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Assessment Materials in Maths for Economists MathCentre is a very large repository of tutorial videos, interactive assessments and PDF handouts to help with maths topics, roughly at A-level. This link is to a range of topics selected as relevant to Economics. The materials are categorised by area (such as Algebra, Arithmetic and Differentiation) and by individual topic. Fowad Murtaza, University of Essex, Domenico Tabasso, University of Essex This course webpage supports an introductory module on quantitative economics as taught by Fowad Murtaza and Domenico Tabasso at the University of Essex in 2009/10. It introduces students to the methods of quantitative economics, i.e. to how data are used in economics. Beginning from an elementary level (assuming no background in statistics), the course shows how economic data can be described and analysed. The elements of probability and random variables are introduced in the context of economic applications. The probability theory enables an introduction to elementary statistical inference: parameter estimation, confidence intervals and hypothesis tests. With these foundations, students are then introduced to the linear regression model that forms a starting point for econometrics. It includes a course outline / handbook, lecture presentations, lecture notes, coursework assignments, problem sets with solutions and statistical data. Mathematics for economists is a course webpage produced by Dieter Balkenborg of the University of Exeter, the 2008 version of the course was taught by Juliette Stephenson. The material includes lecture slides, class exercises and solutions, homework tasks, and exam papers, usually made available as PDF files. Also includes links to previous versions of the course stretching back to 2001. This is an online tool that creates paper exams in the key mathematical skills required for Economics. It generates questions randomly, lets you choose which ones to include and then print out separate question and answer sheets.
Intermediate Algebra (Paper) - 4th edition Summary: Offering a uniquely modern, balanced approach, Tussy/Gustafson/Koenig's INTERMEDIATE ALGEBRA, Fourth Edition, integrates the best of traditional drill and practice with the best elements of the reform movement. To many developmental math students, algebra is like a foreign language. They have difficulty translating the words, their meanings, and how they apply to problem solving. Emphasizing the "language of algebra," the text's fully integrated learning pr...show moreocess is designed to expand students' reasoning abilities and teach them how to read, write, and think mathematically. It blends instructional approaches that include vocabulary, practice, and well-defined pedagogy with an emphasis on reasoning, modeling, communication, and technology44368 Good condition INSTRUCTOR EDITION of Book! May have highlighting and or stickers on front and back cover! All day low prices, buy from us sell to us we do it all!! $9.45 +$3.99 s/h Acceptable SellBackYourBook Aurora, IL 14390443689.45 +$3.99 s/h VeryGood SellBackYourBook Aurora, IL 1439044368 Item in very good condition and at a great price! Textbooks may not include supplemental items i.e. CDs, access codes etc... All day low prices, buy from us sell to us we do it all!! $9.4751
Standard POW Write-Up Intent This reference page introduces students to Problems of the Week and to the standard POW write-up. Students will also refer to this reference page throughout the year to aid with their POW write-ups. Mathematics Communicating about mathematical thinking is an important part of doing mathematics. This reference page is designed to support students' written communication about their findings when exploring large mathematical problems. Stating the problem, discussing one's methods, and concluding succinctly and with justification, so that a reader will understand what has been written, should be the goal of every student writer. By suggesting extensions to the problem, students will be saying that the mathematics has not been fully explored, given the time constraints. Their self-assessment will be an evaluation of the effort and quality of their work, what they take pride in, and what they wish they could have done better. Progression Initially, this reference page will support students as they assemble a paper that communicates the work they did and what they learned. As they become more comfortable with the process of writing about mathematics, the page should be returned to and discussed occasionally. It will prompt students to think more deeply and to share ideas with other students about what each section of the POW write-up means, to evaluate each others' papers, and to focus on improving portions of their own
Advertising Get help with inequality word problems and then put what you learn into practice with practice problems. Use Education.com to study math word problems. Get Linear Inequality Applications help and reviews then put what you learn into practice with practice problems. Use Education.com to study algebra. Algebra word problems are very useful to solve real-life problems. You CAN do them. Remember the famous words of Albert Einstein "Do not worry about your difficulties ... Description: In this course we will investigate what causes inequality between women and men: how does it arise, why does it take different forms, why does it ... An inequality is a statement about the relative size and used to compare two statements. Math problems contain <, >, <= and >= are called inequalities.
General Math Workbook This workbook consists of practice problems based on essential fundamental math concepts focusing primarily on number sense standards from grades one through six. The 80 problem... More > sets are designed to work in tandem with our General Math Curriculum but can also be utilized to remediate basic math ideas. For curriculum information, please contact us at info@ssformath.com< study guide provides parents, teachers and students with multiple opportunities to practice and master the math content areas on the CAHSEE. The lessons use plain language to define academic... More > concepts and simplify seemingly complicated ideas within the California state standards. The topics covered within the workbook mirror the test itself: number sense, statistics, data analysis and probability, measurement and geometry, algebra and functions, mathematical reasoning and algebra I. All questions are formatted to match the CAHSEE and there are three complete practice tests included. This is the ideal solution for tutorial, home study or independent study students " and also discusses the continuum hypothesis. Invites the reader to form his own unbiased opinion based on his own thinking and understanding and expresses an interest in the general consensus of opinion on this issue.< Less THE present work is essentially one of constructive criticism. It is, we believe, the first attempt made on any extensive scale to examine critically the fundamental conceptions of Mathematics as... More > embodied in the current definitions. The purpose of our examination is not solely or even chiefly to show the presence of error, but to pro mote the development of a more scientific doctrine. In expounding our own views we have often been obliged to find fault with those of others; but we have not gone out of our way for the sake of mere criticism; we have merely cleared away false doctrine preparatory to replacing it with true.< Less From the PREFACE: ""The present book is intended, as far as possible, to give an exact insight into the theory of Relativity to those readers who, from a general scientific and... More > philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics. The work presumes a standard of education corresponding to that of a university matriculation examination, and, despite the shortness of the book, a fair amount of patience and force of will on the part of the reader. The author has spared himself no pains in his endeavour to present the main ideas in the simplest and most intelligible form, and on the whole, in the sequence and connection in which they actually originated. In the interest of clearness, it appeared to me inevitable that I should repeat myself frequently, without paying the slightest attention to the elegance of the presentation." -Albert Einstein< Less How better to learn the Special Theory of Relativity and the General Theory of Relativity than directly from their creator, Albert Einstein himself? In Relativity: The Special and the General Theory,... More > "The present book is intended," Einstein wrote in 1916, "as far as possible, to give an exact insight into the theory of Relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics."< Less
Beginning Algebra (Gustafson/ Karr/ Massey) 9780495831419 ISBN: 0495831417 Edition: 9 Pub Date: 2010 Publisher: Brooks Cole Summary: Gustafson, R. David is the author of Beginning Algebra (Gustafson/ Karr/ Massey), published 2010 under ISBN 9780495831419 and 0495831417. Three hundred twenty eight Beginning Algebra (Gustafson/ Karr/ Massey) textbooks are available for sale on ValoreBooks.com, one hundred fifty used from the cheapest price of $38.94, or buy new starting at $218 was very useful except for the teaching technique of my instructor. Math isn't my strong point. This book gives great examples that guides you to understanding. I do recommend this book. This book gives great examples and also gives answers in the back to reference to. This does not mean to misuse this information because I am certain your instructor will want work show for the answers.
Product Description Mathematical Reasoning helps your child devise strategies to solvea wide variety of math problems. These books emphasize problem solvingand computation to build the math reasoning skills necessary for success inhigher level math and math assessments. This book written to the standardsof the National Council of Teachers of Mathematics. Book 2 is supplemental at the higher grade levels. These highly effective activities take students far beyond drill-and-practiceby using step-by-step, discussion-based problem solving to developa conceptual bridge between computation and the reasoning required forupper-level math. Activities and units spiral slowly, allowing students tobecome comfortable with concepts but also challenging them to continuebuilding their math skills. Publisher: The Critical Thinking Company Format: 296 pages, paperback ISBN: 978-0-89455-402-5
Teach Yourself Trigonometry Book Description: Teach Yourself Trigonometry is suitable for beginners, but it also goes beyond the basics to offer comprehensive coverage of more advanced topics. Each chapter features numerous worked examples and many carefully graded exercises, and full demonstrations of trigonometric proofs are given in the answer key
Using the Cauchy-Schwarz inequality as the initial guide, this text explains the concepts of mathematical inequalities by presenting a sequence of problems as they might have been discovered, the solutions to which can either be found with one of history's great mathematicians or by the reader themselves.
How might Hercules, the most famous of the Greek heroes, have used mathematics to complete his astonishing Twelve Labors? From conquering the Nemean Lion and cleaning out the Augean Stables, to capturing the Erymanthean Boar and entering the Underworld to defeat the three-headed dog Cerberus, Hercules and his legend are the inspiration for this book... more... Mathematical Applications and Modelling is the second in the series of the yearbooks of the Association of Mathematics Educators in Singapore. The book is unique as it addresses a focused theme on mathematics education. The objective is to illustrate the diversity within the theme and present research that translates into classroom pedagogies.The book,... more... As a result of the editors' collaborative teaching at Harvard in the late 1960s, they produced a ground-breaking work -- The Art Of Problem Posing -- which related problem posing strategies to the already popular activity of problem solving. It took the concept of problem posing and created strategies for engaging in that activity as a central theme... more... The new edition of this classic book describes and provides a myriad of examples of the relationships between problem posing and problem solving, and explores the educational potential of integrating these two activities in classrooms at all levels. The Art of Problem Posing, Third Edition encourages readers to shift their thinking about problem... more... Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other areas. The book gives an overview of major results, methods and ideas of convex and discrete geometry and its applications. Besides being a graduate-level introduction to the field, it is a practical source... more... solution each and every time, no matter the kind or level... more... The first two chapters of this book are devoted to convexity in the classical sense, for functions of one and several real variables respectively. This gives a background for the study in the following chapters of related notions which occur in the theory of linear partial differential equations and complex analysis such as (pluri-)subharmonic functions,... more...... more...
Business MathBUSINESS MATH, 17E provides comprehensive coverage of personal and business-related mathematics. In addition to reviewing the basic operations of arithmetic, students are prepared to understand and manage their personal finances, as well as grasp the fundamentals of business finances. BUSINESS MATH, 17E prepares students to be smart shoppers, informed taxpayers, and valued employees. Basic math skills are covered in a step-by-step manner, building confidence in users before they try it alone. Spreadsheet applications are available on the Data Activities CD, and a simulation activity begins every chapter. Chapters are organized into short lessons for ease of instruction and include algebra connections, group and class activities, communication skills, and career spotlights.
fundamental goal in Tussy and Gustafson's PREALGEBRA, Third Edition is to teach students to read, write, and think about mathematics through ...Show synopsisThe fundamental goal in Tussy and Gustafson's PREALGEBRA, 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 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.Hide synopsis This textbook is clear, concise, and does a great job of demonstrating how math principles relate to real world applications. It is well organized and encourages learning by repetition, which allows the student to master each new process before moving on. While it is intended as a college textbook,
Fundamentals of Algebraic Modeling : An Introduction to Mathematical Modeling with Algebra and ...FUNDAMENTALS OF ALGEBRAIC MODELING 5e presents Algebraic concepts in non-threatening, easy-to-understand language and numerous step-by-step examples to illustrate ideas. This text aims to help you relate math skills to your daily as well as a variety of professions including music, art, history, criminal justice, engineering, accounting, welding and many others. A Review of Algebra Fundamentals Mathematical Models Real Numbers and Mathematical Equations Solving Linear Equations Formulas Ratio and Proportion Percents Word Problem Strategies Graphing Rectangular Coordinate System Graphing Linear Equations Slope Writing Equations of Lines Applications and Uses of Graphs Functions Functions Using Function Notation Linear Functions as Models Direct and Inverse Variation Quadratic Functions and Power Functions as Models Exponential Functions as Models Mathematical Models in Consumer Math Mathematical Models in the Business World Mathematical Models in Banking Mathematical Models in Consumer Credit Mathematical Models in Purchasing an Automobile Mathematical Models in Purchasing a Home Mathematical Models in Insurance Options and Rates Mathematical Models in Stocks, Mutual Funds, and Bonds Mathematical Models in Personal Income Additional Applications of Algebraic Modeling Models and Patterns in Plane Geometry Models and Patterns in Right Triangles Models and Patterns in Art and Architecture: Perspective and Symmetry Models and Patterns in Art, Architecture, and Nature: Scale and Proportion
From... Math in the "real world" happens all the time, and it can involve everything from buying a car to following a simple (or complex) recipe. The "Math in Daily Life" site offers up a series of interesting ways to get... Created by Joanna DelMonaco and Dona Cady at Middlesex Community College, this resource presents the basics of ratio and proportion as they relate to the visual arts during the Classical, Renaissance, and Modern... Created by artist Cynthia Wilson at Spokane Falls Community College, this lesson combines art, geometry, and algebra to create two-dimensional models for abstract paintings. On this page, visitors will find a very... Created by artist Melissa Tomlinson Newell and mathematician Deann Leoni, this page presents lecture-studio courses in both 2-dimensional and 3-dimensional design. These courses allow students to explore elements and...
1 APStatistics Syllabus 2010-2011 COURSE DESCRIPTION APStatistics is the high school equivalent of a one semester, introductory college statistics course. Introduction Th ese Calculator Notes are written to help you eff ectively use the Texas Instruments TI-83 Plus and TI-84 Plus graphing calculators to support ... APSTATISTICS SYLLABUS 2008-2009 APSTATISTICS COURSE OUTLINE Prerequisites: All students each year come into APStatistics after taking minimum Algebra 2 the ... APStatistics - Syllabus Course Overview This course covers all topics included in the APStatistics topic outline as it appears in the APStatistics Course ... APStatistics 2006 Scoring Guidelines Form B The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose ... CREEKVIEW HIGH SCHOOL APSTATISTICS COURSE SYLLABUS 2009-2010 Course Design This APStatistics course is taught as an activity-based course in which students actively ... Syllabus -2009-2010.pdf APStatistics Syllabus Course Material Course Design One of the greatest differences between teaching statistics and teaching most other mathematics courses is the flexibility ... Syllabus.pdf
Development of theoretical tools for rigorous mathematics; Topics include: proof techniques, sets, logic, functions, relations, countable and uncountable sets. This course is designed to give students an introduction to the major and to provide the basic knowledge, overview and foundation for the curriculum.
Learn Mathematics Covers computational alternatives, such as mental computation, estimation, written techniques, and calculators. Emphasizes problem solving, the most ...Show synopsisCovers computational alternatives, such as mental computation, estimation, written techniques, and calculators. Emphasizes problem solving, the most important skill in mathematics. Demonstrates effective classroom practices while providing a look into a variety of mathematical lessons at different grade levels. Cites and discusses specific books that can be used to complement and supplement mathematics learning.Hide synopsis Description:100% BRAND NEW ORIGINAL US PAPERBACK STUDENT 10th Edition / ISBN...100% BRAND NEW ORIGINAL US PAPERBACK STUDENT 10th Edition / ISBN-10: 111800180X / Mint condition / Never been read / Shipped out in one business day with free tracking. This book is so informative, it is a must for children who need to learn math. It has so many different and unqiue ways for children of all ages! I would strongly recommend this book! It's great for teachers and parents
Summary: CONTEMPORARY MATHEMATICS FOR BUSINESS AND CONSUMERS, BRIEF is a 14-chapter educational adventure into today's business world and its associated mathematical procedures. The book is designed to provide solid mathematical preparation and foundation for students going on to business courses and careers. It begins with a business-oriented review of the basic operations, including whole numbers, fractions, and decimals. Once students have mastered these operations, they a...show morere introduced to the concept of basic equations and how they are used to solve business problems. From that point, each chapter presents a business math topic that utilizes the student's knowledge of these basic operations and equations. In keeping with the philosophy of "practice makes perfect," the text contains over 2,000 realistic business math exercises--many with multiple steps and answers designed to prepare students to use math to make business decisions and develop critical-thinking and problem-solving skills. Many of the exercises in each chapter are written in a "you are the manager" format, to enhance student involvement. The exercises cover a full range of difficulty levels, from those designed for beginners to those requiring moderate to challenge-level skillsBreakTimeBooks
AP Central After beginning the last seven or eight years of both AB and BC Calculus classes with an exploration of local linearity, I am delighted with how well the students respond and with the level of understanding of the concept of derivative that they develop in this unit. It is never the same -- from year to year and from class to class -- and I continue to refine the unit as new questions from students prompt new insights into how to make the conceptual components even more accessible. So it keeps me fresh and excited about teaching as well. In this article, I have included a brief overview that I share with teachers in my summer institutes. I often spend two or three weeks in exploration mode and in having student questions and comments direct "next steps" (which is why the unit is not preprogrammed and thus transferable to the printed page). In recent years, it is often well into week three (of 45-minute classes) before we actually get to developing formal derivative rules or take on concepts/applications related to the derivative. However, in those first weeks, the discussions are rich and much is learned. Note that I do not introduce a formal definition of limit until close to the end of this unit, and I only do so to be sure that students get a glimpse of how the definition "tightens up" the "closeness" issue. In addition, I have tried to outline for you other specific activities (in the section "Next Steps in Local Linearity") that I pick and choose from as the exploration continues. is constant over that interval. Although few functions (other than linear functions) are linear over an interval, all functions that are differentiable at some point where x = c are well modeled by a unique tangent line in a neighborhood of c and are thus considered locally linear. Local linearity is an extremely powerful and fertile concept. Most students feel comfortable finding or identifying the slope of a linear function. Most students understand that a linear function has a constant slope. Our goal should be to build on this knowledge and to help students understand that most of the functions they will encounter are "nearly linear" over very small intervals; that is, most functions are locally linear. Thus, when we "zoom in" on a point on the graph of a function, we are very likely to "see" what appears to be a straight line. Even more important, we want students to understand the powerful implications of this fact! The Derivative If shown the following graph and asked to write the rule, most students will write f(x) = x. This shows some good understanding, but not enough skepticism. If the viewing window [-.29,.29] x [-.19,.19] were known, some students might actually question whether enough is known to conjecture about the function presented. In the viewing window [-4,4] x [-2,2], a very different graph is observed: As teachers, we understand that the first window gets at the idea of local linearity (in the neighborhood of x = 0) of the differentiable function we see in the second window. In fact, the two windows are also supportive of an important limit result: Our ultimate goal, however, is to have students come upon at least an intuitive understanding of the formal definition of the derivative of a function f for themselves. They should be able to say, "Of course!" rather than question, "What is that?" when presented with that formal definition. It is technology that makes this approach possible, and that helps students understand the concept of derivative rather than merely memorizing some obscure (to them) notation. Technology to the Rescue: Discovering Local Linearity of Common Functions Start with a simple nonlinear function, say . Select an integer x-value and have students "zoom in" on that point on the graph until they "see" a line in their viewing window. Ask them to use some method to estimate the slope of the "line" and be ready to describe their process. Most will pick two nearby points and use the slope formula. If they have done as instructed, they should all be finding a slope value very nearly the same. If not, ask them to work in small groups until everyone has agreed on some common, reasonable estimate. This will allow them to check their method and become comfortable with the technology. Next, assign pairs of students their own, personal x-coordinate. In fact, if the class is small, you might assign two or more x-coordinates to each pair. Be sure to assign both positive and negative x-coordinates within an interval, say [-4,4]. Most of the assigned values will be given in tenths. Make a table of results (either on the board or using the statistics capabilities of your overhead calculator). The class should discover on their own that there appears to be a predictable relationship between the x-coordinate and the resulting slope. In fact, they are likely to make a conjecture about the general derivative function without even realizing what they are doing. This conjecture can be confirmed using the difference quotient and an intuitive idea of limit as follows: If a student group was assigned the x-value of a, then they would have predicted the slope of a line containing the point (a,a2). When they zoomed in, a nearby coordinate might have been (x, x2). Thus, their predicted slope would have been , which can be easily simplified to . If x is "very close" to a in value, then the predicted slope should have been almost 2a! Next Steps in Local Linearity Other days are spent on the following activities. I have tried to put them in a logical order, but I really do let the student questions and comments dictate which of these I use and in what order. Some of these explorations make wonderful homework assignments, by the way. When I use them as such, students gather the data and make conjectures, but class discussion always follows to uncover what students are beginning to understand and how they are understanding the concepts. Explore other simple power functions as we did . This is often done as portions of homework assignments. I will often introduce another notation, specifically leading to , and have students confirm conjectures using this notation as well. Thus we review factoring polynomials of the form xn - an and expanding binomial powers of the form (x + a)n in context. Almost always, students will want to know if the pattern they observe will always hold, and thus (to answer that question) we actually prove the Power Rule for positive integers. Explore . This is often done as a class project. I assign each student a decimal value and have them zoom in on the curve at the x-value. They are to find the slope of a good linear model for the graph by using the "zooming in until you think you are viewing a linear function" approach. Then we collect the data and plot the results. I do not try to confirm their conjectures with a formal proof at this point, but they are firmly convinced that Dx(sin x) = cos xat this stage! If the mood seems right, I often lay the groundwork for the Chain Rule by asking them to follow this activity up with one that explores the functions and . We get to think about why there appear to be factors of 2 and , respectively. Have students enter the function in their (TI-83) calculators and explore other functions. Of course, I check to make sure they understand that this allows the calculator to easily do exactly what we have been very tediously doing -- and we get a whole screenful of results. We often begin by verifying that this yields the same "pictures" that we had been painstakingly getting by plotting individual student data with functions already explored above. However, I often begin to insert functions involving other simple transformations, such as , , and . Students quickly recognize many of the patterns that such variations generate, and they do a lot of algebra review in the process of confirming their conjectures -- not to mention developing other derivative rules rather painlessly and within context. Explore . This function is much harder for students to deal with than previous functions, but most students, using the approach above, "guess" that the SlopeFinding function (a.k.a. the derivative) is exponential. Some will even hone in on the constant factor that appears to be the stretch factor involved. There is a wonderful exploration that leads students to discover, with very little help from the teacher, that Dx(bx) = b x 1nb. It's a little too long to include here, but ask questions if you want to know more. Explore functions that aren't differentiable at all points on their domain. (For example, or .) We use these to delve more deeply into the definition of the derivative to find where in the definition we find support for the fact that the derivative does not exist at a particular x-value on each domain. It is here that I often explain the Symmetric Difference Quotient used by the TI-83 to determine derivative values, because that calculator will actually determine a value for and for . This whole exploration raises many questions, and we often take off on tangents (no pun intended) at this point. This is just a sampling of some of the exploring we do, and I hope that this outline has helped clarify why I might spend three weeks on local linearity. In these first weeks, I often (but not always) find myself introducing Newton's Method or L'Hopitals Rule as merely extensions of local linearity. We, of course, always cover using the tangent line to approximate nonlinear function values. And, thinking about tangent lines, students understand that the good linear models they have created throughout the early stages of this unit lead naturally to "tangent lines" that we define to be the best linear models (if they exist) for a function at a particular point. That "best" linear model for f at is the line that contains and that has as its slope. J. T. Sutcliffe holds the Founders Master Teaching Chair at St. Mark's School of Texas in Dallas. A recipient of the Presidential Award for mathematics teaching, as well as Siemens and Tandy Technology Scholars awards, she has served as a member of the AP Calculus Development Committee and as an AP Calculus Table Leader. In addition, J. T. has served on advisory and developmental boards for the College Board Vertical Team and Building Success committees and has also helped develop Pacesetter: Mathematics with Meaning, a teacher professional development project for the College Board.
9780321442321 ISBN: 0321442326 Edition: 9 Publisher: Pearson Summary: Addison Wesley Staff is the author of Problem Solving Approach to Mathematics for Elementary School Teachers - Rick Billstein - Hardcover, published under ISBN 9780321442321 and 0321442326. One hundred twenty three Problem Solving Approach to Mathematics for Elementary School Teachers - Rick Billstein - Hardcover textbooks are available for sale on ValoreBooks.com, nineteen used from the cheapest price of $5.53, or b...uy new starting at $111Textbook-Sound copy, mild reading wear. May or may not have untested CD or Infotrac. May contain highlighting, underlining or writing in text. No international shipping. Purc [more] Textbook-Sound copy, mild reading wear. May or may not have untested CD or Infotrac. May contain highlighting, underlining or writing in text. No international shipping. Purchasing this item helps us provide vocational opportunities to people with barriers to employment.[less] Glued binding. Paper over boards. Contains: Illustrations. Audience: General/trade. Cover has wear with a letter on inside front cover and a label on back cover; pages are unm [more] Glued binding. Paper over boards. Contains: Illustrations. Audience: General/trade. Cover has wear with a letter on inside front cover and a label on back cover; pages are unmarked with some pages having a crease mark. SHIPS NEXT DAY1442321 ISBN:0321442326 Edition:9th Publisher:Pearson Valore Books is the top book store for cheap Problem Solving Approach to Mathematics for Elementary School Teachers - Rick Billstein - Hardcover rentals, or used and new condition books available to purchase and have shipped quickly.
