It demonstrates how to encourage, develop, and foster the processes which seem to come naturally to mathematicians.

    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.

    The work of English clergyman, educator and Shakespearean scholar Edwin A. Abbott (1838-1926), it describes the journeys of A. Square [sic – ed.], a mathematician and resident of the two-dimensional Flatland, where women-thin, straight lines-are the lowliest of shapes, and where men may have any number of sides, depending on their social status.Through strange occurrences that bring him into contact with a host of geometric forms, Square has adventures in Spaceland (three dimensions), Lineland (one dimension) and Pointland (no dimensions) and ultimately entertains thoughts of visiting a land of four dimensions—a revolutionary idea for which he is returned to his two-dimensional world. Charmingly illustrated by the author, Flatland is not only fascinating reading, it is still a first-rate fictional introduction to the concept of the multiple dimensions of space. "Instructive, entertaining, and stimulating to the imagination." — Mathematics Teacher.

    For the first time, these books are available as a boxed, three-volume set. The handsome slipcase makes this set an ideal gift for the recent computer science graduate or professional programmer. Offering a description of classical computer science, this multi-volume work is a useful resource in programming theory and practice for students, researchers, and practitioners alike. For programmers, it offers cookbook solutions to their day-to-day problems.

    The presentation stresses analytical methods, concrete examples, and geometric intuition. A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with mathematical theory.About the Author:Steven Strogatz is in the Center for Applied Mathematics and the Department of Theoretical and Applied Mathematics at Cornell University. Since receiving his Ph.D. from Harvard university in 1986, Professor Strogatz has been honored with several awards, including the E.M. Baker Award for Excellence, the highest teaching award given by MIT.

    Johnson. It was the first book exclusively on the theory of NP-completeness and computational intractability. The book features an appendix providing a thorough compendium of NP-complete problems (which was updated in later printings of the book). The book is now outdated in some respects as it does not cover more recent development such as the PCP theorem. It is nevertheless still in print and is regarded as a classic: in a 2006 study, the CiteSeer search engine listed the book as the most cited reference in computer science literature.

    This book helps you even the odds. Using easy-to-understand explanations and examples, it demystifies probability -- and even offers savvy tips to boost your chances of gambling success Discover how to* Conquer combinations and permutations* Understand probability models from binomial to exponential* Make good decisions using probability* Play the odds in poker, roulette, and other games

    The focus is on algorithms and hence the book is well suited for students in computer science and engineering. Motivation is provided from the application areas: all solutions and techniques from computational geometry are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. For students this motivation will be especially welcome. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement. All the basic techniques and topics from computational geometry, as well as several more advanced topics, are covered. The book is largely self-contained and can be used for self-study by anyone with a basic background in algorithms. In the second edition, besides revisions to the first edition, a number of new exercises have been added.

    And this language is mathematics." In The Language of Mathematics, award-winning author Keith Devlin reveals the vital role mathematics plays in our eternal quest to understand who we are and the world we live in. More than just the study of numbers, mathematics provides us with the eyes to recognize and describe the hidden patterns of life—patterns that exist in the physical, biological, and social worlds without, and the realm of ideas and thoughts within.Taking the reader on a wondrous journey through the invisible universe that surrounds us—a universe made visible by mathematics—Devlin shows us what keeps a jumbo jet in the air, explains how we can see and hear a football game on TV, allows us to predict the weather, the behavior of the stock market, and the outcome of elections. Microwave ovens, telephone cables, children's toys, pacemakers, automobiles, and computers—all operate on mathematical principles. Far from a dry and esoteric subject, mathematics is a rich and living part of our culture. An exploration of an often woefully misunderstood subject, The Language of Mathematics celebrates the simplicity, the precision, the purity, and the elegance of mathematics.

