Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. Intended for undergraduate courses in abstract algebra, it is suitable for junior- and senior-level math majors and future math teachers. This second edition features additional exercises to improve student familiarity with applications. An introductory chapter traces concepts of abstract algebra from their historical roots. Succeeding chapters avoid the conventional format of definition-theorem-proof-corollary-example; instead, they take the form of a discussion with students, focusing on explanations and offering motivation. Each chapter rests upon a central theme, usually a specific application or use. The author provides elementary background as needed and discusses standard topics in their usual order. He introduces many advanced and peripheral subjects in the plentiful exercises, which are accompanied by ample instruction and commentary and offer a wide range of experiences to students at different levels of ability.

    This book will offer students a broad outline of essential mathematics and will help to fill in the gaps in their knowledge. The author explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The topics include linear algebra, vector calculus, differential and analytical geometry, real analysis, point-set topology, probability, complex analysis, set theory, algorithms, and more. An annotated bibliography offers a guide to further reading and to more rigorous foundations.

    In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13, 21, ad infinitum). Far from being just a curiosity, this sequence recurs in structures found throughout nature - from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world. With admirable clarity, two veteran math educators take us on a fascinating tour of the many ramifications of the Fibonacci numbers. They begin with a brief history of a distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms (pineapples, sunflowers, and daisies are just a few examples). In art, architecture, the stock market, and other areas of society and culture, they point out numerous examples of the Fibonacci sequence as well as its derivative, the "golden ratio." And of course in mathematics, as the authors amply demonstrate, there are almost boundless applications in probability, number theory, geometry, algebra, and Pascal's triangle, to name a few.Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings.

    . . like a pendulum? These may not look like math questions, but they are-because they all have to do with patterns. And mathematics, at heart, is the study of patterns. That realization changed Eddie Woo's life-by turning the "dry" subject he dreaded in high school into a boundless quest for discovery. Now an award-winning math teacher, Woo sees patterns everywhere: in the "branches" of blood vessels and lightning, in the growth of a savings account and a sunflower, even in his morning cup of tea! Here are twenty-six bite-size chapters on the hidden mathematical marvels that encrypt our email, enchant our senses, and even keep us alive-from the sine waves we hear as "music" to the mysterious golden ratio. This book will change your mind about what math can be. We are all born mathematicians-and It's a Numberful World.

    The material is arranged chronologically beginning with archaic origins and covers Egyptian, Mesopotamian, Greek, Chinese, Indian, Arabic and European contributions done to the nineteenth century and present day. There are revised references and bibliographies and revised and expanded chapters on the nineteeth and twentieth centuries.

    Yet Euler's formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea.From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map.Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast.

    So it's not surprising that we persist in thinking that we're in with a chance, whether we're playing the lottery or working out the likelihood of extra-terrestrial life. In Chance, a (not entirely) random selection of the New Scientist's sharpest minds provide fascinating insights into luck, randomness, risk and probability. From the secrets of coincidence to placing the perfect bet, the science of random number generation to the surprisingly haphazard decisions of criminal juries, it will explore these, and many other, tantalising questions.Following on from the bestselling Nothing and Question Everything, this book will open your eyes to the weird and wonderful world of chance - and help you see when some things, in fact, aren't random at all.

    To reach this unique audience, Whitlock and Schluter motivate learning with interesting biological and medical examples; they emphasize intuitive understanding; and they focus on real data. The book covers basic topics in introductory statistics, including graphs, confidence intervals, hypothesis testing, comparison of means, regression, and designing experiments. It also introduces the principles behind such modern topics as likelihood, linear models, meta-analysis and computer-intensive methods. Instructors and students consistently praise the book's clear and engaging writing, strong visualization techniques, and its variety of fascinating and relevant biological examples.

    The Second Edition of Trading Chaos is a cutting edge book that combines trading psychology and Chaos Theory and its particular effect on the markets. By examining both of these facets in relation to the current market, readers will have the best of all possible worlds when trading. Bill Williams, PhD, CTA (Solana Beach, CA), is President of Profitunity.com, a leader in the field of education for traders and investors. Justine Gregory-Williams (Solana Beach, CA) is President of the Profitunity Trading Group and a full-time trader.

    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.

    Topics include: Trigonometric Identities & Equations, Circular Functions, and Polar Equations & Complex Numbers.

    Bell, a leading figure in mathematics in America for half a century. Men of Mathematics accessibly explains the major mathematics, from the geometry of the Greeks through Newton's calculus and on to the laws of probability, symbolic logic, and the fourth dimension. In addition, the book goes beyond pure mathematics to present a series of engrossing biographies of the great mathematicians -- an extraordinary number of whom lived bizarre or unusual lives. Finally, Men of Mathematics is also a history of ideas, tracing the majestic development of mathematical thought from ancient times to the twentieth century. This enduring work's clear, often humorous way of dealing with complex ideas makes it an ideal book for the non-mathematician.

    Purchasers are entitled to a free trial membership in the General Books Club where they can select from more than a million books without charge. Subjects: Astronomy; History / General; Juvenile Nonfiction / Science

    Yet the mathematical language of symmetry-known as group theory-did not emerge from the study of symmetry at all, but from an equation that couldn't be solved. For thousands of years mathematicians solved progressively more difficult algebraic equations, until they encountered the quintic equation, which resisted solution for three centuries. Working independently, two great prodigies ultimately proved that the quintic cannot be solved by a simple formula. These geniuses, a Norwegian named Niels Henrik Abel and a romantic Frenchman named Évariste Galois, both died tragically young. Their incredible labor, however, produced the origins of group theory. The first extensive, popular account of the mathematics of symmetry and order, The Equation That Couldn't Be Solved is told not through abstract formulas but in a beautifully written and dramatic account of the lives and work of some of the greatest and most intriguing mathematicians in history.

    For mathematicians, physicists, engineers, and everyone else with an interest in mathematics' cutting edge, The Millennium Problems is the definitive account of a subject that will have a very long shelf life.