Find a Munster CalculusSome of these concepts include: linear equations, inequalities, graphing, quadratic functions, exponents, logarithmic and exponential equations, and factoring. Algebra 2, also known as Intermediate Algebra, is the next step in the mathematical maturity of a student. Many of the skills learned in Algebra 1 are reviewed during the early stages.
intellectually stimulating set of non-routine algebra problems. The non-routine algebra problems in this text provide a stimulating intellectual workout. By non-routine, I mean that the problems require insight and, in some cases, ingenuity to solve. Rather than teaching you a skill and asking you to practice it, the authors assume that you have already developed those skills and ask you to apply them to unfamiliar and difficult problems. The problems draw upon topics taught in elementary, intermediate, and advanced algebra classes. Those topics include equations and inequalities; systems of linear equations; arithmetic, geometric, and harmonic means; relations and functions; maxima and minima; the relationship between algebra and geometry; sequences and series; combinatorics and probability; number theory; and Diophantine equations. Answers to all the problems in which a numerical answer or an algebraic expression is sought are given in an answer key, which gives you a chance to check your answer before reading the authors' solutions. However, not all those answers are correct. Solutions to all of the principal problems are given in a solution key, which is more reliable than the answer key. However, no solution is given to some of the problems that are variations on or extensions to the principal problems. While the authors label these variations and extensions "Challenges," they are generally no more challenging than the principal problems. The solution key is worth reading even if you have solved a problem correctly. The authors often solve not only the problem at hand but show you solve an entire class of related problems. Reading the solutions is also useful since the techniques developed there can sometimes be applied to subsequent problems in the text. Reading the appendices before commencing work on the problems is advisable since the relationships and techniques discussed in the appendices are useful in solving the problems. The appendices address terminating digits; the remainder and factor theorems; maximum product, minimum sum problems; arithmetic, geometric, and harmonic means; divisibility tests; the binomial theorem; some useful algebraic relationships; and how to write a proof by mathematical induction. Working through this text will enhance your problem-solving skills and extend your knowledge of algebra. The level of difficulty of the problems is similar to those in the American Mathematics Competition (AMC), which is not surprising since Charles T. Salkind was the editor of the American High School Mathematics Examination (AHSME), as the AMC was then known, from its inception in 1950 until his death in 1968. Unlike those problems, these problems are not multiple choice. While in many problems a numerical answer or an algebraic expression is sought, these problems also include proofs and investigations of algebraic relationships. While some editing errors detract from the quality of this text, the quality of the problems makes working through it worthwhile. Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged.
Standards in this domain: Represent and model with vector quantities. HSN-VM.A.2 (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. HSN-VM.A.3 (+) Solve problems involving velocity and other quantities that can be represented by vectors. Perform operations on vectors. HSN-VM.B.4 (+) Add and subtract vectors. Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum. UnderstandHSN-VM.C.9 (+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. HSN-VM.C.11 (+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. HSN-VM.C.12 (+) Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.
This paper describes mathematics problems that can be made in Geogebra using Polya's problem solving phases. We describe three ways to use Polya's phases in Geogebra: explaining, exploring and modeling. As an example, we focus on the derivative of a function using a dynamic worksheet. We present an outline for secondary school teachers to use to explain the geometric interpretation of a derivative at a given point. The five stages of symbolism from Moreno-Armella, Hegedus and Kaput are used to describe the interpretation of the dynamic worksheets. Using these techniques, teachers can help students to visualize mathematical objects and to develop a visual understanding of mathematics concepts and the relationship between them.
Appendix B. Linear algebra - Pg. 335 appendix B: Linear algebra To understand advanced machine learning topics, you need to know some linear algebra. If you want to take an algorithm from an academic paper and implement it in code or investigate algorithms outside of this book, you'll probably need a basic understanding of linear algebra. This appendix should serve as a light refresher or introduction if you've had this material before but it's been a while and you need a reminder. If you've never had this material before, I recommend that you take a course at a university, work through a self-study book, or watch a video. Free tuto- rial videos are available on the internet 1 as well as full recordings of semester-long courses. 2 Have you ever heard "Math is not a spectator sport"? It's true. Working through examples on your own is necessary to reinforce what you've watched oth- ers do in a book or video. We'll first discuss the basic building block of linear algebra, the matrix. Then we'll discuss some basic operations on matrices, including taking the matrix inverse. We'll address the vector norm, which often appears in machine learning,
More About This Textbook Overview The Mathematical Association of America's Committee on the Undergraduate Program in Mathematics (CUPM) is charged with making recommendations to guide mathematical sciences departments in designing undergraduate curricula. Undergraduate Programs and Courses in the Mathematical Sciences: CUPM Curriculum Guide 2004 is based on four years of work, including extensive consultation with hundreds of mathematicians and more than one hundred members of partner disciplines. The Introduction contains six recommendations for departments, programs, and all courses in the mathematical sciences. Briefly, these recommendations direct mathematical sciences departments to: _ understand the student population and evaluate courses and programs _ develop mathematical thinking and communication skills _ communicate the breadth and interconnections of the mathematical sciences _ promote interdisciplinary cooperation _ use computer technology to support problem solving and to promote understanding _ provide faculty support for curricular and instructional improvement Part I elaborates on these recommendations and suggests ways that a department can evaluate its progress in meeting them. Part II contains additional recommendations concerning particular student audiences: _ students taking general education or introductory courses in the mathematical sciences _ students majoring in partner disciplines, including those preparing to teach mathematics in elementary or middle school _ students majoring in the mathematical sciences _ mathematical sciences majors with specific career goals: secondary school teaching, entering the non-academic workforce, and preparing for post baccalaureate study in the mathematical sciences and allied disciplines Many recommendations in CUPM Guide 2004 echo those in previous CUPM reports, but some are new. In particular, previous reports focused on the undergraduate program for mathematics majors, although with a steadily broadening definition of the major. CUPM Guide 2004 addresses the entire college-level mathematics curriculum for all students, even those who take just one course. It therefore provides both encouragement and support for conversations not only among mathematics faculty but also between mathematicians and faculty in other disciplines. CUPM has not prescribed specific methods for implementation nor selected particular models of good practice. However, the online document Illustrative Resources for CUPM Guide 2004 gathers a variety of experiences and resources associated with these recommendations. These examples may serve as a starting point for departments considering enhancement of their programs. Pointers to additional resources, such as websites and publications, are also given
Developmental Mathematics for College Students - With CD - 2nd edition Summary: Tussy and Gustafson's fully integrated learning process is designed to expand students' reasoning abilities and teach them how to read, write, and think mathematically. In this text, students get a thorough review of arithmetic and geometry along with all the topics covered in a standard elementary algebra course. The authors build the strong mathematical foundation necessary to give students confidence to apply their newly acquired skills in further mathematics cour...show moreses, at home, or on the job. ...show less Used - book in POOR condition - cover shows extensive wear - pages soiled from use - has many creased pages - this is the student on a budget money saver copy - we ship immediately - our goal is to se...show morerve you! ...show less $200090.37
Mathematical Thinking and Writing A Transition to Abstract Mathematics 9780124649767 ISBN: 0124649769 Pub Date: 2001 Publisher: Elsevier Science & Technology Books Summary: Constructing concise and correct proofs is one of the most challenging aspects of learning to work with advanced mathematics. Meeting this challenge is a defining moment for those considering a career in mathematics or related fields. Mathematical Thinking and Writing teaches readers to construct proofs and communicate with the precision necessary for working with abstraction . It is based on two premises : composing... clear and accurate mathematical arguments is critical in abstract mathematics, and that this skill requires development and support. Abstraction is the destination , not the starting point. Maddox methodically builds toward a thorough understanding of the proof process, demonstrating and encouraging mathematical thinking along the way. Skillful use of analogy clarifies abstract ideas. Clearly presented methods of mathematical precision provide an understanding of the nature of mathematics and its defining structure. After mastering the art of the proof process, the reader may pursue two independent paths. The latter parts are purposefully designed to rest on the foundation of the first, and climb quickly into analysis or algebra. Maddox addresses fundamental principles in these two areas, so that readers can apply their mathematical thinking and writing skills to these new concepts. From this exposure, readers experience the beauty of the mathematical landscape and further develop their ability to work with abstract ideas. Maddox, Randall A. is the author of Mathematical Thinking and Writing A Transition to Abstract Mathematics, published 2001 under ISBN 9780124649767 and 0124649769. Twenty three Mathematical Thinking and Writing A Transition to Abstract Mathematics textbooks are available for sale on ValoreBooks.com, eighteen used from the cheapest price of $4.61, or buy new starting at $29.189780124649767 ISBN:0124649769 Pub Date:2001 Publisher:Elsevier Science & Technology Books is unbeatable for cheap Mathematical Thinking and Writing A Transition to Abstract Mathematics rentals, or used and new condition books available to purchase and have shipped quickly.
This text from the author team of Aufmann and Nation offers the same engaging style and support for students as the Aufmann College Algebra series, all in a brief format that covers the entire course in a single semester. Interactive learning techniques incorporated throughout the text help students better understand concepts, focus their study habits, and achieve greater success.In this First Edition, the authors have also integrated many components into the textbook to help students diagnose and remediate weak algebra skills. Prerequisite review in the textbook and supporting materials allows students to fill in gaps in their mathematical knowledge, and keeps instructors from having to spend time on review. Extra support also comes from the Aufmann Interactive Method, featuring Try Exercises that allow students to practice math as it is presented and to more easily study for tests. In the seven years since the publication of his first book, Functional Training for Sports, new understanding of functional anatomy created a shift in strength coaching. With this new material, Coach Boyle presents the continued evolution of functional training as seen by a leader in the strength and conditioning field. Helping graphic designers expand their 2D skills into the 3D space The trend in graphic design is towards 3D, with the demand for motion graphics, animation, photorealism, and interactivity rapidly increasing. And with the meteoric rise of iPads, smartphones, and other interactive devices, the design landscape is changing faster than ever.2D digital artists who need a quick and efficient way to join this brave new world will want 3D for Graphic DesignersIf you're familiar with HTML, using the information in Learning PHP, MySQL, javascript and CSS, you will quickly learn how to build interactive, data-driven websites with the powerful combination of PHP, MySQL, javascript and CSS - the top technologies for creating modern sites. This hands-on guide explains each technology separately, shows you how to combine them, and introduces valuable web programming concepts such as objects, XHTML, cookies, and session management. This book assumes familiarity with threads (in a language such as Ada, C#, or Java) and introduces the entity-life modeling (ELM) design approach for certain kinds of multithreaded software. ELM focuses on "reactive systems," which continuously interact with the problem environment. These "reactive systems" include embedded systems, as well as such interactive systems as cruise controllers and automated teller machines. Written for students who need a refresher on Plane Euclidean Geometry, Essentials of Geometry for College Students, Second Edition, incorporates the American Mathematical Association of Two-Year Colleges (AMATYC) and National Council of Teachers of Mathematics (NCTM) Standards on geometry, modeling, reasoning, communication, technology, and deductive proof. To make learning interactive and enjoyable, this new edition includes exciting new features such as Technology Connections and Hands-on Activities. Knowledge of beginning algebra and a scientific calculator are required for this text.
The class meets six times a week: four times in lecture, once in conference, and once in the computer laboratory. You are responsible for any and all material discussed in lecture, conference, and lab. Aside from the 6 hours that you spend in class each week, you should expect to spend at least 8 hours more each week working on your own: reading the book, reading and organizing your notes, solving problems. Conferences: In the Friday conference sessions, you will meet with the Peer Learning Assistant (PLA) for the class. You will be able to ask the PLA questions on the material covered and homework. The PLA may lso give you in-class assignments and review course material. Homework: Written Homework: Problems will be assigned for each section of the book covered and will be posted on the class web page. It is necessary to do, at a minimum, the assigned problems so that you can learn and understand the mathematics. You should do additional problems for further practice. Working the exercises will help you learn, and give you some perspective on your progress. You are welcome to discuss homework problems with one another but you must write up your homework solutions on your own. Be mindful of your academic integrity. Your homework will be collected at the beginning of lecture on the date posted on the course website. Late homework will not be accepted. If you must miss that day's class, you should have your work turned in before class time in order for it to be graded. Work on the problems daily as we go through the relevant topics! Your work should be very legible and done neatly. If the work is not presentable, and is illegible, you will not receive credit for it. Please staple the sheets of your assignment together. Discipline yourself to write clear readable solutions, they will be of great value as review. You need to show both your answer and the work leading to it. Merely having the right answer gets no credit - we can all look them up in the back of the book. Online Homework: There will be occasionally be homework using the online tool WebWork. This is the same software that you used for the Math Placement Exam that you took during the summer. Go to Do not use the WebWork system to email for help on problems for such an email will be sent to all the professors and assistants for all the sections of MA1022! Instead, contact Prof. Weekes directly. Quizzes: Each week, there will be a 15-20 minute in-class quiz emphasizing the most recently covered topics. If you miss a quiz for any reason (illness, travel, etc.), you will receive a score of zero. However, don't worry, the lowest quiz score will be dropped. Make-up quizzes will, thus, never be given. Labs: Each week, students will meet in the computer lab (SH003) with the Instructor's Assistant (IA) who is Dina Rassias. We will use the computer algebra system, Maple V, as a visual and computational aid to help you explore the mathematical theory and ideas of the calculus. You will not be given credit for a lab report if you did not attend the lab. There are no make-up labs. The first lab will be on Nov 6th. The final lab will be on Dec. 11th. Final Exam/Basic Skills Test: On Wednesday 12th December from 7-9 pm, you will have a 2 hour comprehensive final examination. Make arrangements now so that there are no conflicts with the final exam. The Final Assessment will consist of two parts. The first part is the Final Exam which is used in determining your course average score as detailed before. The other part is the Basic Skills Exam. You cannot pass the course if you do not pass the Basic Skills Exam. Students with failing averages in the course are given grades of NR, whether or not they passed the Basic Skills exam. If you pass the Basic Skills component, then your course average will be used by the professor to determine your grade for the course. If you fail the Basic Skills Exam, yet have what the instructor determines to be a course average high enough to pass the course, you will be given a grade of I (incomplete). You will be given the opportunity to re-take the Basic Skills exam at a later date; if you pass it, you will receive the grade that is based on your course average. MAS*H: The university also offers Math and Science Help (MASH) for MA1022. The MASH leader for MA1022 is Katie Picchione and her sessions will be: Tuesdays 7-8pm in the Exam Proctoring Center (EPC) Thursdays 11am-noon in the Academic Resource Center Sundays 8-9pm in the EPC. Academic Dishonesty Please read WPI's Academic Honesty Policy and all its pages. Make note of the examples of academic dishonesty; i.e. acts that interfere with the process of evaluation by misrepresentation of the relation between the work being evaluated (or the resulting evaluation) and the student's actual state of knowledge. Each student is responsible for familiarizing him/herself with academic integrity issues and policies at WPI. All suspected cases of dishonesty will be fully investigated. Ask Prof. Weekes if you are in any way unsure whether your proposed actions/collaborations will be considered academically honest or not. Students with Disabilities Students with disabilities who believe that they may need accommodations in this class are encouraged to contact the Disability Services Office (DSO), as soon as possible to ensure that such accommodations are implemented in a timely fashion. The DSO is located in the Student Development and Counseling Center and the phone number is 508-831-4908, e-mail is DSO@WPI. If you are eligible for course adaptations or accommodations because of a disability (whether or not you choose to use these accommodations), or if you have medical information that I should know about please make an appointment with me immediately.
Math Center Level 2 1.0.1.2 description Math software for students studying precalculus and calculus. Math Center Level 2 consists of a Scientific Calculator, a Graphing Calculator 2D Numeric, a Graphing Calculator 2D Parametric, a Graphing Calculator 2D Polar, an Integer Calculator, and a Rational Calculator. The Scientific Calculator works in scientific mode. There are options to save and print calculation history, to change font, and standard editing options. Graphing Calculator 2D Numeric is a further development of Graphing Calculator2D from Math Center Level 1. It has extended functionality: hyperbolic functions are added. There are also added new capabilities which allow calculating series, product series, Permutations, Combinations, Newton Binomial Coefficients, and Gauss Binomial Coefficients . Graphing Calculator 2D Numeric has capability to build graphs for first and second derivatives, definite integral (area under curve) and length integral (length of curve). Since these calculations are done numerically, not symbolically, the calculator is called Numeric. Graphing Calculator 2D Parametric is a generalization of Graphing Calculator 2D Numeric. Now x and y are functions on parameter tau. Since all calculations are done twice, for x and y, there was some sacrificing of precision in order to keep speed of calculations. So, although it is possible to build the same graph of y=f(x) in parametric calculator using x=?, y=f(?), the Graphing Calculator 2D Numeric will build it with greater precision. Graphing Calculator 2D Polar is a specialization of Graphing Calculator 2D Numeric. Enhancements: Formulas similar to sin(x)^2 are allowed and handled as (sin(x))^2. Easy-to-use 3D grapher that plots high quality graphs for 2D and 3D functions and coordinates tables. Graphing equations is as easy as typing them down. Graphs are beautifully rendered with gradual colors and lighting and reflection effects. Free Download
9780813631 Curriculum Press Mathematics Level B Emphasizing basic math skills and problem-solving strategies, this teacher-, student-, and parent-friendly K-6 math program provides students with the solid math foundation they need to succeed. Affordable and easy-to-use, with direct instruction embedded throughout these full-year texts can be used on their own or as an outstanding supplement to any math
Girls Get Curves: Geometry Takes Shape Book Description: New York Times bestselling author and mathemetician Danica McKellar tackles all the angles—and curves—of geometry In her three previous bestselling books Math Doesn't Suck, Kiss My Math, and Hot X: Algebra Exposed!, actress and math genius Danica McKellar shattered the "math nerd" stereotype by showing girls how to ace their math classes and feel cool while doing it. Sizzling with Danica's trademark sass and style, her fourth book, Girls Get Curves, shows her readers how to feel confident, get in the driver's seat, and master the core concepts of high school geometry, including congruent triangles, quadrilaterals, circles, proofs, theorems, and more! Combining reader favorites like personality quizzes, fun doodles, real-life testimonials from successful women, and stories about her own experiences with illuminating step-by-step math lessons, Girls Get Curves will make girls feel like Danica is their own personal tutor. As hundreds of thousands of girls already know, Danica's irreverent, lighthearted approach opens the door to math success and higher scores, while also boosting their self-esteem in all areas of life. Girls Get Curves makes geometry understandable, relevant, and maybe even a little (gasp!) fun for girls
A brief description (by chapter) of the book QUATERNIONS & ROTATION SEQUENCES Chapter 01 - Historical Matters The quaternion is presented as an element in the set of all numbers. The history of the quaternion as a hyper-complex extension of the familiar complex number of rank 2 is discussed. Those readers with strong or sufficient mathematical background may wish to peruse the first three chapters rather lightly. Chapter 02 - Algebraic Preliminaries A brief review of some basic algebraic operations, required in later chapters, is presented. Simple but fundamental rotations in the plane, R2 are introduced. Those with a background in these matters may go directly to Chapter 4 or Chapter 5. Chapter 03 - Rotations in 3-space Rotations in the plane are extended and generalized to define rotations in R3. Various notations are adopted, and sometimes used interchangeably in order to emphasize or specifically focus on certain important attributes of rotation operators. Algorithms are developed for relating independent coordinate frames in R3. Chapter 04 - Rotation Sequences in R3 Rotation sequences are defined and developed. Their underlying ideas are extended in some applications in later chapters. The important notions of a closed-loop rotation sequence, and equivalent sequences, fundamental when developing mathematical models for certain applications in kinematics and dynamics, are introduced. Applications of the Aerospace and other Euler angle rotation sequences are considered in some detail in this and later chapters. Chapter 05 - Quaternion Algebra The algebraic properties of the quaternion are defined. The use of the quaternion in rotation operators is developed in detail, and the geometric interpretation of the quaternion-based rotation operator is discussed. This rotation operator is the primary application of the quaternion in applied mathematics. \newpage Chapter 06 - Quaternion Geometry The composite quaternion axis and angle for a two-rotation quaternion operator sequence are determined. When applied to the familiar tracking example, the expected result which was achieved algebraically is confirmed geometrically. Chapter 07 - Algorithm Summary Here we summarize the algorithms which relate the alternative matrix and quaternion rotation operators. Included are direction cosines, Euler angles, quaternion operators, rotation matrices, eigenvalues, and eigenvectors. This gives a more comprehensive view of these matters when addressing applications. Chapter 08 - Quaternion Factors Given composite rotations in either matrix or quaternion form, the factorization of rotation matrices and quaternion rotation operators is investigated. This is motivated by possible real application requirements and/or their constraints. Chapter 09 - More Quaternion Applications Aerospace and other alternative Euler angle sequences are related, using rotation matrices and quaternion operators. Great circle navigation and Orbit ephemeris determination are studied. In this same context, some simple celestial earth-sun models, which explain and model the seasons of the year, are developed. Chapter 10 - Spherical Trigonometry The development of familiar (some not so familiar) formulas in spherical trigonometry are obtained, using rotation sequences of both rotation matrices and quaternion rotation operators. Interesting exercises provide some comparative insight into these analytical alternatives. Chapter 11 - Calculus for Kinematics/Dynamics The time-derivative of the direction-cosine rotation matrix and of the quaternion and the quaternion rotation operator are derived. The propagation of errors through rotation sequences is introduced and developed. Examples are studied. Body axes angular rates are related to their resulting Euler angle angular rates. The perturbation method is introduced as an alternative for deriving various angular rate relationships. Orbit ephemeris and orbit parameter sensitivities are developed and applied in an example, of some current interest, in order to demonstrate the analytical techniques. Chapter 12 - Rotations in Phase Space A new comprehensive view into the solution space for Ordinary Differential Equations is presented. After some preliminary review of the conventional and familiar phase plane techniques, we develop in some detail the R3 geometry of the solution space, within which reside the solutions of all 2nd order ODE's: Linear, Non-linear, Autonomous and Non-Autonomous! Chapter 13 - A Quaternion Process A mathematical model for an electromagnetic six degree-of-freedom transducer, first conceived, defined, developed and patented by the author, is presented in detail. This new technology is used in several USAF Aerospace applications, as well as in a variety of commercial applications. Its design strategy and mathematical model are developed, both in terms of rotation matrices and quaternion rotation operators. Chapter 14 - Computer Graphics The current interest in computer generated images begs for efficient rotation operators or incremental rotation operators. Perspectives on these matters are presented using the quaternion rotation operator. After a review of the canonical computer graphics operators in homogeneous coordinates the design of an application in Virtual Reality is considered. The six degree-of-freedom transducer, which was discussed in Chapter 13, is implicitly required and integrated in this design.
Synopses & Reviews Publisher Comments: This is a logically self-contained introduction to analysis, suitable for students who have had two years of calculus. The book centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration. Topics discussed include the classical test for convergence of series, Fourier series, polynomial approximation, the Poisson kernel, the construction of harmonic functions on the disc, ordinary differential equation, curve integrals, derivatives in vector spaces, multiple integrals, and others. One of the author's main concerns is to achieve a balance between concrete examples and general theorems, augmented by a variety of interesting exercises. Some new material has been added in this second edition, for example: a new chapter on the global version of integration of locally integrable vector fields; a brief discussion of L1-Cauchy sequences, introducing students to the Lebesgue integral; more material on Dirac sequences and families, including a section on the heat kernel; a more systematic discussion of orders of magnitude; and a number of new exercises. Synopsis: "Synopsis" by Springer,
The Oxford User's Guide to Mathematics in Science and Engineering represents a comprehensive handbook on mathematics. It covers a broad spectrum of mathematics including analysis, algebra, geometry, foundations of mathematics, calculus of variations and optimization, theory of probability and mathematical statistics, numerical mathematics and scientific computing, and history of mathematics Oxford English Grammar Course: Advanced: With Answers CD-Rom /by Collectif. Oxford English Grammar Course Basic and Intermediate are revisions and expansions of the highly successful Good Grammar Book and How English Works.
More About This Textbook Overview Make math a snap with ALGEBRA FOR COLLEGE STUDENTS. Using everyday language and lots of examples, Kaufman and Schwitters show you how to apply algebra concepts and ace the test. This volume also comes with Interactive Skillbuilder CD-ROM. This program is packed with over 8 hours of video instruction to help it all make sense. Plus, you'll get the powerful web-based iLrn Homework program that makes your assignments a breeze. Get the grade you need with ALGEBRA FOR COLLEGE STUDENTS. Kaufmann and Schwitters have built this text's reputation on clear and concise exposition, numerous examples, and plentiful problem sets. This traditional text consistently reinforces the following common thread: learn a skill; use the skill to help solve equations; and then apply what you have learned to solve application problems. This simple, straightforward approach has helped many students grasp and apply fundamental problem solving skills necessary for future mathematics courses in an easy-to-read format. The new Eighth Edition of Algebra For College Students includes new and updated problems, revised content based on reviewer feedback and a new function in iLrn. This enhanced iLrn homework functionality was designed specifically for Kaufmann/Schwitters' users. Textbook-specific practice problems have been added to iLrn to provide additional, algorithmically-generated practice problems, along with useful support and assistance to solve the problems for students. Editorial Reviews From the Publisher "Kaufmann/Schwitters textbook, Algebra for College Students remains to be a good textbook for our students. It is clear in its procedural approach; as well as the number of word problems discussed in each section." "Quite frankly, I have used Kaufmann/Schwitters for the last three editions. This probably covers the last 8 years or so. I believe it is the most readable, straightforward algebra text on the market. I have examined the others. None compare to this one." "We found the textbook to be easy to read and there were lots of examples in each section 2000 Very Few Solutions While the student supplement solution book does solve some problems in detail, it does not solve any of the even problems or even give the solutions. I think for the price it reduces the value of the book. Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged.
