume. • Mathematical Reasoning: These questions deal with approaching problems, determining that a solution is complete, and using strategies, skills, and concepts. • Algebra: This section deals with finding the reciprocal, taking a root, the rules of exponents, absolute values, expressions and inequalities in one variable, multi-step problems involving linear equations and inequalities in one variable, graphing linear equations and computing the x- and y-intercepts, verifying that a point lies on a line, the relationship of parallel slopes, systems of two linear equations, solving a system of two linear inequalities in two variables, performing basic operations on monomials and polynomials, and applying algebraic techniques to solve rate, work, and percent mixture problems. About the Review Sections The review in this book is designed to help you sharpen the basic skills needed to pass the Mathematics section of the CAHSEE. You will find test-taking strategies, a review of arithmetic, algebra, geometry, and word problems, and questions and tasks to strengthen your abilities in these areas. By using the reviews in conjunction with the practice tests, you will better prepare yourself for the CAHSEE itself. Test-Taking Strategies Although you may not be familiar with standardized tests such as the CAHSEE, there are many ways to acquaint yourself with this type of examination and help alleviate your test-taking anxieties. Listed below are ways to help you get to know the CAHSEE, some of which may be applied to other standardized tests. What to Do Before the Test • Pay attention in class. • Carefully work through the review sections of this book. Mark any topics that you find difficult, so that you can focus on them while studying and get extra help if necessary. • Take the practice tests and become familiar with the format of the CAHSEE. When you are practicing, simulate the conditions under which you will be taking the actual test. Stay calm and pace yourself. After simulating the test only a couple of times, you will feel more confident, and this will boost your chances of doing well. • Students who have difficulty concentrating or taking tests in general may have severe test anxiety. Tell your parents, a teacher, a counselor, the school nurse, or a school psychologist well in advance of the test. They may be able to help you learn some useful strategies that will help you feel more relaxed, so that you can do your best on the test. What to Do During the Test • Read all of the possible answers. Just because you think you have found the correct response, do not automatically assume that it is the best answer. Read through each answer choice to be sure that you are not making a mistake by jumping to conclusions. • Use the process of elimination. Go through each answer to a question and eliminate as many of the answer choices as possible. By eliminating two answer choices, you have given yourself a better chance of getting the item correct, since there will only be two choices left from which to make your guess. Sometimes a question will have one or two answer choices that are a little odd. These answers will be obviously wrong for one of several reasons: they may be impossible given the conditions of the problem, they may violate mathematical rules or principles, or they may be illogical. • Work on the easier questions first. If you find yourself working too long on one question, make a mark next to it on your test booklet and continue. After you have answered all of the questions that you know, go back to the ones you have skipped. • Be sure that the answer oval you are marking corresponds to the number of the question in the test booklet. Since the multiple-choice sections are graded by machine, marking one wrong answer can throw off your answer key and your score. Be extremely careful. • Work from answer choices. You can use a multiple-choice format to your advantage by working backward from the answer choices to solve a problem. This strategy can be helpful if you can just plug the answers into a given formula or equation. You may be able to make an educated guess based on your elimination of choices that you know do not fit into the problem. • If you cannot determine what the correct answer is, guess anyway. The CAHSEE does not subtract points for wrong answers, so be sure to fill in an answer for every question. It works to your advantage, because you could guess correctly and increase your score. Table of Contents Contents Independent Study Schedule Passing the CAHSEE Mathematics Exam About This Book and TestWare® About the Test How to Use This Book and TestWare® Format of the CAHSEE Math Scoring the CAHSEE About the Review Sections Test-Taking Strategies The Day of the Test CAHSEE Raw-Score-to-Scale-Score Conversion CAHSEE Mathematics Content Standards PART 1: Number Sense The Lowest Common Denominator Computations Converting a Fraction into a Decimal and a Percent Finding the Prime Factored Form of a Number Exponents The First Law of Exponents The Second Law of Exponents Multiplying and Dividing Monomials Scientific Notation The Square Root of a Number Absolute Value Adding Positive and Negative Numbers PART 2: Measurement and Geometry Measurement Making a Scaled Drawing Reading a Scaled Drawing Converting Units of Measurement Word Problem Finding the Perimeter of a Rectangle Finding the Area of a Triangle Finding the Circumference Around a Circle Finding the Area of a Circle Finding the Area of a Complex Figure Finding Volume More Converting Units of Measurement Graphing The Pythagorean Theorem More Pythagorean Theorem Congruent Triangles Degrees in a Triangle Reflecting an Image Across the x or y Axis PART 4: Algebra and Functions Algebra Basics Multiplying Two Binomials Solving an Equation with One Variable Solving an Equation with Two Variables Solving an Inequality Estimation Evaluating an Equation Expressions and Equations Grouping Symbols Order of Operations Reading a Bar Graph Percent Savings Sale Price Graphing a Function The Slope of a Line Reading a Line Graph More Reading a Line Graph PART 5: Algebra Solving a Linear Equation Word Problem Opposites and Reciprocals More Absolute Value More About Solving a Linear Equation Word Problem Graphing a Line A Point on a Line Coordinates of x- and y-Intercepts Parallel Lines Solving a System of Two Linear Equations and Understanding the Solution Graphically Simplifying Expressions Word Problem Finding an Equivalent Equation Formulas
More About This Textbook Overview This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of the exercises will have a sound knowledge base for upper division mathematics, science, and engineering courses where detailed models and applications are introduced. J. David Logan is Professor of Mathematics at University of Nebraska, Lincoln. He is also the author of numerous books, including Transport Modeling in Hydrogeochemical Systems (Springer 2001). Editorial Reviews From the Publisher From the reviews of the second edition: "This second edition of the short undergraduate text provides a fist course in PDE aimed at students in mathematics, engineering and the sciences. The material is standard … . Strong emphasis is put on modeling and applications throughout; the main text is supplied with many examples and exercises." (R. Steinbauer, Monatshefte für Mathematik, Vol. 150 (4), 2007) "This book contains an elementary introduction of partial differential equations to undergraduate students in mathematics, engineering, and physical sciences. … This is a unique book in the sense that it provides a coverage of the main topics of the subject in a concise style which is accessible to science and engineering students. … Reading this book and solving the problems, the students will have a solid base for a course in partial differential equations … ." (Tibor Krisztin, Acta Scientiarum Mathematicarum, Vol. 74
'm not very good at math and haven't studied it since high school. I'm forty now. This was our designated text. My course is offered online, so I basically had to learn from this book alone with very little outside help. The text was very readable and explanatory. There are many examples that
introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples. The book is organized into two main sections and a set of appendices. Part I addresses steady-state boundary value problems, starting with two-point boundary value problems in one dimension, followed by coverage of elliptic problems in two and three dimensions. It concludes with a chapter on iterative methods for large sparse linear systems that emphasizes systems arising from difference approximations. Part II addresses time-dependent problems, starting with the initial value problem for ODEs, moving on to initial boundary value problems for parabolic and hyperbolic PDEs, and concluding with a chapter on mixed equations combining features of ODEs, parabolic equations, and hyperbolic equations. The appendices cover concepts pertinent to Parts I and II. Exercises and student projects, developed in conjunction with this book, are available on the book s webpage along with numerous MATLAB m-files. Readers will gain an understanding of the essential ideas that underlie the development, analysis, and practical use of finite difference methods as well as the key concepts of stability theory, their relation to one another, and their practical implications. The author provides a foundation from which students can approach more advanced topics and further explore the theory and/or use of finite difference methods according to their interests and needs. Audience: This book is designed as an introductory graduate-level textbook on finite difference methods and their analysis. It is also appropriate for researchers who desire an introduction to the use of these methods. Contents: Preface; Part I: Boundary Value Problems and Iterative Methods. Chapter 1: Finite Difference Approximations; Chapter 2: Steady States and Boundary Value Problems; Chapter 3: Elliptic Equations; Chapter 4: Iterative Methods for Sparse Linear Systems; Part II: Initial Value Problems. Chapter 5: The Initial Value Problem for Ordinary Differential Equations; Chapter 6: Zero-Stability and Convergence for Initial Value Problems; Chapter 7: Absolute Stability for Ordinary Differential Equations; Chapter 8: Stiff Ordinary Differential Equations; Chapter 9: Diffusion Equations and Parabolic Problems; Chapter 10: Advection Equations and Hyperbolic Systems; Chapter 11: Mixed Equations; Appendix A: Measuring Errors; Appendix B: Polynomial Interpolation and Orthogonal Polynomials; Appendix C: Eigenvalues and Inner-Product Norms; Appendix D: Matrix Powers and Exponentials; Appendix E: Partial Differential Equations; Bibliography; Index.
I rstother books you may want to look at are Herstein, AbstractAlgebra, Prentice-Hall, 3rd edition, and Fraleigh, A First Course in AbstractAlgebra, published by Addison-Wesley. My feeling is that Artin's book presents AbstractAlgebra by I. N. Herstein Contemporary AbstractAlgebra by Joseph Gallian A First Course in AbstractAlgebra by John Fraleigh AbstractAlgebra by John A. Beachy and William D. Blair A Book of AbstractAlgebra by Charles C. Pinter I firstPrerequisite: A one semester undergraduate course in AbstractAlgebra (covering group theory and perhaps a little ring theory), ... others are the easier algebra book of Herstein (used recently at BC for the undergraduate course, Math 310), AbstractAlgebra, and the ABSTRACTALGEBRA I 22m:120, Fall 2005 Instructor: Fred Goodman Office: 325G McLean Hall Phone: 335-0791 Office Hours: To be arranged. Course goals: The goals of this course will be for you to develop a systematic knowledge of fundamentally geometric idea of perpendicularity is quite visible in Herstein's "abstract" algebra, but is hidden in Bocher's algebraic "geometry." The explanation behind this difference, as mentioned above, of course, is this: ... Algebra Review 1 Finite Groups The study of algebra is motivated by a desire to abstract away from the familiar notions of arith-metic, numbers, and algebra to develop a theory that is general and applies to different structures For an introduction to group theory, I recommend AbstractAlgebra by I. N. Herstein. This is a wonderful book with wonderful exercises (and if you are new to group theory, you should do lots of the exercises). If Text: AbstractAlgebra 3. rd Edition . by I. N. Herstein (available in . This is an introductory course in AbstractAlgebra. The core of the course will be the theory of groups, covered in Chapters 2 and 3 of the textbook. Additional topics from Textbook and Scope: Our text is Topics in Algebra, by I.N. Herstein (2nd edition), John Wiley & Sons. We'll cover most of Chapters 2 (Groups) and 3 (Rings). ... AbstractAlgebra: Theory and Applications seems the closest to the spirit of this course. Algebra of which we speak is the "Modern," or "Higher," or "Abstract" Algebra of the upper division and post graduate curriculum (although we need to be careful when speaking with the ... Herstein, Topics in Algebra, Blaisdell, Waltham, MA, 1964. 6. G.
Asvab Math? Answer ASVAB mathematics can be scary and difficult for some, but there are many exercises and ways to prepare for the assessment. The ASVAB mathematics portion may include algebra equations, fractions, exponent problems, inequalities, and the need to know the different types of numbers. For a complete list of what you may find on the ASVAB mathematics portion, see this link:
Students can look at graphs of degrees 0 through 5 and see the effects of changing the coefficients a, b, c, d and e on each graph by moving sliders. Allows students to see how the different cubic fu... More: lessons, discussions, ratings, reviews,... Discussion of polynomials, including properties of linear and quadratic polynomials. Investigate the way the roots and graph of a quadratic polynomial ax^2 + bx + c changes as a and the square root o... More: lessons, discussions, ratings, reviews,... This applet solves only the real roots of polynomial equations up to a maximum of order five. Complex number solutions are not available, however it can be included in the future if users request s... More: lessons, discussions, ratings, reviews,... This model represents the interactions between members of a food chain; in this case, vegetation, rabbits and foxes. This simulation can be used to answer questions such as: What happens when vegetati
Linear Algebra With for undergraduate first courses in Linear Algebra. Assumes the user has had calculus. Renowned for thoroughness and accessibility, this top-selling text by one of the leading figures in linear algebra education offers students a challenging and enjoyable study of linear algebra that is infused with an abundance of applications. Balancing coverage of mathematical theory and applied topics, Professor Leon explains concepts with precision so that students at any level can understand the material. Worked examples are heavily integrated into each chapter. The book stresses the important role geometry and visualization play in understanding the subject. This edition will continue to be packaged with the ancillary ATLAST computer exercise guide, as well as new MATLAB and Maple guides.
Related Courses The focus is on building algebraic thinking with an emphasis on modeling real-world phenomena and the meanings represented by algebraic expressions. Topics include linear relationships; slope; linear, quadratic, and exponential functions. Connections will be drawn between algebra and geometry through patterns and other areas of overlap. Prerequisite: MATH 172, MATH 225, or MATH 270. Spring.
Learn Math Interactive Differential Equations (IDE) — CODEE IDE is available, for free, at When we first, in the 1990s, became acquainted with Hubert Hohn and his wonderful interactive illustrations we knew immediately that he had found a real key to making our subject (and many others) come alive--not only for students, but for ourselves and our faculty colleagues. Hohn is a master educator. Ordinary Differential Equations - Resources The sources below are among some of the best locations of sites dedicated to ordinary differential equations, online and on the computer. General Sources Math Forum: Differential Equations. Daniel Kopsas Daniel Kopsas (pronounced "Copsis") E-mail: kopsasd@otc.edu Office Phone: (417) 447 - 8263 Twitter: I teach mathematics at Ozarks Technical Community College in Springfield, Missouri. I was inspired by Maria Andersen from Muskegon Community College to create this site and continue to pursue the use of technology in the mathematics classroom. For each of the courses in the sidebar to the left, I have built or I am currently building math video libraries. Statistics Correlation examples Statistics is an applied branch of Mathematics. A knowledge of statistics is like a knowledge of foreign languages or of algebra; it may prove of use at any time under any circumstances. - A. L. Bowley Courses[edit] Welcome to the Wikibook of Statistics Statistics - Area of applied mathematics concerned with the data collection, analysis, interpretation and presentation. Statistics is used in almost every field of research: the discovery of the Higgs particle, social sciences, climate research,... With this, and with its well established foundations, it is very well suited for a wikibook. Statistics - Wikibooks, collection of open-content textbooks All of Statistics All of Statistics A Concise Course in Statistical Inference by Larry Wasserman Get the book from Springer or Amazon Errata (last updated April 3 2013) New England Complex Systems Institute 238 Main Street Suite 319, Cambridge, MA 02142 Phone: 617-547-4100 Fax: 617-661-7711 Textbook for seminar/course on complex systems.View full text in PDF format The study of complex systems in a unified framework has become recognized in recent years as a new scientific discipline, the ultimate of interdisciplinary fields. Breaking down the barriers between physics, chemistry and biology and the so-called soft sciences of psychology, sociology, economics, and anthropology, this text explores the universal physical and mathematical principles that govern the emergence of complex systems from simple components. Dynamics of Complex Systems September 2007 This is the second installment of a new feature in Plus: the teacher package. Every issue contains a package bringing together all Plus articles about a particular subject from the UK National Curriculum. Whether you're a student studying the subject, or a teacher teaching it, all relevant Plus articles are available to you at a glance. Teacher package: Mathematical Modelling
Intermediate Algebra : Graphs and Models - 3rd edition Summary: The Third Edition of the Bittinger Graphs and Models series helps students succeed in algebra by emphasizing a visual understanding of concepts. This latest edition incorporates a new Visualizing the Graph feature that helps students make intuitive connections between graphs and functions without the aid of a graphing calculator. 3.1 Systems of Equations in Two Variables 3.2 Solving by Substitution or Elimination 3.3 Solving Applications: Systems of Two Equations 3.4 Systems of Equations in Three Variables 3.5 Solving Applications: Systems of Three Equations 3.6 Elimination Using Matrices 3.7 Determinants and Cramer's Rule 3.8 Business and Economics Applications 0321416163 Instructors edition! Item has some cover wear but otherwise in good condition!!Used texts may not include supplemental matieral. All day low prices, buy from us sell to us we do it all!! $110.89
More About This Textbook Overview This text is a generic computer activities book in which students use software applications to build math, communication, and information skills. Activities are also provided for students to explore the power and scope of the Internet. The four units of the book cover word processing, spreadsheet, database, and Internet skills for beginning and intermediate level users. The focus of the book is learning through application. Using these activities helps students build both software and business skills in a hands-on
This series of videos, created by Salman Khan of the Khan Academy, features topics covered from very basic algebra all the way through algebra II. This is the best algebra playlist to start at if you've never seen... This series of videos contains 180 Worked Algebra I examples (problems written by the Monterey Institute of Technology and Education). You should look at the "Algebra" playlist if you've never seen algebra before or if... This lesson helps students understand financial topics (interest rates, FICO scores and loan payments) in a mathematical context. Students will calculate monthly payments for a car or home based on the best interest... This lesson involves economics and mathematical materials. Students will use their knowledge of exponents to compute an investment's worth using a formula and a compound interest simulator. They may also use the model... This algebra unit from illuminations provides an in depth exploration of exponential models in context. The model of light passing through water is used to demonstrate exponential functions and related mathematical...
ELEMENTARY STATISTICS: A STEP BY STEP APPROACH" is for general beginning statistics courses with a basic algebra prerequisite. The book is non ...Show synopsisELEMENTARY STATISTICS: A STEP BY STEP APPROACH" is for general beginning 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. This edition places more emphasis on conceptual understanding and understanding results. This edition also features increased emphasis on Excel, MINITAB, and the TI-83 Plus and TI-84 Plus graphing calculators; computing technologies commonly used in such courses.Hide synopsis Description:Acceptable. Ships same or next business day with delivery...Acceptable. Ships same or next business day with delivery confirmation. Acceptable condition. Contains highlighting. Expedited shipping available. Sewn binding. Cloth over boards. Contains: Illustrations. Audience: General/trade. Description:Good. Elementary Statistics: A Step By Step Approach. This book...Good. Elementary Statistics: A Step By Step
Elementary Linear Algebra With Applications - 9th edition Summary: This book presents the basic ideas of linear algebra in a manner that users will find understandable. It offers a fine balance between abstraction/theory and computational skills, and gives readers an excellent opportunity to learn how to handle abstract concepts.Included in this comprehensive and easy-to-follow manual are these topics: linear equations and matrices; solving linear systems; real vector spaces; inner product spaces; linear transformations and matrices; determinants; e...show moreigenvalues and eigenvectors; differential equations; and MATLAB for linear algebra.Because this book gives real applications for linear algebraic basic ideas and computational techniques, it is useful as a reference work for mathematicians and those in field of computer
The first half of the course will focus on first learning how to analyze & reason (through the study of logic) and then moves on to the basics of geometry, being lines & angles. Afterward, the concept of lines & angles is used to understand the principles of polygons such as triangles and quadrilaterals. Finally, the first semester ends with applying the coordinate plane to this basic geometric knowledge. The second half of the course focuses on more advanced topics such as shapes, figures, and their properties. Even more advanced topics will be discussed such as the properties of circles and triangles, trigonometry, and graph theory. Other less intimidating topics such as perimeter, area, volume, and surface area will also be discussed. Additionally, algebra, statistics, and probability will be reviewed in order to prepare students for the mathematical sections of both the College Board and SAT exams. Students will also learn a bit of the history of mathematics such as ancient numeral systems, numerical superstitions, and the biographies of important mathematicians.
