Haskell emerged in the last decade as a standard for lazy functional programming, a programming style where arguments are evaluated only when the value is actually needed. Haskell is a marvellous demonstration tool for logic and maths because its functional character allows implementations to remain very close to the concepts that get implemented, while the laziness permits smooth handling of infinite data structures.This book does not assume the reader to have previous experience with either programming or construction of formal proofs, but acquaintance with mathematical notation, at the level of secondary school mathematics is presumed. Everything one needs to know about mathematical reasoning or programming is explained as we go along. After proper digestion of the material in this book the reader will be able to write interesting programs, reason about their correctness, and document them in a clear fashion. The reader will also have learned how to set up mathematical proofs in a structured way, and how to read and digest mathematical proofs written by others.

    

    The work is predicated on the idea that studying mathematics can generate the same enthusiasm as playing a team sport - without necessarily being competitive.

    This is done in a way that is not only easy to understand, but is actually fun! Professors and engineers, with high school and college students following closely, comprise the largest percentage of our readers. It is a must-have for anyone interested in music, mathematics, physics, engineering, or complex science. Dr. Yoichiro Nambu, 2008 Nobel Prize Winner in Physics, served as a senior adviser to the English version of Who is Fourier? A Mathematical Adventure.

    Underpinning both math and science, it is the foundation of every major advancement in knowledge since the time of the ancient Greeks. Through adventure stories and historical narratives populated with a rich and quirky cast of characters, Mazur artfully reveals the less-than-airtight nature of logic and the muddled relationship between math and the real world. Ultimately, Mazur argues, logical reasoning is not purely robotic. At its most basic level, it is a creative process guided by our intuitions and beliefs about the world.

    This introductory text is suitable for use in a course on the subject or for self-study, featuring broad coverage and a readable exposition, with many examples and exercises. The four main chapters present the basics: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature is the inclusion of many optional topics not usually part of a first course due to time constraints: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and Steenrod squares and powers.

    Persi Diaconis and Ron Graham provide easy, step-by-step instructions for each trick, explaining how to set up the effect and offering tips on what to say and do while performing it. Each card trick introduces a new mathematical idea, and varying the tricks in turn takes readers to the very threshold of today's mathematical knowledge.Diaconis and Graham tell the stories--and reveal the best tricks--of the eccentric and brilliant inventors of mathematical magic. The book exposes old gambling secrets through the mathematics of shuffling cards, explains the classic street-gambling scam of three-card Monte, traces the history of mathematical magic back to the oldest mathematical trick--and much more.

    It can be freely downloaded and it works on multiple computer platforms. This book provides an elementary introduction to R. In each chapter, brief introductory sections are followed by code examples and comments from the computational and statistical viewpoint. A supplementary R package containing the datasets can be downloaded from the web.

    This supplement will cater to the requirements of students by covering all important topics of Laplace transformation, Matrices, Numerical Methods. Further enhanced is its usability by inclusion of chapter end questions in sync with student needs. Table of contents: 1. Basic Concepts 2. An Introduction to Modeling and Qualitative Methods 3. Classification of First-Order Differential Equations 4. Separable First-Order Differential Equations 5. Exact First-order Differential Equations 6. Linear First-Order Differential Equations 7. Applications of First-Order Differential Equations 8. Linear Differential Equations: Theory of Solutions 9. Second-Order Linear Homogeneous Differential Equations with Constant Coefficients 10. nth-Order Linear Homogeneous Differential Equations with Constant Coefficients 11. The Method of Undetermined Coefficients 12. Variation of Parameters 13. Initial-Value Problems for Linear Differential Equations 14. Applications of Second-Order Linear Differential Equations 15. Matrices 16. eAt 17. Reduction of Linear Differential Equations to a System of First-Order Equations 18. Existence and Uniqueness of Solutions 19. Graphical and Numerical Methods for Solving First-Order Differential Equations 20. Further Numerical Methods for Solving First-Order Differential Equations 21. Numerical Methods for Solving Second-Order Differential Equations Via Systems 22. The Laplace Transform 23. Inverse Laplace Transforms 24. Convolutions and the Unit Step Function 25. Solutions of Linear Differential Equations with Constant Coefficients by Laplace Transforms 26. Solutions of Linear?Systems by Laplace Transforms 27. Solutions of Linear Differential Equations with Constant Coefficients by Matrix Methods 28. Power Series Solutions of Linear Differential Equations with Variable Coefficients 29. Special Functions 30. Series Solutions N

    Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    Linear Equations; Vector Spaces; Linear Transformations; Polynomials; Determinants; Elementary canonical Forms; Rational and Jordan Forms; Inner Product Spaces; Operators on Inner Product Spaces; Bilinear Forms For all readers interested in linear algebra.

    This proven and accessible text speaks to beginning engineering and math students through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and group projects. Using a straightforward, readable, and helpful style, this book provides a thorough treatment of boundary-value problems and partial differential equations.

    In Burn Math Class, Jason Wilkes takes the traditional approach to how we learn math -- with its unwelcoming textbooks, unexplained rules, and authoritarian assertions-and sets it on fire. Focusing on how mathematics is created rather than on mathematical facts, Wilkes teaches the subject in a way that requires no memorization and no prior knowledge beyond addition and multiplication. From these simple foundations, Burn Math Class shows how mathematics can be (re)invented from scratch without preexisting textbooks and courses. We can discover math on our own through experimentation and failure, without appealing to any outside authority. When math is created free from arcane notations and pretentious jargon that hide the simplicity of mathematical concepts, it can be understood organically -- and it becomes fun! Following this unconventional approach, Burn Math Class leads the reader from the basics of elementary arithmetic to various "advanced" topics, such as time-dilation in special relativity, Taylor series, and calculus in infinite-dimensional spaces. Along the way, Wilkes argues that orthodox mathematics education has been teaching the subject backward: calculus belongs before many of its so-called prerequisites, and those prerequisites cannot be fully understood without calculus. Like the smartest, craziest teacher you've ever had, Wilkes guides you on an adventure in mathematical creation that will radically change the way you think about math. Revealing the beauty and simplicity of this timeless subject, Burn Math Class turns everything that seems difficult about mathematics upside down and sideways until you understand just how easy math can be.

    The Art of Problem Solving, Volume 1, is the classic problem solving textbook used by many successful MATHCOUNTS programs, and have been an important building block for students who, like the authors, performed well enough on the American Mathematics Contest series to qualify for the Math Olympiad Summer Program which trains students for the United States International Math Olympiad team.Volume 1 is appropriate for students just beginning in math contests. MATHCOUNTS and novice high school students particularly have found it invaluable. Although the Art of Problem Solving is widely used by students preparing for mathematics competitions, the book is not just a collection of tricks. The emphasis on learning and understanding methods rather than memorizing formulas enables students to solve large classes of problems beyond those presented in the book.Speaking of problems, the Art of Problem Solving, Volume 1, contains over 500 examples and exercises culled from such contests as MATHCOUNTS, the Mandelbrot Competition, the AMC tests, and ARML. Full solutions (not just answers!) are available for all the problems in the solution manual.

    The author has sought to utlilize the technology now available for the teaching and learning of calculus. The hand-held graphics calculator is one such form of technology that has been integrated into the book. Topics in algebra, trigonometry, and analytical geometry appear in the Appendix.