... Show More 10: Pre-Algebra: from basic number skills to data analysis and probability and on to beginning algebra, this book covers material necessary to pass many educational and occupational tests
South Orange PhysicsIn some curricula, pre-calculus would be more informatively labeled "Algebra 3." It is a last-minute maintenance check-up to ensure that students can perform algebraic operations involving polynomials, radicals, and exponents as will be necessary for calculus. Many students regard course textbo
Basic Math and Pre-Algebra - (rev edition Summary: When it comes to pinpointing the stuff you really need to know, nobody does it better than CliffsNotes. This fast, effective tutorial helps you master core mathematical concepts -- from fractions, decimals, and statistics to graphs, integers, and exponents -- and get the best possible grade. Jerry Bobrow, PhD, is an award-winning teacher and educator. He is a national authority in the field of test preparation. As executive directory of Bobrow Test Preparation Services, Dr. Bobrow has been administering the test preparation programs for most California State Universities for the past 27 years. Dr. Bobrow has authored more than 30 national best-selling test preparation books including Cliffs Preparation Guides for the GRE, GMAT, MSAT, SAT I, CBEST, NTE, ACT, and PPST. Each year he personally lectures to thousands of students on preparing for these important exams. View Table of Contents Introduction. Why You Need This Book. How to Use This Book. Visit Our Web Site. Very good condition book with only light signs of previous use.Sail the Seas of Value $1.99 +$3.99 s/h New GIANTBOOKSALE BAY SHORE, NY 0764563742 SHIPS TODAY!! GREAT BOOK!! $1.99 +$3.99 s/h Good books&more4less Northridge, CA 0764563742 CREASE FO...show moreLD FRONT COVER
Product Details: The two-line display scientific calculator combines statistics and advanced scientific functions and is a durable and affordable calculator for the classroom. The two-line display helps students explore math and science concepts in the classroom. Ideal for: General Math Algebra 1 & 2 Geometry Trigonometry Statistics Science Display Two-Line Shows entries on the top line and results on the bottom line. Scrolling Entry line (top) shows up to 11 characters and can scroll left and right up to 88. Result line (bottom) shows up to a 10-digit answer and 2-digit exponent. Key features for math and science Previous entry Lets you review previous entries and look for patterns.
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 eases you into "trig," starting with angles and triangles. As you progress, you will master essential concepts such as mapping, functions, vectors, and more. You will learn to transform polar coordinates as well as apply trigonometry in the real world. Detailed examples make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce key ideas. It's a no-brainer! You'll learn about: Right triangles Circular functions Hyperbolic functions Inverse functions Geometrical optics Infinite-series expansions Trigonometry on a sphere Simple enough for a beginner, but challenging enough for an advanced student, Trigonometry DeMYSTiFieD, Second Edition, helps you master this essential subject.
CFCC General Education Competencies Will Incorporate All or Some of the Following: Written Communication Understanding Social Structure Oral Communication Problem Solving Critical Thinking Understanding Scientific Concepts & Application Basic Computer Usage OPTIONAL TEXT: You may either purchase the text and access code from the bookstore or you may use the e-book available online after you register into the Course Compass part of your course. The text is Precalculus Algebra and Trigonometry, 4th Edition, Bittinger, Beecher, Ellenbogen, Penna. Addison, Wesley Longman Publishing and an accompanying Student Access Code for MyMathLab. You must have a graphing calculator. Instructions for the TI-83/TI-84 are provided online and in the text; however, all other makes and models will be your responsibility to learn to operate. YOU MUST COMPLETE THE ONLINE ENROLLMENT VERIFICATION NO LATER THAN MIDNIGHT, AUGUST 24TH OR YOU WILL BE ADMINISTRATIVELY WITHDRAWN. COURSE DESCRIPTION: This is the first of two courses designed to emphasize topics that are fundamental to the study of calculus. Emphasis is placed on equations and inequalities, functions (linear, polynomial, rational), systems of equations and inequalities, and parametric equations. This course also includes a laboratory. Emphasis in the lab is placed on experiences that enhance the materials presented in the class. Upon completion of the course, students should be able to solve practical problems and use appropriate models for analysis and predictions. Upon completion of the lab, students should be able to solve problems, apply critical thinking, work in teams, and communicate effectively. COURSE OBJECTIVES: Upon completion, students should be able to: identify whether an equation represents a function; identify the domain and range of a function; evaluate a function; find the inverse of a function; graph linear, polynomial, piece-wise defined, exponential and logarithmic functions, as well as apply basic translation techniques; write the equation of a line incorporating the relationship between parallel and perpendicular lines; solve a multitude of equations manually and graphically, to include but not limited to: linear, quadratic, radical, rational, exponential and logarithmic; analyze rational expressions; identify vertical, horizontal and/or oblique asymptotes as well as any x- and y-intercepts; use technology to fit regression lines/curves to given data; and, be able to distinguish which is the 'best' model; write the equation of a circle in standard form using the midpoint and distance formulas. Identify the center and radius of a circle; determine equivalent rectangular equations for parametric equations and graph parametric equations; solve systems of linear equations EVALUATION: You will have 5 unit tests weighing 11% of your grade each for a total of 50%. THERE ARE NO MAKE UP OR LATE TESTS!IF YOU MISS A TEST, YOU WILL RECEIVE A GRADE OF "0". You may replace the lowest test grade with your final exam grade. You will have 14 online homework assignments which will average 20% of your course grade. THERE WILL BE NO MAKE UP OR LATE WORK. You will have a proctored comprehensive final exam worth 25% of your course grade. You will have two opportunities to take the final exam. The final exam will be given at the Downtown Campus. You must take the final exam to pass the course. THERE WILL BE NO MAKE UP OR LATE HOMEWORK OR LABS ACCEPTED! The grading scale is as follows: 92 - 100 A 84 - 91 B 76 - 83 C 68 - 75 D 67 - below F We will be covering chapters 1 – 5 and sections 9.1, 9.2, and 10.7. ONLINE ASSIGNMENTS: Homework assignments are grouped together containing two or three sections each. The homework is set up for you to have three attempts at each problem. You can enter an answer three times before the system counts that problem wrong, then you can click on "Similar Exercise" at the bottom of the page and try again. If you use the "Help Me Solve This" feature it will count as one of your attempts. You may open and close the homework any number of times prior to the due date and time. Tests must be completed in one setting, you will not be able to close a test and reopen it. Also, there are no aids associated with the tests. This is not a self-paced course. The due dates are final dates, not suggested ones. The technology required to take this course is your responsibility. Computer glitches or problems are not acceptable excuses for late or incomplete work. PROCTORED FINAL EXAM: You have two options for the proctored final exam. You will need to make arrangements at the beginning of the semester to free your schedule of any possible conflicts for one of these dates and time. If you live more than 50 miles from the CFCC campus, you may secure a proctor at your local community college or university to take this exam. The site and proctor must be preapproved by your instructor. Be prepared to present a photo ID before beginning the exam. This exam is comprehensive and contains 15 open ended questions. MATH LAB and LEARNING LAB: Extra help is available at either the MATH LAB or the Learning Lab. The MATH LAB is located in room S-606. You may go there at any time without an appointment, but you will have to fill out a form the first time you go in. The Learning Lab is located in the L building near the Library. You are encouraged to go to the Learning Lab on a regular basis if you are having difficulty with the work. ATTENDANCE: "Students must be in attendance at least eighty (80%) percent of the clock hours of a course to receive credit for the course. Those who do not meet minimum attendance requirements will be given the grade of "F", which will be computed in the students' grade point average as a failing grade." "Attendance in online (Internet) courses is measured not only by the initial log-in (enrollment verification due within the first 8 days of the semester) but also by completion of 80% of the required course work." (CFCC Catalog, page 19) Therefore, you cannot miss any combination of assignments that result in more than 20% of the course work. Students will be allowed two days of excused absence each academic year for religious observances required by the faith of the student. These excused absences will be included in the twenty (20%) percent of allowable clock hour absences. Students are required to provide written notice of the request for an excused absence by completing the Religious Observance Absence form available in Student Development. The completed form must be submitted to the Vice President of Student Development or his/her designee a minimum of ten (10) school days prior to the religious observance. The Vice President of Student Development or his/her designee will notify the instructor within three (3) school days of receiving the request. Students will be given the opportunity to make up any tests or other work missed due to the excused absence and should work with their instructors in advance of the excused absence to delineate how to make up the missed coursework. HONOR CODE: Upon logging onto this course, you are agreeing to complete all graded assignments independently. You will not solicit nor secure assistance on tests or homework assignments. Furthermore, if there is just cause, your instructor may require some or all of your graded assignments to be proctored. STUDENT EMAIL: You have a CFCC email account. Access the website and click on the myCFCC link. You will see the My Classes link, which houses your course websites. You will also see the email icon, which is your student email. Your username is part of your email address: user@mail.cfcc.edu. (Note if you've had a CFCC email address in the past, this one differs because we've changed 'email' to 'mail' in the address.) Your email account may be used for personal or academic reasons, up to three years after you leave the college, and is subject to the CFCC Computer Acceptable Use Policy. Tobacco use is prohibited on all CFCC property. The first offense is a warning and the second offense may result in disciplinary action. DISABILITY SERVICES: If you are a person with a disability and anticipate needing accommodations of any type in order to access or participate in this class, you must contact the Disability Support Services Office (Galehouse Bldg. room A215, 362-7012 or 362-7158), provide the necessary documentation of the disability and arrange for the appropriate authorized accommodations. All information shared with the Disability Support Services Office is protected as confidential. DISCLAIMER: Information contained in this syllabus was, to the best knowledge of the instructor, considered correct and complete when distributed for use at the beginning of the semester. The instructor reserves the right, acting within the policies and procedures of Cape Fear Community College, to make changes in course content or instructional techniques without notice or obligation.
More About This Textbook Overview This fourth volume of Research in Collegiate Mathematics Education (RCME IV) reflects the themes of student learning and calculus. Included are overviews of calculus reform in France and in the U.S. and large-scale and small-scale longitudinal comparisons of students enrolled in first-year reform courses and in traditional courses. The work continues with detailed studies relating students' understanding of calculus and associated topics. Direct focus is then placed on instruction and student comprehension of courses other than calculus, namely abstract algebra and number theory. The volume concludes with a study of a concept that overlaps the areas of focus, quantifiers. The book clearly reflects the trend towards a growing community of researchers who systematically gather and distill data regarding collegiate mathematics' teaching and learning. Editorial Reviews Booknews This collection of essays focuses on student learning of mathematics, primarily calculus but also looks at student understanding of abstract algebra and number theory. Two of the chapters explore, through overviews, differing learning and teaching techniques of France and the United States, especially as they pertain to calculus reform. Other articles explore why students have difficulty applying their knowledge to solving non-routine problems, the lasting effects of the integrated use of graphing technologies in precalculus, and visual confusion in permutation representations
5xx's: Related Names (4) 551 _ _ ‎‡a Bristol‏ 510 2 _ ‎‡a City and Guilds of London Institute‏ ‎‡e Affiliation‏ 551 _ _ ‎‡a London‏ 551 _ _ ‎‡a York‏ Selected Titles Elementary lessons in electricity & magnetism ‎(11) Calculus made easy : being a very-simplest introduction to those beautiful methods of reckoning which are generally called by the terrifying names of the differential calculus and the integral calculus ‎(11)
LinearAlgebra by KennethHoffman & RayKunze ATLAST Computer Exercises for LinearAlgebra by Leon, et al Topic: Introduction to Vectors ... To enable students to use linearalgebra to formulate and solve problems and to communicate solutions. 6. Some LinearAlgebra knowledge from MA 405 will be assumed. If this is your first LinearAlgebra course, you should take MA 405 instead. Text: LinearAlgebra, by Kenneth M. Hoffman and RayKunze, 2nd edition, Prentice Hall, 1971, ISBN: 978-0135367971. A basic result in linearalgebra is that the row and column spaces of a matrix have ... linear functionals and dual spaces, ... KennethHoffman and RayKunze, LinearAlgebra, 2nd edition, Prentice-Hall, Englewood Cliffs, NJ,
This is a calculus textbook at the college Freshman level based on Abraham Robinson's infinitesimals, which date from 1960.... see more This is a calculus textbook at the college Freshman level based on Abraham Robinson's infinitesimals, which date from 1960. Robinson's modern infinitesimal approach puts the intuitive ideas of the founders of the calculus on a mathematically sound footing, and is easier for beginners to understand than the more common approach via limits.The First Edition of this book was published in 1976, and a revised Second Edition was published in 1986, both by Prindle, Weber & Schmidt. The book is now out of print and the copyright has been returned to the author. ״At first blush one might think that of all areas of mathematics certainly arithmetic should be the simplest, but it is a... see more ״At first blush one might think that of all areas of mathematics certainly arithmetic should be the simplest, but it is a surprisingly deep subject. We assume that students have some familiarity with basic set theory, and calculus. But very little of this nature will be needed. To a great extent the book is self-contained. It requires only a certain amount of mathematical maturity. And, hopefully, the student's level of mathematical maturity will increase as the course progresses. Before the course is over students will be introduced to the symbolic programming language Maple which is an excellent tool for exploring number theoretic questions.״ Euclid's Elements form one of the most beautiful and influential works of science in the history of humankind. Its beauty... see more Euclid's Elements form one of the most beautiful and influential works of science in the history of humankind. Its beauty lies in its logical development of geometry and other branches of mathematics. It has influenced all branches of science but none so much as mathematics and the exact sciences. The Elements have been studied 24 centuries in many languages starting, of course, in the original Greek, then in Arabic, Latin, and many modern languages.The text of all 13 Books is complete, and all of the figures are illustrated using the Geometry Applet, even those in the last three books on solid geometry that are three-dimensional. forall x is an introduction to sentential logic and first-order predicate logic with identity, logical systems that... see more The materials here form a textbook for a course in mathematical probability and statistics for computer science students.״Why... see more The materials here form a textbook for a course in mathematical probability and statistics for computer science students.״Why is this course different from all other courses?״ * Computer science examples are used throughout, in areas such as: computer networks; data and text mining; computer security; remote sensing; computer performance evaluation; software engineering; data management; etc. * The R statistical/data manipulation language is used throughout. Since this is a computer science audience, a greater sophitication in programming can be assumed. It is recommended that my R tutorial, R for Programmers, be used as a supplement. * Throughout the units, mathematical theory and applications are interwoven, with a strong emphasis on modeling: What do probabilistic models really mean, in real-life terms? How does one choose a model? How do we assess the practical usefulness of models? * There is considerable discussion of the intuition involving probabilistic concepts. However, all models and so on are described precisely in terms of random variables and distributions.For topical coverage, see the book's detailed table of contents. A textbook that covers the traditional topics studied in a modern prealgebra course, as well as topics of estimation,... see more A textbook that covers the traditional topics studied in a modern prealgebra course, as well as topics of estimation, elementary analytic geometry, and introductory algebra. It is intended for students who (1) have had a previous course in prealgebra, (2) wish to meet the prerequisite of a higher level course such as elementary algebra, and (3) need to review fundamental mathematical concepts and techniques Intermediate Algebra carefully builds on the basics learned in Elementary Algebra and introduces the more advanced topics,... see more Intermediate Algebra carefully builds on the basics learned in Elementary Algebra and introduces the more advanced topics, enhancing it all with with the modern amenities that only a free online text can deliver.It is essential to lay a solid foundation in mathematics if a student is to be competitive in today's global market. The importance of algebra, in particular, cannot be overstated, as it is the basis of all mathematical modeling used in applications found in all disciplines. Traditionally, the study of algebra is separated into a two parts, Elementary and Intermediate Algebra. This textbook by John Redden, Intermediate Algebra, is the second part. Written in a clear and concise manner, it carefully builds on the basics learned in Elementary Algebra and introduces the more advanced topics required for further study in applications found in most disciplines. Used as a standalone textbook, Intermediate Algebra offers plenty of review as well as something new to engage the student in each chapter. Written as a blend of the traditional and graphical approaches to the subject, this textbook introduces functions early and stresses the geometry behind the algebra. While CAS independent, a standard scientific calculator will be required and further research using technology is encouraged. Intermediate Algebra is written from the ground up in an open and modular format, allowing the instructor to modify it and leverage their individual expertise as a means to maximize the student experience and success. A more modernized element, embedded video examples, are present, but the importance of practice with pencil and paper is consistently stressed. Therefore, this text respects the traditional approaches to algebra pedagogy while enhancing it with the technology available today. The importance of Algebra cannot be overstated; it is the basis for all mathematical modeling used in all disciplines. After completing a course sequence based on Elementary and Intermediate Algebra, students will be on firm footing for success in higher-level studies at the college level.
Introductory Mathematics-With Access - 10 edition Summary: This textbook provides students with a solid foundation in basic mathematics, and an excellent preparation for algebra. The format, examples, and problems in this book have been refined through more than 20 years of classroom testing. As with all McKeague titles, his emphasis on study skills and his positive tone toward success are reflected in the presentation. Published by XYZ textbooks67 +$3.99 s/h Good SellBackYourBook Aurora, IL 193636804825.0025.19 +$3.99 s/h VeryGood Blue Fog Books IL Chicago, IL 2010 Soft cover VERY GOOD Book No highlighting or marks in text. Excellent service & fast shipping. t5. $47
More About This Book Pretest The 50-question pretest contains a question for each of the 50 skills most likely to be seen on the GED Mathematics Test. Each question has been organized around the four major content areas of the GED Test. This test is designed to accurately assess which skills require additional study. Each question number is directly correlated to the lesson skill number in the text. Lesson Structure Each lesson is presented in a two-page format. The top of the two-page spread contains the title of the skill. The left page contains instruction and any information relevant to successfully understand the skill. That skill is then applied to an example problem illustrating a step-by-step solution. The right page of the lesson is the GED Readiness page. That page of the lesson is divided into three practice question types: Concept, Procedure, and Application. The bottom of the page references related skills throughout the text. Posttest The posttest in Top 50 Math Skills for GED Success is formatted just like the GED Test, and is designed to assess student's readiness for the GED. An evaluation chart correlates each question to a specific skill as well as to specific review pages within the text. This chart also correlates to the GED Math Satellite book for further instruction and practice. Computation Review Section Students can use the Computation Review section for a quick review of the basic math skills important for GED success. Each math skill is presented with an explanation, examples, and brief practice problems. Other Features Top 50 Math Skills for GED Success contains a detailed Annotated Answer Key, which not only shows the correct answer for each problem in the text but a step-by-step illustration of how the answer was derived. Casio fx-260 instructions are included with an illustration of the calculator face that shows which functions are used on the GED Test. Instructions on using the basic functions and step-by-step examples using the calculator for certain functions are included. An Estimation section illustrates guidelines for estimation using whole numbers, mixed numbers, decimals, and formulas involving Pi. A detailed explanation when to use and when not to use estimation during the GED Test is included along with example problems that illustrate each estimation guideline. Top 50 Math Skills for GED Success contains a special instructional section on the use of Alternative Answer Formats. Illustrations and instructions on using the grids with whole numbers, decimals, and fractions are included as well as right, left, or center justification explanations. An instruction on using the coordinate plane grid
0155923igonometry/Student Solution Manual Problem-solving oriented, the material in this text, is carefully presented in a step-by-step process using numerous examples, detailed solutions, and figures to illustrate the concepts. The organization allows the instructor considerable flexibility in making assignments for the class or individual students. Learning aids include a summary of key terms, definitions, concepts organized by topic, and review
College Prep Algebra 2A Mrs. Manor Contact Information Email: smanor@londonderry.org VoiceMail: 432-6941 x2873 If possible, I prefer to be contacted via email as it is easier to respond in a timely manner. Expectations  Be Ready Be Respectful Be Responsible  Be on time and prepared for class. Expect to work bell to bell.  Math class must be utilized doing math. Materials Bring your textbook (covered); notebook, folder, or binder; scientific or graphing calculator; and a pencil to class EVERY day. NOTE: Other devices cannot be used in lien of an approved graphing calculator. Homework Homework will be assigned almost daily and is due at the beginning of the next class period. Homework will be checked and recorded periodically. To receive full credit, you must make a reasonable attempt to complete each problem AND you must check to see if your answers are correct. Answers to homework are either provided or in the back of the textbook. Incomplete, illegible, unchecked, and answers-only homework will receive no credit. Homework plays a critical role in understanding the concepts of this course. Each homework builds on previous homework – so it is important to do your homework daily and not get behind. If you don't get it – get help – quickly. You will be assigned sections from the book to read periodically. You should read the other sections covered as well to better prepare for class and for deeper understanding. Class Work/GroupWork You will occasionally work on in-class assignments. They must be turned in by the end of the period for full credit. You will periodically work in small groups in and out of class. Some projects require independent thinking by the groups. The entire group must participate to get credit. Homework/Class Work/Group Work Format Copy the original problem from the text onto your paper (not necessary if a worksheet). Beneath the problem – show ALL steps necessary to solve the problem (or provide a detailed written explanation). Don't say, "I did it in my head." I cannot read your mind. I need to see your thinking process on your paper. Clearly identify the answer by circling/boxing. Skip a line and go on to the next problem. All work must be shown AND the work shown must support the answer given. Your final answer should be circled if possible and checked if answers are available. All work must be neat, organized, readable, and in pencil. All answers must include labels/units if appropriate. Name, date, unit, and day are required on all assignments. Reviews A review assignment is given prior to most tests for preparation and practice. Answers are provided. Reviews are not collected. In-class review time must be used to work on the review. Quizzes and Tests Quizzes and tests will be given periodically. They must be done in pencil. Non-pencil assessments will lose one letter grade. There are no retakes. Make-ups are scheduled in accordance with days missed. If absent one day – you have one day to make up. If absent two days – you have two days to make up. Etc. You will lose one letter grade off your score for every day late on make-ups. If you are absent on a review day – you are expected to take the test upon return – so be prepared. All quizzes and tests will be collected and kept in student folders. Attendance/Tardiness Attendance is expected. Reference student handbook for attendance policies. If absent – YOU are responsible for:  getting all missed notes and work  handing in any work due during your absence  scheduling any make-ups for missed tests, quizzes or competencies I will not pursue you about your missed work or make-ups. Unexcused tardiness will not be tolerated. You are allowed one warning for an unexcused tardiness. All subsequent tardies will result in time AFTER school. Class Rules and Regulations Be respectful of self and others. Disrepsect will not be tolerated. Be responsible for your actions. Cheating (as defined in the student handbook) will not be tolerated. Bathroom/locker passes will not be issued while I am teaching unless it is an emergency. Please ask for a pass before class starts or after the lesson. Whenever you leave the room for any reason, you must sign out in the log book and have a pass. Upon returning, sign back into the log book and return the pass. Passes to the café are not allowed. Please do not ask for one. Extra Help Math Lab: The math lab is a resource that can be utilized by all students during lunch and/or study. It is located next to the Main Office (room 146). There is always a math teacher on duty. Extra Help: I am available for extra help on a daily basis with the exception of Tuesdays and an occasional personal appointment. Make sure to let me know what time to expect you. Peer Tutoring: After school every Tuesday in room 157 by Math Honor Society. If you don't get it – GET HELP. Your success depends on
This Office Administration course was created by a team of educators at Florida Community College at Jacksonville to combine business and math. In-depth lessons are provided that address mathematics in consumer finance... Created by Joanna DelMonaco and Dona Cady at Middlesex Community College, this resource presents the basics of ratio and proportion as they relate to the visual arts during the Classical, Renaissance, and Modern... Patty Amick, Cheryl Hawkins, and Lori Trumbo of Greenville Technical College created this resource to connect the art of public speaking with the task of demographic data collection. This course will help students... The American Mathematical Association of Two-Year Colleges (AMATYC) has compiled a collection of mathematics resources related to various subjects and disciplines. ?Math Across the Community College Curriculum? is the... The American Mathematical Association of Two-Year Colleges (AMATYC) has compiled a collection of mathematics resources related to various subjects and disciplines. ?Math Across the Community College Curriculum? is the...