)... MoreDiscussion for Mathematics Tutorials and Problems (with applets) Katie Larkin (Faculty) Great resource. Great organization and scope of material. 4 years ago Seamus Beall (Student) this is a straight forward site which uses graphs to demonstrate different math concepts. I think that students who prefer a direct visual example of what they are learning would appreciate this site and I believe it would stand to benefit a teacher who might want to show graphically what small changes in input numbers can do to graphs. I would have really liked to have known about this particular site when i took my intermediate algebra class because it covers so many topics in a fair ammount of depth. Time spent reviewing site: 1 half hour. 4 years ago Thomas Brown (Faculty) Contains applets which can help students develop an intuition for boxplots and the normal distribution.
This is going to be my summary of the freely available* Linear Algebra course from MIT. I watched the lectures of this course in the summer of 2008. This was not the first time I learned linear algebra. I had already had two terms of linear algebra when I studied physics back in 2004. But it was not enough for a curious mind like mine. I wanted to see how it was taught at the world's best university. The rationale of why I am posting these mathematics lectures on my programming blog is because I believe that if you want to be a great programmer and work on the most exciting and world changing problems, then you have to know linear algebra. Larry and Sergey wouldn't have created Google if they didn't know linear algebra. Take a look at this publication if you don't believe me "Linear Algebra Behind Google." Linear algebra has also tens and hundreds of other computational applications, to name a few, data coding and compression, pattern recognition, machine learning, image processing and computer simulations. The course contains 35 lectures. Each lecture is 40 minutes long, but you can speed them up and watch one in 20 mins. The course is taught by no other than Gilbert Strang. He's the world's leading expert in linear algebra and its applications and has helped the development of Matlab mathematics software. The course is based on working out a lot of examples, there are almost no theorems or proofs. I'll write the summary in the same style as I did my summary of MIT Introduction to Algorithms. I'll split up the whole course in 30 or so posts, each post will contain one or more lectures together with my comments, my scanned notes, embedded video lectures and a timeline of the topics in the lecture. But, not to flood my blog with just mathematics, I will write one or two programming posts in between. You should subscribe to my posts through RSS here. Lecture 1: The Geometry of Linear Equations The first lecture starts with Gilbert Strang stating the fundamental problem of linear algebra, which is to solve systems of linear equations. He proceeds with an example. The example is a system of two equations in two unknowns: There are three ways to look at this system. The first is to look at it a row at a time, the second is to look a column at a time, and the third is use the matrix form. If we look at this equation a row at a time, we have two independent equations 2x - y = 0 and -x + 2y = 3. These are both line equations. If we plot them we get the row picture: The row picture shows the two lines meeting at a single point (x=1, y=2). That's the solution of the system of equations. If the lines didn't intersect, there would have been no solution. Now let's look at the columns. The column at the x's is (2, -1), the column at y's is (-1, 2) and the column at right hand side is (0, 3). We can write it down as following: This is a linear combination of columns. What this tells us is that we have to combine the right amount of vector (2, -1) and vector (-1, 2) to produce the vector (0, 3). We can plot the vectors in the column picture: If we take one green x vector and two blue y vectors (in gray), we get the red vector. Therefore the solution is again (x=1, y=2). The third way to look at this system entirely through matrices and use the matrix form of the equations. The matrix form in general is the following: Ax = b where A is the coefficient matrix, x is the unknown vector and b is the right hand side vector. How to solve the equations written in matrix form will be discussed in the next lectures. But I can tell you beforehand that the method is called Gauss elimination with back substitution. For this two equations, two unknowns system, the matrix equation Ax=b looks like this: The next example in the lecture is a system of three equations in three unknowns: We can no longer plot it in two dimensions because there are three unknowns. This is going to be a 3D plot. Since the equations are linear in unknowns x, y, z, we are going to get three planes intersecting at a single point (if there is a solution). Here is the row picture of 3 equations in 3 unknowns: The red is the 2x - y = 0 plane. The green is the -x + 2y - z = -1 plane, and the blue is the -3y + 4z = 4 plane. Notice how difficult it is to spot the point of intersection? Almost impossible! And all this of going one dimension higher. Imagine what happens if we go 4 or higher dimensions. (The intersection is at (x=0, y=0, z=1) and I marked it with a small white dot.) The column picture is almost as difficult to understand as the row picture. Here it is for this system of 3 equations in 3 unknowns: The first column (2, -1, 0) is red, the second column (-1, 2, -3) is green, the fourth column (0, -1, 4) is blue, and the result (0, -1, 4) is gray. Again, it's pretty hard to visualize how to manipulate these vectors to produce the solution vector (0, -1, 4). But we are lucky in this particular example. Notice that if we take none of red vector, none of green vector and one of blue vector, we get the gray vector! That is, we didn't even need red and green vectors! This is all still tricky, and gets much more complicated if we go to more equations with more unknowns. Therefore we need better methods for solving systems of equations than drawing plane or column pictures. The lecture ends with several questions: Can Ax = b be solved for any b? When do the linear combination of columns fill the whole space?, What's the method to solve 9 equations with 9 unknowns? The examples I analyzed here are also carefully explained in the lecture, you're welcome to watch it: [24:00] Solution (x=0, y=0, z=1) from the column picture by noticing that z vector is equal to b vector. [28:10] Can Ax=b be solved for every b? [28:50] Do the linear combinations of columns fill the 3d space? [32:30] What if there are 9 equations and 9 unknowns? [36:00] How to multiply a matrix by a vector? Two ways. [36:40] Ax is a linear combination of columns of A. Here are my notes of lecture one. Sorry about the handwriting. It seems that I hadn't written much at that time and the handwriting had gotten really bad. But it gets better with each new lecture. At lecture 5 and 6 it will be as good as it gets. Notes of Linear Algebra lecture 1 on The Geometry of Linear Equations. Have fun with this lecture! The next post is going to be about a systematic way to find a solution to a system of equations called elimination. Feedburner used to have a really nice RSS subscriber growth graph. I loved it. But then one day they were acquired by Google and they changed their nice chart to an interactive flash thing that was slow and looked just awful. This graph was taken from Feedburner stats dashboard today. Choose "Show stats for" -> "all time" to generate this graph. This critter takes 35MB of RAM, responds in 4 seconds and worst of all, looks very, very ugly. I don't know why would anyone replace a nice 6.5KB image with a 35MB monster. I don't want to see this ugliness anymore, therefore I'll create a Perl program that generates the awesome graph they used to have. I'll write my thought process in creating this program in this post. Here it goes. First I need to get the data somehow. I remember they had some kind of an API to get the data. A quick Google search for feedburner api returns this link Feedburner Awareness API. Ya, that's it. This is the documentation of their API. Accessing the following URL gets me subscriber count data from July 1, 2007 to November 17, 2009: Excellent, now I can write the Perl program. It will need to parse the XML data, draw the chart and save the image to a file. Hmm, how should I invoke my program? Ok, here is how: $ generate_feedburner_graph.pl <<strong>feed name</strong>> [<<strong>start date</strong>> [<<strong>end date</strong>>]] # if <strong>end date</strong> is not specified, it's set to today. # if <strong>start date</strong> is not specified, it's set to first # day when the feed had at least one subscriber. This program will use LibGD to generate the image. It will save it to a file called feed_name-start_date-end_date.png. Now I need to find the colors used in the awesome feedburner graph. For this purpose I'll use ColorZilla Firefox plugin. The green one is #95CF9C, the background is #F2F8FC, the light grid is #CCCECE, the one that separates the green area from background is #687279, and the x-y axis are #808080. Alright, now I have everything I need to create the program. ... Several hours later ... Done! One thing I forgot to mention is that you will need DejaVuSans TrueType font to run this program (it uses it to draw text). Download it and put the DejaVuSans.ttf in the same directory as the program. As I was writing this I had the coolest idea to make a set of tools for probloggers. I added this idea to my idea-list and will try to make it happen. This tool could be the first in problogger tool suite! As you all may know, I watched and posted my lecture notes of the whole MIT Introduction to Algorithms course. In this post I want to summarize all the topics that were covered in the lectures and point out some of the most interesting things in them. Actually, before I wrote this article, I had started writing an article called "The coolest things that I learned from MIT's Introduction to Algorithms" but quickly did I realize that what I was doing was listing the topics in each article and not really pointing out the coolest things. Therefore I decided to write a summary article first (I had promised to do so), and only then write an article on really the most exciting topics. Talking about the summary, I watched a total of 23 lectures and it resulted in 14 blog posts. It took nearly a year to publish them here. The first blog post in this series was written in August 2008, and the last in July 2009. Here is a list of all the posts: I'll now go through each of the lectures. They require quite a bit of math knowledge to understand. If you are uncertain about your math skills, I'd suggest reading Knuth's Concrete Mathematics book. It contains absolutely all the necessary math to understand this course. Lecture 1: Analysis of Algorithms If you're a student, or even if you're not, you must never miss the first lecture of any course, ever! The first lecture tells you what to expect from the course, how it will be taught, what it will cover, who the professor is, what the prerequisites are, and a bunch of other important and interesting things. In this lecture you also get to know professor Charles E. Leiserson (author of CLRS) and he explains the following topics: Why study algorithms and their performance? What is the analysis of algorithms? What can be more important than the performance of algorithms? The sorting problem. Insertion sort algorithm. Running time analysis of insertion sort. Asymptotic analysis. Worst-case, average-case, best-case running time analysis. Analysis of insertion sort's worst-case running time. Asymptotic notation - theta notation - Θ. Merge sort algorithm. The recursive nature of merge sort algorithm. Running time recurrence for merge sort. Recursion trees. Running time analysis of merge sort by looking at the recursion tree. General recurrence for divide and conquer algorithms. I personally found the list of things that can be more important than the performance of the program interesting. These things are modularity, correctness, maintainability, security, functionality, robustness, user-friendliness, programmer's time, simplicity, extensibility, reliability, scalability. Lecture 2: Analysis of Algorithms (continued) The second lecture is presented by Eric Demaine. He's the youngest professor in the history of MIT. Here are the topics that he explains in the second lecture: Asymptotic notation. Big-o notation - O. Set definition of O-notation. Capital-omega notation - Ω. Theta notation - Θ. Small-o notation - o. Small-omega notation - ω. Solving recurrences by substitution method. Solving recurrences by recursion-tree method. Solving recurrences by the Master's method. Intuitive sketch proof of the Master's method. An interesting thing in this lecture is the analogy of (O, Ω, Θ, o, ω) to (≤, ≥, =, <, >). For example, if we say f(n) = O(n2) then by using the analogy we can think of it as f(n) ≤ c·n2, that is, function f(n) is always smaller than or equal to c·n2, or in other words, it's bounded above by function c·n2, which is exactly what f(n) = O(n2) means. Lecture 3: Divide and Conquer The third lecture is all about the divide-and-conquer algorithm design method and its applications. The divide and conquer method solves a problem by 1) breaking it into a number of subproblems (divide step), 2) solving each problem recursively (conquer step), 3) combining the solutions (combine step). Lecture 4: Sorting Lecture four is devoted entirely to the quicksort algorithm. It's the industry standard algorithm that is used for sorting in most of the computer systems. You just have to know it. Topics explained in lecture four: Divide and conquer approach to sorting. Quicksort algorithm. The partition routine in the quicksort algorithm. Running time analysis of quicksort. Worst-case analysis of quicksort. Intuitive, best-case analysis of quicksort. Randomized quicksort. Indicator random variables. Running time analysis of randomized quicksort in expectation. I loved how the idea of randomizing the partition subroutine in quicksort algorithm led to a running time that is independent of element order. The deterministic quicksort could always be fed an input that triggers the worst-case running time O(n2), but the worst-case running time of randomized quicksort is determined only by the output of the random number generator. I once wrote another post about quicksort called "Three Beautiful Quicksorts" where I summarized what Jon Bentley's had to say about the experimental analysis of quicksort's running time and how the current quicksort algorithm looks in the industry libraries (such as c standard library, which provides qsort function). Lecture 6: Order Statistics Lecture six deals with the order statistics problem - how to find the k-th smallest element among n elements. The naive algorithm is to sort the list of n elements and return the k-th element in the sorted list, but this approach makes it run in O(n·lg(n)) time. This lecture shows how a randomized, linear-time algorithm (in expectation) for this problem can be constructed. Topics explained in lecture six: Order statistics. Naive order statistics algorithm via sorting. Randomized divide and conquer order statistics algorithm. Expected running time analysis of randomized order statistics algorithm. Worst-case linear-time order-statistics. An interesting point in this lecture is that the worst-case, deterministic, linear-time algorithm for order statistics isn't being used in practice because it performs poorly compared to the randomized linear-time algorithm. Lecture 8: Hashing (continued) The second lecture on hashing. It addresses the weakness of hashing - for any choice of hash function, there exists a bad set of keys that all hash to the same value. An adversary can take an advantage of this and attack our program. Universal hashing solves this problem. The other topic explained in this lecture is perfect hashing - given n keys, how to construct a hash table of size O(n) where search takes O(1) guaranteed. Lecture 9: Search Trees This lecture primarily discusses randomly built binary search trees. (It assumes you know what binary trees are.) Similar to universal hashing (see previous lecture), they solve a problem when you need to build a tree from untrusted data. It turns out that the expected height of a randomly built binary search tree is still O(lg(n)), more precisely, it's expected to be 3·lg(n) at most. Topics explained in lecture nine: What are good and bad binary search trees? Binary search tree sort. Analysis of binary search tree sort. BST sort relation to quicksort. Randomized BST sort. Randomly built binary search trees. Convex functions, Jensen's inequality. Expected height of a randomly built BST. The most surprising idea in this lecture is that the binary search tree sort (introduced in this lecture) does the same element comparsions as quicksort, that is, they produce the same decision tree. Lecture 10: Search Trees (continued) This is the second lecture on search trees. It discusses self-balancing trees, more specifically, red-black trees. They balance themselves in such a manner that no matter what the input is, their height is always O(lg(n)). Lecture 11: Augmenting Data Structures The eleventh lecture explains how to build new data structures out of existing ones. For example, how to build a data structure that you can update and query quickly for the i-th smallest element. This is the problem of dynamic order statistics and an easy solution is to augment a binary tree, such as a red-black tree. Another example is interval trees - how to quickly find an interval (such as 5-9) that overlaps some other intervals (such as 4-11 and 8-20). Topics explained in lecture eleven: Dynamic order statistics. Data structure augmentation. Interval trees. Augmenting red-black trees to have them perform as interval trees. Correctness of augmented red-black tree data structure. Augmenting data structures require a lot of creativity. First you need to find an underlying data structure (the easiest step) and then think of a way to augment it with data to make it do what you want (the hardest step). Lecture 12: Skip Lists This lecture explains skip lists, which is a simple, efficient, easily implementable, randomized search structure. It performs as well as a balanced binary search tree but is much easier to implement. Eric Demaine says he implemented it in 40 minutes before the class (10 minutes to implement and 30 to debug). In this lecture Eric builds this data structure from scratch. He starts with a linked list and builds up to a pair of linked lists, to three linked lists, until it finds the optimal number of linked lists needed to achieve logarithmic search time. Next he continues to explain how to algorithmically build such a structure and proves that the search in this data structure is indeed quick. Lecture 13: Amortized Analysis Amortized analysis is a technique to show that even if several operations in a sequence of operations are costly, the overall performance is still good. A good example is adding elements to a dynamic list (such as a list in Python). Every time the list is full, Python has to allocate more space and this is costly. Amortized analysis can be used to show that the average cost per insert is still O(1), even though Python occasionally has to allocate more space for the list. Lecture 14: Self-Organizing Lists and Competitive Analysis This lecture concentrates on self-orginizing lists. A self-organizing list is a list that reorders itself to improve the average access time. The goal is to find a reordering that minimizes the total access time. For example, each time an element is accessed, it's moved to the front of the list, hoping that it might be accessed soon again. This is called move-to-front heuristic. Competitive analysis can be used to theoretically reason how well such a strategy as moving items to front performs. Lecture 15: Dynamic Programming This lecture is about the dynamic programming algorithm design technique. It's a tabular method (involving constructing a table or some part of a table) that leads to a much faster running time of the algorithm. The lecture focuses on the longest common subsequence problem, first showing the brute force algorithm, then a recursive one, and finally a dynamic programming algorithm. The brute force algorithm is exponential in the length of strings, the recursive one is also exponential, but the dynamic programming solution is O(n·m) where n is the length of one string, and m is the length of the other. Topics explained in lecture fifteen: The idea of dynamic programming. Longest common subsequence problem (LCS). Brute force algorithm for LCS. Analysis of brute-force algorithm. Simplified algorithm for LCS. Dynamic programming hallmark #1: optimal substructure. Dynamic programming hallmark #2: overlapping subproblems. Recursive algorithm for LCS. Memoization. Dynamic programming algorithm for LCS. The most interesting thing in this lecture is the two hallmarks that indicate that the problem may be solved with dynamic programming. They are "optimal substructure" and "overlapping subproblems". The first one means that an optimal solution to a problem contains the optimal solution to subproblems. For example, if z = LCS(x,y) - z is the solution to the problem LCS(x,y) - then any prefix of z is a solution to LCS of a prefix of x and prefix of y (prefix of z is a solution to subproblems). The second one means exactly what it says, that the problem contains many overlapping subproblems. Lecture 16: Greedy Algorithms This lecture introduced greedy algorithms via the minimum spanning three problem. The minimum spanning tree problem asks to find a tree that connects all the vertices of a graph with minimum edge weight. It seems at first that dynamic programming solution could solve it effectively, but if analyzed more carefully, it can be noticed that the problem exhibits another powerful property -- the best solution to each of the subproblems leads to globally optimal solution. Therefore it's called greedy, it always chooses the best solution for subproblems without ever thinking about the whole problem in general. Lecture 17: Shortest Path Algorithms This lecture starts a trilogy on shortest path algorithm. In this first episode single-source shortest path algorithms are discussed. The problem can be described as following -- how to get from one point on a graph to another by traveling the shortest distance (think of a road network). The Dijkstra's algorithm solves this problem effectively. Topics explained in lecture seventeen: Paths in graphs. Shortest paths. Path weights. Negative path weights. Single-source shortest path. Dijkstra's algorithm. Example of Dijkstra's algorithm. Correctness of Dijkstra's algorithm. Unweighted graphs. Breadth First Search. The most interesting thing here is that the