    For decades your teachers, authority figures and textbooks have been lying to you. You do not have five senses. Your tongue doesn't have neatly segregated taste-bud zones. You don't know what the pyramids really looked like. You're even pooping wrong - Jesus, you're a wreck!But it's going to be okay. Because we're here to help. Packed with more sexy facts than the Encyclopedia Pornographica, the Cracked De-Textbook will teach you about the true stars of history, why you picture everything from Velociraptors to Ancient Rome incorrectly, and finally, at long last - how to pop a proper squat. This book was built from the ground up to systematically seek out, dismantle and destroy the many untruths that years of misguided education have left festering inside of you, and leave you a smarter person...whether you like it or not. The De-Textbook is a merciless, brutal learning machine. It can't be bargained with. It can't be reasoned with. It doesn't feel pity, or remorse, or fear. And it absolutely will not stop, ever, until you are informed.

    For the calculus-based General Physics course primarily taken by engineers and scientists.

    This book provides an introduction to the field of solid state physics for undergraduate students in physics, chemistry, engineering, and materials science.

    Read a concise history of South Africa in just one hour.South Africa is a nation that has been ravaged by oppression and racial inequality. After years of concentrated violence and apartheid, Nelson Mandela led the country to unite ‘for the freedom of us all’ as the country’s first black President.SOUTH AFRICA: HISTORY IN AN HOUR gives a lively account of the formation of modern South Africa, from the first contact with seventeenth-century European sailors, through the colonial era, the Boer Wars, apartheid and the establishment of a tolerant democracy in the late twentieth century. Here is a clear and fascinating overview of the emergence of the ‘Rainbow Nation’.Love your history? Find out about the world with History in an Hour…

    Admittedly real life wasn’t like that. But only, they argued, because we didn’t have enough data to be certain.Then the cracks began to appear. It proved impossible to predict exactly how three planets orbiting each other would move. Meteorologists discovered that the weather was truly chaotic – so dependent on small variations that it could never be predicted for more than a few days out. And the final nail in the coffin was quantum theory, showing that everything in the universe has probability at its heart.That gives human beings a problem. We understand the world through patterns. Randomness and probability will always be alien to us. But it’s time to plunge into this fascinating, shadowy world, because randomness crops up everywhere. Probability and statistics are the only way to get a grip on nature’s workings. They may even seal the fate of free will and predict how the universe will end.Forget Newton’s clockwork universe. Welcome to Dice World.

    Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures. KEY TOPICS: Sets and Relations; GROUPS AND SUBGROUPS; Introduction and Examples; Binary Operations; Isomorphic Binary Structures; Groups; Subgroups; Cyclic Groups; Generators and Cayley Digraphs; PERMUTATIONS, COSETS, AND DIRECT PRODUCTS; Groups of Permutations; Orbits, Cycles, and the Alternating Groups; Cosets and the Theorem of Lagrange; Direct Products and Finitely Generated Abelian Groups; Plane Isometries; HOMOMORPHISMS AND FACTOR GROUPS; Homomorphisms; Factor Groups; Factor-Group Computations and Simple Groups; Group Action on a Set; Applications of G-Sets to Counting; RINGS AND FIELDS; Rings and Fields; Integral Domains; Fermat's and Euler's Theorems; The Field of Quotients of an Integral Domain; Rings of Polynomials; Factorization of Polynomials over a Field; Noncommutative Examples; Ordered Rings and Fields; IDEALS AND FACTOR RINGS; Homomorphisms and Factor Rings; Prime and Maximal Ideas; Gr�bner Bases for Ideals; EXTENSION FIELDS; Introduction to Extension Fields; Vector Spaces; Algebraic Extensions; Geometric Constructions; Finite Fields; ADVANCED GROUP THEORY; Isomorphism Theorems; Series of Groups; Sylow Theorems; Applications of the Sylow Theory; Free Abelian Groups; Free Groups; Group Presentations; GROUPS IN TOPOLOGY; Simplicial Complexes and Homology Groups; Computations of Homology Groups; More Homology Computations and Applications; Homological Algebra; Factorization; Unique Factorization Domains; Euclidean Domains; Gaussian Integers and Multiplicative Norms; AUTOMORPHISMS AND GALOIS THEORY; Automorphisms of Fields; The Isomorphism Extension Theorem; Splitting Fields; Separable Extensions; Totally Inseparable Extensions; Galois Theory; Illustrations of Galois Theory; Cyclotomic Extensions; Insolvability of the Quintic; Matrix Algebra MARKET: For all readers interested in abstract algebra.