Geometric algebra is a powerful mathematical language with applications across a range of subjects in physics and engineering. This book is a complete guide to the current state of the subject with early chapters providing a self-contained introduction to geometric algebra. Topics covered include new techniques for handling rotations in arbitrary dimensions, and the links between rotations, bivectors and the structure of the Lie groups. Following chapters extend the concept of a complex analytic function theory to arbitrary dimensions, with applications in quantum theory and electromagnetism. Later chapters cover advanced topics such as non-Euclidean geometry, quantum entanglement, and gauge theories. Applications such as black holes and cosmic strings are also explored. It can be used as a graduate text for courses on the physical applications of geometric algebra and is also suitable for researchers working in the fields of relativity and quantum theory. less
Find a Vallejo PrecalculusThe following topics from calculus 2 and calculus 3 can also be covered: Partial differentiation, directional derivatives, total derivative, vector and scalar fields, tangent planes, matrix form of chain rule, line integrals, the gradient, multiple integrals, Green's theorem in the plane, surface
Coryoth asks: "If you're taking computer science then getting as much mathematics as you can is probably a good idea. Ultimately, however, there are only so many math courses you an squeeze in. Given that, what areas of mathematics should we be teaching CS students for maximum benefit? Traditionally university math courses are structured around the needs of the physical sciences and engineering, which means calculus is what gets offered. While a decent calculus course can teach a certain amount of formality in reasoning, wouldn't CS students be better served with a course in mathematical logic and foundations with its greater degree of formal reasoning and obvious connections to fundamental concepts in computer science? Are courses in abstract algebra and graph theory going to be useful to CS students? Should courses in category theory (yes, it applies to computer science) be required of students going on in theoretical computer science? In short — what areas of mathematics are going to be the most useful and most applicable to computer science students? What courses were of the most value to you?" Oops! You do not appear to have javascript enabled. We're making progress in getting things working without JavaScript. You may prefer to switch to Slashdot Classic for now. Some Math greater than Other Math (4, Insightful) For CS students, the fundamentals of discrete math and set theory are probably some of the most important. More focus on these in a CS context would be helpful to people such as myself who find math more interesting when it has a purpose. I did not mind the physics and statistical math courses. I could see the point behind them clearly. But doing math just for the sake of doing math never seem to have a purpose. Re:Some Math greater than Other Math (3, Insightful) Yep, operations research, cryptography, matrix algebra, stats, logic and some physical stuff like trig and calculus were all in my CS degree (89-91). I don't remeber much about the formulas but it has served me well to know what can and can't be done and why. When I was in college (90 to 94) at an engineering school, my CS degree required Calculus through the third one (because it was in the Engineering department) and statistics (because otherwise, noone in their right mind would ever take statistics) and an elective "math" the your advisor would point you towards based on what type of work you were interested in doing. I think this approach has worked out well for me. Re:It realy doesn't matter (4, Informative) I am VP of software development at a software company. I hire a lot of recent graduates (and am always looking for more good talent). What I look for as a starting point is a solid understanding of how programs work, and enough programming experience that I am not teaching the basics. Experience with both lower level languages (C++) and higher level languages (Java, VB, etc) is required just to get past HR. Also, knowledge of the context (networks, operating systems, databases) is required. The above just gets you to the point that HR will really read your resume, and possibly pass it on to me. Once I get a resume, I assume those skills are present. What I look for are things that are more intangible. Passion (The love of the art of programming) Communication skills (The ability to understand and be understood, both written and verbal) flexibility (If the decision is made to accomplish something that does not agree with your idea of the best way, attack the problem as if you believe it truly is the best way. This does not mean silencing your opinion before a decision is made) teamwork, cooperation, social skills. I don't want prima donnas Potential. Hard to judge in a recent grad, but I want people who strive to accomplish more than their current position. Business Knowledge. Since our software is designed to solve business problems, it is essential that all of our staff understands what a business is. The graduates that can show these traits are very likely to be hired. Those that don't, won't. Some of these characteristics can be taught in formal courses, others have more to do with personal development and maturity. Specific languages can be taught to the right person very quickly. A solid background in math is also essential (Algebra, Statistics and Calculus) but I have yet to use n-dimensional calculus in non-cartesian space for practical business applications. computational statistics (3, Insightful) Well, perhaps because it has something with what I do, but I was surprised computational statistics isn't on that list. Perhaps it's the other way around, statisticians need to learn to program. Regardless there is quite a bit of overlap. This is also one of the few areas remaining where the speed of your program actually matters. Re:computational statistics (4, Interesting) I'm willing to assert something stronger. Instead of requiring undergrads to spend a year learning calculus, the requirement for all undergrads should be basic statistics. In the decade or so since I completed a math degree, I've used calculus only rarely (the intended implication being that even a mathematician might find little need for calculus). Statistics, on the other hand, are needed to correctly interpret newspaper articles. Re:computational statistics (2, Interesting) I think most everyone would be improved by more exposure to statistics. Business is one degree that most needs more calculus (most of what businessmen deal with is rates of change). For example the income statement contains the first derivative of most of the balance sheet, but I've never heard the term even broadly hinted at in any business classes. Re:computational statistics (1) I had both. I've used far more calculus than statistics over the past 20 years. But what I've used most is linear algebra. I suppose it depends upon what you do as to what you'll need. Since what I do now is radically different than what I'd thought I'd be doing when I graduated, I'd say requiring a basic set of math skills (algebra, calculus, statistics) is appropriate. Re:computational statistics (1) I agree that statistic are needed. In my undergraduate CS work, though, we couldn't escape without BOTH a year of calculus AND a semester of probability and statistics. I've found them both very useful. Actually, in my work, there is a lot of calculation of rates of flow and such, so the calc has been more useful than the statistics. Stats, in general, though, are just as important, especially when it comes to computer learning applications. I think that what math will come in handy is heavily dependent on where you end up in your career, but having the right tools will also help steer you in a good direction in that career. And, definitely, if you want to go further in school than a bachelor's, you'll need all the math you can get. The problem at most universities is that they can only really have so many required courses and still have students graduating on time, so they leave the rest up to electives. While I'm on the subject, I'd recommend discrete math, linear algebra, and at least one course that teaches you the fundamentals of logic and proof writing. And, like I said, calculus and statistics. Re:computational statistics (5, Interesting) In my biased opinion, that is a course that MUST NOT be taught to CS students unless they have the full one year worth of Probability Theory before that. In fact it is a course that MUST NOT be taught to any scientific student who has not taken a full probability theory course first. Unfortunately, many universities especially in the US tend to do that - teaching stats without teaching the probability theory which makes them possible. As far probability theory itself is concerned its knowledge is essential for nearly any task in CS starting from an OS and all the way to transaction systems especially if the system is operating under a resource constraint. The time your request traverses the system, the completion rate, etc are all described by Markov chains and there is a appallingly low percentage of CS people who actually know them and can understand how their systems behave. There is no way in hell you can optimise or even understand a complex system without this knowledge. Unfortunately most Unis now prefer to use this time to teach marketing buzzword bollocks also known as Unified Process, Agile, etc instead. The second most important math area for a CS student is possibly optimal control. This one is also nowdays omitted from some university curicullae which IMO is an absolute madness. Re:computational statistics (1) In my experience, statistics has always been combined with probability. I agree that statistics is useless without probability. I'll amend my assertion to state that instead of (a year of) calculus, undergrads should be required to have (a year of) probability and statistics. ballpark (4, Informative) probability (heavily skewed towards combinatorics), number theory, geometry (the plain euclidean one because this is really the best way to train a human brain for logic that's been found in the past few thousand years), calculus (of 1 and 2 variables... the rest is a waste of time unless you are specifically training programmers whose skills will be heavily computational in nature), linear algebra, and formal logic. Category theory (which is really just object-oriented math) could be familiarized with, but showing its applications would be more useful than going rigourously through proofs. Re:ballpark (1) Add discrete mathematics (especially graph theory) to that list. I'm quite surprised you didn't mention it in the first place, and even more surprised that you mentioned calculus of 2 variables instead. That's a whole lot less useful than being able to think about problems in graph terms. Re:ballpark (1) I mentioned calculus of two variables for a very specific reason. You cannot understand the gaussian curve without it. "Discreet math" was covered under combinatorics which I said should be covered in probability. Graph theory (from combinatorial rather than topological point of view) would be part of an extensive linear algebra course (or series of courses). I should have made it clear that I think that rather than having the usual Calc 1,2,3 there should be Calc 1,2 and Linear Algebra 1,2,3. What I am on the fence about is whether or not abstract algebra would be too far off field. Certainly it would help to understand linear algebra on a much deeper level... but it might be too deep for anyone who wants to concretly compute network-traversal times to care. Re:ballpark (1) Either you don't know or understand category theory, or you don't know what object-oriented means. At best you could claim your statement is a ridculous simpification (on par with "Algebra (which is really just math with letters)"), at worst its a fundamental misunderstanding of categry theory due to, most likely, a lack of ever actully having dealt with it. Re:ballpark (1) I live to learn. Do tell what differences they have. I am sure if you try to write them out coherently, you will find that the differences are in details. By as an abstraction (something the removes the details to look ideas pertenant to a subject matter discussed) they are similar in that they deal with study of relations (in plain english rather than math sense of the word) between objects. Therefore, to think about either cat theory or obj oriented programming one may adapt a very similar method of thinking. I was not comparing them feature-to-feature. I was saying that thinking about concrete categories may be a useful training for thinking about classes. Thinking about categories ("at large", so to speak) may be a useful training for thinking about abstract classes. I liked oenology, personally (1, Insightful) Personally, I found a great deal of education in my oenology courses. Well, they weren't really courses. Or at school. Mostly at home with friends. But to get back to your question, I don't find any of the math that I took applicable to any of the work I do. I don't write 3D software, music synthesizer software, or calculate missile trajectories, so all that math is lost on me. The most applicable mathy CS thing I learned was covered in an hour regarding big O notation. Along with a good course on data structures, that has been the most beneficial thing I can say I learned. But that is besides the point. What you do in the real world doesn't necessarily have to be relevant when choosing curriculums (curriculi? curricula?) Give them the works! Everything from Calc through Topo and everything in between. Not all of them are going to grow up to be rocket scientists, but so what? The more knowledge you give these kids the better. I'm not saying you need to wipe them out or flunk them out or even use the math as a weeding tool, just that what you want to do is give them the tools to look at other sciences and not be befuddled. There's nothing worse than a CS graduate that doesn't have a full grasp of math. Anonymous Coward \| more than 6 years ago All of them! (1) Seriously, what useful work ever gets done without mathematics? Maybe pushing bulk data around into and out of databases, but who other than a C-grade CS student in a third world outsource farm is interested in doing that? Re:All of them! (1) That's because there are so few CS graduates that actually can do much more than just push the data around. In my old University, the CS students took different classes than the engineering students, with focus on discrete math, statistics, and matrix math (such as methods for solving complex problems using matrices). Basically, they learned how to perform the real math that computers and programs use. Could there be more? Probably, but most higher match classes require a very good background in calculus. Re:Core Math for Comp Sci. (2, Interesting) I agree with Linera Algebra, if you know linear algebra, you can pick up on 3D rendering APIs easily, and making 3D games is great fun, and you learn a lot about programming in general, like the need to structure your code (source code of 3D games without good structure is hell to modify). Also, a lot of geometrical problems can be solved using Linear Algebra, things that can be useful in GUI code for instance (like, which of these arbitrary line segments are closest to the cursor, what angle does these lines form, etc etc). How far are they going in CS? (5, Informative) (For the benefit of members of institutions with other sizes of courses: When I write "one course" below, I mean "1/40th of a standard Bachelor's degree".) For students who just want to get a job as a programmer, I'd say that a first year course in discrete mathematics should be enough; it won't actually teach them anything by itself, but it will increase the odds of them understanding what the smart guy on their team is talking about when he says "this is a standard graph theory problem...". For students who want to be that guy who tells the rest of the team how to solve problems, I'd suggest two discrete math courses, two calculus courses, a linear algebra course, and either a number theory course or a statistics course. For students who want to actually do research in computer science: They're in the wrong department. The best preparation for graduate work in computer science is an undergraduate degree in mathematics. If they insist on getting their undergraduate degree in computer science, I'd recommend as an absolute minimum three calculusRe:How far are they going in CS? (2, Insightful) The best preparation for graduate work in computer science is an undergraduate degree in mathematics. If they insist on getting their undergraduate degree in computer science, I'd recommend as an absolute minimum three calculusWow. I do have an undergraduate degree in mathematics, and I'm not sure it covered everything you described there. You'd certainly be lucky to get things like Galois theory taught routinely at undergrad level these days, at least here in the UK. Re:How far are they going in CS? (1) I have an undergraduate degree in math and I know for sure it didn't cover everything described there. However, with independent studies, summer research programs, and semesters abroad at schools with a stronger math program, I was able to shore up those weaknesses. If I had been at a school that had a decent graduate program in mathematics I could've moved onto that during my senior year. More advanced topics in algebra are certainly not out of reach though, my school only had one semester of algebra, but I had a lot of friends at schools with two semesters, and in two semesters there's no reason you can't get to Galois theory. Each provides a quite different approach to CS education. Just remember that you did not learn everything you will ever need to know in college. Hopefully your undergrad taught you how to learn new information quickly. Re:How far are they going in CS? (0) This comment was hidden based on your threshold setting. Anonymous Coward \| more than 6 years ago I would agree. For those who say "what undergraduate courses teach all that?", I studied Math(s) at Cambridge University. They teach all these subjects at undergraduate level with the possible exception of formal languages (which I taught myself whilst at Cambridge anyway - you can't beat those libraries!) These are my experiences of doing Math rather than CS, looking back 15 years later: 0. Math was hard. CS looked way easier. 1. Most of what I learned in my Math degree has come in use at one time or another (not that I would have known at the time) - Galois Theory being the exception, although I did have cause to review my Galois Theory notes just last month because I thought it might be relevant to something I was working on (it wasn't) 2. I've picked up everything I need to know about CS since by self-teaching; I didn't know the web would take off when I studied Math but it did and now most of CS can be learned online (the rest from books) 3. Learning graduate-level CS with a Math degree looks a lot easier than learning graduate-level Math with a CS degree The question for me therefore is not "how much Math should a CS student do" but "how much CS should a CS student do"? CS and Math are two sides of the same coin, but the knowledge transfer only goes one way. I didn't go into CS research, though. I find all this Math useful just for being a games programmer. CompSci maths... (3, Insightful) being able to use asymtotic notation for bounds on algorithm running times, and a good basis in proofs in order to prove them once you've come up with something. Also solving recurences, and proving them is invaluable. There are some other things that are very usesfull on a day to day basis, like linear algebra (spesifically coding theroy), geometry, graph theroy, counting and probability (but thats more of an ai thing) Re:CompSci maths... (1) Also solving recurences, and proving them is invaluable. There are some other things that are very usesfull on a day to day basis, like linear algebra (spesifically coding theroy), geometry, graph theroy, ... I guess spelling isn't one of those things you find "very usesfull on a day to day basis"... Statistics & Basic Economics (1) Statistics is the only maths course that I wish had been treated with more care in my CS degree, and in my Software Engineering related job(s) it's the one that I have had the most use and need of. Whether it's relevant for "pure" CS I have no idea, but would suppose that proper understanding and use of statistics is relevant for all science and engineering disciplines. Adding to that, though it's not exactly maths or CS as such, a better understanding of economics and the practical economic or accounting mechanisms and tools used in business and life would come in handy. Depends on what you want to do with it (2, Insightful) I was a math minor at Penn State, and I decided to concentrate on Stat because that is what interested me, but everyone is different. I would say that if you are interested mostly in "pure"(not pure!=better) CS, then courses like graph theory and combinatorics are probably best. If you are interested in applying your CS degree to problems in engineering and science, then differential equations and numerical analysis is your best bet. If you want to go into the business/actuarial side of things, statistics is obviously best. The most important thing is that you take a lot of math, and hopefully math that actually interests you. Re:Depends on what you want to do with it (1) I am currently a CS major with a minor in business at Penn State. I feel that we are basically required to take a well rounded number of math related classes. Many of them are under the guise of CSE classes or CSE/MATH classes but were are required to take 2 Stat classes, 3 Calc classes, 2 Logic classes, 1 Algorithms class and a few others that aren't very relevant. Unless you know before you graduate a specific field of study that you want to go into great depth about, I think that the key is to be well rounded so that you have at least a general understanding of the biggest amount of things. Lets say I come to a problem about very complex statistics. Since I didnt specialize in statistics, I may not know how to work it out exactly, but when I search and find items to read up on to understand the complex statistics, they will most likely use many statistical references that I do understand. You can never really know exactly what kind of work you will be doing and what experience you will need to accomplish it until you get to that point so it is important to be well rounded and prepared for anything. Hard to decide (2, Insightful) As a current student majoring in both (CS-Math), I've found useful all of my Math courses to CS. I'd say that Analysis, and Measure Theory have helped too. However, we should not forget that it's suposed to be a CS major, so I'd recommend as "priority" ones: Calculus (one-many variables), Linear Algebra, Probability, Statistics, Linear Optimization, Non-linear Optimization, Combinatorial Optimization, Numerical Analysis, Computational Complexity, Graph Theory and Information Theory. As subjects of further study I'd choose some Logic, Abstract Algebra, Functional Analysis, Set Theory and Category Theory. It is important that a CS student could get as much Math as he/she can, because it helps to provide a useful mental framework for thinking, and because helps to get chances of right use of some mathematical tools. As I see it, many engineering majors are as teaching a student to battle with some weapon, teach some mathematical tecniques related to the subject, and some practical things about the tecnique ("the weapon"). But learning as much as Math as you can, is like to learn how to use a swiss knife: if you know how to use it properly, sky is the limit (you can be a "science McGyver":-) ) Re:Hard to decide (0) Anonymous Coward \| more than 6 years ago As a current student majoring in both (CS-Math), I've found useful all of my Math courses to CS. As a geezer in his late 30s returning to school majoring in math with a minor in CS I'd have to agree. It is important that a CS student could get as much Math as he/she can, because it helps to provide a useful mental framework for thinking, and because helps to get chances of right use of some mathematical tools. Exactly. And unlike current languages, paradigms, etc math doesn't go obsolete in five years. It's all about exercising the noggin and then getting enough CS coursework in to actually do something with it. When I worked for the Department of Defense, all of the contract coders who were shit hot software people were almost all math or physics people. There were a few CS folks, EEs, and one "Systems Engineering" major who were skilled as well, but math and physics folks seemed to dominate. Why do CS? (3, Insightful) I think the first question you need to answer is why you're doing a CS degree in the first place. Personally, I don't see any point in them. It's not the best way to learn to program (how can you really learn Java in a lecture theatre? It just doesn't work. Just get a good reference book, find some good code to copy the syntax from, and work it out as you go along.), if you want to know the maths side of it, do a maths degree (picking courses that are useful for the job you have in mind - you might have to pick a uni accordingly), you'll understand it far better (doing a few courses in maths is much harder than doing lots, because so many parts of maths interlink). If you want to be a Systems Administrator, or something, then I can't see why you would need a degree at all, it's experience that counts in those kinds of jobs. Can anyone name a job for which a CS degree is the best qualification? Re:Why do CS? (2, Insightful) This must be one of the dumbest answers I have seen so f... oh.. this is SlashDot... I forget.:P I don't have a B.Sc./M.Sc. in CS. Yet. I have under the hood as you so skilfully describe, a self-education in programming and system administration. And, I have been working as a systems administrator, dba and network technician for the past decade at universities and major corporations/banks. I do have experience, of that there's no doubt. A year ago I decided that a CS degree would be of benefit. All too often I had discussions with my teammates and had little or no understanding when it came to mathematical reasoning used in our work. Now, I'm finishing the first half of my second year in CS. I have so far learnt more in these 12 months ( 3 terms a year ) then I have in the past 10 years, and today I can say that I have a grasp on a helluva lot of issues that I didn't while I was actively working on them ( monkey see, monkey do - me being the monkey at that time ). A CS degree must be the one thing that truly should have some meaning for computer enthusiasts. If not to get a better salary, then for your greater mental good. And to be on topic, I've taken so far: Discrete Mathematics I. Next term I'm taking Discrete Mathematics II and Linear Algebra. Term after that comes Calculus and Algorithm Design. Of course, the mathematics CS students take should echo the usability of the mathematics within the sector. Re:Why do CS? (1) In terms of being a programmer, I agree 100%, although I can't speak for SysAdmins. Before I came to Uni, I was considering doing a joint honours Maths & CS degree. I was advised against it by my A-Level (UK qualification; normally taking ages 16-18) computing teacher, who said that by doing just maths I'd actually end up being a better programmer. If I compare stuff I've written recently, with stuff I did for A-level projects, I'd say this is true - and there was a good year and a half gap where I wasn't programming anything, so the improvement is not just experience. I think this is the case because, as is so often pointed out, the logic behind mathematics and programming is the same. Maths forces you to learn the logic, whereas CS tends to teach you factual details on how it works etc. So, what maths modules should be part of a CS degree? It depends on what you want to do with your degree. I would imagine Linear Algebra, Discrete and Logic (at least Propositional, possibly Predicate) to be good in general. Re:Why do CS? (4, Informative) Actually, I didn't learn how to code in my CS classes. That was expected knowledge. Yes, CS doesn't teach coding here, instead they expect you to know how to write code and why x=x+5 isn't completely insane. What I did get taught was how to write good code. How to make use of binary trees and how to optimize algorithms. How to plan software projects and what problems to expect. How to plan, lay down and manage a network. As a low level SysAdmin, you certainly won't need a degree to figure out a subnet mask for a single router lan. But networks don't simply scale, they tend to get very tricky and complicated as soon as you have a few layers of routing between them. Not to mention that you won't be able to even plan such a network sensibly if you don't know the theory behind it, how to streamline it and what happens "inside". And yes, that's where the math comes in. A good university education will give you a heavy dose of theory. And while you won't be able to apply this directly, you will know WHY something works, not just how. And, more important, when it stops working you'll have a clue why it did. And you'll have a plan how to fix it, or at the very least, you'll know where to look. I have a Master's in CS. Yes, I agree that at the higher end CS is basically a specialized math degree. But there is that touch of applied math thrown in that separates it from a mathematician or statistician. Even better, if you pair up a CS degree with something applied (physics, mech engineering, chemistry) you suddenly become someone very valuable to any organization trying to build advanced software. Yes, a biologist could hack out some code to study protein folding, but if you're also a CS guru then you can make a very efficient protein folding algorithm and save zillions of computing hours. Basic math skills ... (-1, Troll) Basic math skills. I mean, come on, if you can't see that a result is obviously off by several orders of magnitude ("gee... what's magnitude?") by having a rough idea of the desired result in your head... And learning the difference between kilometers and miles wouldn't hurt... Earth to Mars... oops, missed the damn planet!Some basic reading and writing skills wouldn't hurt, either ("OMG I don't want to write any documentation... the code is the documentation!"... 