Dijkstra's algorithm for unweighted graphs reduces to breadth first search algorithm which uses a FIFO instead of a priority queue because there is no longer a need to keep track of the shortest distance (all the paths have the same weight). Lecture 18: Shortest Path Algorithms (continued) The second lecture in trilogy on shortest paths deals with single-source shortest paths that may have negative edge weights. Bellman-Ford algorithm solves the shortest path problem for graphs with negative edges. Topics explained in lecture eighteen: Bellman-Ford algorithm for shortest paths with negative edges. Negative weight cycles. Correctness of Bellman-Ford algorithm. Linear programming. Linear feasibility problem. Difference constraints. Constraint graph. Using Bellman-Ford algorithm to solve a system of difference constraints. Lecture 19: Shortest Path Algorithms (continued) The last lecture in trilogy deals with all-pairs shortest paths problem -- determine of the shortest distances between every pair of vertices in a given graph. Topics explained in lecture nineteen: Review of single source shortest path problem. All-pairs shortest paths. Dynamic programming. Idea from matrix multiplication. Floyd-Warshall algorithm for all-pairs shortest paths. Transitive closure of directed graph. Johnson's algorithm for all-pairs shortest paths. An interesting point here is how the Floyd-Warshall algorithm that runs in O((number of vertices)3) can be transformed into something similar to Strassen's algorithm to compute the transitive closure of a graph (now it runs in O((number of vertices)lg7). Lecture 20: Parallel Algorithms This is an introductory lecture to multithreaded algorithm analysis. It explains the terminology used in multithreaded algorithms, such as, work, critical path length, speedup, parallelism, scheduling, and others. Topics explained in lecture twenty: Dynamic multithreading. Subroutines: spawn and sync. Logical parallelism and actual parallelism. Multithreaded computation. An example of a multithreaded execution on a recursive Fibonacci algorithm. Lecture 22: Cache Oblivious Algorithms Cache-oblivious algorithms take into account something that has been ignored in all the algorithms so far, particularly, the cache. An algorithm that can be transformed into using cache effectively will perform much better than a one that doesn't. This lecture is all about how to lay out data structures in memory in such a way that memory transfers are minimized. Lecture 23: Cache Oblivious Algorithms (continued) This is the final lecture of the course. It continues on cache oblivious algorithms and shows how to store binary search trees in memory so that memory transfers are minimized when searching in them. It wraps up with cache oblivious sorting. Topics explained in lecture twenty-three: Static search trees. Memory efficient layout of static binary search trees in memory. Analysis of static search trees. Cache aware sorting. Cache-oblivious sorting. Funnel sort. K-funnel data structure. This is the most complicated lecture in the whole course. It takes a day to understand the k-funnel data structure. That's it. This was the final lecture. I hope you find this summary useful. Upcoming on my blog -- review of MIT's Linear Algebra course. At first I thought I'd post Linear Algebra to a separate blog section that does not appear in the RSS feed but then I gave it another thought and came to a conclusion that every competent programmer must know the linear algebra and therefore it's worth putting them in the feed. You can surely be a good programmer without knowing linear algebra, but if you want to work on great problems and make a difference, then you absolutely have to know it. This is the fifth post in the article series "Vim Plugins You Should Know About". This time I am going to introduce you to a nifty plugin called "a.vim". A.vim allows you to quickly switch between related source code files. For example, if you're programming in C, you can alternate between source.c and the corresponding header source.h by just typing :A. It saves you only a few seconds every time you use it, but don't forget that these seconds can add up to hours during several weeks. After I'm done explaining all these one-liners, I'll publish an ebook. Subscribe to my blog to know when that happens! The one-liners will make heavy use of Perl special variables. A few years ago I compiled all the Perl special variables in a single file and called it Perl special variable cheat-sheet. Even tho it's mostly copied out of perldoc perlvar, it's still handy to have in front of you, so print it. Awesome news: I have written an e-book based on this article series. Check it out: Calculations This one-liner uses an ingenious regular expression to detect if a given number is a prime or not. Don't take it too seriously, though. I included it for its artistic value. First, the number is converted in its unary representation by " (1x$_) ". For example, 5 gets converted into " 1x5 ", which is " 11111 ". Next, the unary number gets tested against the ingenious regular expression. If it doesn't match, the number is a prime, otherwise it's a composite. The regular expression works this way. It consists of two parts " ^1?$ " and " ^(11+?)\1+$ ". The first part matches " 1 " and empty string. Clearly, empty string and 1 are not prime numbers, therefore this regular expression matches, which indicated that they are not prime numbers. The second part determines if two or more 1s repeatedly make up the whole number. If two or mores 1s repeatedly make up the whole number, the regex matches, which means that the number is composite. Otherwise it's a prime. Let's look at the second regex part on numbers 5 and 6. The number 5 in unary representation is " 11111 ". The " (11+?) " matches first two ones " 11 ". The back-reference " \1 " becomes " 11 " and the whole regex now becomes " ^11(11)+$ ". It can't match five ones, therefore it fails. But since it used " +? ", it backtracks and matches the first three ones " 111 ". The back-reference becomes " 111 " and the whole regex becomes " ^111(111)+$ ". It doesn't match again. This repeats for " 1111 " and " 11111 ", which also don't match, therefore the whole regex doesn't match and the number is a prime. The number 4 in unary representation is " 1111 ". The " (11+?) " matches the first two ones " 11 ". The back-reference " \1 " becomes " 11 " and the regex becomes " ^11(11)+$ ". It matches the original string, therefore the number is not a prime. The " -lne " command line options have been explained in parts one and two. 22. Print the sum of all the fields on a line. perl -MList::Util=sum -alne 'print sum @F' This one-liner turns on field auto-splitting with " -a " command line option and imports the "sum" function from "List::Util" module with " -MList::Util=sum " option. The "List::Util" is in the Perl core so you don't need to worry about installing it. As a result of auto-splitting the split fields end up in the " @F " array and the " sum " function just sums them up. The -Mmodule=arg option imports arg from module and is the same as writing: This one-liner keeps pushing the split fields in " @F " to the " @S " array. Once the input is over and perl is about quit, END { } block gets called that outputs the sum of all items in @F. This sum is the sum of all fields over all lines. This solution isn't too good - it creates a massive array @S. A better solution is to keep just the running: perl -MList::Util=sum -alne '$s += sum @F; END { print $s }' 24. Shuffle all fields on a line. perl -MList::Util=shuffle -alne 'print "@{[shuffle @F]}"' This is almost the same as one-liner #22 above. Instead of summing all fields, it shuffles and prints them. The " @{[shuffle @F]} " construct creates an array reference to the contents of " shuffle @F " and " @ { ... } " dereferences it. This is a tricky way to execute code inside quotes. It was needed to get the values of shuffled @F separated by a space when printing them out. Another way to do the same is join the elements of @F by a space, but it's longer: perl -MList::Util=shuffle -alne 'print join " ", shuffle @F' 25. Find the minimum element on a line. perl -MList::Util=min -alne 'print min @F' This one-liner uses the "min" function from "List::Util". It's similar to all the previous ones. After the line has been automatically split by " -a ", the "min" function finds minimum element and prints it. 26. Find the minimum element over all the lines. perl -MList::Util=min -alne '@M = (@M, @F); END { print min @M }' This one-liner is a combination of the previous one and the #23. The "@M = (@M, @F)" construct is the same as "push @M, @F". It appends the contents of @F to the array @M. This one-liner stores all the data in memory. If you run it on a 10 terabyte file, it will die. Therefore it's better to keep the running minimum element in memory and print it out at the end: It finds the minimum of each line and stores in $min, then it checks if $min is smaller than the running minimum. Once the input ends, it prints the running minimum, which is the smallest value over all input. This one-liner auto-splits the line by " -a " command line option. The split fields, as I already explained, end up in the @F variable. Next it calls the absolute value function "abs" on each field by the help of "map" function. Finally it prints it joins all the fields by the help of array interpolation in double quotes. The " @{ ... } " construct was explained in one-liner #24. 30. Find the total number of fields (words) on each line. perl -alne 'print scalar @F' This one-liner forces to evaluate the @F in scalar context, which in Perl means "the number of elements in @F." Therefore this one-liner prints out the number of elements on each line. 31. Print the total number of fields (words) on each line followed by the line. perl -alne 'print scalar @F, " $_"' This is exactly the same as #30, except " $_ " is added at the end that prints out the whole line. (Remember that " -n " option caused each line to be put in the $_ variable.) 32. Find the total number of fields (words) on all lines. perl -alne '$t += @F; END { print $t}' Here we just keep adding the number of fields on each line to variable " $t ", and at the end we print it out. The result is number of words on all lines. 33. Print the total number of fields that match a pattern. perl -alne 'map { /regex/ && $t++ } @F; END { print $t }' This one-liner uses the " map " function that applies some operation on each of the elements in @F array. In this case the operation checks if each element matches /regex/ and if it does, it increments variable $t. At the end it prints this variable $t that contains the number of fields that matched /regex/ pattern. A better way to do it is by looping: perl -alne '$t += /regex/ for @F; END { print $t }' Each element in @F is tested against regex. If it matches, /regex/ returns 1 (true), which gets added to variable $t. This way the number of matches get counted in $t. The best way is to use grep in scalar context: perl -alne '$t += grep /regex/, @F; END { print $t }' Grep in scalar context returns the number of matches. This number gets accumulated in $t. 34. Print the total number of lines that match a pattern. perl -lne '/regex/ && $t++; END { print $t }' The /regex/ evaluates to true if the current line of input matches this regular expression. Writing /regex/ && $t++ is the same as if ($_ =~ /regex/) { $t++ }, which increments variable $t if the line matched the pattern. Finally in the END block the variable $t contains the total number of pattern matches and it gets printed out. Remember that localtime returns a 9-list (see above) of various date elements. The 4th element in the list is current month's day. If we subtract one from it we get yesterday. The "mktime" function constructs a Unix epoch time from this modified 9-list. And "scalar localtime" construct prints out the new date, which is yesterday. The POSIX package was needed because it exports mktime function. It's supposed to normalize negative values. This one-liner modifies 0th, 4th, and 7th elements of @now list. The 0th is seconds, the 4th is months and 7th is days (see the table of 9 element time list above). Next, mktime creates Unix time from this new structure, and localtime, evaluated in scalar context, prints out the date that was 14 months, 9 days and 7 seconds ago. 41. Calculate factorial. perl -MMath::BigInt -le 'print Math::BigInt->new(5)->bfac()' This one-liner uses bfac() function from Math::BigInt module that is in the Perl core (no need to install). Math::BigInt->new(5) construction creates a new Math::BigInt object with value 5, then a method bfac() is called on the newly created object to calculate the factorial of 5. Change 5 to any number you wish to find factorial for the value you are interested in. Another way to calculate factorial is by just multiplying numbers from 1 to n together: perl -le '$f = 1; $f = $_ for 1..5; print $f' Here we initially set $f to 1. Then do a loop from 1 to 5 and multiply $f by each of the values. The result is 12345, which is the factorial of 5. 42. Calculate greatest common divisor. perl -MMath::BigInt=bgcd -le 'print bgcd(@list_of_numbers)' Math::BigInt has several other useful math functions. One of them is bgcd that calculates the greatest common divisor of a list of numbers. For example, to find gcd of (20, 60, 30), you'd execute the one-liner this way: perl -MMath::BigInt=bgcd -le 'print bgcd(20,60,30)' Surely, you can also use Euclid's algorithm. Given two numbers $n and $m, this one-liner finds the gcd of $n and $m. The result is stored in $m. perl -le '$n = 20; $m = 35; ($m,$n) = ($n,$m%$n) while $n; print $m' 43. Calculate least common multiple. Another function from Math::BigInt is lcm - the least common multiplicator. This one-liner finds lcm of (35, 20, 8): perl -MMath::BigInt=blcm -le 'print blcm(35,20,8)' If you know some number theory, then you'll recall that there is a connection between gcd and lcm. Given two numbers $n and $m, their lcm is $n$m/gcd($n,$m), therefore one-liner follows: It exports the powerset function, which takes a list of elements and returns a reference to a list containing references to subset lists. In the for() loop, I call the powerset function, pass it the list of elements in @l. Next I dereference the return value of powerset, which is a reference to a list of subsets. Next, I dereference each individual subset @$_ and print it. For a set of n elements, there are exactly 2n subsets in the powerset. This one-liner converts the IP address 127.0.0.1 into unsigned integer (which happens to be 2130706433). It does it by first doing a global match of (\d+) on the IP address. Doing a for loop over a global match iterates over all the matches. These matches are the four parts of the IP address. Next the matches are added together in the $u variable, with first being bit shifted 83 = 24 places, the second being shifted 82 = 16 places, the third 8 places and the last just getting added to $u. But this one-liner doesn't do any error checking on the format of an IP address. You may use a more sophisticated regular expression to add checking, such as /^(\d+)\.(\d+)\.(\d+)\.(\d+)$/g. I had a discussion about this with a friend and we came up with several more one-liner: This one-liner utilizes the fact that 127.0.0.1 can be easily converted to hex as 7f000001 and then converted to decimal from hex by the hex Perl function. Another way is to use unpack: perl -le 'print unpack("N", 127.0.0.1)' This one-liner is probably as short as it can get. It uses the vstring literals (version strings) to express the IP address. A vstring forms a string literal composed of characters with the specified ordinal values. Next, the newly formed string literal is unpacked into a number from a string in Network byte order (Big-Endian order) and it gets printed. If you have a string with an IP (and not a vstring), then you first have to convert the string with the function inet_aton to byte form: perl -MSocket -le 'print unpack("N", inet_aton("127.0.0.1"))' Here inet_aton converts the string " 127.0.0.1 " to the byte form (which is the same as pure vstring 127.0.0.1) and next it unpacks it as the same was as in previous one-liner. Perl one-liners explained e-book I've now written the "Perl One-Liners Explained" e-book based on this article series. I went through all the one-liners, improved explanations, fixed mistakes and typos, added a bunch of new one-liners, added an introduction to Perl one-liners and a new chapter on Perl's special variables. Please take a look:
More About This Textbook Overview An informed understanding of mathematical methods and the skills to make use of them are essential for the aspiring numerate manager of today. An overview of the methods and an awareness of their range and relevance are important parts of a modern education in business management, finance and economics. This comprehensive and user-friendly textbook provides a thorough introduction to mathematical concepts and methods used in the analysis of business management, finance and economics. Much of the coverage is also relevant for students of other social sciences at university level where a quantitative approach is employed. The ten chapters of the book are each carefully designed with a graduated approach to lead students through from a basic level to more advanced concepts and applications, enabling both students and teachers to choose the level appropriate for their course. The text is 'software aware' and most chapters contain illustrative computer programs relevant to the material covered, without making prior knowledge or extensive use of computers a requirement. Student exercises and comprehensive worked solutions are provided throughout
rigorous two-part treatment advances from functions of one variable to those of several variables. Intended for students who have already completed a one-year course in elementary calculus, it defers the introduction of functions of several variables for as long as possible, and adds clarity and simplicity by avoiding a mixture of heuristic and rigorous arguments.The first part explores functions of one variable, including numbers and sequences, continuous functions, differentiable functions, integration, and sequences and series of functions. The second part examines functions of several variables: the space of several variables and continuous functions, differentiation, multiple integrals, and line and surface integrals, concluding with a selection of related topics. Complete solutions to the problems appear at the end of the text.
College Algebra Demystified: A Self Teaching Guide (Paperback) One of the most valuable tools acquired in a university education, college algebra is essential for courses from the sciences to computing, engineering to mathematics. It can help you do better on plac......more One of the most valuable tools acquired in a university education, college algebra is essential for courses from the sciences to computing, engineering to mathematics. It can help you do better on placement exams, even before college, and it's useful in solving the computations of daily life. Now anyone with an interest in college algebra can master it. In College Algebra Demystified, entertaining author and experienced teacher Rhonda Huettenmueller breaks college algebra down into manageable bites with practical examples, real data, and a new approach that banishes algebra's mystery. With College Algebra Demystified, you master the subject one simple step at a time—at your own speed. Unlike most books on college algebra, general concepts are presented first—and the details follow. In order to make the process as clear and simple as possible, long computations are presented in a logical, layered progression with just one execution per step. This fast and easy self-teaching course will help you: Perform better on placement exams Avoid confusion with detailed examples and solutions that help you every step of the way Get comfortable with functions, graphs of functions, logarithms, exponents, and more Master aspects of algebra that will help you with calculus, geometry, trigonometry, physics, chemistry, computing, and engineering Reinforce learning and pinpoint weaknesses with questions at the end of every chapter, and a final at the end of the book Rhonda Huettenmueller (Sanger, TX) has taught mathematics at the college level for over 14 years. Popular with students for her ability to make higher math understandable and even enjoyable, she incorporates many of her teaching techniques in this book. She received her Ph.D. in mathematics from the University of North
Algebra and Trigonometry with Modeling and Visualization - 3rd edition Summary: Gary Rockswold focuses on teaching algebra in context, answering the question, ''Why am I learning this?'' and ultimately motivating the students to succeed in this class. In addition, the author's understanding of what instructors need from a text (great 'real' examples and lots of exercises) makes this book fun and easy to teach from. Integrating this textbook into your course will be a worthwhile endeavor. Applications: The author believes that students become more effective problem-solvers by being exposed to applications throughout the course. Therefore, a wide variety of unique, data-based, contemporary applications are included in nearly every section. Making Connections: This feature points out how concepts presented throughout the course are interrelated. It also provides students with a perspective on how previously learned material applies to the new material they have learned. Checking Basic Concepts: This feature consists of a small set of exercises provided after every two sections. These exercises can be used by students for review purposes, or by the instructor as group activities. They require 10-15 minutes to complete and could be used during class if time is available. End of Chapter Material: Each chapter ends with a summary of key concepts, review exercises, and extended and discovery exercises. Chapter R Reference: Basic Concepts from Algebra and Geometry: This contains much of the material from intermediate algebra and basic geometry in a separate appendix at the back of the text. This material is referenced by Algebra and Geometry Review Notes in the margins of the text. Graphing Calculator Appendix: This allows students to work more easily on their own with the calculator and frees up class time for the instructor. This material is referenced by Graphing Calculator Help Notes in the margins of the text.Goodwillnyonline Astoria, NY Good $12.99 +$3.99 s/h Good NationwideText Three Rivers, MI 2005-03-19 Hardcover Good In Good Condition! ! Addison Wesley: Algebra and Trigonometry with Modeling and Visualization (Hardcover) Copyright-2005, ISBN: 0321279107. We Ship Daily, Mon-Sat. (KS)Cus...show moretomer service is always our top priority! WE WILL NOT PROCESS INTERNATIONAL ORDERS! These orders will be cancelled automatically! Thank you for your cooperation!
