It presents in a unified manner an introduction to the mathematical theory underlying computer graphic applications. It covers topics of keen interest to students in engineering and computer science: transformations, projections, 2-D and 3-D curve definition schemes, and surface definitions. It also includes techniques, such as B-splines, which are incorporated as part of the software in advanced engineering workstations. A basic knowledge of vector and matrix algebra and calculus is required.

    Far from the thankless, pointless exercises they are often thought to be, mathematics and logic are indispensable guides to ridding ourselves of dominant opinions and making possible an access to truths, or to a human experience of the utmost value. That is why mathematics may well be the shortest path to the true life, which, when it exists, is characterized by an incomparable happiness.

    Pose the same question to students and many will use words like "boring", "useless", and even "humiliating". In  Becoming the Math Teacher You Wish You'd Had , author Tracy Zager helps teachers close this gap by making math class more like mathematics. Tracy has spent years working with highly skilled math teachers in a diverse range of settings and grades. You'll find this book jam-packed with new ideas from these vibrant classrooms.  How to Teach Student-Centered Mathematics: Zager outlines a problem-solving approach to mathematics for elementary and middle school educators looking for new ways to inspire student learningBig Ideas, Practical Application: This math book contains dozens of practical and accessible teaching techniques that focus on fundamental math concepts, including strategies that simulate connection of big ideas; rich tasks that encourage students to wonder, generalize, hypothesize, and persevere; and routines to teach students how to collaborateKey Topics for Elementary and Middle School Teachers:  Becoming the Math Teacher You Wish You'd Had  offers fresh perspectives on common challenges, from formative assessment to classroom management for elementary and middle school teachersAll teachers can move towards increasingly authentic and delightful mathematics teaching and learning. This important book helps develop instructional techniques that will make the math classes we teach so much better than the math classes we took.

    Among the old chestnuts he cracks wide open are the following classics: Knights and knaves The monk and the mountain The dominoes and the chessboard The unexpected hanging The Tower of HanoiUsing real-world analogies, infectious humor, and a fresh approach, this deceptively simple volume will challenge, amuse, enlighten, and surprise even the most experienced puzzle solver.

    Judy Willis responds with an emphatic yes in this informative guide to getting better results in math class. Tapping into abundant research on how the brain works, Willis presents a practical approach for how we can improve academic results by demonstrating certain behaviors and teaching students in a way that minimizes negativity.With a straightforward and accessible style, Willis shares the knowledge and experience she has gained through her dual careers as a math teacher and a neurologist. In addition to learning basic brain anatomy and function, readers will learn how to* Improve deep-seated negative attitudes toward math.* Plan lessons with the goal of achievable challenge in mind.* Reduce mistake anxiety with techniques such as errorless math and estimation.* Teach to different individual learning strengths and skill levels.* Spark motivation.* Relate math to students' personal interests and goals.* Support students in setting short-term and long-term goals.* Convince students that they can change their intelligence.With dozens of strategies teachers can use right now, Learning to Love Math puts the power of research directly into the hands of educators. A Brain Owner's Manual, which dives deeper into the structure and function of the brain, is also included--providing a clear explanation of how memories are formed and how skills are learned. With informed teachers guiding them, students will discover that they can build a better brain . . . and learn to love math!

    I just wish I had known all of this twelve years ago...'When you speak to the likes of Dylan Wiliam, Doug Lemov, Daisy Christodoulou, Kris Boulton and the Bjorks, you are bound to learn a thing or two. But when he started his Mr Barton Maths Podcast, Craig Barton wasn't expecting to have his whole outlook on teaching and learning turned upside down. How I Wish I'd Taught Maths is the story of an experienced and successful maths teacher's journey into the world of research, and what it looks like in the classroom.Along the way we meet practical, easy-to-implement strategies including Supercharged Worked Examples, Silent Teacher, SSDD problems, low-stakes quizzes, diagnostic questions, Purposeful Practice, self-explanations, harnessing the power of the hypercorrection effect, how to (and how not to) teach problem-solving and much more. No matter your experience, teaching style or favourite number, every maths teacher will find something to think about in this book.