6 day/weeks/months later... "I haven't got a clue how this works. Who wrote this piece of shit? Me? Oops...") Re:Basic math skills ... (1) And learning the difference between kilometers and miles wouldn't hurt... Earth to Mars... oops, missed the damn planet! Get your facts straight. Aside from what the article mentions, the error would not have caused mission failure if either (a) they had not decided to go from 2 solar panels to 1 (which resulted in more AMDs because of unbalanced radiation pressure) or (b) they had been tracking the trajectory of the spacecraft with ground instruments rather than dedicating them to other science. (I learned about these while interning at JPL.) Re:Basic math skills ... (1) The article you quote bears me out... it was an error in failing to do a conversion between standard and metric units. The conversion factor from pound-seconds to newton-seconds was buried in the original equation and not immediately identifiable, and so it was not included in the updated equation.Thus, the ground software reported calculated "impulse bits" which were a factor of 4.45 too large (1 pound force = 4.45 newtons). Subsequent processing of the calculated impulse bit values from the AMD file by the navigation software underestimated the effect of the thruster firings on the spacecraft trajectory by this factor. This mixup was exacerbated by two factors: The lack of end-to-end testing of the AMD data flow before launch The lack of an independent navigation algorithm to cross-check the AMD-based algorithm in flight Note my original post, where I said that one of the problems is people not being able to recognize errors that are one or more magnitudes in size from the correct answer... Re:Basic math skills ... (0) This comment was hidden based on your threshold setting. Anonymous Coward \| more than 6 years agoSo tell me Tom, how's the Canadian space program? Oops, that's right, you've got to ride shotgun with the US since you don't really have one eh? Right about now is when you should trot out the argument about how the US stole the Avro Arrow engineers who helped put the US on the moon. Too bad fools like you never seem to mention that they were almost all of UK extraction and immigrants to Canada after WWII and not indigenously developed. Then you can follow up with the work on the shuttle arm for an encore. Re:Basic math skills ... (1)I have heard that this joke works when you are studing for obstetrician, too. And for eugenetics, too. Re:Maybe I just misunderstand CS (1) At my school (in the US), my required math courses for my CS major were enough to be a minor, but of course didn't get credit for the minor. I think I was 3 math courses shy of a double major in CS and Math, but I had enough of math by that point that it was not going to happen. I thought most of the math was useless, though I'm sure some of it rubbed off into various problem solving skills. I can't tell you how other schools are in the US, but at mine, I definitely was given a big emphasis on math. Re:Maybe I just misunderstand CS (0) This comment was hidden based on your threshold setting. Anonymous Coward \| more than 6 years ago I think it's rare for CS majors in the US to get much analysis at all, although a little formal real analysis may be lumped into their last calculus course. More common is calculus, linear algebra, discrete math (combinatorics, graph theory), maybe some numerical analysis, etc. Re:Maybe I just misunderstand CS (1) I don't know if our universities synch up exactly with yours in terms of meaning, but in the U.S. at the bachelor's level, it'd be very rare for anyone to have six semesters of analysis. Maybe if you count the calculus sequence and basic ODEs, but there's very little serious analysis generally occuring in those classes. Re:Maybe I just misunderstand CS (1) The "old" system I was studying in is equivalent of a Masters, it was one five year block. Then lately they changed to the Bolognese system of 3 years batchelor and 2 years masters. As far as I know they still have 6 semesters of analysis in the first 3 years of a batchelor degree. Re:Maybe I just misunderstand CS (1) Hmm... if I (European) remember correctly, first year was 8 hours/week math, second was about the same (plus 4h MathLogic), after that it tapers off sharply if you (unlike me) don't go for the statistics branch. Re:Maybe I just misunderstand CS (1) One reason why mathmatics is so heavily emphasized is because the CS departments were often appendages to the mathmatics departments, or were started in the mathmatics departments. About 30 years ago (showing my age here) when you couldn't even get a CS degree, most computer programmers had a BS degree in mathmatics. Almost all of the older CS professors usually had a PhD in Mathmatics, although one of my best CS profs had his PhD in Biology (and turned out to be the graphics algorithms teacher at my university... go figure). I believe that largly due to this early emphasis on mathmatics, it has skewed the emphasis by some of those professors to more pure mathmatics concepts. While not bad by itself, I did find it boring after a fashion when one of these professors would get caught up with making a mathmatical proof of some CS theory.... particularly when you were in a class like compilers or data algorithms that had little to do with very abstract mathmatical proofs. Those younger professors who had a PhD in CS and spent time working "in the industry" tended to be much more grounded on coding fundimentals and teaching finite number theory instead. For myself, while I think advanced mathmatics may have usefulness for hardcore computer science, that is the study of computer algorithms and computational theory, it doesn't have much of a practical application. Of course I view myself as a software engineer seeking practical development of computer algorithms as opposed to a computer scientist that explores theoretical directions of computational concepts. In this regard, I consider software engineers to be very different from computer scientist. Or more to the point, I think there ought to be a ratio of about 1 computer scientist to about 50 software engineers. Unfortunately, it is presumed that you would get a CS degree if you want to become a computer programmer. But if your school doesn't offer a software engineering degree (very, very rare) you are trained as a computer scientist first and a software engineer maybe as a supplimentary (sometimes optional) course. Personally, (1) In relation to computer science, I got a huge boost from linear algebra, probability & statistics, and a very discrete level of calculus material like riemann sums, taylor/maclaren series, root-finding algorithms (newton's method), etc. I also found that taking a logic course was very beneficial. It was from a philosophy standpoint, but was mathematical in nature, and boolean algebra was developed out of it after all. My uni also has a discrete math course which covered things like the fundamental theorem of arithmetic, set theory, counting laws, graph theory, and some other things useful in comp sci. Formal grammar, predicate calculus, statistics (2, Interesting) Start by making sure you understand the distinction between Computer Science and its related disciplines, and that this is a CS course. Read the overview report from the ACM Curricula Recommendations.. It is apparent from the ACM's recommendations (amongst others) that a lot of mathematics traditionally covered at universities(such as calculus) is not strongly related to Computer Science. That said, there are many applications of computing that require strong skills in these areas (scientific computing and cryptography for example) so they are not a bad option. Important numerical and logical fundamentals that support the learning and use of undergraduate Computer Science include: Basic computing theory (formal grammars and finite automata). Understanding the qualities and use of state machines and formal grammars is essential in many fields of computer science including algorithm and protocol design, modeling robust systems, and creating parsers (e.g. for domain specific languages). It is also necessary to understand the halting problem and turing theory. Most of the theory requires the use of proof by induction or construction, which (in my experience) are the most common proof techniques in CS. First-order logic (predicate calculus). Also exceptionally valuable in the development of data structures and algorithms, and for communicating between domains. Statistics. You will use it in most forms of analysis, at least to verify that a real-world realisation matches the predictions of a theory. Also valuable for performance analysis and optimisation to determine performance distribution and bounds. Re:Formal grammar, predicate calculus, statistics (1) I'd have to agree with the beginning of your post: Calculus isn't all that useful to a CS major. Don't get me wrong, calculus is useful in and of itself, but since computers can't do integrals or derivatives, it's kinda useless. Calculus combined with something like numerical methods, which teach you how to use various methods of approximation and interpolation to get a computer to understand calculus...well... that's a different story. Even then though, I don't tend to use calc or numerical methods for much. Algebra and Galois Fields tend to be the maths I use the most. GFs are especially nice for crypto since GF(2^8) and the operations that are closed over it represent everything you can do to a byte... Mind you, I'm mostly interested in ai and crypto. Crypto is mostly a hobby, but for ai having a rock solid understanding of lin alg helps in performing things like computer vision (lin alg for the pixel manipulations, trig ftw for the angular calculations), path planning (okay, some calc, but mostly lin alg as we're, again, approximating a continuous curve over a discrete space, so it's summations instead of integrals) motion prediction (same as last)... etc... So again, I'd have to say, Algebra is the math that a CS major should be the strongest in. The formal languages, automata, graph theory, etc... is all fairly standard CS stuff. None of it is as much a cornerstone of good coding as lin alg IMHO, but they're all really really nice to have sometimes. As for the rest of your post, it's pretty obvious that your experience has been with parsers and compilers (or something similar), in which case, the rest of your post is 100% true. However, for my corner of the CS world (ai and robotics) lin alg and trig are t3h sh!t... followed by probs/stats (for stochastic modelling/simulations).... I guess a "YMMV" belongs at the end of each post in this topic as everyone needs different math tools based on what they're working with. This should provide a bit of an answer to both the OP and the people asking "what do you need maths for if you're going to be a sysadmin?" (You're either trolling or confused as to what CS guys actually do, so I'll give the benefit of the doubt to you and shed some more insight into what some of us do...) Re:Formal grammar, predicate calculus, statistics (1) I have worked with parsers and compilers in the past, but most of my time now is working with crypto;) That said, I'm an SE by practice although a CS by qualification. In my line of work SE and CS come together when I get to protocols and algorithms. Formal grammars are essential in describing protocols (think BNF) and modeling for robustness. As an example, getting FIPS certification for crypto hardware requires submitting a finite state model of the firmware. I have a poor grounding in graph theory and linear algebra (I just apply the crypto algorithms) but have found it useful in optimisation of algorithms. Statistics, IMHO, is the bridge between theory and reality when it comes to performance. A constant time algorithm can really suck if the constant is large enough;) Sometimes it is better to use a slow-but-simple algorithm (easy to develop, debug & maintain) and optimise special but common cases, rather than using a complex but higher performance algorithm. Statistics can help you to understand the performance bounds of the application, how it will scale in the real world, etc. It also helps you to understand how numbers can lie, and the difference between good sampling and bad sampling (this microbenchmarks). None of it is as much a cornerstone of good coding as lin alg IMHO, but they're all really really nice to have sometimes. ...but then CS isn't about good coding, it's about taking over the world (y'know, "science"). IMHO there is nothing better for good coding than to slow down, do a tiny thing at a time, and wonder what path execution will follow when your assumptions are wrong. DSP (maybe I'm a bit biased) (1) I'm not a Computer Scientist- I'm an EE- and I may be biased towards the engineering type courses, but I think some digital signal processing type courses would be incredibly useful (beyond just engineers). Of course, there are a whole bunch of prerequisites, including calculus, differential equations, signals, and probability/stochastic processes. Not every CS major is going to be working on making new OSes- there has to be some application processing going on, and if you are working on data derived from meatspace, DSP and all the prerequisites are vital. There are lots of electrical engineers forced into programming because the Computer Science guys just don't have the math background- and what we often end up with is pretty poorly done code because the coursework behind the engineering degree is lots of math and relatively little code. What I'd really like to see is a combination of better code and better systems to run that code. Re:DSP (maybe I'm a bit biased) (1) I second the idea that you need calculus for many CS applications, for example probability and DSP, but there are also less obvious reasons to take calculus. For example, understanding the Fourier transform framework (with convolution theorem etc.) is a great eye-opener in many ways, and it comes up in surprising places. For example, Shor's factorizing algorithm depends on FT. What do you want to do with your degree? (1) If you want to go onto grad school, double major in math and take everything you can. Electives and even core requirements probably have heavy overlap. It tends to be one of the easiest combinations in terms of course load. Also consider testing out a fall semester grad class or two in your senior year. These will probably look a lot like math classes. If you can't hack an undergrad math degree, odds are very good that the graduate CS program will kill you. I have to confess that I have limited experience in computer science myself, but I've seen a couple uses for various areas of mathematics. I was doing an optimization problem where I was trying to find the maximal distance apart of two points on a given surface along the surface itself. To begin with, in these kinds of optimization problems you want to know when you've found the answer and what kind of accuracy you have. To answer those questions you're going to need estimates and approximations, things that you learn in analysis. If your calculation is of critical importance, you don't want to just eyeball something, you want to know that you've got an answer with the appropriate accuracy. The surface was basically defined in two different pieces glued together along their boundaries. I needed to calculate lengths along these boundaries where they were joined together. To calculate these lengths explicitly was literally impossible given the types of curves, and I ended up with an integral equation I couldn't resolve. So I used a combination of approximations for the values of the integrals and something like Newton's method from calculus to get a quickly converging answer to a problem that ground Maple to a halt when I tried the naive solution of just plugging it in. If you're sampling data and using it to estimate the behavior of something, say a flow (like the movement of the wind or a river), you're going to want to know how accurate your data needs to be for your model to produce good results. This is a question in dynamical systems. Granted, this analysis may not be performed by the CS guy, but being able to do this sort of thing combined with having a good knowledge of computers opens a lot of exciting possibilities in science. Similarly, in robotics, the configuration space of things like different joints on robot arms is a multi-dimensional surface, an object that is studied in differential geometry and topology. Using methods from calculus you can find the critical points in the configuration space, which it is generally a Good Idea to avoid (like a robot with its arm extended straight out) because of the fragility of the tolerance there (again, back to dynamics). If you have a recursion, there are some fairly standard tricks you can try to apply to obtain a generating function, which can often lead to an easier computation or even a closed-form solution. There is a free text available on the internet, generatingfunctionology, which could be used as the basis for an independent study. Things like encryption algorithms have found good uses for number theory. Graph theory can model relations between data or routes over a network. Statistics and probability are very useful for all sorts of things. Straight-up algebra and logic courses are great tools to get your mind working, though admittedly a lot of topics in your standard undergrad algebra course might be of limited use unless you're planning on pursuing a graduate degree. DEs and their solutions are great for most scientific applications. Discrete Math is usually the name they give to the mathematics course that is tailored towards computer science applications, so that's almost a no-brainer. Statistics and Experimental Design (2, Insightful) "Statistics" (2 semesters at least) and "experimental design". "Modeling and simulation" is closely related, but is somewhat covered if you take the stats and experimental design courses. Here's why... When starting on my PhD research, I pretty naively thought I'd just write a network simulator to try out my idea and to compare its performance to other network protocols. That would be fairly acceptable in today's CS climate, but STUPID. People using simulators face a number of questions that they often don't ask, and therefore make their conclusions nearly meaningless. Are there specific hypotheses they're trying to test? How do they know they've performed enough simulation runs to draw conclusions at an acceptable confidence level? Exactly what is the distribution over which the inputs are randomized, and why was distribution chosen? To what extent is the model even validated (ok, this is more of a Modeling and Simulation issue than a stats issue)? Psych and biology majors have been forced to rigorously answer these questions for a long time. We, the supposedly "mathematically superior" CS majors, have often ignored these details as though they're irrelevant. But if left un-tackled, we can produce crap research whose conclusions have little clear connection to reality. These is even true for when we can afford to do real-world tests and thus are less at the mercy of simulation model inaccuracies. How many real-world tests do we perform before we draw our conclusions? How do we randomize the inputs? Much of today's network-related research sucks. Not because the ideas being generated are bad, but because the analysis of the new ideas and their comparison to the performance of pre-existing ideas is crap. Without taking stats and experimental design courses, even the reviewers of these papers don't realize that those weaknesses exist. If you want your network research to be meaningful, test your ideas with meaningful experiments and analysis. Lots (2, Informative) The CS students who make it through a lot of math often end up being better programmers. I'm not sure if that's a true statement, but it certainly seems to be true where I go to school. Calculus Calculus Calculus! So important! At least one semester of calc is necessary, but I would say if you can squeeze in multi variable calculus, you're good. Multi variable + Linear Algebra (matrix math) is really good. I would say the matrix math is much more important though. And discrete! Now, we actually have a class in our CS department that is our own little private discrete class, but I'm totally planning on taking the math department's discrete. Plus, my math department has this computer programming class for math majors. It's all logic problems. I'm taking that too. Statistics. Now, this one isn't as important because if you get the basic concept then you can just look stuff up, but consider it an easy A (hopefully). I am so glad I took AP Stat in high school. I have used information from that class in almost every class I have had here in college. In short, if you can fit in a math minor (or major), go for it. My CS department has you take 3 math courses, and then you only need 4 more for a minor. Anonymous Coward \| more than 6 years ago All Major Mathematics Courses Should Be Taught (1) I think all major mathematics courses should be taught within a computer science curriculum. There is real-world purpose for all forms of mathematics. A software developer with a strong foundation in mathematics can develop programs to efficiently analyze or simulate real-world phenomena. I think the most important are the following: Discrete mathematics, otherwise finite mathematics should be taught because it is the best way to represent a finite machine. A computer is a finite machine with many countable sets. Calculus is great for computer science. Students who take calculus develop strong problem solving skills. Multivariable calculus should be optionally taught to those who want to design 3D games. Statistics and probability theory should be taught. Statistics is used to analyze, interpret and present data. Computers are used to perform calculations on data. The combination of statistics and computers facilitate decisions in all areas of science, business and government. Math courses (2, Informative) I recently graduated from NJIT with a BS in Computer Science and a minor in Applied Mathematics. The fundamental courses were 3 semesters of Calc(I/II/II). Probability & Statistics, Discrete Analysis, Differential Equations as per the engineering requirements and enforce formal thought (except maybe discrete, that is considerably more out of the box). One of the most important courses I took was Linear Algebra. Dealing with matrices is fundamental... but more to the point: anyone even considering graphic theory needs linear algebra. OpenGL models / graphing simulations rely heavily on constructing matrices and working with them to represent 3D images in a 2D world. Another class that provides some very deep insight is Numerical Methods. This study of mathematics requires some programming knowledge to automate error analysis (particularly the big question is always: You all have an answer to a set of problems, but just how accurate is your answer and within what bounds? 10^-6... 8?). The class also provides insight and formulas for detecting propogation of errors. Any computer scienctist is going to deal with computational math and at some point you will goto another research or a project lead and they will ask "are your results correct?"; You will comfortable with your results, given some background to know that they are correct. Life, not CS (1) Not related to CS or Engineering, but I think that the most amazing piece of math is Cantor's diagonal argument. So simple, so beautiful, so insightfull. And such a strong conclusion: infinite comes in many sizes. It's 10 years since I been first exposed to the proof and I am still filled with joy when I contemplate the simplicity and power of its truth. Graphics Guy (1) I've got a CS degree. When I began taking graduate courses for 3D graphics, I was quite upset that numerical analysis wasn't pushed onto me in undergrad. It would have been nice to not have to learn monte-carlo integration alongisde ray tracing. That way I could have given enough time to both to fully understand. Instead I felt rushed through both topics:\ To contribute to the topic, here is what I took: Calculus 1-3 (3 was most important for me since it was about 3D analytical geometry) Differential Equations Discrete I (combinatorics), Discrete II (Finite Automata & Language Theory) What I wish I had taken: Linear algebra (matrix stuff) Numerical Analysis SOMETHING THAT TAUGHT QUATERNIONS!!!! All of them. (1) Every math course I've taken has in some way been useful to me as a computer scientist (this is partially because the area I'm interested in researching is applying mathematical concepts to CS topics, however). I would recommend at least minoring in math if you're going to do a CS degree. 3 words... (3, Insightful) Algebra, geometry, calc, who cares. It's the Proofs that make math apply to Comp Sci. Having obscure formulas memorized means squat. But being able to look at a problem and break it down into the most simple of building blocks, that is a critical skill. The useful maths I took back in the day... (1) ... were Boolean algebra, numerical analysis, matrices, queueing theory, and a semester of descriptive stat. I didn't find linear algebra of any use to me, nor the year of formal stat. Calculus is kinda like long division -- I don't use it much (if at all), but it's good to know it's there. Oh, and some of my pals recommended formal logic. I skipped that, 'cause I wasn't terribly interested in spending a semester playing word games. I don't think I've ever missed it, but someone else who actually took the class might straighten me out here. Bar none, the best math class I ever took was a freshman seminar with no textbook, no lecture, no assignments and no exams. You were graded 100% on class participation, and the topic was... math. The prof stood off to the side and would start the conversation: "How many integers are there?" might be a typical query. He'd sit back while we discussed the matter in Socratic fashion, sometimes nudging us in a particular direction. That semester we "invented" limits, cardinalities, discontinuous functions and other groovy things. I doubt that this particular class had much direct application in my professional life, but it was the first fun math I'd ever done in my short life. At my university... (1) At my university, for the Computer Science students, the core math classes taught are Calculus I, Calculus II, Discrete Mathematics, Linear Algebra, and Probability and Statistics. Then, depending on the track you choose, you will either take Differential Equations and Numerical Analysis, or Theory of Numbers or Discrete Mathematics II. From what I have been told, multiple semesters of Numerical Analysis used to be required. I don't know why it was changed. Maybe they thought it was overkill for an undergraduate? I have heard good arguments for placing Linear Algebra above Calculus in importance in today's digital world, however, it looks like Calculus is still what is being required for a full year. I personally would like to be able to fit in some sort of Computer Statistical Analysis/Computational Statistics course before I graduate (I am a Software Engineering student, not a Computer Science major, and interested in sports statistics) but I doubt I'll be able to. There is just too much material to cover these days in an undergraduate Engineering curriculum, especially if you, like me, switched your major at some point. I hear that probability theory is a good one to take if you are interested in getting a job in some sort of prediction-based industry. It seems like there are never too many possibly useful math classes one can take. I'd like to know myself which ones are the most practical, by their industrial application, however. Prob and Stat (1) Which was required for my degree. As a DBA today, you have to use this, as even single machines are going into parallel processors. So one has to use Prob and Stat to calculate what the machine is going to do. And while I was working on Teradatas, with as many as 150 parallel processors, I lived in that world. Even the micros today are going to parallel processors. Calculas? Haven't touched it in 25+ years in the business world of CS. The other course that was useful was data structures. Tought me to think in linked lists. In one case it taught me to look at the problem from the link point of view. So the process I was on was codeable in 4n lookups, instead of n! + 3n lookups! Oh, and to all the doubters there. When calculating the processing power of multiple processors, don't forget to subtract off the OS on each processors. Most venders won't tell you about that little probelm when calculating the machine size. My most useful classes (1) I received both a BS and an MS in computer science at Stevens Institute of Technology back in 1993. Most of the classes people are suggesting here were all required to earn the undergrad degree there; in addition to 3 semesters of Calculus, you also had to pass discrete mathematics, statistics (two semesters of that), and linear algebra as part of the standard program. Out of the required math classes, two stood out as being particularly helpful for my career in software development. The introductions to logic, graph theory, proof, and other topics in the discrete math course were absolutely vital to understanding more complicated computer science constructs. I recall trying to understand how compilers were built before that time and being completely confused, but everything made perfect sense after completing that class. The other class was in operations research, a subject I didn't notice anyone bringing up here yet. OR really made an impression on me as it provided a bridge for how to apply several types of mathematical approaches that had seemed completely theoretical to solving the kinds of real-world problems computers are good at helping with. As the most obvious example, I feel that having a solid practical understanding of how to model a complicated queue or flow across a series of queues is wildly more useful for building software than anything related to big-O analysis will ever be, unless you're one of the rare people writing basic algorithm libraries. My experience is that you'll see dozens of messaging queue issues in business software design for every problem that requires an understanding of complexity analysis. And learning how formally construct decision trees turns into a great tool when you get far enough along that you're managing projects instead of just working on them. I considered it unfortunate that I didn't discover this class of mathematics until very late into my time at school, as I would have gladly taken more of it and benefitted from--something I can't say about statistics or linear algebra, where I felt the basic introduction gave sufficient understanding for normal programming tasks. Crypto (1) When I was in college, I struggled with Calculus. It got to the point where I really thought I was "not good at math" because I wasn't good at calc. Then I discovered I didn't need to take Calc II/III or Differential Equations. I could substitute more "advanced" classes like Graph Theory, Number Theory, and Cryptology. Suddenly I was good at math. Not only that, but I got a whole lot better at computer science. The more advanced classes focus more on how to think logically, and how to operate in procedures. Cryptology is especially important because it is one of those items which most computer scientists will use, but only in passing, and using it badly is often worse than not using it at all. An understanding of cryptology brings with it a lots of logic, set theory, and optimization skills. I would hope (1) That boolean algebra/logic be taught as well. You would think that would be a 'no-brainer', but that's the phrase I used to describe some code recently. And I can't tell you how many times I've had to fix someone else's program because they had a series of conditions totally messed up. At least one, I rewrote the whole thing, because not only did the other coder have the wrong logic in place to try and solve what he wanted to solve, it was also ordered very poorly. At least one class on probability and statistics would be good, vector math/algebra, a topology course (ok I took that and oddly it helps), trigonometry if going into graphics processing/modeling, and a number of other courses I took but can't remember. The only thing I haven't used in the last year, the rest of the above I have, is some of the higher level calculus. Double! (0) This comment was hidden based on your threshold setting. Anonymous Coward \| more than 6 years ago You've already acknowledged the constraints: there are only so many math courses that one can "squeeze in". I assume you mean, "squeeze into a four year CS degree". So stop doing that: take the Math/CS double major, and take an extra year if you need it. For students coming into the university with AP, IB or dual-enrollment hours, they may even get back onto a four year schedule. I can't speak for the entirety of the technical industry, but I feel pretty comfortable with the following statement: anyone who considers herself a professional Computer Scientist would most likely have benefited from a double major in an appropriate field: stats, math, physics, chemistry, engineering (probably won't have time for one of these), biology, meteorology, oceanography or philosophy. I listed here the subjects with strong analytical or computational components.
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Course Description MA 1025 Mathematical Problem Solving Prerequisite: C or above in MA1000. Topics in algebra including exponents and their properties, and addition, subtraction, and multiplication of variable expressions are central to the work of this course. Solving and applying linear equations and applying exponential equations are studied. Other course topics include: graphing lines and linear inequalities using slope-intercept form, solving systems of equations and inequalities, and displaying data. Throughout the course business, social science, and finance application problems and use of appropriate technology are emphasized.