Table of Contents "Many students come to believe that school mathematics consists of mastering formal procedures that are completely divorced from real life, from discovery, and from problem solving.' - Alan Schoenfeld Background Alan Schoenfeld is currently the Elizabeth and Edward Conner Professor of Education and Affiliated Professor of Mathematics at the University of California, Berkeley. He has also been the President of the American Education Research Association. In 2008, he was awarded the Senior Scholar Award by the AERA's Special Interest Group for Research in Math Education. Much of his work has focused on problem solving. Degrees Professor Schoenfeld has acquired numerous degrees from both Stanford and Queens College. He first received his B.S. in Mathematics from Queens College in 1968. He then received his M.S. in mathematics from Stanford University in 1969, followed by his Ph.D. in 1973. He is currently teaching mathematics and education courses at the University of California, Berkeley. Theory Dr. Schoenfeld began studying math and how students learned. He wanted to find a new way for students to approach math in order to make it more meaningful for them. Many children don't know how useful math can be in the real world, simply because they have always been taught only how to master formulas. Alan Schoenfeld is known best for his studies of mathematics and how students should learn it. This theory, known as Mathematical Problem Solving, focuses on solving problems through a variety of ways to help students understand the subject better. He believes that teaching mathematics does not only mean educating children on the basic equations and how to plug numbers into them, but how to analyze and understand the meaning behind the formulas. Students must be taught to seek solutions rather than just memorizing procedures, expore patters rather than memorizing formulas, and formulating conjectures rather than doing exercises. Students must have a broader understanding of mathematics in order to excel in it. According to Dr. Schoenfeld, four categories of skills are necessary in order to be successful in math: successinmath.png As the above image shows, students must have control, resources, heuristics, and beliefs in order to be successful in mathematics. Control includes being able to determine when certain strategies should be used. Resources are the procedural knowledge that a student has. This is basically the equations taught in a typical math class. Heuristics are the different strategies that students have to solve these math problems, including drawing figures, working backwards, identifying patterns, etc. Finally, the beliefs that a student has are the views that the student has when approaching a problem. Another main element in Dr. Schoenfeld's mathematical problem solving theory deals with metacognition, or "thinking about thinking." Basically, metacognition means having the knowledge to know when to use particular strategies for problem solving. With the mathematical metacognition that students need, they will be able to apply mathematics to real life situations that they face every day. It can also create a community of learners outside of the classroom that use math in different contexts. The following image show a complex view of the Mathematical Problem Solving Theory that Schoenfeld is known for: mathematicalproblemsolving.jpg Since this image can be difficult to read and extremely confusing to the eye, let's analyse it further to make sense of it and extract the most important points. To begin with, we see that this is a basic summary of Alan Schoenfeld's publication Learning to Think Mathematically. In this writing, he examines the goals of teaching math. Teaching needs enculturation, or using the values of the community. This theory uses sociology, anthropology, and constructivism. Constructivism is a method of teaching in the classroom in which students are engaged in activities, teachers serve as facilitators to learning, and learning is more social. Mathematical teaching also needs problem solving. Problem solving includes exercises that require thinking, and he wants students to view these problems as real life situations. In the next portion of the chart, we see that Schoenfeld then looks at the effect of these goals on mathematical thinking. In this chart, mathematical thinking is defined as developing a mathematical point of view and developing competence with the tools of the trade. He wants these goals to empower students in their mathematical thinking. From this, he proposes a new framework for exploring mathematical thinking. The critical components of this framework are core knowledge, problem solving strategies, effective use of resources, having a mathematical perspective, and engagement in mathematical practices. Core knowledge includes perceptual knowledge, formulas, and basic math skills that are required to solve problems. Problem solving strategies are the heuristics that were discussed previously. It is critical for students to have an effective use of resources, which involves using metacognition. Having a mathematical perspective involves being able to look at problems with a mathematical mindset. Finally, engagement in mathematical practices is crucial in order for students to retain the knowledge that they have obtained in learning how to critically solve problems. Pedagogy One of the best ways to apply this to the classroom is to focus on giving students word problems that are relevant to the students. Real life problems will focus students' attention on how the math concept can be applied to the world they live in. The best teaching method to use to support the Mathematical Problem Solving method is constructivism. A good example that Schoenfeld used to show how teachers can help students master difficult formulas is to use flashcards. Below shows some examples of the flashcards used. Students can work alone or in pairs to fill in the blanks in each card. Blank cards can be used for students to write their own. flashcards1.png flashcards2.png In the first figure, students could work together in groups to first find the pattern, then fill in the blanks. While finding the answers to the blanks, students will be learning how to discover patterns at the same time. In the second figure, students can work together to write the equations for the area of each figure. These area equations will help them to expand their view of area to include variables rather than only numbers. In these examples, the role of the student is to discover patterns and equations, work together as a team, and use their metacognition to solve the puzzles. The role of the teacher would be to guide the students as needed, as well as to introduce and explain simple problems to the students and work through them to give them the idea of what is expected. The teacher then can assess the students on the completion of the puzzles, as well as the work done to show their understanding. Finally, students can be assessed on teamwork and collaboration. Assessment alanschoenfeld1.jpg When reading through Professor Schoenfeld's works, it is easy to tell what he expects the curriculum of math classes to look like. After all, he is still a practicing math professor himself. What is interesting to see is that his views of mathematics curricula have been criticized, because he wants to teach students how to think, rather than force equations onto students. To Schoenfeld, "mathematical 'content' depends on one's point of view" ( He believes that the typical math class curriculum is familiar and comfortable, because it shows exactly what a student will be exposed to and can clearly show what courses they will be prepared for. However, this is dangerous. Mathematical thinking is composed of much more than simply knowing facts, formulas, and processes. There is a big difference between what a person can mathematically do and what they know. In other words, it is about using what you know. The curriculum of a math class taught under this theory will be dramatically different than others. One of the main differences in the curriculum will be the amount of real-life problems that are presented to the class. The curriculum of a typical direct instruction classroom contains lessons with lecture, followed by example problems, followed by rigorous practice by the students. Using Schoenfeld's theory, a mathematics class will be based more on asking general questions about a broad topic, then gradually come to more specific conclusions and derive formulas from this. This will enable students to become more enthusiastic about the topic when they discover the equations on their own. The curriculum cannot take on a minimalistic approach to the basics, however. Students still need to learn the content in some form. Therefore, curricula can be created that contains a good mix of both basic skills and discovery work. A constructivist approach will be the main method of teaching students. Most of the lessons can consist of class discussions, in which students will contribute to the discovery of mathematical procedures. Assessing the curriculum, according to Schoenfeld, will be based on student success. If students can successfully solve unfamiliar problems with the knowledge they have attained, then the curriculum is successful. Assessments for the students can include their contributions to in-class discussions, as well as content knowledge assessments such as tests and quizzes. The impact that this new curriculum will have on teaching will change the way educators think about teaching math altogether. Lessons will be taught through class discussions, and teachers will become more passive. They will present the topic, and coax students when needed to discover the material on their own. They will also present real-life problems that can help students problem solve. This is completely different from the "drill and kill" method that has been used in the past.
From the preface: The material in the handbook is presented so that key information can be located and used quickly and easily. Each chapter includes a glossary that provides succinct definitions of the most important terms from that chapter. Individual topics are covered in sections and subsections within chapters, each of which is organized into clearly identifiable parts: definitions, facts, and examples. The definitions included are carefully crafted to help readers quickly grasp new concepts. Important notation is also highlighted in the definitions. Lists of facts include: information about how material is used and why it is important; historical information; key theorems; the latest results; the status of open questions; tables of numerical values, generally not easily computed; summary tables; key algorithms in an easily understood pseudocode; information about algorithms, such as their complexity; major applications; pointers to additional resources, including websites and printed material. Facts are presented concisely and are listed so that they can be easily found and understood. Extensive crossreferences linking parts of the handbook are also provided. Readers who want to study a topic further can consult the resources listed. The material in the handbook has been chosen for inclusion primarily because it is important and useful. Additional material has been added to ensure comprehensiveness so that readers encountering new terminology and concepts from discrete mathematics in their explorations will be able to get help from this book. Examples are provided to illustrate some of the key definitions, facts, and algorithms. Some curious and entertaining facts and puzzles that some readers may find intriguing are also included. Each chapter of the book includes a list of references divided into a list of printed resources and a list of relevant websites.
Questions About This Book? The Used copy of this book is not guaranteed to inclue any supplemental materials. Typically, only the book itself is included. Summary Key Message: The Third Edition of the BittingerGraphs and Modelsseries helps readers succeed in algebra by emphasizing a visual understanding of concepts. This latest edition incorporates a new Visualizing for Success feature that helps readers make intuitive connections between graphs and functions without the aid of a graphing calculator. In addition, readers learn problem-solving skills from the Bittinger hallmark five-step problem-solving processcoupled with Connecting the Concepts and Aha! Exercises. As you have come to expect with any Bittinger text, we bring you a complete supplements package including MyMathLabtrade; and the New Instructor and Adjunct Support Manual. Key Topics: Introduction to Algebraic Expressions; Equations, Inequalities, and Problem Solving; Introduction to Graphing and Functions; Systems and Graphing; Polynomials; Polynomial Factorizations and Equations; Rational Expressions, Equations, and Functions; Inequalities; More on Systems; Exponents and Radical Functions; Quadratic Functions and Equations; Exponential and Logarithmic Functions; Conic Sections; Sequences, Series, and the Binomial Theorem; Elementary Algebra Review Market: For all readers interested in Algebra. Table of Contents Note: every chapter concludes with a Chapter Summary and Review and a Chapter Test. Chapters 3, 6, 9, 12, and 14 also have a Cumulative Review
Elementary Statistics - With CD - 6th edition Summary: Elementary Statistics is appropriate for a one-semester introductory statistics course, with an algebra prerequisite. ES has a reputation for being thorough and precise, and for using real data extensively. Students find the book readable and clear, and the math level is right for the diverse population that takes the introductory statistics course. The text thoroughly explains and illustrates concepts through an abundance of worked out examplesTEXTBOOKFETCHER! Cortland, NY 0201771306 This is a used item2.10 +$3.99 s/h Good Wonder Book Frederick, MD Good condition. With CD! Writing inside. 6th edition. $2.10 +$3.99 s/h VeryGood Wonder Book Frederick, MD Very Good condition. With CD! 6th edition94
... More The main goal of this project is to improve student understanding of the geometric nature of multivariable calculus concepts, i.e., to help them develop accurate geometric intuition about multivariable calculus concepts and the various relationships among them. To accomplish this goal, the project includes four parts: · Creating a Multivariable Calculus Visualization applet using Java and publishing it on a website: web.monroecc.edu/calcNSF · Creating a series of focused applets that demonstrate and explore particular 3D calculus concepts in a more dedicated way. · Developing a series of guided exploration/assessments to be used by students to explore calculus concepts visually on their own. · Dissemination of these materials through presentations and poster sessions at math conferences and through other publications. Intellectual Merit: This project provides dynamic visualization tools that enhance the teaching and learning of multivariable calculus. The visualization applets can be used in a number of ways: - Instructors can use them to visually demonstrate concepts and verify results during lectures. - Students can use them to explore the concepts visually outside of class, either using a guided activity or on their own. -. - Instructors will be able to use CalcPlot3D to create lecture demonstrations containing particular functions they specify and/or guided explorations for their own students using a scripting feature that is being integrated with this applet. The guided activities created for this project will provide a means for instructors to get their students to use these applets to actively explore and "play" with the calculus concepts. Broader
Oak Ridge North, TX PrecalculusAlgebra II extends the concepts of Algebra I to a more formal level. The course of study is designed to extend the development of numbers to include the study of the complex numbers as a mathematical system, to expand the concept of functions to include quadratic, exponential and logarithmic fun...
Book DescriptionCustomers Who Viewed This Item Also Viewed Editorial Reviews From the Publisher The only book devoted solely to least square adjustments. Early chapters define terms and introduce the fundamentals of errors and methods for analyzing them. The next chapters deal with error propagation in diverse types of basic surveying instruments, followed by those which describe observation weighting and introduce the least squares method for adjusting observations. Applications of least squares in adjusting basic types of surveys are presented in separate chapters. The more advanced topics of blunder detection, the general least squares approach and computer optimization are covered in the last chapters. Example problems, ranging from the analysis of a single observation to adjustment of complex data networks, illustrate statistical analyses and least squares adjustment of typical surveying measurements. The accompanying disk contains programs for statistical evaluations, the performance of least square adjustments and basic matrix operations. From the Back CoverThis is an excellent and relevant book. It is well structured, and the examples are very much practice oriented. However, when I tried to install the included software under Windows 98 and Windows 2000 Prof I failed. Only under Windows 95 it runs! Did I something wrong or it is just like that! I would appreciate any helpful comment! Starts off with some basic principles before going in to more developed mathematical and stochastic models and even includes topics include in the use of constraint equations and blunder detection. Explanations are supported by clear & practical problems. Excellent book for surveyors and photogrammetrist.
Soal Soal Un Matematika Smp Kelas 9
A pre-calculus class involves using critical thinking skills to analyze a problem, not just coming up with a single answer. Basic algebra, geometry, and trigonometry topics along with their graphs are used as the foundation. The level of difficulty is increased as multiple concepts are related
Learning Exercise This assignment will get the solutions to the many problems you do in an elementary algebra course. The procuder is not given, but the site provides the answers to many of the questions. Specially topics as multiplying, factoring and solving equations.
Math is fun! It is full of applications, yet enjoyable in its own right. And you'll get the answer to the question, "What comes after Calculus?" Mathematics is a field with a surprising variety of specialties. You can learn about Abstract Algebra, Number Theory, Cryptography, non-Euclidian Geometry, Probability and Statistics, Combinatorics, Differential Equations, and Graph Theory, just to name a few. The list of career options for math majors is nearly endless. Employers in just about every field love to hire math majors because of the amazing skill set they bring to the job. Math majors are critical, creative and logical thinkers. Studying math develops such skills as arguing logically and rigorously, thinking abstractly, formulating and solving problems, analyzing data, and creating and analyzing mathematical models. Engineering, biotech, actuarial, and computer companies need employees with mathematical knowledge and abilities. Math majors become very successful management consultants, doctors, and lawyers. Companies in the computer and communications industries employ many mathematicians, as do oil companies, banks, insurance companies, consulting firms, and the federal government (the NSA is the country's leading employer of mathematicians). Wall Street has also become a major employer of math majors. Having a degree in math is a necessity for some fascinating very math-specific careers as well. Statisticians are needed by a wide variety of companies. The (highly paid) professionals responsible for computing insurance rates are specialized statisticians called actuaries. The computer industry provides many lucrative jobs for math majors. Many sophisticated applications of computers, such as the graphics you see in the movies and the compressed video and audio signals for your phone, involve a great deal of advanced mathematics. Many biotech companies hire mathematics majors because of the highly mathematical nature of the field.Teaching mathematics is an incredibly rewarding career, and every year roughly half of the positions advertised for secondary school teachers in math go unfilled. Really hot today is the area of cryptography - the making and breaking of codes. Cryptography is used by many businesses. Cable TV companies encode their signals, requiring customers to have decoding boxes. Online businesses must encrypt their customers' credit card information. Even your ECampus sessions are encrypted. Ooh, and math is a good pre-med major! In fact, math majors enjoy higher acceptance rates to medical school than many more traditional majors like biology. Professional graduate schools in business, law, physical sciences, engineering, and medicine think mathematics is a great major because it develops analytical skills and the ability to work in a problem-solving environment. Consistently, students majoring in mathematics score substantially higher than average on both the LSAT (law school admissions test) and GMAT (business school admissions test). When ranking scores by major, mathematics is typically ranked number one. Knowing advanced math can only lead to great things. In addition to higher pay, a math major's employment promises higher levels of job satisfaction. In The Jobs Rated Almanac, 250 jobs are ranked according to six criteria: income, stress, physical demands, potential growth, job security, and work environment. Mathematician consistently ranks in the top 5%. Moreover, some of the jobs rated higher than mathematician, such as actuary, also involve significant mathematical reasoning and knowledge and therefore are likely filled by math majors as well. Mathematicians have an opportunity to make a lasting contribution to society by helping to solve problems in such diverse fields as medicine, management, economics, government, computer science, physics, psychology, engineering, and social sciences. So the question really is, why would you choose not to major in mathematics?
Encyclopedia of Mathematics Education This title is a Work in Progress Here you will find the online-first version of articles. For this reason, not all articles are available yet; but return frequently - the collection is growing daily! Welcome to the home page of the Encyclopedia of Mathematics Education. This new project is a Springer initiative and follows the development of the Encyclopedia of Science Education, already at a quite advanced stage. The Encyclopedia is intended to be a comprehensive reference text, covering every topic in the field with entries ranging from short descriptions to much longer pieces where the topic warrants more elaboration. The entries will provide access to theories and to research in the area and will refer to some of the leading publications for further reading. The Encyclopedia will be aimed at graduate students, researchers, curriculum developers, policy makers, and others with interests in the field of mathematics education. It is planned to be two volumes in its hard copy form but the text will subsequently be up-dated and developed on-line in a way that retains the integrity of the ideas, the responsibility for which will be in the hands of the Editor-in-Chief and the Editorial Board.
MATH 2243: LINEAR ALGEBRA AND DIFFERENTIAL EQUATIONS SAMPLE FINALEXAM INSTRUCTOR: SASHAVORONOV Some of the problems on the actual final will be multiple-choice. PENNSYLVANIA DEPARTMENT OF EDUCATION Keystone exams Program overview General information The Keystone Exams are end-of-course assessments designed to assess ... Pre-Algebra Practice FinalExam Free Response 1. Write a proportion to model the problem; then show an equation that could solve the problem. Solve. INTERMEDIATE ALGEBRA (MA-140) FINALEXAM REVIEW This practice exam is designed to help you focus your studying for the final. If you have trouble with a ... MULTIPLECHOICE REVIEW WORKSHEET FOR COLLEGE ALGEBRAFINALEXAM The multiplechoice questions included in this review worksheet are intended to be a sampling of ...