    Collected here to keep your wits sharp, The Best Brain Teasers of All Time features the cleverest brain teasers from around the world and throughout history.The Best Brain Teasers of All Time gives you hours of fun-filled entertainment with brain teasers that develop your problem-solving skills in math, logic, and wordplay. Organized as an integrated challenge, these brain teasers build in momentum as they increase in difficulty from classic nursery rhymes to the riddle of the sphinx.The Best Brain Teasers of All Time puts your mind to the test with: 125 Brain Teasers that require no special skills to solve. Plus, each question comes with an optional clue in case you get stumped and a handy answer key in the back to test yourself or play with friends Brain Teasers for Every Level that cater to beginners and advanced masterminds alike, with brain teasers organized by level of difficulty to improve your skills as you move forward Hints of History that provide fun facts and background information for every brain teaser Get ready to sharpen your wit with every “aha” moment. The Best Brain Teasers of All Time is a go-to source for timeless fun and mind-blowing challenges.

    Your guide to a higher math score on standardized tests*SATACT(R)ASVABGMAT(R)GRE(R)CBEST(R)PRAXIS I(R)GED(R) And More!Why CliffsNotes?Go with the name you know and trustGet the information you need-fast!About the Contents:IntroductionHow to use this bookOverview of the examsPart I: Basic Skills ReviewArithmetic and Data AnalysisAlgebraPart II: Strategies and PracticeMathematical AbilityQuantitative ComparisonData SufficiencyEach section includes a diagnostic test, explanations of rules, concepts withexamples, practice problems with complete explanations, a review test, and aglossary!Test-Prep Essentials from the Experts at CliffsNotes(R)For more test-prep help, visit CliffsNotes.com(R)*SAT is a registered trademark of the College Board, which was not involved inthe production of, and does not endorse, this product.

    The discussion of problem solving strategies is extensive. It is written for trainers and participants of contests of all levels up to the highest level: IMO, Tournament of the Towns, and the noncalculus parts of the Putnam Competition. It will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", "problem of the month", and "research problem of the year" to their students, thus bringing a creative atmosphere into their classrooms with continuous discussions of mathematical problems. This volume is a must-have for instructors wishing to enrich their teaching with some interesting non-routine problems and for individuals who are just interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. Very few problems have no solutions. Readers interested in increasing the effectiveness of the book can do so by working on the examples in addition to the problems thereby increasing the number of problems to over 1300. In addition to being a valuable resource of mathematical problems and solution strategies, this volume is the most complete training book on the market.

    The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo MCMC. Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.

    The Clay Mathematics Institute is offering a prize of $1 million to anyone who can discover a general solution to the problem. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem.The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet they arise from some very deep--and often very mystifying--mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and in the process venture to the very frontiers of modern mathematics. Along the way, they give an informative and entertaining introduction to some of the most profound discoveries of the last three centuries in algebraic geometry, abstract algebra, and number theory. They demonstrate how mathematics grows more abstract to tackle ever more challenging problems, and how each new generation of mathematicians builds on the accomplishments of those who preceded them. Ash and Gross fully explain how the Birch and Swinnerton-Dyer Conjecture sheds light on the number theory of elliptic curves, and how it provides a beautiful and startling connection between two very different objects arising from an elliptic curve, one based on calculus, the other on algebra.

    Not anymore. The best-selling author of The Complete Idiot's Guide® to Calculus has taken what appears to be a typical calculus workbook, chock full of solved calculus problems, and made legible notes in the margins, adding missing steps and simplifying solutions. Finally, everything is made perfectly clear. Students will be prepared to solve those obscure problems that were never discussed in class but always seem to find their way onto exams.--Includes 1,000 problems with comprehensive solutions--Annotated notes throughout the text clarify what's being asked in each problem and fill in missing steps--Kelley is a former award-winning calculus teacher

    This book discusses real sequences and series, continuity, functions of several variables, elementary and implicit functions, Riemann and Riemann-Stieltjes integrals, and Lebesgue integrals.

    Sousa discusses the cognitive mechanisms for learning mathematics and the environmental and developmental factors that contribute to mathematics difficulties. This award-winning text examines:Children's innate number sense and how the brain develops an understanding of number relationships Rationales for modifying lessons to meet the developmental learning stages of young children, preadolescents, and adolescents How to plan lessons in PreK-12 mathematics Implications of current research for planning mathematics lessons, including discoveries about memory systems and lesson timing Methods to help elementary and secondary school teachers detect mathematics difficulties Clear connections to the NCTM standards and curriculum focal points

    Emphasis on developing algebraic skills is extended to the exercises--including both drill problems and applications. The authors work through examples and explanations with a blend of rigor and accessibility. In addition, they have refined the flow, transitions, organization, and portioning of the content over many editions to optimize learning for readers. The table of contents covers a wide range of topics efficiently, enabling readers to gain a diverse understanding.