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Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software, including complete details that are missing from most textbooks. Using an inquiry-based learning approach, Numerical Analysis is written in a narrative style, provides historical background, and includes many of the proofs and technical details in exercises. Students will be able to go beyond an elementary understanding of numerical simulation and develop deep insights into the foundations of the subject. They will no longer have to accept the mathematical gaps that exist in current textbooks. For example, both necessary and sufficient conditions for convergence of basic iterative methods are covered, and proofs are given in full generality, not just based on special cases. The book is accessible to undergraduate mathematics majors as well as computational scientists wanting to learn the foundations of the subject. Presents the mathematical foundations of numerical analysis Explains the mathematical details behind simulation software Introduces many advanced concepts in modern analysis Self-contained and mathematically rigorous Contains problems and solutions in each chapter Excellent follow-up course to Principles of Mathematical Analysis by Rudin
Advanced, four-line scientific calculator, with higher-level math and science functionality, that is ideal for computer science and engineering courses in which graphing technology may not be permitted
to the Saxonmath program. ... Math 65, Math 76, Math 87, and Algebra 1/2. Please note that this placement test is not infallible. It is simply one indicator that teachers may use to place new students. The best placement for most new students is to A Harcourt Achieve Correlation Of SaxonMathAlgebra To The Pennsylvania State Content Standards 1 GRADE EIGHT PENNSYLVANIA STATE CONTENT STANDARDS SAXONMATHALGEBRA Mathematics 2.1 Numbers, Number Systems and Number Relationships Available now for Algebra 1, Algebra 2, Geometry, Advanced Math, Saxon 5/4, 6/5, 7/6, and 8/7, Saxon has provided a user-friendly format – CD-ROMs used on a computer. There are four lesson CDs and one Test CD for each course. algebra and geometry, including circumference and pi, angles, coordinate graphing, and prime factorization. ... Particularly useful to students who are new to SaxonMath or who need ongoing practice with addition, subtraction, multiplication, and division. SaxonMath Course 1 Standards Success is a companion to SaxonMath Course 1 (Intermediate 6). The first section, the Table of Contents, lists the Common Core focus of each lesson. The second section, Correlation of SaxonMath Course 1 to the Common SaxonMath 4 Patterns, Algebra, and Functions, continued Readiness for Algebraic Reasoning, continued Graphs large numbers on a number line 55-2 33 Shows addition, subtraction, and/or multiplication on a number line 126 93 Locates and graphs points (ordered SAXONMATH , a mathematics program designed for use in kindergarten through grade 12. ... with algebra and other advanced math courses (National Association for the Education of Young Children and National Council of Teachers of Mathematics, Saxon program should start in Saxon's Math 54, Math 65, Math 76, Math 87, Algebra 1/2, or Algebra 1 textbook. Please note that this placement test is not a fool-proof placement ... in the Saxonmath program should skip a textbook. The Rules 1. Allow the student up to one hour to take Algebra 1, like all SaxonMath courses, includes five instructional components; introduction of the new incre-ment; examples with complete solutions, practice of the increment, daily problem sets, and cumulative assessments. Algebra 1 covers all Teachers using SaxonMath 5/4 - Algebra I can now use Accelerated Math to generate individualized daily assignments for all students, automatically score the assignments, and create new assignments based on which skills the student has mastered and which ones he or she needs Contents of SaxonAlgebra II: An Incremental Development: Preface Basic Course A Geometry review; Angles; review of absolute value; Properties and definitions ... Math (especially percentages and fractions) and science skills are important in training to be an Algebra 1, like all SaxonMath courses, in-cludes five instructional components; introduction of the new incre-ment; examples with complete solutions, practice of the increment, daily problem sets, and cumulative assessments. Algebra 1 covers all ALGEBRA 1 (3RD EDITION) The Saxonmath program has two important aspects. It uses incremental development and continuous practice. Incremental development refers to the division of concepts into small, easy to understand pieces that are taught over several lessons.
Fourier Analysis - Dave Rusin; The Mathematical Atlas A short article designed to provide an introduction to Fourier analysis, which studies approximations and decompositions of functions using trigonometric polynomials. Of incalculable value in many applications of analysis, this field has grown to include many specific and powerful results, including convergence criteria, estimates and inequalities, and existence and uniqueness results. Extensions include the theory of singular integrals, Fourier transforms, and the study of the appropriate function spaces. Also approximations by other orthogonal families of functions, including orthogonal polynomials and wavelets. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. more>> An Introduction to Wavelets - Amara Graps; Institute of Electrical and Electronics Engineers, Inc. A paper giving an overview of wavelets: mathematical functions that cut up data into different frequency components, and then study each component with a resolution matched to its scale. Wavelets have advantages over traditional Fourier methods in analyzing physical situations where the signal contains discontinuities and sharp spikes. This paper include information about signal processing algorithms, Orthogonal Basis Functions, and wavelet applications. more>> Wavelet Digest: wavelet.org - Wim Sweldens A free monthly newsletter with all kinds of information concerning wavelets; announcement of conferences, preprints, software, questions, etc. The latest issue and searchable copies of back issues (beginning in 1992) are available; links to other wavelet sites are provided. more>> The Wavelet Tutorial - Robi Polikar The engineer's ultimate guide to wavelet analysis: a tutorial that explains basics of signal processing with a focus on the technique of wavelet transformations (WT). Basic concepts of importance in understanding wavelet theory; Short Term Fourier Transform (STFT) (used to obtain time-frequency representations of non-stationary signals); continuous wavelet transform (CWT) (how problems inherent to the STFT are solved); discrete wavelet transform (a very effective and fast technique to compute the WT of a signal). Bibliography included. more>> All Sites - 103 items found, showing 1 to 50 1ucasvb's lab - Lucas Vieira Diagrams and animations from a longtime contributor to Wikipedia's math and physics articles. Posts, which date back to February 2013 and feature graphics coded in POV-Ray and PHP, include "Experimenting with sound: the polygonal trigonometric functionsDrums That Sound Alike - Ivars Peterson (MathLand) Peterson writes that physicists and mathematicians have long recognized that the shape of the boundary enclosing a membrane plays a crucial role in determining the membrane's spectrum of normal-mode vibrations. He outlines the progress made on Mark Kac's ...more>> The Fast Lifting Wavelet Transform - C. Valens A tutorial on wavelet filters aimed at engineers. Focusses on "lifting," a technique for creating a general framework to design filters for every possible wavelet transform. May be read online or downloaded in PostScript format. ...more>> FFTW - Matteo Frigo and Steven G. Johnson FFTW is a C subroutine library for computing the discrete Fourier transform (DFT) in one or more dimensions, of arbitrary input size, and of both real and complex data. Download FFTW; read about its features; subscribe to its mailing list for announcements. ...more>> Fourier Synthesis - Manfred Thole A periodic signal can be described by a Fourier decomposition as a Fourier series, i.e. as a sum of sinusoidal and cosinusoidal oscillations. By reversing this procedure a periodic signal can be generated by superimposing sinusoidal and cosinusoidal waves. ...more>> Gamelan - The Official Java Directory - EarthWeb, Inc. Gamelan's primary mission is to serve as a central registry and directory of Java resources. Much like Yahoo!, Gamelan collects links to resources stored on other sites across the Web. However, unlike Yahoo!, Gamelan's mission is specific - Gamelan collects ...more>> Jeffrey C. Lagarias A member of the University of Michigan Department of Mathematics. List of publications, with many available for download in PostScript format; Lagarias' research interests include Number Theory, also Computational Complexity Theory, Cryptography, Discrete
Mathematical Modeling Offering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 5th Edition delivers an excellent balance of ...Show synopsisOffering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 5th Edition delivers an excellent balance of theory and practice, and gives you relevant, hands-on experience developing and sharpening your modeling skills. Throughout, the book emphasizes key facets of modeling, including creative and empirical model construction, model analysis, and model research, and provides myriad opportunities for practice. The authors apply a proven six-step problem-solving process to enhance your problem-solving capabilities -- whatever your level. In addition, rather than simply emphasizing the calculation step, the authors first help you learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving you in the mathematical process as early as possible -- beginning with short projects -- this text facilitates your progressive development and confidence in mathematics and modeling
Vendors/Publishers Saxon Geometry Teacher Lesson CDs $97.35 Sale: $77.88 Save: 20% off Give your Saxon Geometry students support and reinforcement! Comprehensive lesson instructions feature complete solutions to every practice problem, problem set, and test problem with step-by-step explanations and helpful hints. These user-friendly CD-ROMs contain hundreds of hours of instruction, allowing students to see and hear actual textbook problems being worked on a computer whiteboard. A slider button allows students to skip problems they don't need help on, or rewind, pause, or fast-forward to get to the sections they'd like to access. Problem set questions can be watched individually after the being worked by the student; the practice set is one continuous video that allows for easy solution review. For use with the 1st Edition. Four Lesson CDs and 1 Test Solutions CD are included
Art And Craft of Problem Solving 9780471789017 ISBN: 0471789011 Edition: 2 Pub Date: 2006 Publisher: John Wiley & Sons Inc Summary: You' ve got a lot of problems. That's a good thing. Across the country, people are joining math clubs, entering math contests, and training to compete in the International Mathematical Olympiad. What's the attraction? It's simple--solving mathematical problems is exhilarating! This new edition from a self-described "missionary for the problem solving culture" introduces you to the beauty and rewards of mathematical p...roblem solving. Without requiring a deep background in math, it arms you with strategies and tactics for a no-holds-barred investigation of whatever mathematical problem you want to solve. You'll learn how to: get started and orient yourself in any problem. draw pictures and use other creative techniques to look at the problem in a new light. successfully employ proven techniques, including The Pigeonhole Principle, The Extreme Principle, and more. tap into the knowledge gained from folklore problems (such as Conway's Checker problem). tackle problems in geometry, calculus, algebra, combinatorics, and number theory. Whether you're training for the Mathematical Olympiad or you just enjoy mathematical problems, this book can help you become a master problem-solver! About the Author Paul Zeitz studied history at Harvard and received a Ph.D. in mathematics from the University of California, Berkeley. He currently is an associate professor at the University of San Francisco. He won the USA Mathematical Olympiad (USAMO) and was a member of the first American team to participate in the International Mathematical Olympiad (IMO) in 1974. Since 1985, he has composed and edited problems for several national math contests, including the USAMO and helped train severalAmerican IMO teams, most notably the 1994 "Dream Team" which, for the first time in history, achieved a perfect score. In 2003, he received the Deborah Tepper Haimo award, a national teaching award for college and university math, given by the Math Association of America. Zeitz, Paul is the author of Art And Craft of Problem Solving, published 2006 under ISBN 9780471789017 and 0471789011. Three hundred eighty one Art And Craft of Problem Solving textbooks are available for sale on ValoreBooks.com, one hundred twenty two used from the cheapest price of $32.76, or buy new starting at $53.00.[read more]
Geometry Seeing, Doing, Understanding 9780716743613 ISBN: 0716743612 Edition: 3 Pub Date: 2003 Publisher: W H Freeman & Co Summary: Jacobs innovative discussions, anecdotes, examples, and exercises to capture and hold students' interest. Although predominantly proof-based, more discovery based and informal material has been added to the text to help develop geometric intuition. Jacobs, Harold R. is the author of Geometry Seeing, Doing, Understanding, published 2003 under ISBN 9780716743613 and 0716743612. One hundred twenty five Geometry... Seeing, Doing, Understanding textbooks are available for sale on ValoreBooks.com, thirteen used from the cheapest price of $76.04, or buy new starting at $207.86.[read more
AMERICAN SCHOOL FOUNDATION OF GUADALAJARA APPLIED MATH 12TH GRADE Ms. June Mitsuhashi E-mail: june.mitsuhashi@asfg.mx Webpage: Curriculum The Applied Mathematics course is focused on real life applications of mathematics. In the first semester students will learn basic statistics, while in the second semester students will work on financial mathematics topics such as linear programming, and loans and investments. The course is heavily based on using technology, specifically Microsoft Excel software. Beside the Excel, students will learn how to use graphing calculator for statistical purposes, and how to use Winplot software to graph systems of equations and inequalities. 1. Introduction to Statistics: This introduction unit focuses on statistics vocabulary. In addition, it discusses the positive sides of statistics, as well as its misuse. 2. Frequency Distributions and Graphs: The step that follows data collection is organizing and presenting the data in a meaningful way. This unit explores different ways of presenting data. 3. Data Description: in this unit students will learn how to analyze data by finding the measures of central tendency, variation, and position. 4. Correlation and Regression: This unit explains the methods of finding the correlation between two numerical variables. For example, if you're math grades are good, would you expect your science grades to be god as well? 5. Probability: This unit focuses on basic probability rules for simple and compound events. 6. Systems of Linear Equations and Inequalities: In this unit students will learn how to solve systems of linear equations, how to graph systems of linear inequalities, and how to solve linear programming problems. 7. Matrices: In this unit students will learn how to perform basic matrix operations. In addition, they will learn how to use matrix multiplication to solve systems of linear equations. 8. Review for Ceneval: Stepping out of the main objective of this course, a substantial amount of time will be used to prepare students for the Ceneval exam. 9. Loans and Investments: Simple interest, compound interest, annuities, amortization are the main topics of this financial mathematics unit. Grading Criteria Tests Homework Quizzes Participation Projects 40% 15% 15% 10% 20% There will always be at least two chapter tests per quarter and two quizzes per chapter. The student will also be assigned one project per quarter as follows: 1. Graphs of trigonometric functions and their variations 2. Trigonometry and real world applications. 3. Conic sections and art or Conic Sections Around Us 4. Applications of exponential and logarithmic functions Extra Credit: Extra credit work will be given to students before the test date. Extra Credit is optional. It will give you 10 extra points on the test if it is complete. Exemptions: Students can exempt the semester or final exams with a 95 or above in both quarters. Material Pencil Eraser Sharpener Two letter size folders TI-89 Graphing Calculator Notebook (squares) Letter size pad (squares) (block de cuadrícula) Ruler Textbook: Advanced Mathematical Concepts: Pre-calculus with applications. Each student is expected to bring its own material to class every day. Material cannot be shared specially during quizzes or tests. Homework Notebook The notebook should be divided into two sections: one for notes and the other one for homework. Each homework assignment must include the following: 1. Name of chapter 2. Chapter section 3. Date 4. Instructions 5. Problems with process and answers circled or underlined. Homework grade will be based on completion on time and 10 % on neatness and organization. No late homework will be accepted unless there is an excused absence. It will be corrected on a daily basis. Questions and doubts will be answered during class before going into a new objective. Homework will either be from the textbook or from worksheets. You are responsible to go to the Calculus website and print a copy of the homework worksheet that you will paste in your notebook. Homework will be signed at the beginning of each class period. If the teacher does not sign the homework during this time then it will count as a late homework and you will only get 50% of the credit. Make up work Make up work can only be done if you have an excused absence or tardy. You can copy the notes from a classmate's notebook. You are responsible to look on the website for the homework, quiz, or test that you missed during your absence. Homework must be signed within 3 days after your absence. Extra Help I will gladly help you any week day but Wednesday, from 2:35 to 3:05. Course expectations 1. Respect your classmates, the classroom environment and yourself. 2. Be responsible by being prepared and on time, by doing the homework and consciously studying. 3. Be honest with yourself and with everyone. 4. Do your best at all times. 5. Learn and enjoy math. See The Five "R's" for more information. Mathematics is not just numbers and symbols: it is a language for
Not a C Minus is a comprehensive study aid for senior high school Mathematics. It covers topics such as calculus, probability, finance and trigonometry, and uses a conversational, informal teaching style. Every topic is explained in detail, with sample questions and worked solutionsMcCaulay's Pension Actuarial Mathematics covers topics such as (I) interest and mortality, (II) cost methods, (III) amortization and contributions, and (IV) duration and convexity. Each of the four parts has an exercise set with an answer key and explanations. This book teaches the mechanics and methodology of long division, a procedure for dividing numbers without the need for an electronic calculator. Starting with basic concepts, the book explains the method step by step, and then reinforces these concepts using extensive examples and problems with complete solutions. A Tarrington Math Series Book. Most appropriate for grades 5 to 8.
books.google.com - It provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis.... Analysis From inside the book User ratings Review: Mathematical Analysis User Review - Goodreads Probably the only mathematical text I have ever read cover-to-cover. A very good introduction to Analysis as long as you already have some maths background. Naturally as a pure maths text it is very dry, with some positively arid sections, even for one interested in learning the subject. MATH-4210, MATHEMATICAL ANALYSIS II I have ordered the book Strichartz, because Mathematical Analysis I was taught from it. It has a very intuitive approach and presents important results from ... ~kovacg/ classes/ analysis2/ 421.html Mathematical Analysis - tripatlas.Com Analysis has its beginnings in the rigorous formulation of calculus. It is the branch of mathematics most explicitly concerned with the notion of a limit, ... tripatlas.com/ Mathematical_analysis Less About the author (1974) Tom M. Apostol joined the California Institute of Technology faculty in 1950 and is now Professor of Mathematics, Emeritus. He is internationally known for his textbooks on Calculus, Analysis, and Analytic Number Theory, which have been translated into 5 languages, and for creating Project MATHEMATICS!, a series of video programs that bring mathematics to life with computer animation, live action, music, and special effects. The videos have won first-place honors at a dozen international video festivals, and have been translated into Hebrew, Portuguese, French, and Spanish. His list of publications includes 98 research papers, 46 of them published since he retired in 1992. He has received several awards for his research and teaching. In 1978 he was a visiting professor at the University of Patras in Greece, and in 2000 was elected a Corresponding Member of the Academy of Athens, where he delivered his inaugural lecture in Greek.
Spectrum Geometry, Grades 6-8 (Resource Book Only) eBook Grade 6\|Grade 7\|Grade 8 Sale! Ships Free! Price:6.99$5.94Spectrum Geometry Grades 6-8 help young learners improve and strengthen their math skills, such as perimeter and area, triangles and polygons, and points, lines, rays, and angles. The best-selling SpectrumT series provides standards-based exercises developed to supplement and solidify the skills students learn in school. Each full-color title includes an answer key.
MATH 453 Introduction to Real Analysis An introduction to real analysis and its development: infinite series, differentiability, continuity, the Riemann and Cauchy integrals, uniform convergence. Computer exploration and visualization are an essential part of the course
Problem solving in meaningful contexts, language and communication, connections within and outside mathematics, and formal and informal reasoning underlie all content areas in mathematics. Throughout mathematics in Grades 6-8, students use these processes together with graphing technology and other mathematical tools such as manipulative materials to develop conceptual understanding and solve problems as they do mathematics
This commercial website, developed by GCSE Answers Ltd., offers short tutorials on various topics in mathematics, such as algebra, trigonometry, and measurement. The tutorials include a short overview of the topic... This mathematics tutorial gives users an introduction to functions, functional notation and terminology. The site explains how a function is defined, and the correct way to read and write functional notation. Resources... The Open University had long been dedicated to the proposition of providing high-quality educational materials for persons all over Britain and the world. They were one of the first universities to place such materials... Few calculus resources, either online or offline, can match the sheer depth and user-friendliness of Karl's Calculus Tutor. The site contains educational material that is covered in a standard introductory calculus... Created by Alexander Bogomolny, this site is a clearinghouse of fun and engaging mathematics exercises, puzzles, and other such activities that teachers can utilize in their classrooms. Of course, students might happen...
Using Paul Foerster's Algebra and Trigonometry, this course in Algebra II is targeted for high schoolers who have finished Algebra I. We will be focusing on the first 8 chapters of this book. The second half of the book covers Trigonometry and Advanced Algebra, which will be taught the following year. In completing this book, your child will be ready for Calculus. Class time will be spent in answering question from the previous week's materials and then an introduction to the new material. A schedule, with homework for each week, as well as tests for parents to administer at home, will be made available. The tests can be corrected by the instructor if desired. Susi has a B.S. in mathematics and previously taught in high school. She has tutored private schooled and homeschooled students through the years. Required Materials We will be using Paul Foerster's Algebra and Trigonometry by Prentice Hall Classics. This book can be ordered from Veritas Press for $56.76. The link to the book is: number=015041
Niels Lauritzen Niels Lauritzen's new book Undergraduate Convexity has an intriguing title. What about such a book would make it suitable for undergraduates? Convexity is not often taught as its own subject, especially at an undergraduate level. But convexity is an important concept — it is a common form of nonlinearity, and often the most tractable form — and perhaps should be given its own course more often. To assume that undergraduate in the title means elementary would be somewhat misleading. The book is not so much elementary as concrete. It is filled with computational examples and exercises, mostly computations that can be carried out by hand. A graduate student wanting more hands-on experience with convexity could use this book to complement a more theoretical book long on theorems and proofs but short on algorithms and examples. And while Undergraduate Convexity stresses calculations, it does not skimp on theory. It has a number of theorems not always included in books on convexity, particularly results on polyhedra. The book is divided evenly into two parts, devoted to convex sets and convex functions. The former is more substantial because the latter devotes a fair amount of space to reviewing multivariate calculus. This makes the book more self-contained, but it uses up space that could have been used to discuss convex functions in more depth. Also, much of the section on convex functions is more specifically about the optimization of convex functions. Undergraduate Convexity would make an excellent textbook. An instructor might choose to have students present some of the examples while he or she provides commentary, perhaps alternating coaching and lecturing. A course taught from this book could be a good transition into more abstract mathematics, exposing students to general theory then giving them the familiar comfort of more computational exercises. One could also use the book as a warm-up to a more advanced course in optimization.
Taking Math Notes Everybody knows that it's important to take good math notes, but do you really know how to take notes that really make a difference? The old rules may not work for modern students. For example, we've always heard that you should use a sharp pencil to take math notes. But these days it's much better to use a smart pen! Record your lecture as you take notes. No matter how quickly you copy notes in class, you are likely to miss something. If you record the lecture as you write, you can review the teacher's words as you work through the class problems. The best tool for recording math class is the Pulse Smartpen, by LiveScribe. This pen will enable you to tap on any note and hear the lecture that took place while you were writing it. If you can't afford a smart pen, you may be able to use a recording feature on your laptop, iPad, or tablet. If these tools aren't accessible, you can use a digital recorder. Copy every single step of every problem, and in the margins of your notes, jot down anything the teacher says that may give additional clues to the process. Rewrite each problem or process at night as you study. Re-listen to the lecture. Before you leave a class, ask for extra sample problems that are similar to the problems your teacher works through. Try to work through the extra problems on your own-but seek advice online or from a tutoring center if you get stuck. Buy a used math textbook or two with more sample problems. Use these textbooks to supplement your lectures. It is possible that one book author will describe things in a more comprehensible manner than another.
...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered... Read more > Success your children catch up... Read more > Richard Elwes is a writer, teacher and researcher in Mathematics, visiting fellow at the University of Leeds, and contributor to numerous popular science magazines. He is a committed and recognized popularizer of mathematics. Of Elwes, Sonder Books 2011 Standouts said, "Dr. Elwes is brilliant at giving the reader the broad perspective... Everyone knows what a triangle is, yet very few people appreciate that the common three-sided figure holds many intriguing "secrets." For example, if a circle is inscribed in any random triangle and then three lines are drawn from the three points of tangency to the opposite vertices of the triangle, these... Read more > THE PRINCETON REVIEW GETS RESULTS. Get all the prep you need to ace the AP Calculus AB & BC Exams with 5 full-length practice tests, thorough topic reviews, and proven techniques to help you score higher. This eBook edition has been optimized for on-screen viewing with cross-linked questions, answers, and explanations. Inside...Read more > Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall. Just how calculus makes these thingsSuccess in math requires children to make connections between the real world and math concepts in order to solve problems. Extra practice can help young problem solvers advance to more complex topics with confidence. The activities in this workbook are designed to help your children catch up, keep up, and get... Read more >
review of the most important test-taking strategies students should need to know to succeed on this exam Topic review chapters covering all the math students need to know for this test, including: arithmetic, algebra, plane geometry, solid and coordinate geometry, trigonometry, functions and their graphs, probability and statistics, real and imaginary numbers, and logic Three full-length model tests with complete solutions for every problem The manual comes with an optional CD-ROM that presents two additional full-length practice tests with answers, explanations, and automatic scoring
Find a Studio City ACT Tutor Subject: Zip:In introductory linear algebra, this is done using the technique of elimination which works for systems of two or three equations. However, when more than three equations need to be solved simultaneously, one needs to begin using arrays and matrices. Thus, central to linear algebra is the study of matrices and how to perform basic operation such as matrix multiplication.
These include: classical mechanics, electricity and magnetism, and quantum mechanics. Mathematics: Mathematics education includes calculus at the undergraduate level: both single and multi-variate, pre-calculus, trigonometry, and algebra. These subjects are a necessary foundation for physics.
: A Human Endeavor For instructors of liberal arts mathematics classes who focus on problem-solving, Harold Jacobs's remarkable textbook has long been the answer, ...Show synopsisFor instructors of liberal arts mathematics classes who focus on problem-solving, Harold Jacobs's remarkable textbook has long been the answer, helping teachers connect with of math-anxious students. Drawing on over thirty years of classroom experience, Jacobs shows students how to make observations, discover relationships, and solve problems in the context of ordinary experience.Hide synopsis Description:Very Good. 0716704390 Book is lightly used with little or no...Very Good. 0716704390 Book is lightly used with little or no noticeable damage. Unbeatable customer service, and we usually ship the same or next day. Over one million satisfied customers 1350grams, ISBN: 0716704390. Reviews of Mathematics: A Human Endeavor Discussions about Mathematics: A Human Endeavor I love the Jacobs books - I've used Algebra and Geometry with my oldest daughter and had the teachers guide. I'm going to use the 1971 Mathematics book with my younger kids and need to get the answers for this book. Any ideas on where I could get these
9780534419417 ISBN: 0534419410 Edition: 4 Pub Date: 2006 Publisher: Thomson Learning Summary: The Fourth Edition of Yoshiwara and Yoshiwara's MODELING, FUNCTIONS, AND GRAPHS: ALGEBRA FOR COLLEGE STUDENTS includes content found in a typical algebra course, along with introductions to curve-fitting and display of data. Yoshiwara and Yoshiwara focus on three core themes throughout their textbook: Modeling, Functions, and Graphs. In their work of modeling and functions, the authors utilize the Rule of Four, which... is that all problems should be considered using algebraic, numerical, graphical, and verbal methods. The authors motivate students to acquire the skills and techniques of algebra by placing them in the context of simple applications that use real-life data. Yoshiwara, Katherine is the author of Modeling, Functions, And Graphs Algebra for College Students (With Printed Access Card Ilrn Tutorial Student), published 2006 under ISBN 9780534419417 and 0534419410. Five hundred ninety one Modeling, Functions, And Graphs Algebra for College Students (With Printed Access Card Ilrn Tutorial Student) textbooks are available for sale on ValoreBooks.com, three hundred sixty five used from the cheapest price of $1.24, or buy new starting at $97534419417 ISBN:0534419410 Edition:4th Pub Date:2006 Publisher:Thomson Learning is the college student's top choice for cheap Modeling, Functions, And Graphs Algebra for College Students (With Printed Access Card Ilrn Tutorial Student) rentals, or used and new copies that can get to you quickly.