A student writing an article for an on-campus magazine about whether higher math (ie, algebra on) should be required or optional in high school contacted me for my thoughts. I thought my off-the-cuff response was worth sharing: I agree that making math optional would be harmful, for the reasons you described. Without learning high school math, many future paths are blocked off, so if math is optional, the stereotypes will end up getting reinforced. There's may in the the computer world who believe that this is part of why programing and software engineering has stayed so overwhelming male: computer programming is treated as an elective, and only the nerdy/geeky take it. Most students -- particularly girls -- never have the opportunity to see what it's like, and if they would actually enjoy it. (This is tangential at best to your original question, but there is a movement to incorporate computer programing and algorithmic though into the standard math curriculum, which I absolutely support.) Back to you question: I think that, at its best, algebra teaches important patterns of thought. Let's think about high school English class for a moment. You'll probably never analyze a piece of literature after college, but learning to write an essay involves learning to organize your evidence and use it to and make a coherent argument -- valuable ways of approaching the world in situations far outside the English classroom. Similarly, algebra should be teaching people to learn to recognize and describe patterns, identify and isolate an unknown quantity, and model a real world situation with symbols and graphs are valuable skills, and are ideally applicable far outside the confines of a math or science classroom. Unfortunately, at its worst, algebra becomes a series of tricks to memorize and perform, taught with little attention to concept or understanding. In that form, math serves as little more than a gatekeeper, baring the door to college and further advancement to people who failed to make it through a series of arbitrary hoops. In other words, it's not math, it's the way it can be taught that is the problem. I'd love to see a deep and broad re-think of the order and content of the high school math curriculum. The basic structure of college-prep math was set long in a world where calculations were done with pencil and paper, and laborious use of tables for things like logs and square roots. I don't think this makes sense any more. Here's one example: Every time someone writes about how useless high school math is, factoring or the quadratic equation come up as examples. Why do we make polynomials such an important part of algebra? It's actually really hard to motivate a reason to care about quadratics, cubics, etc. (Well, quadratics do come up naturally in physics, but only once you're using calculus modes of thought -- a 12th grade topic, not a 9th grade one.) On the other hand, exponential functions and logarithms (think interest, or population growth) are actually really easy to make relevant and meaningful. But they're shunted off to 10th and 11th grade, and taught as a series of arcane steps. Why? I believe it's because polynomials are far more accessible to pencil and paper calculations. But we're not no longer living in a world where ease of calculating should be driving the curriculum. Let's not throw away math; let's refocus on making sure that we're teaching math in a way that's appropriate and connected to the 21st century world we live in. Give students the skills that they would need to go forward in any field, and don't cut off pathways in high school, but also make sure that we're teaching relevant and meaningful content. I would love to see this quote plastered on Billboards from sea to shining sea ... "Once again, the American financial industry is proving that there's nothing they can't screw up. For the last two decades they've been just about the least consumer-enhancing industry in the country, and they're continuing their value-destroying ways in the transition to smart cards. I guess we shouldn't really be surprised." ... and once this lesson has been drummed into everyone's head, maybe then we'd be allowed to dismantle our utterly useless, mega-destructive financial industry and rebuild it from scratch.
books.google.com - This... mathematics Discrete mathematics This complete coverage of: Logic and Proofs; Algorithms; Counting Methods and the Pigeonhole Principle; Recurrence Relations; Graph Theory; Trees; Network Models; Boolean Algebra and Combinatorial Circuits; Automata, Grammars, and Languages; Computational Geometry. For individuals interested in mastering introductory discrete mathematics. From inside the book LibraryThing Review User Review - LibraryThing Why is this book so tall? Good grief, it's like a notebook. I guess it's easier to fit into one's backpack though. Introduces all the basic concepts of the "science" of computer science. Logic, probability, relations, graphs, algorithm efficiency, it's all here. There's even a little bit of combinatorial math, which I've lately come to love. And yes, of course, our favorite: the pigeonhole principle. I swear, computer science textbooks make such a big deal about it, that for weeks after I first "learned" it, I thought I had to be missing something. Surely, such an OBVIOUS statement isn't something that they need to TEACH people? They must mean something else. Nope. That's it. Oh well. Review: Discrete Mathematics User Review - Joecolelife - Goodreads I am only 1 chapter in but I can say I understand everything up until now it is very well written and has nice examples. I will give it only 4 stars because I have not gotten to the rest yet and most of the complaints range in the area of proofs.Read full review Discrete Mathematics The student will be acquainted with basic facts and knowledge from the set theory, topology and especially the discrete mathematics with focus on the ... study/ course-l.php?id=5865 More nationmaster - Encyclopedia: Discrete mathematics Discrete mathematics, also called finite mathematics, is the study of mathematical structures that are fundamentally discrete, in the sense of not ... encyclopedia/ Discrete-mathematics About the author (1990) Richard Johnsonbaugh" is Professor Emeritus of Computer Science at DePaul University. He has degrees in computer science and mathematics from the University of Oregon, Yale University, and the University of Illinois at Chicago. He is the author of numerous articles and books, including "Discrete Mathematics, Fifth Edition," and, with co-author Martin Kalin, "Object-Oriented Programming in C++, Second Edition, Applications Programming in C++," and "Applications Programming in ANSI C, Third Edition." "Marcus Schaefer" is Assistant Professor of Computer Science at DePaul University. He holds degrees in computer science and mathematics from the University of Chicago and the Universitat Karlsruhe. He has authored and co-authored several articles on complexity theory, computability, and graph theory.
BEGINNING ALGEBRA 9780131444447 ISBN: 0131444441 Edition: 4 Pub Date: 2004 Publisher: Prentice Hall Summary: Clearly explained concepts, study skills help, and real-life applications will help the reader to succeed in learning algebra. Martin-Gay, K. Elayn is the author of BEGINNING ALGEBRA, published 2004 under ISBN 9780131444447 and 0131444441. Eighty seven BEGINNING ALGEBRA textbooks are available for sale on ValoreBooks.com, sixty two used from the cheapest price of $0.01, or buy new starting at $5 Great condition for a used book! Minimal wear. Experience the best customer ca... [more]Sorry, CD missing. Great condition for a used book! Minimal wear. Experience the best customer care, fast shipping, and a 100% satisfaction guarantee on all orders
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for).
Course Description: Designed for those who want to improve their attitude toward mathematics. Explores feelings and develops strategies to overcome math phobia. Emphasis will be placed on problem-solving approaches to diagrammed, descriptive, and symbolic number problems. This course is open to students at all levels of mathematical skills, whether preparing for a job, college courses, a test, or living in a world where numbers matter. One hour lecture/discussion each week.
The pedagogical benefits of using computer aided dynamic geometry software in classrooms are well understood among educators. MathDisk, the latest entrant into this foray, has all the essential aspects one could expect from interactive mathematical software. MathDisk goes beyond the conventional feature set which defines this class of software and implements proven learning techniques found in other disciplines. One such technique in MathDisk called "Progressive Discovery" is a concept found extensively in user interface design to improve the readability and usability of software. Progressive discovery (or disclosure) is an information presentation pattern, where the focus of the audience is centered on one point at a time eliminating wordiness or overwhelming and distracting information. MathDisk provides a simple and systematic approach for applying this concept into mathematical presentations. Using this principle, a certain part of given Mathematical model is displayed or animated before revealing the entire model. This approach of progressively disclosing the model not only demystifies complex concepts, but by highlighting basic constructs it also reinforces that the underlying concepts behind many advanced topics are essentially the interplay of the same fundamental mathematical operations. In this paper we have illustrated this concept using couple of examples in 2D and 3D. The paper also provides a brief overview of the tools available within MathDisk to achieve progressive discovery and how to effectively apply this as a teaching aid. ..When it comes to engaging students,format plays far more of an important role than the content according to a research conducted by the leading US textbook publisher Houghton Mifflin Harcourt.A growing number of researchers are uncovering evidence that students are better able to remember what they read in printed textbooks…MathDisk could play a vital role in bridging this divide as it brings the format of traditional textbook like appearance on worksheet using its equation editor, multi-graph sheet and free form layout capabilities… ..The equal emphasis to both the symbolic and visual representations of Mathematics makes MathDisk an ideal tool to create online interactive textbook for teaching mathematics…
goal in Tussy and Gustafson's INTRODUCTORY ALGEBRA, Third Edition is to teach students to read, write, and think about mathematics ...Show synopsisThe fundamental goal in Tussy and Gustafson's INTRODUCTORY ALGEBRA, Third Edition is to teach students to read, write, and think about mathematics through building a conceptual foundation in the language of mathematics. The book blends instructional approaches that include vocabulary, practice, and well-defined pedagogy, along with an emphasis on reasoning, modeling, communication, and technology skills to develop students' fluency in the "language of algebra." Tussy and Gustafson understand the challenges of teaching developmental students and this book reflects a holistic approach to teaching mathematics that includes developing study skills, problem solving and critical thinking alongside mathematical concepts. New features in this edition include a pretest for students to gauge their understanding of prerequisite concepts, problems that make correlations between student life and the mathematical concepts and study skills information designed to give students the best chance to succeed in the course. Additionally, the texts widely acclaimed Study Sets at the end of every section are tailored to improve students' ability to read, write and communicate mathematical ideas Sorry, CD missing. Great condition for a used book!...Very Good. Sorry, CD missing. Great condition for a used book! Minimal wear. Find out why millions of customers rave about Better World Books. Experience the best customer care and a 100% satisfaction guarantee. Description:Good. Sorry, CD missing. Shows some signs of wear, and may have...Good. Sorry, CD missing. Shows some signs of wear, and may have some markings on the inside. Experience the best customer care, fast shipping, and a 100% satisfaction guarantee on all orders. Description:Good. Cover scuffed, cd & unused access code included 070 Item...Good. Cover scuffed, cd & unused access code included
Beginning Algebra - With CD - 4th edition Summary: For college-level courses in beginning or elementary algebra. Elayn Martin-Gay's success as a developmental math author and teacher starts with a strong focus on mastering the basics through well-written explanations, innovative pedagogy and a meaningful, integrated program of learning resources. The revisions provide new pedagogy and resources to build student confidence, help students develop basic skills and understand concepts, and provide the highest ...show morelevel of instructor and adjunct support. Martin-Gay's series is well known and widely praised for an unparalleled ability to: Relate to students through real-life applications that are interesting, relevant, and practical. Martin-Gay believes that every student can: Test better: The new Chapter Test Prep Video shows Martin-Gay working step-by-step video solutions to every problem in each Chapter Test to enhance mastery of key chapter content. Study better: New, integrated Study Skills Reminders reinforce the skills introduced in section 1.1, "Tips for Success in Mathematics" to promote an increased focus on the development of all-important study skills. Learn better: The enhanced exercise sets and new pedagogy, like the Concept Checks, mean that students have the tools they need to learn successfully. Martin-Gay believes that every student can succeed, and with each successive edition enhances her pedagogy and learning resources to provide evermore relevant and useful tools to help students and instructors achieve success. ...show less Sorry, CD missing. Great condition for a used book! Minimal wear. Experience the best customer care, fast shipping, and a 100% satisfaction guarantee on all orders
More About This Book Overview Higher and Standard Level fully revised for the 2012 syllabus, these are 2nd editions of the highly regarded textbooks used successfully by teachers worldwide. More than just printed books This comprehensive offering comprises a textbook covering the core material and the additional higher level material, all the options via an online link, and an e-book containing a wealth of extension material, full worked solutions, and downloadable files of each chapter. Higher and Standard Level Mathematics features: Written by experienced IB teachers, examiners, and experts in mathematics and educational
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Chapters one through five would be studied in a precalculus class, and chapters six through ten would be probably be studied in a Trigonometry class, which is classified as precalculus. Chapters eleven through thirteen would probably be skipped over entirely, although all of this would vary from school to school and teacher to teacher Yep, that almost exactly what we covered in my Pre-calc - chapters one through 10 - with a huge emphasis on being able to find domains and ranges for functions. The only real difference was that we primarily studied unit-circle based trigonometry rather than the right-triangle-based version in my class.
algebra honors I was placed into algebra honors instead of advanced math.. I am in 7th grade.. I have to maintain an 80% for the entire year or go to virtual school all summer.. My question is: Is there a special technique, formula, or very useful site that might help me grasp the concepts ... Tuesday, October 5, 2010 at 11:24am by Jarrad Honors Algebra Is this all you have to do in "honors algebra?" In my opinion, riddles are a waste of your valuable time. Tuesday, January 27, 2009 at 9:25pm by Ms. Sue 7th grade Honors Math Although I don't understand your second question, try some of the following links for information on the first part: Sra Monday, December 13, 2010 at 7:01pm by SraJMcGin algebra 2 honors math what is the inverse of the function f(x)=2x2+2? Sunday, May 2, 2010 at 11:52am by deja algebra honors (MATH) what happens when the smog lifts in los angeles, california? Monday, April 26, 2010 at 7:51pm by jasmine World History Honors Since you're in an honors section, I'm sure you have a lot of good ideas. We'll be glad to comment on them. Wednesday, February 23, 2011 at 11:03pm by Ms. Sue Probabilities A team has 10 players named A, B, C, ... . Before each game an oŽensive captain, a defensive captain, and a water-boy are determined by chance. No one may have more than one of these honors per game. The probability the C and D both win honors for the sixth game is closest to... Friday, May 1, 2009 at 10:38pm by Andrey L Algebra 2 honors sorry.im not very good at algebra =[ Wednesday, September 10, 2008 at 8:23pm by bex Algebra 1 HaHa i am in Algebra 1 Honors in the 8th GRADE!!!!! Thursday, November 13, 2008 at 3:05pm by Anoymous Honoirs Algebra Hello - I am afreshman & honors algebra is kicking my butt - I need to simplify the following (-6c)(2-3c) can some on help Monday, October 1, 2007 at 9:38pm by Eddie English Honors I already completed it anyways. I just guessed. My online school is not called english honors... That was one of the subjects I had. I had math, geography, biology, and english honors along with P.E. Reason why I posted it here was because that is true. My parents made the ... Sunday, June 5, 2011 at 9:21pm by Skylar Algebra 1 Honors What Is 45% of 30? Thursday, September 23, 2010 at 11:28pm by Haley Honors Algebra exactly what is a 48x? Thursday, November 4, 2010 at 6:09pm by bobpursley ALGEBRA 1 HONORS Are you solving for x or y? Tuesday, October 11, 2011 at 4:34pm by Ms. Sue honors algebra 1 composition function g(f(x)) so where ever you see x in the g(x) equation plug in f(x) so do the reverse g(x)= (1/2)x so when you check your work g(f(x))= (1/2(2x)) ----> the 1/2 and the 2 cancel and you are left with just x so it checks! Thursday, March 4, 2010 at 9:35pm by math Honors Algebra What do you call a duck that steals? Tuesday, January 27, 2009 at 9:25pm by Anonymous question just stay in the class it is an honors class and your first high school honors class so it it good that your are experiencing a higher work load than a regular. you had a choice to be in the class and from my point of view you should face the consequences of your actions, ... Friday, November 1, 2013 at 10:38pm by Bill Nye the Science Guy Algebra 2 Honors if that confused you, haley and i are working together. Sunday, June 6, 2010 at 10:19pm by Christine Physics Honors If this is an honors class, you clearly need to do some analysis. What time does an object take to fall 22m? in that time, the ball travels 35 m. Velocity=distance/time Sunday, October 23, 2011 at 9:33pm by bobpursley Algebra 1 Honors Answered three hours ago. Set it up as an algebra problem and express the larger number in terms of the smaller. Then set the sum = 45 and solve. Thursday, October 30, 2008 at 1:30am by drwls algebra 2 honors how do you solve problems like : log3x-log5=1 Wednesday, February 11, 2009 at 8:12pm by vanessa Algebra 2 Honors Did you click on the above link? tan(375 degrees) = 0.267949192 Sunday, June 6, 2010 at 10:19pm by Ms. Sue Algebra 2 Honors yes, but that is not an exact answer. i need a fraction of some sort, not a rounded decimal Sunday, June 6, 2010 at 10:19pm by Christine math (algebra honors) #2 If the radius of a circle is increased by 6 cm, the new area is 121 (pi) cm^2. Find the radius of the original border using factoring. Sunday, February 27, 2011 at 5:55pm by K.S.7th grade Algebra 1 Honors 5-2 textbook help How do you solve this for example g(t)-4 and the function is g(x)=x squared +1 . . . . . . .. . .I NEED THIS DONE BY TOMORROW HELP! Wednesday, November 4, 2009 at 5:26pm by Juliana 9th grade honors algebra please help! I can't figure out the function rule for a table that says x=0,1,4,5 and y=9,6,-3,-6 Saturday, November 24, 2012 at 12:05pm by jor.kan Honors Application I am filling out an Honors application for English/History and one of the questions asked why do I wish to take this course.. any ideas? Thanks My ideas are: I want want to take this course because I want to take a class that is a bit more advanced than regular classes. Sunday, February 24, 2013 at 2:10pm by Chris Algebra 2 Honors Find the exact value by using an appropriate sum or difference identity. cos(165) degrees Sunday, June 6, 2010 at 9:49pm by Christine Physics Honors Compute the time it takes for the vertical velocity component to become zero; then double it for the "hang time". It takes just as long going up as coming down. To merit honors for your physics class work, you should attempt more of it. Friday, December 2, 2011 at 12:21am by drwls Honors English : Dr. King's Which speech? Since you're in honors English, I'm sure you can explain how Dr. King's use of figurative language make the speech so powerful. We'll be glad to critique your answers. Sunday, June 1, 2008 at 2:16pm by Ms. Sue math (algebra honors) the edge of one cube is 2 cm shorter than the edge of a second cube. The volumes of the two cubes differ by 386cm^3. Find the edge of the smaller cube. Thursday, February 27, 2014 at 9:19pm by rosa Question Do i really have to be in AP or IB classes in order to get into Yale School of Arts or no don't worry you don't have to take AP or IB but only if you are doing very well in school but you still have to be in honors like regular honors or regents. Saturday, December 31, 2011 at 6:44pm by Laruen Honors Algebra I Fill in the blanks to explain the step below. A=1/2(b to the 1st power + b to the second power)h solve for h Tuesday, September 30, 2008 at 8:09pm by Cherri English Honors English honors in an online school? Were you in the hospital for 2 months? And your school won't honor your medical treatment and give you an extension? This doesn't ring true. If you were so sick for two months and couldn't do this assignment, then your best choice is to ... Sunday, June 5, 2011 at 9:21pm by Ms. Sue honors algebra since 1 ft is 12 in. multiply V=lwh with 12 in. then divide it with w 3 times each feet then you will find the rest easy. THANK YOU! Tuesday, November 13, 2012 at 6:03pm by Anonymous Honors Math This did not help, I am still confused. Wednesday, August 31, 2011 at 6:26pm by Chelsea science honors 1 First -- your class is spelled science HONORS. Assuming you're weighing the same volume of "stuff," you'll need to put the names of the things you're weighing vertically along the left side of the chart. Across the top of the chart, write increments of the weights, such as 1 ... Thursday, August 21, 2008 at 8:25pm by Ms. Sue math (algebra honors) The edge of one cube is 2 cm shorter than the edge of a second cube. The volumes of the two cubes differ by 386 cm^3. Find the edge of the smaller cube using factoring. Sunday, February 27, 2011 at 5:52pm by K.S. Algebra 1 Honors 2x+4=5(x+1) -2(x+2) Would this be identity (all numbers are the solution), No solution (no real number solution), or can it be solved? Sunday, October 9, 2011 at 9:30pm by Stefanie honors chemistry- isotopes... can scientists actually measure the mass and relative abundance of isotopes of an element by counting each particle and measuring their masses? [ i think no because it would be too small ] if not, how could a scientist measure the mass and relative abundance of isotopes of an ... Tuesday, October 31, 2006 at 5:13pm by guitarking4000 honors algebra 2 the product of two negative numbers is 338. one of the numbers is half the other number. find the numbers. Sunday, September 30, 2007 at 6:40pm by ryan