7th Grade English Seventh grade spelling and vocabulary focuses on principles such as meanings of prefixes and suffixes, root words from Greek and Latin, and how to discern the meaning of a new word based on already understood concepts. The comprehensive Analytical Grammar program, a systematic and logical approach to teaching all the basics of grammar in seasonal unit studies, covers parts of speech, parts of the sentence and the basics of sentence diagramming in the first season and all the phrases and clauses in the second season. The Institute for Excellent in Writing (IEW) student intensives breaks down the art of writing into two areas: structure and style. By layering these two components, students develop competency, independence, fluency and creativity all within a system that provides for concrete evaluation and measurable achievement. The literature component of English 7 consists of the reading of four books over the course of the year: The Pearl by John Steinbeck, A Christmas Carol by Charles Dickens, The Jungle Books by Rudyard Kipling, and a book of the student's choice for a combined English and history project. These books are supplemented with poetry, short stories and other writings. Mathematics Students continue to develop skills in adding, subtracting, multiplying, and dividing integers, fractions, mixed numbers, decimal numbers, and integers. They solve problems using percentages, including calculating discounts and markups. Students extend their understanding of numbers to include irrational numbers. They also expand their knowledge of geometric shapes and calculating area of those shapes, as well as their knowledge of geometric solids and volume of solids. A major emphasis in this course is on developing strategies for and expertise in solving word problems. Continuous review of skills learned helps to develop mastery in all areas. Or Pre-Algebra Pre-Algebra lays the groundwork for all upper-level mathematics. It is the bridge between concrete and abstract mathematics. The primary focus of this course is to expose students to the formal notation of abstract mathematics and step by step processing. Problem solving is heavily integrated throughout the entire course in order to connect abstract mathematics to concrete situations. It is desired that students become fluent in basic computations and become fluent in basic computations and develop a solid comprehension of the numbering system, geometric shapes, calculating lengths, areas, and volumes, beginning algebra terminology, data analysis tools and probability techniques, and mathematical reasoning. This course is the key to a successful experience in upper-level mathematics. World Studies 7 Using a textbook by a Christian publisher, the role of God throughout history as well as relationships between God and peoples of a region are explored in this course. Students study examples of people and nations who either followed or failed to follow God's standard and His resulting blessing or judgment. The textbook is divided into four sections and each section is covered during each of the nine weeks periods: Part 1 covers 1100–1650 and includes bits of history from early towns through the developments in Africa. Part 2 (1400–1800) picks up at the age of exploration and the forming of the Americas. Part 3 touches on the time of conquests in Asia and Europe in the 1800′s, and the final section focuses on the last century of major changes in geography, technology and people. Life Science The seventh grade science curriculum is, essentially, biology for middle school. We study many aspects of God's creation; from the complexity of a single cell to overviews of the plant and animal kingdoms. This study begins with learning about the scientific method and creation vs. evolution. Then the students concentrate on the nature of living things: characteristics and needs, structure and function, and interactions. This study continues with the classification of living things into the five kingdoms and an extensive look into the organisms belonging to those kingdoms. The textbook is published by Bob Jones University Press, and life science is taught with a Christian worldview and biblical principles are regularly applied to the concepts. Bible This one-year course consists of an overview of the New Testament, designed to give students a general understanding of who Jesus Christ is and why He came to earth, as well as how the Gospel message of salvation through Christ spread throughout the known world. After examining the Messianic prophecies to discover how they were fulfilled in Jesus Christ, students study the events in Jesus' life and ministry as shown in the four Gospels. Particular attention is given to Jesus' teachings about the kingdom and kingdom living, especially the "Sermon on the Mount," and to his teachings about himself and salvation found in the Gospel of John. Each student learns how he can have a personal relationship with God through Christ and how he can grow in that relationship. Students are expected to memorize at least one Scripture verse per week, and they will be challenged to apply the teachings of Jesus to their lives.
. . . to work independently, complementary to government curriculum development, seeking to develop, pilot and spread alternative approaches and tools for teaching and learning mathematics. MALATI itself later added: and at the same time, to make a direct contribution to Curriculum 2005, e.g. by developing materials as interpretations of Curriculum 2005 and making these available to LACs and publishers for maximum immediate impact. MALATI is a co-operative project of mathematics educators at the Universities of the full-time staff of 12 and part-time involvement of as many university mathematics educators. MALATI philosophy The MALATI University Reference Group developed an initial vision document as a basis for MALATI's work. This grew into a philosophy which underlies MALATI's work and creates the context in which the materials can be used successfully. The main features of this philosophy are: Curriculum Principles: Problem solving as a vehicle for learning and the use of technology (calculators and graphing calculators) as a vehicle for changes in objectives, in content and in pedagogy. MALATI identified the crucial domains of school mathematics as Fractions, Algebra, Datahandling and Probability, Geometry and Introductory Calculus. We organised ourselves into Working Groups on each of these topics, and re-conceptualised each of these content areas through a study of available research, a re-think of appropriate objectives, possible teaching and assessment approaches and an analysis of available materials. Where there was insufficient available research, we did the research ourselves, e.g. we have investigated the development of children's understanding of fractions in the primary school, and their ability to generalise as a basis on which we designed and tested our fraction and algebra materials. Learner activities have thus been developed based on what we know about how children learn these topics, and were updated in the light of experiences of project workers and teachers in the project schools and inputs from other interested parties. The MALATI packages of materials for these five content areas consist of rationale documents, learner activities and accompanying teacher notes reflecting the MALATI approach to the teaching and learning of mathematics in general and the content area in paricular. These packages are designed to cater for the following grades: The MALATI materials have been trialled in seven project schools in the Western Cape in co-operation with the Western Cape Education Department and eight schools in the Northern Province in co-operation with the Mathematics, Science Technology Education College (MASTEC). The trialling process involved observing the use of the materials as well as intensive teacher support in the form of workshops, classroom visits and regular scheduled discussion periods. The packages were continuously revised in the light of the experiences in these schools. Note: All the materials developed by MALATI are in the public domain. They may be freely used and adapted, with acknowledgement to MALATI and the Open Society Foundation for South Africa. To order print copies of the MALATI materials or the MALATI CD, click here MALATI has structured itself into a co-ordinator for each project school in the Western Cape. The co-ordinator regularly visited the school and classrooms and co-ordinates MALATI activities in the school, e.g. arranging for "experts" from our Working Groups to present workshops on that content area, or to give additional classroom support when that specific content area was handled in class. Co-ordinators met all the mathematics teachers in their school on a weekly basis, apart from individual classroom visits and support. Throughout these activities we did not follow a deficit-model, but rather tried to create an atmosphere of co-operation and partnership, to reflect together on our most basic assumptions about the nature of mathematics, of learning mathematics and of teaching mathematics. Evaluation research MALATI decided that the most worthwhile general research would be to investigate, document and analyse classroom culture and changes in the classroom culture over time. We have investigating three areas: 1. Changes in teachers' classroom practices 2. Changes in teachers' beliefs 3. Changes in students' achievement and relationships between these areas. We have developed research tools for each of these areas, have collected and analysed base-line data for each area, and have followed changes in each area through ongoing classroom observations, discussions, interviews, questionnaires and tests.
Elementary Number Theory - 98 edition Summary: This book gives an undergraduate-level introduction to Number Theory with the emphasis on fully explained proofs and examples; exercises (with solutions) are integrated into the text. The first few chapters covering divisibility prime numbers and modular arithmetic assume only basic school algebra and are therefore suitable for first or second year students as an introduction to the methods of pure mathematics. Elementary ideas about groups and rings (summarised in an appendix) are t...show morehen used to study groups of units quadratic residues and arithmetic functions with applications to enumeration and cryptography. The final part suitable for third-year students uses ideas from algebra analysis calculus and geometry to study Dirichlet series and sums of squares; in particular the last chapter gives a concise account of Fermat's Last Theorem from its origin in the ancient Babylonian and Greek study of Pythagorean triples to its recent proof by Andrew Wiles. ...show less Light shelving wear with minimal damage to cover and bindings. Pages show minor use.Help save a tree. Buy all your used books from Green Earth Books. Read. Recycle and Reuse. $16.59 +$3.99 s/h Good Goodwill of Orange County Santa Ana, CA Good $2275 +$3.99 s/h Good Greener Books London, 07/31/1998 Paperback 1st ed. 1998. Corr.
Algebra 1 Activities Overview Welcome to the wonderful world of algebraic computation! This activity book offers puzzles, games, and activities suitable for students who want to have fun while becoming more adept in mathematical skill and ability. Algebra provides many of the core foundations for a large number of career paths. Algebra 1 Activities provides students with a practical, useful, and fun way to learn while preparing for studies in medicine, architecture, computer science, meteorology, media, statistics, accounting, engineering, industry, and parenting. Designed with both the instructor and students in mind, Algebra 1 Activities facilitates meaningful teaching and learning opportunities. It covers various mathematics topics that may be used as follow-up or supplementary activities to guided instruction at the teacher's discretion. Several activities are included for extended practice if required. They are logically arranged for a smooth progression through mastery of mathematics skills and can be adapted to fit the students' needs, abilities, and learning styles. Algebra 1 Activities allows for creativity, flexibility, and the enhancement of learning experiences in mathematics.
Video Summary: This learning video presents an introduction to graph theory through two fun, puzzle-like problems: "The Seven Bridges of Königsberg" and "The Chinese Postman Problem". Any high school student in a college-preparatory math class should be able to participate in this lesson. Materials needed include: pen and paper for the students; if possible, printed-out copies of the graphs and image that are used in the module; and a blackboard or equivalent. During this video lesson, students will learn graph theory by finding a route through a city/town/village without crossing the same path twice. They will also learn to determine the length of the shortest route that covers all the roads in a city/town/village. To achieve these two learning objectives, they will use nodes and arcs to create a graph and represent a real problem. This video lesson cannot be completed in one usual class period of approximately 55 minutes. It is suggested that the lesson be presented over two class sessions
Offering 9 subjects including calculus
Master Math: Probability is a comprehensive reference guide that explains and clarifies the principles of probability in a simple, easy-to-follow style and format. Beginning with the most basic fundamental topics and progressing through to the more advanced, the book helps clarify probability using step-by-step procedures and solutions, along with... more... Like other areas of mathematics, geometry is a continually growing and evolving field. Computers, technology, and the sciences drive many new discoveries in mathematics. For geometry, the areas of quantum computers, computer graphics, nanotechnology, crystallography, and theoretical physics have been particularly relevant in the past few years. There... more...
Post navigation I've made a change in my links: Picalc is gone; it's been replaced by eCalc (shown above) and the link is on the sidebar. This compact, handy calculator has a lot of features which are hidden from sight, giving the calculator a clean interface. The features are available through the "Menu" and "Side Bar" keys and the active features are shown at the top; the eCalc link gives comprehensive documentation. Pressing the "Menu" key lets you change the settings that are shown at the top. The angle choices are degrees, radians, and gradients. The coordinate system is either rectangular or polar. The number format can be either standard, fixed, scientific, or engineering. Last, but certainly not least, you can change the mode from a standard calculator to an RPN calculator. If you've ever had the chance to get comfortable with an RPN calculator, it's really helpful in speeding through calculations because you are able to put numbers and calculations on the stack and use them as needed. Pressing the "Side Bar" key opens up some more options. The options available from pressing "Menu" are shown above the calculator and the options available from pressing "Side Bar" are shown, naturally enough, on the side. I like the unit conversion feature; just enter a number in one of the fields and all the conversions are displayed. This calculator has a lot more features including Complex Numbers, Constants Library, Online Solver (linear and polynomial), and Base Converter; you can read about them in the documentation, Combinatorics and probability are two of the more difficult subjects to learn and to teach. Difficult to learn because it's easy to make a come up with an answer in a logical way which is very, very wrong. It's difficult to teach because students steadfastly resist showing their work. Combining those two facts results in a mess unless the curriculum has a lot of time to get them trained properly. For almost any problem of reasonable difficulty and you can find your class has come up with 7 or 8 different answers and most answers aren't even close to the correct answer. When you ask how they got their answer they don't have much work to show and struggle to explain it. Breaking that down is problematic. Math IS difficult, especially when you have lousy habits. I try to teach good habits, but getting "good" American students to do it "your" way is more difficult than the overseas students I've taught (not that they're excellent either). An important part of those good habits shows up when a problem uses the Fundamental Principle of Counting. IF you can get students to show steps (find the events, count the number of outcomes for each event, and give an example of what has been ascertained) they can get it. I've posted two examples on theHandoutspage of showing your work in an organized fashion. It's the sort of process I want them to go through, too. The first is determining the probability of 1 pair in poker, and the second is determining 2 pairs. Determining two pairs causes problems for all but the best students so it's a decent example to use in class while you're teaching. 1. Start with the famous Dr. Edward Frenkel: He laments that the math curriculum we have is boring and fails to show the beauty and utility of mathematics. In this article you have a video and podcast as well. Dr Frenkel connects math with hacking e-mail, changing the CPI calculations to raise taxes and cut benefits, and the financial crash in 2008. In this LA Times OP-ED piece, Dr Frenkel puts the blame on a curriculum of studying mathematics that is more than a thousand years old. The LA Times article says, "For." and leads to his point, ".". Personal comment: Many students lack the basics (multiplication tables and fractions) needed for the course they're in and many math teachers (thanks to certification requirements that don't care about math qualifications) don't have that knowledge or appreciation of "power and exquisite harmony of modern math". Add on top of that the a curriculum that is stuffed full of too many topics (a "firehose approach" to learning). In my case I have to cover 1100+ pages of text for the accelerated class I teach. Dr Frenkel's approach is the right prescription IF the students in a class have the proper foundation and IF the teacher has the requisite knowledge and IF (a really big if) there was time in the curriculum. As such it wouldn't fly very well in a typical public school. The need for a teacher to cover the material so the students are prepped for the multiple choice state test that measures their knowledge (which then determines whether the teacher has done their job) precludes that. 2. More typical of today's public school is this article where I found a lot of valid points: "The latest educational fad term is "STEM," which stands for a curriculum in the areas of science, technology, engineering and mathematics. GOOGLE reports over 174 million pages on "STEM education" alone. The problem is that adults, including some educators, still haven't figured out how to make peace with the "mathematics" in STEM. Everyone applauds classes in high-tech robotics as the sine qua non of a good STEM program, but ask them to explain how they integrate any mathematics content into the robotic curriculum and you may be surprised that most of these programs do not even work with mathematics teachers to legitimize themselves."...."The NASA brand has become synonymous with inspiring students, making them feel excited about what they know, and enticing them to learn more about STEM careers. The problem is that in our society, mathematics tends not to make people feel they are competent; it does not excite our emotions in a positive way, and often engenders a sense of dread. Any marketing expert will tell you that mathematics is the poison-pill for any brand, and so over the years NASA and other agencies have largely hidden their mathematics expertise from public view. ... There are no down-sides to students building robots out of parts from a box, and watching as these battery-powered critters scurry around the classroom floor. There is also little or no math involved in these curricula."....."But if you think that NASA is alone in some sinister plot to de-emphasize mathematics you are wrong. Virtually every federal agency that offers STEM resources to teachers does so by minimizing the mathematical content. They do this, for example, by creating middle and high school STEM activities that cover math skills far below what the students see in their corresponding math classes. The rush to make activities "hands-on" has seemingly created legions of resources that have students measure and plot and take a few percentages, but never delve into math concepts above grade eight such as linear equations, statistics and mathematical modeling.". Personal comments: The "regular" Algebra 2 and Geometry classes I've taught have students who still haven't mastered their multiplication tables. They've been passed along through the system even though they don't know what they're doing. In one school I was at, the guidance counselors decided the math classes the student would take for the next year---in many cases over-riding the opinions of the math teacher who had just taught them. That meant students who complained enough would be put into honors classes (even though they didn't belong) and since there were too many students like that, the overall quality of the course suffered. Welcome to today's world of education; the emphasis is not on setting standards. It's more about placating parents and students. 3. Canada has problems that sound just like our math problems and they've identified discovery education as a culprit in why there math scores are going down: "Ontario's curriculum, however, does not require students to memorize multiplication tables or learn basic algorithms such as long division. They are instead encouraged to break problems down into smaller portions to work through them.". Likewise, here you'll find: " "If you look at what's been happening, predominantly over the last decade, there's been an unprecedented emphasis on discovery learning," said Donna Kotsopoulos, an associate professor in Wilfrid Laurier University's education faculty and former teacher. Robert Craigen, a University of Manitoba mathematics professor who advocates basic math skills and algorithms, said Canada's downward progression in the international rankings – slipping from sixth to 13th among participating countries since 2000 – coincides with the adoption of discovery learning....Parents in Alberta, Ontario and British Columbia, for example, launched petitions over the Christmas holidays, calling on their governments to revamp curriculums with a greater emphasis on basic math skills.". Finally, this article summarizes the problem: "The one side says, "drill and kill." The other says "drill for skill." Basically, though, just about every mathematician and math education researcher who was interviewed for this story agrees that the perfect math class should have a mix of skills and problem solving. They just can't agree on the amounts of each, when to add them, and what to skip."...."How does Shanghai do so well? They devote an average of 14 hours a week to homework (versus three for the Canadians) and 70 per cent have parents willing to pay for extracurricular math classes (versus 28 per cent in Canada). And those students who seem to spend so little class time on math also have teachers trained more rigorously and subject to greater supervision."....." top-performing Asian countries typically cover fewer subjects more deeply, especially in the early grades. A 2004 study found that Grade 1 teachers in Canada were expected to cover 18 topics versus just five in Hong Kong, where even textbooks may be hundreds of pages shorter.". Personal comments: Understand that the poor educational results our country has are inflated. They're pulled up by students who are getting extra tutoring outside of class to fill in the deficiencies of the educational system. Most students that I've encountered lack basic skills (multiplication tables and fractions) and then the schools put calculators into their hands to avoid the drudgery of calculations; they never learn their arithmetic or algebra. But no big deal, pass them through the system and onto the college level. Complaints from parents are minimized, students can claim they're taking accelerated classes even when they lack the math skills of an accelerated student. Now the college has to figure out what to do with them. In previous posts, here, here, and here, we've seen how Sage's ability to calculate points for functions makes it a viable engine (and convenient alternative due to Sagemath Cloud) to generate Tikz/pgfplots pictures, rather than gnuplot. Actually, Sage and sagetex are an improvement over gnuplot. Don't believe me? Take a look at this post here at TexStackExchange and you might get the impression that for complicated graphs you're "better off" with Asymptote/PSTricks because pgfplots doesn't have any "numerical integration schemes". Now look at the post which it is said to be a duplicate of and you'll see more discussion of why pgfplots is not as effective as PSTricks. In both questions the users specifically asked a question about how they should plot something in Tikz/Pgfplots and in the only case where an answer was accepted the user settled for a PSTricks solution. In that second post a comment to the original questions says, "If you want to use TikZ then, you could use gnuplot. It doesn't support integration natively, but you can find examples easily googling them.". If you've ever seen this post you'll get more details on things that PSTricks can do that Tikz struggles at. In the comments to that question, Alain Mathes (the designer of the Altermundus packages) writes, "The limits actually of TikZ is pgfmath. Calculus with Tex are not efficient and often very slow. We can do a lot of things with TeX but we can't compare calculus and programming with postscript and the same thing with TeX. Now perhaps lua and luatex can change something. With lua and some modules we can do I think everything but I don't how if the compilation is not too slow ?". It should now be clear that there are weaknesses with the math skills of Tikz and gnuplot; the only issue seems to be overhead (Sage is big, Lua is small...perhaps a stripped down Sage version can be made?). But go back to that first post I mentioned. I submitted the only answer that answered the question using pgfplots by relying on Sage and the sagetex package. Sagemath Cloud gets them to work with LaTeX. So it seems clear (gnuplot's limitations of integration aren't a problem with Sage) that Sage should, at the very least, be an option in Tikz/Pgfplots. See, for example, the gallery of pgfplots examples and check out how gnuplot is called: \begin{tikzpicture} \begin{axis}[view={0}{90}] \addplot3[contour gnuplot] {xy}; \end{axis} \end{tikzpicture} Why not an option for contour Sage and have Sage do the work? That is: \addplot3[contour sage] {xy}; That built in support is needed because the work-arounds like I showed are just a little too difficult--the PSTricks answer was not only accepted by the user (who wanted a pgfplots solution) but it got more upvotes than the only solution that answered the question. What's up with that?!?!? I've added another "proof of concept" example using sagetex, sage and pgfplots to the Plotting with Sagetex page. The example, shown above, illustrates how 3D graphs can be created. The extra complication with 3D graphs is you need to indicate the number of rows of data; but Sage can take care of that as well. Change step from 0.20 to 0.25 and the mesh will adjust. You can find the code here that you can use as a template. If and when these package developers start using Sage (with/without gnuplot) as the computational engine then plotting in LaTeX will take a big step forward. I've added another problem to the Sagetex: Combinatorics/Probability page. For this problem the user chooses a word (in capital letters), such as CALCULUS shown above, and the problem asks how many different arrangements are there using all the letters. The solution will create a table showing the distribution of the letters and print out the answer both as a formula and as a number. Complications arise from trying to get the the answer in both forms: if you try to typeset the answer outside of sagesilent then you don't have knowledge of which letters were repeated how many times. This needs to be done inside sagesilent and is calculated here (formatting is not accurate). I've created a new page for sagetex problems involving combinatorics and probability. The first problem is a classical balls drawn from an urn problem. The output is shown above and it can be found on the Sagetex: Combinatorics/Probability page. Infinity, you say (or maybe "that's a divergent series")? Actually, it's , and the Numberphile website has the math to prove it. They've been mentioned in an article by the NY Times and the video I'm talking about is embedded there. The answer of , "as absurd as it sounds, has been verified to many decimal places in lab experiments."...."But there is broad agreement that a more rigorous approach to the problem gives the same result, as shown by a formula in Joseph Polchinski's two-volume textbook "String Theory."" Continuing from the NY Times article, "In modern terms, Dr. Frenkel explained, the gist of the calculations can be interpreted as saying that the infinite sum has three separate parts: one of which blows up when you go to infinity, one of which goes to zero, and minus 1/12. The infinite term, he said, just gets thrown away. And it works. A hundred years later, Riemann used a more advanced and rigorous method, involving imaginary as well as real numbers, to calculate the zeta function and got the same answer: minus 1/12.". That's all over my head, but throwing away "the infinite term" doesn't sound quite correct mathematically, even if it makes the physics work. 3. If you are following the world of Common Core, the opposition keeps growing. It's been a mess from my first row seat, too, and the criticism is coming from all sides: But ultimately, it's not that surprising. Education movements come and go, each one promising to make things better before it is ultimately abandoned for something else. This is the year "... all U.S. public schools were going to reach 100 percent student proficiency, thanks to No Child Left Behind (NCLB).". I liked the opinion voiced here, "When students complete eight years of learning (elementary and middle school) and are unable to achieve the percentile of literacy that is required, they should then be permitted to attend a tech school where the emphasis would be on learning a job skill that would help them become employable when they graduate." 4. Nevada has addressed the issue of the inability of students to meet proficiency exams head on (yes, that's sarcasm) by making them easier to pass. "Board member Dave Cook of Carson City said research has shown no evidence that students who pass the exams are more successful in college or career, so "why prolong them?" "This is a totally subjective process forced upon students when it is of no benefit," he said.". Which makes you wonder why they forced students to go through the "totally subjective process" to begin with. Sounded like a good idea at the time, I'll bet. "The board will likely decide on what the new passing score will be Feb. 26, when a test vendor presents the estimated minimum score needed to maintain a 54 percent pass rate among sophomores. Students first take the test their sophomore year and can retake the test throughout high school until they pass. This year, 56 percent of sophomores scored at least 252 on their first, so the new minimum will likely be around there, state officials said.". So set the standard low enough that it can be met now, whether or not (it's not) that level is an appropriate standard. Sigh. In earlier posts I used the sagetex package to force sage do the calculations for the Altermundus packages (rather than gnuplot). With Sagemath Cloud putting Sage at your fingertips you don't need to go through the hassle of gnuplot. Although the Altermundus packages let you insert the output string between \begin{tizpicture}...\end{tikzpicture}, pgfplots isn't so obliging. I've managed to get that working as well but it requires making the output string contain everything from \begin{tizpicture} to \end{tikzpicture}. This use of sagetex creates the data on the fly, so there's no need for an external data file. You can see the code running above; the Plotting with Sagetex page has more details and the code to download. Just change the function and plotting parameters to what you want and you'll have Sage crunching the math. The Plotting with Sagetex page also includes Dr. William Stein's instructions on how to increase the buffer for Sagemath Cloud. In trying to adapt the sagetex package to the beautiful packages of Altermundus there are some rough patches: so many macros rely on (at some level) the Gnuplot program. I added an example to the Plotting with Sagetex page to address some issues that come up. The biggest problem is that if a function has a large derivative then there is an issue that the graph (red curve above) doesn't go to the edge of the screen because the step size is too small--but increasing the step size results in too many points and it can't be graphed. I can fix this on my local tex installation of by changing the buffer size to a bigger number (from 200000 to 1000000). It takes a longer time for sagetex to process but eventually you can get the desired output: I don't know how to fix that on Sagemath Cloud, though. You can read more of the details by clicking here.