I never intended to write a textbook and certainly not one in geometry. It was not until I taught a course to future high school teachers that I discovered that I have a view of the subject which is not very well represented by the current textbooks. The dominant trend in American college geometry courses is to use geometry as a medium to teach the logic of axiomatic systems. Though geometry lends itself very well to such an endeavor, I feel that treating it that way takes a lot of excitement out of the subject. In this text, I try to capture the joy that I have for the topic. Geometry is a fun and exciting subject that should be studied for its own sake. Though the primary target audience for this text is the future high school teacher, this text is also suitable for math majors, both because of the challenging problems throughout the text, and because of the quantity of material. In particular, I think this would make an excellent text for an undergraduate course in hyperbolic geometry. To the Student In the Republic, Plato (ca. 427 - 347 B.C.) wrote that his ideal State should be ruled by philosophers educated first in mathematics. He believed that the value of mathematics is how it trains the mind, and that its practical utility is of minor importance. This philosophy is as valid now as it was then. A modern education might include vocational or technical training (such as engineering, medicine, or law), but at its core, there are the English and mathematics courses which make up a liberal education. Though mathematics has rather surprising utility, for many students, the most important lesson to be learned in their math classes is how to think analytically, creatively, and rigorously. Keep this in mind as you read this book. Recognize that the exercises are a fundamental and integral part of the text. This is where the most important lessons are learned. You will not solve them all, perhaps not even most, but I hope that the exercises you do solve will leave you with a feeling of satisfaction. Chapter 2 on Greek astronomy provides some interesting material which can be mixed in with Chapter 1, or used on 'optional' days, such as the Wednesday before Thanksgiving. I usually begin integrating Sketchpad (Chapter 4) after I have completed the first few sections on constructions (Chapter 3). A laptop and computer projector come in handy. Polyhedra (Chapter 5) might be considered optional, but I think it can be very valuable for a future high school teacher. In particular, Exercise 5.14 should not be missed, both as a class project and again as an exercise. These are lessons which can be easily brought into the high school classroom and have the potential to be memorable. I usually skip most of Chapter 6, and only introduce the 'crutch,' the concepts of parallel and ultraparallel lines, and the concept of asymptotic triangles. The beginning of Chapter 7 poses a bit of a dilemma. Most of my students are not familiar enough with path integrals and differentials to understand the arguments of Sections 7.2 and 7.3. I could not see a way of introducing the Poincaré upper half plane model that avoids these arguments or something as difficult. I usually ask those students to accept these results and not worry too much if they do not understand the proofs. If I reach Chapter 8, it is usually covered during the last week of classes. I think of it as a cushion which allows the-students a little extra time to absorb the difficult material of Chapter 7 before their final. One of the constraints I face when I teach this course is the weak background of some of our students. Education students who have chosen mathematics as their second teaching field are required to take our geometry course. Outside of this course, the most sophisticated course they are currently required to take is the first semester of calculus. We are in the process of changing this, so that these students must also take a course in linear algebra. I think a rather nice alternative for a class of these students would be to omit Chapters 6 and 7, and instead introduce the pseudosphere (Chapter 12) as the model of hyperbolic geometry, after covering spherical geometry (Sections 10.1 - 10.5). With such a course, I would not overly emphasize the axioms of geometry. I would instead emphasize the relations between these geometries through the similar results, most notably in the different trigonometries. Such a plan would require a little more thought on the part of the instructor, since Chapter 12 was not written with this organization in mind. Nevertheless, a good instructor thoroughly familiar with the contents of Chapter 7 should be able to pull it off. Special Notes There are many places where the treatment of this subject could have been done differently. I would like to take a moment to explain some of my choices, as well as draw attention to and justify some of the unusual placements of material. Instructors may wish to occasionally return to this section as they teach. In Chapter 1, I never do define the measure of an angle. Though I use degrees earlier, there is no real need to talk about the measure of an angle until the Law of Cosines is introduced. Before that, for example in the Star Trek lemma, we only need a notion of congruent angles, which is defined via isometries. Since I already assume knowledge of trigonometry when I introduce the Law of Cosines, I do not see the point of formally defining the measure of angles. The student is eventually asked to formally define the measure of angles in Exercise 9.21. In Chapter 1, when we do use the measure of angles, we use degrees, which is the measure most commonly used in high schools. Later, when we introduce hyperbolic geometry, we switch to radians. There is a nice proof of Ceva's theorem (see Exercise 1.120) which does not use Menelaus' theorem. This can be used by an instructor who wishes to skip Menelaus' theorem. One advantage of the proof of Ceva's theorem using Menelaus' theorem is that it also works in both spherical and hyperbolic geometry. There is a very nice proof that cos(2p/5) is constructible (see Exercise 3.18). The advantage of the algebraic proof given in the text is that similar arguments are required in the proof that cos(2p/7) and similar quantities are not constructible. There are a number of programs similar to Geometer's Sketchpad (like Cabri and Cinderella), but I believe Sketchpad currently dominates the market, particularly in the high schools. This is why I chose to learn and write about Sketchpad. I have grown to appreciate the value of Geometer's Sketchpad and encourage instructors and readers to not just shrug off Chapter 4. It can be very useful for weak students and can be very valuable for future high school teachers. It can also be very fascinating and instructive for talented students. There are a lot of questions about constructions that I would never have considered had I not been familiar with Sketchpad. For example, which tilings of the Poincaré plane can be drawn using only a straightedge and compass? How can we construct a regular 7-gon using a straightedge, compass, and something else (see Exercise 3.39)? Some theorems, for example Feuerbach's theorem, are also a little more satisfying when played with using dynamic software (see Exercise 4.22). Results in hyperbolic trigonometry are included in Section 7.16. It is appropriate to first read about spherical trigonometry, which appears later in Sections 10.2 and 10.3. I chose to introduce hyperbolic trigonometry first only because I wanted to keep it together with the rest of Chapter 7. This could have been avoided by introducing spherical geometry first, but because we introduce new geometries via a change in Euclid's axioms, hyperbolic geometry naturally comes first. Tilings are first introduced in the exercises of Chapter 5 together with the regular and semiregular polyhedra. They are introduced again in Chapter 8, together with things of hyperbolic geometry. Chapter 9 is an unusual treatment of the foundations of geometry. It is intended for students who have already taken a course in analysis and assumes an axiomatic development of the real line. When compared to contemporary textbooks, the placement of Chapter 9 might also seem unusual, but it is not so unusual when compared with history. A sound axiomatic system for geometry was not developed until the late nineteenth century, well after the development of models for hyperbolic geometry. Though the logical order of geometry begins with the axioms, I do not believe that it should be taught that way. A strong intuitive understanding of geometry is necessary for anyone to understand the subtleties of the axiomatic foundation. As mentioned earlier, the placement of Chapter 10 is a matter of taste. If the instructor wishes to introduce spherical geometry earlier, there is no problem. The only prerequisites for Sections 10.1 - 10.5, other than Chapter 1, are trigonometry and some vector geometry (dot products and cross products). Parts of Chapter 5 should be done before Section 10.6, and Chapter 9 is a prerequisite for Sections 10.7 and 10.8. If the instructor really wishes to emphasize axiomatic systems, I encourage them to look closely at Chapter 13. In this chapter, the finite affine and projective planes are first introduced as algebraic objects. 'We then define them as incidence geometries together with Desargues' theorem and eventually show that the two definitions are equivalent. This beautiful result due to Hilbert really emphasizes the relationship between algebra and geometry. Chapter Dependence Though most of this book is meant to be read in order, there are only a few chapters which have a heavy dependence on earlier chapters. Depending on course objectives, several chapters can be safely skipped, and in particular, spherical geometry (Chapter 10) can immediately follow Chapter 1. I expect that the reader has at least a decent high school education, including trigonometry, and that they have some mathematical sophistication. I also expect that all readers cover the bulk of Chapter 1 (say, Sections 1.1 - 1.11) before moving on. More background is required for some of the text, as outlined in Table 2. Errata and Web Support Supporting material for this textbook will be made available at I anticipate that this page will include further exercises, perhaps solutions, links to related sites, and an errata sheet. Comments and reports of errors are sincerely appreciated and can be sent to baragar@nevada.edu Acknowledgments This text evolved from a course I taught several times at the University of Nevada Las Vegas. I would like to thank all the students who took this course, and in particular, I would like to thank the class of fall '97. They showed a great deal of character by embracing this subject with nothing but classroom notes and a text we never used. Their enthusiasm was inspirational and helped motivate the creation of this text. I would like to extend special thanks to Robin Fulmer and Brenda Walker, who both lent me their notes from the fall class. I would like to thank my advisor, Joseph Silverman, and my editor, George Lobell, whose encouragement helped transform those classroom notes into a textbook. I would like to thank Peter Shine and Dorette Pronk, who both provided feedback after they used versions of this text in courses they taught. I would like to thank Jeff Johannes, who also carefully read the text and who participated in frequent conversations about geometry and the history of mathematics. I would like to thank the reviewers too for their input. I would like to thank my production and copy editors, Barbara Mack and Martha Williams, who taught me a little about grammar. I would like to thank John Scherk, from whom I took my first undergraduate course in geometry at the University of Alberta. I would like to thank the members and coaches of the '98 and '99 Canadian IMO (International Mathematical Olympiad) teams. Some of the more sophisticated gems in this book are due to my association with these teams. It was also through my association with the IMO that I was exposed to Kiran Kedlaya's beautiful book Ke. I highly recommend this text to anyone with a serious interest in competition mathematics. I would like to thank Hanns-Heinrich Langmann of Germany, Ake H. Samuelsson of Sweden, and Bogdan Enescu of Romania, for graciously allowing me to use the IMO logos from '89, '91, and '99, the years their respective countries hosted the International Mathematical Olympiad. Finally, I would like to thank my wife Meg, and my son Timothy, whose support and tolerance made writing this text smoother and more enjoyable. Arthur Baragar View Table of Contents Introduction. The Geometry of Our World. A Review of Terminology. Notes on Notation. Notes on the Exercises. 1. Euclidean Geometry. The Pythagorean Theorem. The Axioms of Euclidean Geometry. SSS, SAS, and ASA. Parallel Lines. Pons Asinorum. The Star Trek Lemma. Similar Triangles. Power of the Point. The Medians and Centroid. The Incircle, Excircles, and the Law of Cosines. The Circumcircle and the Law of Sines. The Euler Line. The Nine Point Circle. Pedal Triangles and the Simson Line. Menelaus and Ceva. 2. Geometry in Greek Astronomy. The Relative Size of the Moon and Sun. The Diameter of the Earth. The Babylonians to Kepler, a Time Line. 3. Constructions Using a Compass and Straightedge. The Rules. Some Examples. Basic Results. The Algebra of Constructible Lengths. The Regular Pentagon. Other Constructible Figures. Trisecting an Arbitrary Angle. Models. Results from Neutral Geometry. The Congruence of Similar Triangles. Parallel and Ultraparallel Lines. Singly Asymptotic Triangles. Doubly and Triply Asymptotic Triangles. The Area of Asymptotic Triangles. All text is legible, may contain markings, cover wear, loose/torn pages or staining and much writing. SKU:9780130143181-5-0 $25.97 +$3.99 s/h VeryGood BookCellar-NH Nashua, NH 013014318926.22 +$3.99 s/h VeryGood Texts Direct Lexington, KY 2000 Paperback Very good
Hutchison's Beginning Algebra (The Hutchison Series in Mathematics) Elementary Algebra, 8/e by Baratto/Bergman is part of the latest offerings in the successful Streeter-Hutchison Series in Mathematics. The fourth edition continues the hallmark approach of encouraging the learning of mathematics by focusing its coverage on mastering math through practice. This worktext seeks to provide carefully detailed explanations and accessible pedagogy to introduce beginning and intermediate algebra concepts and put the content in context. The authors use a three-pronged approach (I. Communication, II. Pattern Recognition, and III. Problem Solving) to present the material and stimulate critical thinking skills. Items such as Math Anxiety boxes, Check Yourself exercises, and Activities represent this approach and the underlying philosophy of mastering math through practice. The exercise sets have been expanded, organized, and clearly labeled. Vocational and professional-technical exercises have been added throughout. Repeated exposure to this consistent structure should help advance the student's skills in relating to mathematics. The book is designed for a combined beginning and intermediate algebra course, or it can be used across two courses, and is appropriate for lecture, learning center, laboratory, or self-paced courses. It is accompanied by numerous useful supplements, including McGraw-Hill's online homework management system, MathZone
Beginning Algebra With Applications - 7th edition Summary: Intended for developmental math courses in beginning immediate feedback, reinforcing the concept, identifying ...show moreproblem areas, and, overall, promoting student success. New! Interactive Exercises appear at the beginning of an objective's exercise set (when appropriate), and provide students with guided practice on some of the objective's underlying principles. New! Think About It Exercises are conceptual in nature and appear near the end of an objective's exercise set. They ask the students to think about the objective's concepts, make generalizations, and apply them to more abstract problems. The focus is on mental mathematics, not calculation or computation, and help students synthesize concepts. New! Important Points have been highlighted to capture students' attention. With these signposts, students are able to recognize what is most important and to study more efficiently. New! A Concepts of Geometry section has been added to Chapter 1. New! Coverage of operations on fractions has been changed in Section 1.3 so that multiplication and division of rational numbers are presented first, followed by addition and subtraction New! A Complex Numbers section has been added to Chapter 11, "Quadratic Equations." New Media! Two key components have been added to the technology package: HM Testing (powered by Diploma) and, as part of the Eduspace course management tool, HM Assess, an online diagnostic assessment tool
MATH 102 - Liberal Arts Mathematics (3)Prerequisite: MATH 100 This course is designed for students in liberal arts programs and other fields that do not require a core of mathematics. Topics covered include introductions to logic, sets, counting and combinatorics, and elementary probability and statistics. Additional topics which may be covered will be selected from the areas of finance, voting and apportionment, number systems and number theory, geometries, graph theory, exponential growth and decay, logarithmic scales, matrices and Markov chains, and linear programming. This course counts towards the Analytical and Quantitative Thinking degree requirement. MATH 104 – Precalculus (5)Prerequisite: MATH 101 and Math 103 or ACT score of 23+ Precalculs offers a background for students who intend to major in Science, Technology, Engineering, Mathematics, Economics, or Finance. Precalculus consists of a review of elementary algebra, the concepts of algebraic, trigonometric, logarithmic, exponential functions, applications and modeling, and analytical geometry. MATH 107 – Math Applications (3)Prerequisite: MATH 101 This course investigates a variety of mathematics/science applications using productivity software in a computer lab setting. Topics include types of data and graphs, descriptive statistics, functions, graphing, curve fitting, right triangle trigonometry and functions, math modeling, and programming. The final is a simulated research project, report, and presentation. An added benefit is that the students will become fluent in computer use. This course counts towards the Analytical and Quantitative Thinking degree requirement. MATH 215 - Applied Calculus I (5)Prerequisite: MATH 101 and MATH 103 A study of single variable calculus and analytic geometry, including functions, limits, derivatives, applications of derivatives, exponential growth and decay, and an introduction to integration. MATH 221 – Calculus & Analytic Geometry I (5)Prerequisite: MATH 104 Study of variable and functions with emphasis on the changing properties of relationships that can be described mathematically by algebraic, numeric, and graphical methods. Designed to provide students majoring in mathematics, science, computer programming, engineering and many non-science fields an opportunity to begin a study of analysis. The basic underlying theory and the tools of calculus including differentiation and integration of functions are studied and used in geometric and various applied problems. A TI-83 graphing calculator or equivalent is required for this course. MATH 101 College Algebra (3). This course will transfer to other colleges and universities. MATH 102 Liberal Arts Mathematics (3). Liberal Arts Mathematics is a new course that provides a survey of topics in mathematics. It is designed for students not interested in pursuing more mathematics courses. This course is offered as an alternative to College Algebra to meet requirements for graduation. This course may or may not transfer to other schools, depending on the school's criteria. Math 107 Math Applications (3). This course will transfer as a math elective beyond College Algebra. Math 215 Applied Calculus I (5) Math 216 Applied Calculus II (5)
Age Range Search ResultsSNAP (Student Notes and Problems) Workbooks are packed with lessons covering each of the course objectives , notes, explanations and illustrative examples, they've got everything a student needs to develop a complete understanding of a subject's key concepts. The SNAP workbooks can be used in the…
This course is an introductory graduate level course in numerical methods designed to give engineering, mathematics, and science students the expertise necessary to understand and use computational methods for solving scientific problems. This course is an introductory graduate level course in numerical methods designed to give engineering, mathematics, and science students the expertise necessary to understand and use computational methods for solving scientific problems. The Student Support Edition of IntermediateAlgebra: An Applied Approach, 7 This student focused text addresses individual learning styles through the use of a complete study system that starts with a learning styles inventory and presents targeted learning strategies designed to guide students toward success in this and future college level courses. Comes With13 CDs. Each CD has about an hour of video. Digital Video Tutor is included with the textbook: Elementary and IntermediateAlgebra: Graphs & Models 2nd edition Published by Pearson / Addison Wesley. A study guide is also included.
... More About This Book the definition of limit, and problems related to the computation of limits. Answers and hints to the test problems are provided, and "road signs" appear in the margins, marking passages requiring particular attention. 1969An Introduction to Theory An excellent introduction to sequences,combinations,and limits. The book introduces the theory underlying these concepts to the reader. Very concise. Numerous problems. The book would make an excellent supplement for any text which emphasizes the concepts listed above. Finally, price is right. Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged.
- After, also ..... Dear User, your publication has been rejected because WE DO NOT ACCEPT THIS SORT OF MATERIALS at englishtips.org. Please see our rules here: Thank you After also… Dear User, your publication has been rejected because WE DO NOT ACCEPT THIS SORT OF MATERIALS at englishtips.org. Please see our rules here: Thank you Elementary and Middle School Mathematics: Teaching Developmentallywas written to help teacher candidates and practicing teachers understand mathematics and become more confident in their ability to teach the subject to children in pre-K through eighth grade. Structured for easy reference, offering 23 chapters reflecting the latest research to consult throughout one's teaching career, the revised edition infuses NCTM and Common Core State Standards with the benefits of problem-based mathematics instruction. With an emphasis on real-world math applications, the Sixth Edition of INTRODUCTORY TECHNICAL MATHEMATICS provides readers with current and practical technical math applications for today's sophisticated trade and technical work environments. Straightforward and easy to understand, this hands-on book helps readers build a solid understanding of math concepts through step-by-step examples and problems drawn from various occupations. Mathematics for Elementary Teachers: A Contemporary Approach, 10th Edition makes readers motivated to learn mathematics. With new-found confidence, they are better able to appreciate the beauty and excitement of the mathematical world. The new edition of Musser, Burger, and Peterson's best-selling textbook focuses on one primary goal: helping students develop a true understanding of central concepts using solid mathematical content in an accessible and appealing format. The four sections in this Third International Handbook are concerned with: (a) social, political and cultural dimensions in mathematics education; (b) mathematics education as a field of study; (c) technology in the mathematics curriculum; and (d) international perspectives on mathematics education. These themes are taken up by 84 internationally-recognized scholars, based in 26 different nations. Each of section is structured on the basis of past, present and future aspects. The Learner's Perspective Study ascribes to the premise that the investigation of social practice within the mathematics classrooms must attend to the learners' practice with at least the same priority as that accorded to the teachers' practice. In focusing on student voice within this partnership, as enacted in many different guises across different cultures and socio-political learning environments, we hope that we will be better informed to understand the relationship between pedagogy and learning mathematics, and between pedagogy and the empowerment of diverse learners.
L3.5 Deriving Trig Derivatives Susan Braford, Mathematics Instructor Kings Fork High School, Suffolk Susan Braford created this power point presentation for a classroom activity. The students derived the differentiation rules for the 6 trig functions by using the graphs of sine and cosine, their graphing calculators and what they knew of the reciprocals an ratios. Once they discovered d/dx of sin x was cos x, they then used the quotient rule to discover csc x. She was able to roam about the room with her wireless mouse and monitor their progress. It was the first time she tried this and everything went better than anticipated.
is a new introduction to linear algebra for students who have completed the first year of calculus. In the spirit of modern instruction, this elementary presentation of the important ideas in linear algebra emphasizes conceptual understanding, developing applied examples, and working with realistic numerical data before introducing formal mathematical definition and operations. This text emphasizes geometric, symbolic, and numeric presentations of the subject. The first two chapters cover linear phenomena in both numeric and geometric settings. The symbolic manipulation of vectors and matrices is then introduced as a tool for the study of specific problems. Many examples, student exercises, and group project ideas are included.