ICE-EM Maths Aust Curriculum Ed Year 10 (&10A) Book 2 A complete 5-10A mathematics series for the Australian Curriculum. The ICE-EM Mathematics series was created by the Australian Mathematical Scien... ICE-EM Mathematics Year 7 Book 1 & 2 Australian Curriculum Editions have been rewritten and developed for the Australian mathematics curriculum, while retaining the structure, depth and approach of th... ICE-EM Mathematics Year 8 Book 1 & 2 Australian Curriculum Edition has been rewritten and developed for the Australian mathematics curriculum, while retaining the structure, depth and approach of the ... The aim of the International Centre of Excellence for Education in Mathematics (ICE-EM) is to strength education in the mathematical sciences at all levels - from school to advanced research and conte... A complete 5-10A mathematics series for the Australian Curriculum. The ICE-EM Mathematics series was created by the Australian Mathematical Sciences Institute (AMSI) to provide a mathematics program t...
Browse Results Modify Your Results The Algebra 1/2 course focuses on introductory algebra topics. It is designed to facilitate your transition from the concrete concepts of arithmetic to the abstract concepts of algebra. One feature of Algebra 1/2 that you will find particularly useful is the lesson reference numbers in the problem sets. Beneath each problem number in the problem sets is a number in parentheses; this number refers to the lesson where the concepts and skills required to solve the problem are introduced. Should you have difficulty solving a particular problem, refer to the appropriate lesson for assistance. The book contains daily lessons and investigations. Each lesson begins with practice of basic number facts and mental math that will improve speed, accuracy, and ability of students to do math. The pattern and problem-solving activities give practice using strategies that help solve more complicated problems. Practice problems focus on the topic of each lesson. Following each lesson is a problem set that reviews the day-to-day learning skills. Investigations are variations of the daily lesson. This book is made up of daily lessons and investigations. Each lesson has four parts. The first part is a Warm-Up that includes practice of basic facts and mental math. The second part of the lesson introduces a new mathematical concept and presents examples that use the concept. Third one, the Lesson Practice helps solve problems involving the new concept. The final part is the Mixed Practice which reviews previously taught concepts and solving the problems set gives much benefit to students. This book was written to help you learn mathematics and to learn it well. For this to happen, you must use the book properly. As you work through the pages, you will see that similar problems are presented over and over again. Solving each problem day after day is the secret to success. This book is made up of daily lessons and investigations. Each lesson has four parts. The first part is a Warm-Up that includes practice of basic facts and mental math. This book contains word problems that are often drawn from everyday experiences. It's also made up of daily lessons and investigations. Each lesson has four parts. The first part is a Warm-Up that includes practice of basic facts and mental math
Course MAT202 Introduction to Linear Algebra Introduction to linear algebra, mostly in real n-space. Companion course to MAT201. Introduces more algebraic methods needed to understand real world questions. Whereas MAT201 develops calculus in a multivariable setting, this course develops fundamental algebraic tools involving matrices and vectors to study linear systems of equations and Gaussian elimination, linear transformations, orthogonal projection, least squares, determinants, eigenvalues and eigenvectors and their applications. Emphasizes concrete computations over more theoretical considerations. Because this is an algebra course, it is necessarily more abstract than MAT201, and requires some general arguments and consideration of exceptional cases on exams, mostly in the form of true/false questions, an intermediate between formal proofs and concrete computational questions. Matrices, linear transformations on real n-space, linear independence and dimension, bases and coordinates, determinants, orthogonal projections, least squares, eigenvalues and eigenvectors and their applications to quadratic forms, dynamical systems and differential equations. Complex eigenvalues and eigenvectors are also covered in the 2 by 2 and 3 by 3 cases. Description of classes Classes meet 3 times per week, for 50 minutes. Sections are generally offered MWF at 9, 10, 11 and 12:30 in both semesters. The course is organized into small sections of 20 to 30 students. There is one course head who coordinates with all the instructors to write the exams. All students have the same homework assignments and take the same midterm and final exam. The midterm and final count for the bulk of the course grade, typically about 70%. These exams are graded by all the instructors and graduate student AI's together to ensure uniformity across all sections. Typically there are two in-class quizzes, the same for all sections. Homework and quizzes together usually account for about 30% of the course grade. In order to do well in the course, we anticipate that most students will need to spend approximately ten hours per week reading the text, reviewing class notes, solving homework problems and working through lots of extra practice problems to prepare for quizzes and exams. The course will be quite fast-paced and it is essential to work steadily throughout the semester. Frequent feedback will be given to help students keep up and monitor progress. Notes MAT201 and MAT202 can be taken in either order, but we recommend you take MAT201 first. The course does not use much calculus, and although it treats many of the same topics as MAT201, it does so more algebraically. Either treatment can reasonably come first. The least abstract and most computational of our three introductory linear algebra courses (MAT202, MAT204, and MAT217); provides a very solid introduction to the subject sufficient for most future engineers and scientists. MAT175 is intended for students who will not take futher mathematics courses at Princeton but in rare cases it may be possible for a highly motivated student who received a grade of at least B+ to attempt MAT202 afterwards. Such a student should expect to work extremely hard in order to succeed as this course demands much greater mathematical maturity than does MAT175. (Students who have already taken MAT175 should not take MAT201.) Although MAT104 is listed as a prerequisite, the course does not require much calculus knowledge, although prior experience with vectors is very useful. This course does however require strong motivation and some mathematical maturity; students who are not following the standard science/engineering tracks should use caution. Who Takes This Course The typical student is an incoming freshman or sophomore with plans to major in engineering or one of the sciences; however, many other students with quantitative interests (e.g. economics or finance) take this course, especially those with possible graduate work in mind. It gives a solid introduction to linear algebra suitable for most students who want to use mathematics as an analytic tool in later studies in other fields. Most students in MAT202 in the fall semester are sophomores who took MAT104 and MAT201 in their freshman year. Most students in the spring are freshmen continuing from MAT201 Students who consider a major in physics should take MAT204 or MAT217 instead, as do many of the more mathematically inclined future scientists and engineers. These are better linear algebra choices for students who plan to take 300-level math courses here at Princeton. Prospective math majors should probably take MAT217 instead (after MAT214 or MAT215). Some students who are more interested in applied math opt instead for MAT204. Students interested in econometrics should take this course instead of (or in addition to) MAT175. AB COS majors are not required to take MAT201. They need only MAT202 (or MAT204 or MAT217). Placement and Prerequisites While MAT201 is normally taken first, it is not a prerequisite. The main requirement is the maturity and self-reliance that students usually learn there. Strong interest in thinking rigorously about problems, rather than learning cook-book type algorithms is required. I already took linear algebra in high school, do I have to take this course? • Many students in MAT202 have had some multivariable calculus and/or linear algebra before, but rarely with the same depth and thoroughness. If you need the course for upper division courses in your major, then you are probably better off to take MAT202 even though some material will be review. And if you really love math, you might be able to consider taking MAT204 or MAT217 instead. • Take the sample final. Can you do any of the problems? For most students, the answer will be no. Review your old notes and try again. Can you do at least 60% of the exam? • In rare cases, the placement officer will decide that your prior work is indeed equivalent to MAT202 at Princeton. It will be helpful if you can bring your graded exams from the course you took to show him/her. You may also need to take an exam to demonstrate your knowledge. Can I take MAT201 and MAT202 in the same semester? • It is not impossible, but we do not recommend it. It makes midterm week particularly unpleasant, but if you have a very good reason for it and you are a very strong student, it can be done. It will likely mean that you will get a lower grade in one of them that you would otherwise have done. How much work is this course? • Most math courses require a steady time commitment. We expect that the weekly problem sets will take at least 3 hours to complete, although this can vary quite a lot depending on your background and goals. To do well on exams, you need to work through a lot of extra problems. All in all you should be ready to spend up to then hours per week working outside of class. Because the material is more abstract than a calculus course, it often takes more time to digest the new material. Last minute cramming is especially unwise for this course. I can't fit this course into my schedule. Can I take this course for Princeton credit at another university? • Yes, but it may be difficult to find an equivalent course. Many linear algebra courses at other universities cover only about half of 202. See our detailed guidelines for summer courses. I have more questions that are not answered here. What should I do? • First, check the undergraduate home page or the general FAQ for more information about how our courses work in general and about who to contact if you need to discuss your situation with someone from the math department. In addition, representatives from the math department will be available at freshman registration.
This is a free online textbook designed for the Advanced Algebra instructor. According to the author, he "developed a set of... see more This is a free online textbook designed for the Advanced Algebra instructor. According to the author, he "developed a set of in-class assignments, homework and lesson plans, that work for me and for other people who have tried them. The complete set comprises three separate books that work together:•The Homework and Activities Book contains in-class and homework assignments that are given to the students day-by-day." "•The" target=״_blank״ Concepts Book provides conceptual explanations, and is intended as a reference or review guide for students; it is not used when teaching the class." •The" target=״_blank״ Teacher's Guide provides detailed lesson plans; it is your guide to how the author "envisioned these materials being used when I created them (and how I use them myself) " target=״_blank״ Instructors should note that this book probably contains more information than you will be able to cover in a single school year." According to the OER Commons, "Word 2007 is a word processor designed by Microsoft This manual will show you some more... see more According to the OER Commons, "Word 2007 is a word processor designed by Microsoft This manual will show you some more advanced features of the program and is aimed at students preparing to write their thesis. The manual covers: Outlining; Using styles; Creating a table of contents; Defining document sections; Effective use of graphics.״ This is a free, online textbook offered by the National Institute of Child Health & Human Development. "Based on decades... see more This is a free, online textbook offered by the National Institute of Child Health & Human Development. "Based on decades of NICHD research on parenting, this 62-page booklet gives parents the tools they need to make their own decisions about successful parenting. The booklet provides real-world examples and stories about how some families include responding, preventing, monitoring, modeling, and mentoring in their own daily parenting activities.״ This is a free textbook by Boundless that is offered by Amazon for reading on a Kindle. Anybody can read Kindle books—even... see more This is a free textbook by Algebra textbook is a college-level, introductory textbook that covers the important subject of Algebra -- one of the basic building blocks of studies in higher mathematics. Boundless works with subject matter experts to select the best open educational resources available on the web, review the content for quality, and create introductory, college-level textbooks designed to meet the study needs of university students.This textbook covers:The Building Blocks of Algebra -- Real Numbers, Exponents, Scientific Notation, Order of Operations, Working with Polynomials, Factoring, Rational Expressions, Radical Notation and Exponents, Basics of Equation SolvingGraphs, Functions, and Models -- Graphing, Functions: An Introduction, Modeling Equations of Lines, Functions Revisited, Algebra of Functions, TransformationsFunctions, Equations, and Inequalities -- Linear Equations and Functions, Complex Numbers, Quadratic Equations, Functions, and Applications, Graphs of Quadratic Functions, Further Equation Solving, Working with Linear InequalitiesPolynomial and Rational Functions -- Polynomial Functions and Models, Graphing Polynomial Functions, Polynomial Division; The Remainder and Factor Theorems, Zeroes of Polynomial Functions and Their Theorems, Rational Functions, Inequalities, Variation and Problem SolvingExponents and Logarithms -- Inverse Functions, Graphing Exponential Functions, Graphing Logarithmic Functions, Properties of Logarithmic Functions, Growth and Decay; Compound InterestSystems of Equations and Matrices -- Systems of Equations in Two Variables, Systems of Equations in Three Variables, Matrices, Matrix Operations, Inverses of Matrices, Determinants and Cramer's Rule, Systems of Inequalities and Linear Programming, Partial FractionsConic Sections -- The Parabola, The Circle and the Ellipse, The Hyperbola, Nonlinear Systems of Equations and InequalitiesSequences, Series and Combinatorics -- Sequences and Series, Arithmetic Sequences and Series, Geometric Sequences and Series, Mathematical Inductions, Combinatorics, The Binomial Theorem, Probability' " Algebra for College Students is designed to be used as an intermediate level text for students who have had some prior... see more " Algebra for College Students is designed to be used as an intermediate level text for students who have had some prior exposure to beginning algebra in either high school or college. This text explains the why's of algebra, rather than simply expecting students to imitate examples online textbook that is linked to the overall site, All About Circuits. This book covers DC circuits,... see more This is a free online textbook that is linked to the overall site, All About Circuits. This book covers DC circuits, including Basic Concepts of Electricity, OHM's Law, Electrical Safety, Scientific Notation, etc., AC circuits,... see more This is a free online textbook that is linked to the overall site, All About Circuits. This book covers AC circuits, including Basic AC Theory, Complex Numbers, Reactance and Impedance, Resonance Semiconductors,... see more This is a free online textbook that is linked to the overall site, All About Circuits. This book covers Semiconductors, Amplifiers and Active Devices, Solid-State Device Theory, Diodes and Rectifiers Direct circuits,... see more This is a free online textbook that is linked to the overall site, All About Circuits. 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Course Description:As suggested by the title of the textbook, this course is about functions, and how to use functions to model situations and contexts, and to solve "real-world" problems.In particular, we will be interested in polynomial, rational, trigonometric, exponential, and logarithmic functions. Goals:Students will understand: ·The definition of function ·Classes (polynomial, rational, trigonometric, exponential, and logarithmic) of functions in terms of their equations, their graphs, and the contexts in which these kinds of functions are relevant ·How to model problems in context with mathematical functions and how to interpret solutions in context ·How to solve problems using problem-solving strategies and metacognition ·How and when to use mathematical reasoning, explanation, and proof Expected Outcomes:Students will be able to: ·Identify functions as such from a given representation of a relation ·Use mathematical reasoning to identify a class of function or a specific choice of function within a class depicted in a graph and explain their choice ·Use mathematical reasoning to predict the behavior (asymptotes, domain, range, behavior "at infinity") of functions from their description with an equation or table ·Set up and justify the use of functions as models for problems set in context and solve and interpret answers appropriately ·Construct examples of functions with given behaviors ·Represent functions in words, with equations, in tables, and with a graph, and construct the other representations from a given one ·Identify problem-solving and metacognitive techniques and use them appropriately to solve problems ·Prove trigonometric identities and derive properties of functions from other properties Assessment: Homework98 Reflective Essay50 Journal150 Quizzes150 Exams300 Final252 Total1000 Homework:Homework is assigned weekly and turned in each Friday.If you cannot be in class, have someone turn your homework in for you or turn it in to my office on the day it is due.Late homework is not accepted.Full credit (7 points) is given if all work is completed and correct.A score of 6 points is given to work that is complete but not all correct.A score of 5 points or fewer indicates that no substantial work was done on one or more assigned problems. Reflective Essay:You will be given an article on metacognition.You will then have two opportunities in class to solve a problem and track your metacognitive processes. Based on evidence from these two opportunities and your other course work, you are to write an essay to defend or refute the statement, "My awareness of metacognition and my experience with teaching through problem-solving in this class has changed my beliefs about mathematics and my ability to do mathematics."The essay is to be three-quarters of a page to one page long, typed and double-spaced in 12-point Times New Roman or Courier font.You will turn in your evidence with your essay. Journal:For each day of class you will have assigned reading, prompts, and exercises (see Reading Prompts and Schedule below).Your responses to the reading prompts and to the exercises are to be kept in a three-ring folder that will be collected every class period and returned the following class.See the schedule for details on the reading prompts and the list of exercises. Quizzes:There will be 3 quizzes, each worth 50 points.Quizzes will be held on the following days:September 9, September 28, and October 28.Each quiz will last approximately 30 minutes and will be given during the last 30 minutes of class. Exams:There will be 2 exams, each worth 150 points.Exams will be held on Monday, October 10, and Monday, November 21. Final:The final will be held Wednesday, December 14, from 11:30-1:30, and will be cumulative. Creating Conditions for Successful Learning:Research shows success in math class depends very much on two factors:the amount of time spent working on the material, and the student's beliefs about mathematics and what it means to understand and do mathematics.With this in mind, here are some suggestions: Be in class, every class, and be on time. Be prepared to participate in group work and discussions every day so that class time is not wasted, and Spend at least 1 hour every day, not including class time, working on homework assignments, readings, journals, and studying. Realize that mathematics is not just a set of procedures, and that mathematical concepts involve a lot of thinking and reasoning.Consequently, being able to execute procedures accurately is only one part of doing well in this class. Realize that success in mathematics is less about "ability" and more about willingness to think and to work hard to make sense of things. In addition, you need to have: your assignments with you and ready to turn in on the day they are due the numbers and emails of at least 2 classmates so that you can be informed if you miss a class. Make-up Policy:I do not accept late or make-up work.If you experience a major emergency, special arrangements may be made at my discretion.Please make every effort to contact me as soon as possible when you know you will miss a class due to an emergency; do not wait until the next class to ask about being excused from an assignment. Classroom Norms:As we will spend a lot of time working in partnerships, in groups, and in class discussions, here are some rules to help you navigate what may be an unfamiliar experience in math class. Never call out an answer until the person leading the classroom has given permission.Raise your hand. This is a safe environment.That means that you should feel free to ask a question or offer an opinion or an answer, and no one will make fun of you for what you say.We will discuss how to disagree with or question fellow students when they are sharing their work. If you are working with classmates, work with them.Do not wait and hope that others will do your work for you, and do not move on to other assignments while your classmates are struggling to understand the current one. Be considerate of others.In addition to the ways to be considerate listed above, do not dominate group or class discussions.Remember that everyone needs an opportunity to share his/her ideas. Do not expect me to validate your answers or those of anyone else.You are responsible for making sense of answers and solution methods, and you should always look for ways to verify your work. Cell phones should be off or set to "vibrate."Do not place a call during class, and do not answer a phone call without first leaving the room. These rules are meant to benefit the entire class, and to ensure that everyone has the opportunity to contribute and to learn. Academic integrity is expected.I enforce university policies on academic integrity.In particular, cheating, fraud, plagiarism or other academic dishonesty is unacceptable and will be cause for disciplinary action. Reading Prompts:You are assigned reading for each class, and you are expected to make sense of the reading on your own time.Traditionally, you have probably had instructors who solved exercises for you in class and then assigned you to do similar problems.Perhaps the instructor didn't even bother with the word problems, or solved them all for you.Unfortunately, this practice does not teach you enough about how to process mathematics or to develop your critical thinking and reasoning skills.Research shows that these practices do not encourage enough people to understand math or to retain the material covered by the instructor. As you do math, expect that you will be confused at times, and that you will get stuck.This is a natural part of learning, and, like a sore muscle, it means you can grow stronger from it.The reading prompts are designed to help you understand the text and to teach you how to make sense of mathematics on your own.As you read the assigned section(s), you should be taking notes, asking questions of yourself and of the text, and answering your questions if possible.You should try to work out the examples in the text on your own (without reading the solution first). List all definitions encountered in your reading. For each definition in (1), create one example and one non-example that illustrate the important features of the definition. Summarize the reading in 50 words or less. Identify the most important concept in the reading and make an analogy to a non-mathematical situation or explain the concept using a real-life situation. List the questions which you were unable to answer during your process of taking notes.Be ready to ask these questions in class. Solve Exercises 1 and 5, and another odd-numbered problem of your choice from the exercises section.
A flexible program with the solid content students need Glencoe Algebra 1strengthens student understanding and provides the tools students need to succeed--from the first day your students begin to learn the vocabulary of algebra until the day they take final exams and standardized tests. From the first day your students begin to learn the vocabulary of algebra until the day they take final exams and standardized tests, these programs strengthen student understanding and provide the tools students need to succeed. THE PROGRAM STUDENTS NEED; THE FOCUS TEACHERS WANT! "Glencoe Algebra 2" is a key program in our vertically aligned high school mathematics series developed to help all students achieve a better understanding of mathematics and improve their mathematics scores on today's high-stakes assessments. "New York Algebra 2 with Trigonometry" is the third of three books in Glencoes New York High School Mathematics Series. This series offers complete coverage of New Yorks Mathematics standards, strands, and performance indicators. As students learn to integrate a comprehensive array of tools and strategies, they become proficient in mastering concepts and skills, solving problems, and communicating mathematically. This series of books helps your students identify and justify mathematical relationships; acquire and demonstrate mathematical reasoning ability when solving problems; use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes; and succeed on the Regents Examinations. ENGAGING MATHEMATICS, SUPPORTING ALL LEARNERS, DELIVERING THE CONTENT NEEDED TO MEET TODAY'S STANDARDS Glencoe Geometrydelivers the depth of content required to meet the new changes in your state's standards; provides relevant applications for teens; unique instructional resources for teachers; and is available in print, online, and on CD-ROM or DVD formats. A flexible program with the solid content students need Glencoe Geometry is the leading geometry program on the market. Algebra and applications are embedded throughout the program and an introduction to geometry proofs begins in Chapter 2
Calendar Description: This course introduces students to technical mathematics with an emphasis on its application to surveying: trigonometric functions of any angle, solution of triangles, identities and trigonometric equations; spherical trigonometry; systems of linear equations; analytic geometry. Date First Offered: 2009-09-01 Hours: Total Hours: 105 Lecture Hours: 5 Laboratory Hours: 2 Total Weeks: 15 This course is offered online: No Pre-Requisites: One of Principles of Math 12, Pre-Calculus 12 or Math 050 Learning Outcomes: Upon successful completion, the student will be able to: - Use basic algebraic rules and operations - Rearrange formulae used in geomatics - Solve line intersection problems - Formulate and solve elementary geometric properties of circles - Solve right-angle triangles using trigonometry - Use right-angle trigonometry to solve applied surveying problems - Use radian measure in the solution of surveying problems involving circular arcs - Use the sine and cosine laws for solving oblique triangles - Apply the sine and cosine laws to elevation problems and traverses - Carry out the simplification of trigonometric expressions using trigonometric identities - Solve simple trigonometric equations - Demonstrate the use of statistical parameters in reducing surveying measurements - Apply area formulae to problems such as finding the area contained in a traverse and the area contained within a lot with an irregular boundary. - Apply volume formulae to problems such as cut and fill. - Solve right-angled spherical triangles. - Solve oblique spherical triangles. - Use spherical triangles for determining azimuth and bearing. - Carry out matrix operations. - Use matrix operations to rotate, translate and scale coordinate systems such as is used in transforming from a ground based system to UTM coordinates. - Solve problems in analytic geometry. - Use analytic geometry in geomatics applications such as vertical curves. Additional Comments: Assignments: Late assignments, lab reports or projects will not be accepted for marking. Assignments must be done on an individual basis unless otherwise specified by the instructor. Makeup Tests, Exams or Quizzes: There will be no makeup tests, exams or quizzes. If you miss a test, exam or quiz, you will receive zero marks. Exceptions may be made for documented medical reasons or extenuating circumstances. In such a case, it is the responsibility of the student to inform the instructor immediately. Ethics: NLC assumes that all students attending the institution will follow a high standard of ethics. Incidents of cheating or plagiarism may, therefore, result in a grade of zero for the assignment, quiz, test, exam, or project for all parties involved and/or expulsion from the course. Attendance: Attendance will be taken at the beginning of each session. Students not present at that time will be recorded as absent. Illness: A doctor's note is required for any illness causing you to miss assignments, quizzes, tests, projects, or exam. At the discretion of the instructor, you may complete the work missed or have the work prorated. Attempts: Students must successfully complete a course within a maximum of three attempts at the course. Students with two attempts in a single course will be allowed to repeat the course only upon special written permission from the Dean. Students who have not successfully completed a course within three attempts will not be eligible to graduate from the appropriate program. Course Outline Changes: The material or schedule specified in this course outline may be changed by the instructor. If changes are required, they will be announced in class. Course Credit: Applications for course credit or course exemption on the basis of previously completed mathematics courses are assessed on a case-by-case basis by the NLC Geomatics Faculty taking into account all of the following: • the correspondence between topics, content and level • recency (generally no more than 3–5 years) • the grade (generally at least a C+ or 65%) • the context (course taken as part of a university or college science or engineering program, rather than, for example, an arts or social science program) Assignment Details: There is a weekly assignment which consists of questions related to the material covered in the lectures of that week. A deadline for submission of these assignments will be established at the beginning of the term..
hi, i need someone who understands any one of the topic below: 1) Introduction Real Functions and Graphs is a reminder of the principles underlying the sketching of graphs of functions and other curves. 2) Group Theory (A) Symmetry studies the symmetries of plane figures and solids, including the five 'Platonic solids', and leads to the definition of a group. 3) Linear Algebra Vectors and Conics is an introduction to vectors and to the properties of conic sections. 4) Analysis ...

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