0071615chaum's Outline of Vector Analysis, 2ed (Schaum's Outline Series) The guide to vector analysis that helps students study faster, learn better, and get top grades More than 40 million students have trusted Schaum's to help them study faster, learn better, and get top grades. Now Schaum's is better than ever-with a new look, a new format with hundreds of practice problems, and completely updated information to conform to the latest developments in every field of study. Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores
Standards (7) AAAS Benchmark Alignments (2008 Version) 2. The Nature of Mathematics 2B. Mathematics, Science, and Technology 9-12: 2B/H3. Mathematics provides a precise language to describe objects and events and the relationships among them. In addition, mathematics provides tools for solving problems, analyzing data, and making logical arguments. 9. The Mathematical World 9B. Symbolic Relationships 9-12: 9B/H4. Tables, graphs, and symbols are alternative ways of representing data and relationships that can be translated from one to another. 9C. Shapes 9-12: 9C/H3a. Geometric shapes and relationships can be described in terms of symbols and numbers—and vice versa. Common Core State Standards for Mathematics Alignments High School — Number and Quantity (9-12) Quantities? (9-12) N-Q.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. Vector and Matrix Quantities (9-12) N-VM.1 (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, \|v\|, \|\|v\|\|, v). Common Core State Reading Standards for Literacy in Science and Technical Subjects 6—12 Key Ideas and Details (6-12) RST.11-12.2 Determine the central ideas or conclusions of a text; summarize complex concepts, processes, or information presented in a text by paraphrasing them in simpler but still accurate terms. Range of Reading and Level of Text Complexity (6-12) RST.11-12.10 By the end of grade 12, read and comprehend science/technical texts in the grades 11—CCR text complexity band independently and proficiently. Disclaimer: ComPADRE offers citation styles as a guide only. We cannot offer interpretations about citations as this is an automated procedure. Please refer to the style manuals in the Citation Source Information area for clarifications.
This is a short eBook that describes how to get free high school Algebra 1 help online without having to spend any money, buy anything, join any free trials, or anything like that. Free High School Algebra 1 Help Online \| Algebra 1 Help.org. A short ebook explaining a simple way to subtract integers for people who have trouble subtracting integers. This uses a method based on simply changing a subtraction problem to an addition problem based on helping people with algebra. How to Subtract Integers Without Getting Confused \| Algebra 1 Help.org
MATH COURSES AT WEST DEPTFORD HIGH SCHOOL (updated for the 2011-2012 school year) To help our students retain the skills they learned this past year, the math department has developed review sheets which all students must complete during the summer months. Every student was given a packet along with instructions. In case you misplaced your copy, please click the following link and print the review for the course you will be entering in September. Algebra I - In this course, the students will learn the Algebra standards put forth by the State of New Jersey in a more concrete ratherthan abstract manner. This college-prep course is designed for students who have not passed the NJ ASK8 or students for whom mathematics is not a strength. Advanced Algebra I - This course is the foundation for all courses in advanced mathematical studies and is designed for students who have a solid foundation in basic arithmetic and knowledge of the real number system. Students must have passed the NJ ASK8. Geometry - In this course, the students will learn the Geometry standards put forth by the State of New Jersey in a more concrete rather than abstract manner.This college-prep course is designed for students who have not passed the NJASK8 or students for whom mathematics is a weakness. Advanced Geometry - a year-long course where students learn and apply the theorems and postulates of plane geometry. Prerequisite: Algebra I, passing with at least a "C" Course registration is based on a number of factors, such as final grade average, standardized test scores, teacher recommendation, etc. Interactive Algebra/Geometry III - This is the third in a series of three courses designed to provide a common core of broadly useful mathematics for all students. Please see the description above. Upon completion of this course, the student is recognized as having completed the standards for Algebra I and Geometry. Accelerated Interactive Algebra/Geometry III -Students will be placed in this level based on teacher recommendation, grades, and testing results. This course is similar in content to Interactive Algebra/Geometry III, but topics will be delved into more deeply, the pace will be faster, and additional concepts will be presented. We strongly recommend that each student own a TI-83 plus graphing We will, however, provide one for use in the math classroom. Students will be assigned a particular one for classroom use only and the student will be responsible for it should they destroy it. Interactive Algebra/Geometry IV - This program will cover the remaining standards addressed in Algebra II and it will also prepare the students for college entrance exams such as the Accuplacer Test and the SAT. A student who completes all four levels of Interactive Algebra/Geometry is recognized as having completed the standards for Algebra I, Geometry, and Algebra II. Accelerated Interactive Algebra/Geometry IV -Students will be placed in this level based on teacher recommendation, grades, and testing results. This course is similar in content to Interactive Algebra/Geometry IV, but topics will be delved into more deeply, the pace will be faster, and additional concepts will be presented. Algebra II - a year-long course which continues and refines Advanced Algebra I. Functions and graphing are stressed as well as applications. Prerequisite: Advanced Algebra I, Geometry, passing with at least a "C" in both courses. Course registration is based on a number of factors, such as final grade average, standardized test scores, teacher recommendation, etc. Math Analysis - this is a year-long pre-calculus course. Trigonometry receives a major emphasis. Prerequisite: Algebra II, passing with at least a "B-". Course registration is based on a number of factors, such as final grade average, standardized test scores, teacher recommendation, etc. Prob/Stat - this is a semester course dealing with such topics as samplings, permutations, combinations, and data analysis. Prerequisite: Algebra II, passing with at least a "C". Course registration is based on a number of factors, such as final grade average, standardized test scores, teacher recommendation, etc. Discrete Math - this semester course deals with the topic of efficiency. Some questions that are addressed are why do you stand in a maze to enter a ride in Disney World, how does a CD player interpret codes correctly, what's the most efficient way to drive through a city with one-way streets. This course is ideal for anyone interested in entering such fields as computer science, telecommunications, biological sciences, social sciences, business, education, or liberal arts. Prerequisite: Algebra II, passing with at least a "C". Course registration is based on a number of factors, such as final grade average, standardized test scores, teacher recommendation, etc. Honors Calculus - in this year-long course differential and integral calculus are studied. The text is a book used by many area colleges and universities.Prerequisite: Mathematical Analysis-Honors, passing with at least a "C" or Mathematical Analysis, passing with at least a "B". Course registration is based on a number of factors, such as final grade average, standardized test scores, teacher recommendation, etc. AP Calculus - this year-long course intensely prepares the students for the examination given in May of each year. (prerequisite is Honors Math Analysis). Students must own a TI-83 Plus graphing calculator. If this poses a problem for any student, he/she should see the department chairperson, Mrs. Fish, as soon as possible so accommodations may be made. SAT Studies - an evening course offered to the students in the spring who wish to prepare for or improve their SAT scores. It is offered jointly with the English department. This carries a no-credit status and their is a charge. Miscellaneous information: Honors levels courses are offered in Geometry, Algebra II, and Math Analysis. AP Calculus carries an honors status. Students are recommended for these courses based on past classroom performance, test scores, and teacher recommendation. If a student was not recommended for an honors level, the math department strongly encourages you to speak with your son/daughter's present math teacher and guidance counselor before signing a waiver. Please note that many students who are not recommended for this level course do not perform successfully and, due to class sizes, may not be able to be placed in the appropriate level once the school year has begun. Every student should own his/her own calculator. A graphing calculator, the Texas Instrument TI-83 Plus, is the one that will be used in most math classes as well as in science classes, HSPA testing, SAT testing and even at the college level. For this reason we strongly recommend all students invest in this Doubling courses: If a student wishes to double up Geometry and Algebra II, it is important to discuss this with his/her current math teacher. Two math courses taken simultaneously is not an easy task for a student. For additional information, please refer to the curriculum guide or contact the guidance department. Commitment to NJ Core Curriculum Content Standards for Mathematics 1.All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a variety of ways. 2.All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe, and analyze phenomena. 3.All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts, and processes. 4.All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze, and analyze and draw appropriate inferences from data. 5.All students will use mathematical processes of problem solving, communication, connections, reasoning, representations, and technology to solve problems, and communicate mathematical ideas. 1.All students will demonstrate interpersonal and self-management skills 2.All students will develop career awareness, planning, and employability. 3.All students will use critical thinking, decision-making, and problem solving skills. 4.All students will use computer applications to manipulate and communicate information. 5.All students will develop an understanding of the nature and impact of technology, engineering, technological design, and the designed world as they relate to the individual, society, and the environment. 6.All students will demonstrate career planning and employability skills, and develop the foundational knowledge and skills necessary for further study in a selected occupational area.
Wolfram Research Mathematica 6 The latest upgrade to the popular math application Mathematica makes your data dynamic. From high-end number theory (there are more than 20 new functions for computations in algebraic number fields) to chemistry (3D graphics of chemical compounds can be turned and viewed from all angles), Mathematica 6 creates 3D graphics and lets you manipulate any parameter with any remote control, including gamepad controllers. The new Manipulate function allows you to dynamically change specified parameters, giving insight into the dependencies of different parts of the computation. Mathematica 6 also includes large collections of data in math, physics, chemistry, astronomy, geography, linguistics, and finance. With these data, a teacher can make plots of chemical properties, word trees, or maps of countries color-coded by population. For those looking to have some fun with Mathematica (math and fun? You better believe it!), version 6 has some new possibilities. Coding is supported, including a debugger with a step-through function and the ability to set arbitrary break points. The new CurrentValue function can check where your mouse is, what buttons are being pushed, how many mouse clicks there have been, low-level data on the states of all controllers, and any other current value of a specified item in the Mathematica system and interface. Despite - or perhaps because of - all these advances, Mathematica 6 is still complicated and difficult to master. To help, Wolfram Research offers classes (both in person and online) to teach you how to use the app. In Mathematica 6 itself, warnings of possible syntactic errors follow you as you type, and error messages appear for incorrect inputs - though the messages don't explain how to correct your work. The bottom line. Wolfram Research has reinvented Mathematica to the benefit of math geeks of all stripes. Mathematica 6 has an amazing variety of ways to interact with graphs, matrices, and data. COMPANY: Wolfram Research CONTACT: PRICE: $2,495, $1,095 academic list price, or $139.95 student version REQUIREMENTS: G4 or faster or Intel processor, Mac OS 10.3 or later Lets math geeks and other smarties manipulate data in ways that allow new insight and imagination. Universal binary. Requires complicated programming-like input that can take time to master
Pre-Algebra Subject Kit (2nd ed.) Pre-Algebra (2nd edition) eases the transition from arithmetic to algebra. Algebraic expressions and linear equations are applied throughout a thorough review of operations on integers, fractions, decimals, percents, and radicals. Students explore relations and functions using equations, tables, and graphs. Chapters on statistics and geometry extend foundational concepts in preparation for high school courses. Problem-solving and real-life uses of math are featured in each chapter. Dominion through Math exercises regularly illustrate how mathematics can be used to manage God's creation to His glory.
Contents CONTENTS include: The quadratic formula leading to the definition of a complex number; The algebra of complex numbers; The Argand diagram; The modulus, argument form for a complex number; Products and quotients; The four operations represented on the Argand diagram; Useful facts; Sample questions; De Moivre's Theorem; The cube roots of unity; The nth roots of any complex number; Locus questions
Post navigation Review: Discovering Mathematics (Singapore Math, Secondary Level) Note: Since beginning Discovering Mathematics, Singapore Math has released a new edition, Discovering Mathematics Common Core. The order of lessons vary a bit, and new topics have been included. At this writing, only levels 7A and 7B are available, with 8A and 8B to be released at the end of 2012. The others should follow soon, I've been told. Yes, movement between the old and new programs are doable, and a switch from the old level 1 to the new level 8 works well, I'm told by their forum guru. Worrier that I am, I have 7B and 1A just to be certain we won't miss anything. In all regards, including, rigor, the new books are quite similar to the old, with additions and a bit of rearranging being the main differences. Providing a challenging mathematics education was one of the key reasons we started homeschooling. Deeply disappointed by the depth of the math provided by two schools, my older son, then seven, assumed he was the problem. "I don't think I've very smart, Mom," he told me. "Why not?" I inquired. "Because they don't give me anything hard to do," came his sad reply. Math (and science) were his loves at age 4 and 5 in Montessori and while at home. He was appropriately challenged in the first at school and free to explore the second at home. First grade ended all that, where math became repetition of previously mastered lessons. Second grade, at our local gifted and talented public school, it was nonexistent which was because, we were informed, he knew all the material for that year already. So once home, math took a starring role. Singapore Math quickly became our preferred curriculum (reviewed here) for the elementary sequence. Even doing the Challenging Word Problem books, we burned through it quickly. Almost 10, my older insisted on Algebra, so we started the standard sequence, happily making our way through a fine text, Jacobs' Algebra. (reviewed here). When my younger finished 6B, I wondered if there was another way. We vamped for much of last year, working through a variety of books while choosing our next course of action. After much consideration, we decided to stay with Singapore, specifically, their Discovering Mathematics series. This four-year series is designed to cover some prealgebra, algebra (I and II), geometry, and a smattering of other topics, like probability and counting. Unlike most American programs, these topics are interwoven throughout the years, with chapters on algebra followed by chapters on geometry with a side trip to data handling. It's challenging, with plenty of problems, tests with answers, and teacher's support books if needed. But I hesitated. Accustomed to the four-year math sequence I'd known as a child and that my older son had followed, I was hesitant to commit to a different path. What if we didn't like it after a year? What then? (Answer: Start a traditional Algebra program and compact or test out of what has already been covered. Ditto the next year with Geometry.) I presented my younger son, then 10, with the options. Singapore, Jacobs, or Art of Problem Solving? He looked at samples of all online and liked the familiarity of the Singapore. Thus, we reached a decision. We've not been disappointed. We started Discovering Mathematics 1A soon after it arrived and found that while it certainly felt like the Singapore Math we'd enjoyed the previous years, it was a step up in challenge and pace. He's enjoying it, but we don't whip through the pages as we did at the elementary level. Concepts aren't broken down in such small parts, and even the sample problems (Try This!) are fairly challenging. Fortunately, this increase in challenge has resulted in an increase of effort. As a result, he's feeling rather accomplished while learning large amounts. At the minimum, the user will need to purchase two textbooks for the year. These paperbacks are affordable and reusable, in keeping with Singapore Math's reputation for affordability. Each of the four levels requires two textbooks, each generally over 200 pages long. The year is broken up into 11 to 17 chapters, roughly evenly divided between the two books. (The fourth level is shorter, with a significant proportion of 4B dedicated to review tests, similar to the elementary level 6B.) The chapters are broken up into shorter sections, some amenable to a single lesson or day of work, others requiring multiple days, given the depth of the lessons. Each section ends with problems in four categories: Basic Practice (the easiest problems), Further Practice (definitely a bit more work), Maths@Work (word problems just as challenging as the aptly named Challenging Word Problems of the elementary series), and Brainworks (sometimes too hard for Mom but worth trying if no one is crying). The so-called Revision Exercise (test) at the end of each chapter is at the level of the Further Practice and Maths@Work level. Aside from the Brainworks problems, all the answers for the problems are in the back of the book. If you desire worked solutions (and so far, I'm good without), there are Teacher's Guides available, which include other teaching assistance, activities, and a breakdown of lessons and timing. An additional workbook is available for each level, providing some extra practice as well as more problems at the more challenging level. Unlike the traditional workbook, these don't provide a place to do the problems, making them more of a reusable problem bank. I assign some of these at the end of each chapter, before the revision (test). The number I assign depends on how well he's handling the material — some sections just require more practice than others. Generally, these workbook problems are more challenging than the textbook ones. They are broken down into sections called Basic Practice, Further Practice (both a bit more involved than the same-named section in the text, it seems), Challenging Practice (and it generally lives up to its name), and Enrichment (excellent problems that we don't get to most of the time). As with the text, answers are in the back, but solutions require the Teacher's Edition of the workbook. I'd strongly suggest the workbook to supplement all learners, with the Teacher's Edition on the shelf if a parent is a bit math wary and wants guidance on the trickier problems. The strengths of the elementary level of Singapore Math continue at the secondary level. The pace is swift, which is excellent for the mathematically talented child but could be overwhelming for others. The problems in the text at the secondary level are far more challenging that what is in the workbooks for the elementary level, but on par with the Challenging Word Problems books. (I've not used the Intensive Practice books at the elementary level, which are designed to increase the challenge at their respective levels.) The depth we've encountered thus far is also impressive. Math is not taught via algorithm but by deep understanding, which, in my opinion, is by far the superior method. It is applied, not simply in one-step word problems, but across the sciences and into the work world. Math lives in these books, with all its complexity and beauty there for the learning. The downside to the Discovering Mathematics series? If one isn't math-comfortable, these could be a challenge to teach. That said, for the math-uncomfortable, these are an excellent way to build a new relationship with math. I know that throughout teaching even the elementary level of Singapore Math to my boys, this math-comfortable mom moved from number capable to number savvy. I've said before that I believe that math is best taught rather than learned solo. Discussion is part of the process, and many times, I've had a child teach me and correct me, thus delighting the child and enlightening me. (For more on thoughts about strong mathematics programs, read my post, Math Matters.) We're early in our exploration of this four-level series, and I'll post again as we move through the program. I'm hoping we continue to enjoy Discovering Mathematics over the next several years, allowing us continuity with a strong mathematics educational program. As always, I only review what we've used, and I never accept compensation of materials or money for my reviews. I, too, have used Singapore Primary Mathematics from the get-go (now finishing up 6A/6B). I found your review to be very helpful in confirming what I already knew–that the Discovering Mathematics would probably hold true to the analytical/critical thinking type math that makes you think and not just plug in numbers. I, too, have noticed that my mental math in particular and understanding of concepts has really sharpened doing this math with my girls. I, too, have had the more than one occasion of my daughter teaching me a problem. My husband always says, who is home schooling whom? It does make for a great confidence builder for your child! Do post later if you end up using Sketchpad–I just read about that today as I was reviewing the Discovery Mathematics series. Thanks for the information! Thanks for this review. We have used Singapore all the way through, and I do think we will stick with Discovering Mathematics after Singapore 6. My husband is a high school math teacher and speaks highly of what the kids have learned so far. I started out with Singapore NEM, but thinking of switching to DM. So, I may be able to only use the textbook and workbook alone without having to buy the teaching notes and solution book and the workbook solutions book?
Students Courses Need Help? MATH BRIDGE THE GAP SECOND GRADE PREP This class will prepare students to take the advanced math test in the spring and prepare them to suceed in honors or regular level math in 7th grade. It will cover in depth prealgebra, fractions, percents, decimals, graphing, and inequalities.
3rd edition. Book is in overall good condition. There is some water damage, causing pages to lightly ripple but does not affect the text. Cover shows some edge wear and corners ...are lightly worn. Pages have a minimal to moderate amount of markings. FAST SHIPPING W/USPS TRACKING!!! Read moreShow Less Hardcover Fair 0495014001Hardcover Fair 0495014001 Good reading copy. No missing pages. * CD seal has not been broken-not sure if works* Please note that it is rated due to likely blemishes such as ...highlighting, underlining, folds, creases. Buy with confidence....Customer Service is our TOP PRIORITY! Quick shipping/Free Tracking.Read moreShow Less More About This Textbook Overview Tussy and Gustafson's fundamental goal is to have students read, write, and talk about mathematics through building a conceptual foundation in the language of mathematics. Their text blends instructional approaches that include vocabulary, practice, and well-defined pedagogy, along with an emphasis on reasoning, modeling, and communication skills. With an emphasis on the "language of algebra," they foster students' ability to translate English into mathematical expressions and equations. Tussy and Gustafson make learning easy for students with their five-step problem-solving approach: analyze the problem, form an equation, solve the equation, state the result, and check the solution. In addition, the text's widely acclaimed study sets at the end of every section are tailored to improve students' ability to read, write, and communicate mathematical ideas. The Third Edition of ELEMENTARY ALGEBRA also features a robust suite of online course management, testing, and tutorial resources for instructors and students. This includes BCA/iLrn Testing and Tutorial, vMentor live online tutoring, the Interactive Video Skillbuilder CD-ROM with MathCue, a Book Companion Web Site featuring online graphing calculator resources, and The Learning Equation (TLE), powered by BCA/iLrn. TLE provides a complete courseware package, featuring a diagnostic tool that gives instructors the capability to create individualized study plans. With TLE, a cohesive, focused study plan can be put together to help each student succeed in math. Meet the Author Alan Tussy teaches all levels of developmental mathematics at Citrus College in Glendora, CA. He has written nine math books — a paperback series and a hard-cover series. An extraordinary author, he is dedicated to his students' success, relentlessly meticulous, creative, and a visionary who maintains a keen focus on his students' greatest challenges. Alan received his Bachelor of Science degree in Mathematics from the University of Redlands and his Master of Science degree in Applied Mathematics from California State University, Los Angeles. He has taught up and down the curriculum from prealgebra to differential equations. He is currently focusing on the developmental math courses. Professor Tussy is a member of the American Mathematical Association of Two-Year Colleges. R. David Gustafson is Professor Emeritus of Mathematics at Rock Valley College in Illinois and co-author of several best-selling math texts, including Gustafson/Frisk's BEGINNING ALGEBRA, INTERMEDIATE ALGEBRA, BEGINNING AND INTERMEDIATE ALGEBRA: A COMBINED APPROACH, COLLEGE ALGEBRA, and the Tussy/Gustafson developmental mathematics series. His numerous professional honors include Rock Valley Teacher of the Year and Rockford's Outstanding Educator of the Year. He earned a Master of Arts from Rockford College in Illinois, as well as a Master of Science from Northern Illinois
The Algebra 1: The Complete Course DVD Series will help students build confidence in their ability to understand and solve algebraic problems. In this episode, students will learn how to derive an algebraic equation using the method of finite differences and how to derive the input/output table of numerical values. Grades 5-9. 30 minutes on DVD.
After A. Ungar had introduced vector algebra and Cartesian coordinates into hyperbolic geometry in his earlier books, along with novel applications in Einstein's special theory of relativity, the purpose of his new book is to introduce hyperbolic barycentric coordinates, another important concept to embed Euclidean geometry into hyperbolic geometry.... more... The mere mention of hyperbolic geometry is enough to strike fear in the heart of the undergraduate mathematics and physics student. Some regard themselves as excluded from the profound insights of hyperbolic geometry so that this enormous portion of human achievement is a closed door to them. The mission of this book is to open that door by making... more... The word barycentric is derived from the Greek word barys (heavy), and refers to center of gravity. Barycentric calculus is a method of treating geometry by considering a point as the center of gravity of certain other points to which weights are ascribed. Hence, in particular, barycentric calculus provides excellent insight into triangle centers.... more...
Sets This plugin is part of set STACK. Plugins from the set work the best when installed together. The STACK system is a computer aided assessment package for mathematics, which provides a question type for the Moodle quiz. In computer aided assessment (CAA), there are two classes of question types. Selected response questions In these questions, a student makes a selection from, or interacts with, potential answers which the teacher has selected. Examples include multiple choice, multiple response and so on. Student-provided answer question In these questions the student's answer contains the content. It is not a selection. Examples of these are numeric questions. STACK concentrates on student-provided answers which are mathematical expressions. For example, a student might respond to a question with a polynomial or matrix. Essentially STACK asks for mathematical expressions and evaluates these using computer algebra. The prototype test is the following pseudo-code. STACK uses a computer algebra system (CAS) to implement these mathematical functions. A CAS provides a library of functions with which to manipulate students' answers and generate outcomes such as providing feedback. Establishing algebraic equivalence with a correct answer is only one kind of manipulation which is possible. Using CAS can also help generate random yet structured problems, and corresponding worked solutions. In STACK a lot of attention has been paid to allowing teachers to author and manage their own questions. The following are the key features. Question versions are randomly generated within structured templates. There are many different kinds of inputs. These are, for example, where the student enters a mathematical expression, or makes a true/false selection. Mathematical properties of students' answers are established using answer tests within the CAS Maxima. Feedback is assigned on the basis of these properties using a potential response tree. This feedback includes: Textual comments for the student. A numerical mark. Answer notes from which statistics for the teacher are compiled. These broadly correspond to formative, summative and evaluative functions of assessment. Which of these outcomes is available to the student, and when, is under the control of the teacher. Multi-part mathematical questions are possible: each question may have any number of inputs and any number of potential response trees. There need not be a one-to-one correspondence between these. Partial credit is possible when an expression only satisfies some of the required properties. Plots can be dynamically generated and included within any part of the question, including feedback in the form of a plot of the student's expression. Comments Hi, This plugin seems very interesting, but I could not find the english language strings in AMOS available for translation. According to David Mudrak (sept 5th 2012): "From now on, whenever a maintainer publishes a new version of their contributed plugin, strings are automatically sent via a web service to the AMOS. This process respects the supported Moodle version setting so the strings appear at the correct Moodle branch in AMOS. This works for new plugins that will be uploaded into Plugins in the future, too. With the exception that the strings appear in AMOS only after when the plugin is approved as a part of its validation. This new mechanism works for all plugins that were uploaded into the Plugins directory and are written for Moodle 2.0 and higher. Contributed plugin maintainers are now encouraged to transfer all their current code to this new scheme: The plugin code itself should now contain just the English strings in the /lang/en folder. All other translations are to be maintained via AMOS and you as the plugin maintainer do not need to look after them any more! Translated strings for contributed plugins are part of the standard language packs generated by AMOS. If your plugin code currently contains some translation, you (as the plugin maintainer) should submit it as a contribution into AMOS prior to dropping it from your plugin's source code. AMOS stage page provides a form to upload strings from an existing PHP file. You are supposed to import all non-English string files you currently have shipped with your plugin (eg. /lang/cs/yourmodule.php) into the AMOS stage and then submit them language pack maintainers. We believe that this new procedure will make translation of contributed plugins much easier than it ever been - for both the plugin maintainer and translators, too. Should you have any questions regarding this new feature, do not hesitate to ask in AMOS support forum at this site. Thank you all for you great work on contributed plugins and their translations!" It is indeed a long time since we uploaded the beta here. We really ought to upload a new version. I will discuss it with Chris, and with any luck we can do that tomorrow. The latest version of the code is available on github, of course, and Chris is now using it for real in his teaching. (We already have some translation too, and I need to transfer those to AMOS.) Hi Christopher. I must confess I am only a veterinary pathologist who enjoys translating Moodle into spanish, and it's been 30 years since I took calculus, but one English language string in qtype_stack seemed odd to me: 2.4 [ddl_empty,qtype_stack] "No choices were provided for this drop-down. Please input a set of values link a,b,c,d" I wonder if the word "link" should not really be "like". I apologize if am asking a silly question and I thank you in advance for your help. Hi, I tried to instal the plugin several times. I think I followed step by steps the instructions but when running STACK healthcheck I get the message: The version of the STACK-Maxima libraries being used (So old the version is unknown!) does not match what is expected (2012122800) by this version the the STACK question type. It is not really clear how that happened. You will need to debug this problem yourself. And CAS result Warning, empty result! unpack_raw_result: no results were returned by the CAS. It looks to me like PHP could not start a CAS process at all. Hence, there is no version number being returned. If you email me the HTML page you get back from the healthcheck, and let me know a little about your system I will be able to help more. If you are on unix you need to ensure maxima is installed and working. Try the command line "maxima". Malik, STACK conforms exactly to the normal Moodle system of language strings for plugins. E.g. Please do get involved in translating STACK. This would be very welcome. If you need STACK specific changes, e.g. splitting up strings for any reason, please let me know. Chris
The Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989) recommend that high school students should be able to do the following: "represent and analyze relationships using tables, verbal rules, equations, and graphs; translate among tabular, symbolic, and graphical representations of functions; recognize that a variety of problem situations can be modeled by the same type of function; and analyze the effects of parameter changes on the graphs of functions" (p. 154). The teaching of functions by emphasizing the tabular, symbolic and graphical representations and the connections between them became known as "The Rule of Three." Functions can also be represented by real-world situations themselves so "The Rule of Three" later was called by some as "The Rule of Four". These representations should not be learned in isolation and that true learning of the concept of function occurs when a person can easily make connections between the various representations and see how changes in one representation effects the other three.
Algebra with Applications This book is for sophomore-level or junior/senior-level first courses in linear algebra and assumes calculus as a prerequisite. This thorough and ...Show synopsisThis book is for sophomore-level or junior/senior-level first courses in linear algebra and assumes calculus as a prerequisite. This thorough and accessible text, from one of the leading figures in the use of technology in linear algebra, gives students a challenging and broad understanding of the subject. The author infuses key concepts with their modern practical applications to offer students examples of how mathematics is used in the real world. Each chapter contains integrated worked examples and chapter tests. The book stresses the important roles geometry and visualization play in understanding linear algebra **...New in new dust jacket
Discrete Mathematics Using a Computer 9781846282416 ISBN: 1846282411 Pub Date: 2006 Publisher: Springer Summary: 'Discrete Mathematics Using A Computer' offers a new, 'hands-on' approach to teaching discrete mathematics. A simple functional language is used to allow students to experiment with mathematical notations which are traditionally difficult to pick up. Odonnell, John is the author of Discrete Mathematics Using a Computer, published 2006 under ISBN 9781846282416 and 1846282411. Two hundred thirty six Discrete M...athematics Using a Computer textbooks are available for sale on ValoreBooks.com, four used from the cheapest price of $30.38, or buy new starting at $56.00
It supports standard scientific calculator functions, including absolute value, logn, and a wide range of trigonometric functions, including hyperbolic sine, cosine, and tangent! In addition to graphing any expression you can throw at it, it can also plot parametric curves (fun!), functions translated to the y-axis (i.e. functions in the form x=f(y)), and that's not all! It also includes the popular Polynomial Calculator, capable of performing lightning-fast operations on polynomials with any number of variables. Now you can factor polynomials with ease! It has every function you'd expect from a much more expensive graphing calculator, but only costs a fraction of the price, and works on the PPC you already own, so why not save yourself the cost of a Texas Instruments TI-81 or a Casio fx-7700.
The primary goal of this lesson is to understand that the costs associated with buying on credit and that making only minimum payments are problematic to long-term financial health. The secondary goal... More: lessons, discussions, ratings, reviews,... This lesson plan presents an activity which demonstrates the birthday paradox, using it as a springboard into a unit on probability. Explanation on the difficulty with probability; Use of the TI-83 gr... book uses the calculator as a problem-solving tool. In each activity, the basic problem could be solved without the calculator; however, the mathematics involved makes the calculator the appropri... More: lessons, discussions, ratings, reviews,... The activities in this book are designed for students to use the calculator as a problem-solving tool. In order for students to increase their problem-solving skills, the teacher needs to let them ... middle and high school Algebra I students with a set of data collection investigations that integrate mathematics and science and promote mathemati... More: lessons, discussions, ratings, reviews,... These mathematics and science-based investigations using the TI-73 with Graph Explorer Software allow students to display and analyze data that they collect. The activities focus on the integration of... More: lessons, discussions, ratings, reviews,... The activities in this book highlight the functional capabilities of the TI-73 calculator, while making mathematical connections to topics applicable to middle school students. The use of the TI-73 is... More: lessons, discussions, ratings, reviews,... This book was written to accompany the TI-73 calculator for teachers teaching 5th or 6th grade. The activities are ordered from easiest to more difficult. Each activity contains the main concept being... More: lessons, discussions, ratings, reviews,... Step-by-step directions on how to use the Logic Ladder App. One activity, Play Factor, involves filling in the prime factorization of a given number. The second activity, Play Classic, involves orderi... More: lessons, discussions, ratings, reviews,... These activities are intended to develop and deepen students' understanding of middle school geometry concepts. They may be woven into the curriculum as an independent geometry investigation or as a r... More: lessons, discussions, ratings, reviews,... These materials describe how to use the Topics in Algebra 1 Calculator Software Application (App) for the TI-73 Explorerô, the TI-83 Plus family, and the TI-84 Plus family. Both the App and the classr... More: lessons, discussions, ratings, reviews,... These activities are intended to help students use the number line and the fraction line to develop both an operations and number sense. Several activities focus on operations with the integers, such
Synopses & Reviews Publisher Comments: This introduction to Laplace transforms and Fourier series is aimed at second year students in applied mathematics. It is unusual in treating Laplace transforms at a relatively simple level with many examples. Mathematics students do not usually meet this material until later in their degree course but applied mathematicians and engineers need an early introduction. Suitable as a course text, it will also be of interest to physicists and engineers as supplementary material. Synopsis: Scientists and engineers who need to model problems must often use mathematical concepts, such as Laplace transforms and Fourier series. This introduction is intended for self-study, and contains many problems and fully worked-out solutions. Synopsis: Gardners, Scientists and engineers who need to model problems must often use mathematical concepts, such as Laplace transforms and Fourier series. This introduction is intended for self-study, and contains many problems and fully worked-out solutions. "Synopsis" by Ingram, , Includes bibliographical references (p. 245-246
1. A Beginner's Guide to the Scholarship of Teaching and Learning in Mathematics This course will introduce participants to the scholarship of teaching and learning (SoTL) in mathematics and help them begin projects of their own. We describe a taxonomy of SoTL questions, provide examples of SoTL projects in mathematics, and discuss methods for investigation. Participants will learn about collecting and analyzing different types of evidence, conducting literature searches, dealing with human subjects' requirements, and selecting venues for presenting or publishing their work. With the presenters' guidance, participants interactively select and transform a teaching problem of their own into a question for scholarly investigation and identify several types of evidence to gather. Participants will be introduced to the importance of Boolean network models in modern biology. They will learn how to build Boolean models and will work in small groups to experience how to use such models to describe, simulate, and control the dynamics of complex biological systems. Participants will learn how to work with the web-based software systems DVD and ADAM for visualization and analysis of Boolean models and how to utilize the materials in courses that do not require Calculus. We will conclude with a discussion on the advantages of Boolean models as tools for an early introduction to modeling. Raina Robeva, Sweet Briar College Robin Davies, Sweet Briar College 3. Enhancing Conceptual Understanding of Multivariable Calculus using CalcPlot3D for Visualization and Exploration It is difficult for students to develop an accurate and intuitive understanding of the geometric relationships of calculus from static diagrams alone. This is especially true for the 3D concepts of multivariable calculus. In this course, we will explore ways to help students make these connections by visualizing multivariable calculus using CalcPlot3D, a versatile applet developed with NSF funding (NSF-DUE-0736968). Participants will learn how to customize this applet to create demonstrations and guided exploration activities for student use. Images created in this applet can be pasted into participants' documents. See Basic HTML experience is helpful. Bring a Java-enabled laptop. This session is designed to support mathematicians interested in implementing an inquiry oriented curriculum. By inquiry-oriented we mean that the students are engaging in authentic mathematical inquiry and the teachers are actively involved in inquiring into students' mathematical thinking. This mini-course will have two components. In the first component participants will engage with mathematical tasks from 3 different research-based inquiry oriented curricula that have been developed for Linear Algebra, Differential Equations, and Abstract Algebra. The goals of this component are to familiarize participants with the curricular tasks, the nature of the instruction, and common ways of student thinking. The second component will focus on high-leverage teaching practices that can be used in any inquiry-oriented setting. Examples of such practices include leading whole class discussions and launching instructional tasks. The goal of this component is to provide instructors with opportunities to develop some of the necessary teaching practices needed to implement inquiry-oriented curricula. Estrella Johnson, Virginia Tech Karen Keene, North Carolina State University Christine Andrews-Larson, Florida State University 5. Teaching Linear Algebra with GeoGebra: Making Connections between Algebra and Geometry Participants will work with GeoGebra applets supporting instruction in elementary Linear Algebra. The workshop will consist of a) an overview of the topics and design, incorporating activities fostering connections between algebra and geometry; b) participant work with selected applets, including a very short introduction to GeoGebra; c) discussion of possible pedagogical approaches incorporating the applets; d) a look at some related application problems; e) summary of preliminary evaluation results; f) wrap-up, including remarks and suggestions by participants. Links to further freely available resources will be provided. James D. Factor, Alverno College Susan F. Pustejovsky, Alverno College This minicourse will permit participants to experience SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations, an online community of teachers and learners of differential equations who use modeling and technology throughout the learning process. Participants will share several learning opportunities using SIMIODE materials; develop models from the student perspective; engage in collegial activities about uses of SIMIODE modeling scenarios; and initiate the creation of their own teaching scenario contributions to SIMIODE through partnering with other participants in and after the minicourse. The web home for SIMIODE is at
Resources For MATLAB Help SCHOOL OF ENGINEERING Need help with MATLAB? MATLAB is a computer program designed for technical calculations. Its name is an abbreviation of "Matrix Laboratory." MATLAB allows users to implement calculations in relatively short programming time. When these calculations have been performed, they can be visualised by means of several plot-routines. If you're just starting out with MATLAB, here are a few useful links: The Eindhoven University of Technology has developed a very nice tutorial for MATLAB. This is good for folks who want to simply jump in with a separate open MATLAB window.
This course is organized around a series of intertwined themes each of which has aspects that are pertinent to primary, secondary and post-secondary mathematics as well as to mathematics as it is employed by those who use it in diverse ways in the pursuit of their livelihoods. These themes are · mathematical objects and actions, · mathematics as a tool for understanding one's world, · mathematics as an intellectual undertaking in its own right, · learning mathematics and/or making mathematics, · meaningful assessment of mathematical attainment, · mathematics and culture - how universal is the subject? There will be both assigned readings and problems in the course. Students will be evaluated on the basis of participation in class discussion and problem-solving sessions as well as a final presentation. This course meets the requirement for a graduate level course in mathematics for purposes of certification. The course is limited to math students in the Midcareer Math and Science Program and math concentrators in the Teaching and Curriculum Program. Mathematics students in MCMS and TAC are expected to enroll in the course. The permission of the instructor is required. Can Technology Help Us Make The Mathematics Curriculum Intellectually Stimulating and Socially Responsible? - Schwartz (paper on reserve in library and available for purchase from ETC secretary in Nichols House). Shuttling between the Particular and the General: Reflections on the Role of Conjecture & Hypothesis in the Generation of Knowledge in Science and Mathematics, J.L.Schwartz, in Software Goes to School, Perkins, Schwartz, West & Wiske, eds. Oxford University Press, 1995

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