Beginning millions of years ago with ancient “ant odometers” and moving through time to our modern-day quest for new dimensions, it covers 250 milestones in mathematical history. Among the numerous delights readers will learn about as they dip into this inviting anthology: cicada-generated prime numbers, magic squares from centuries ago, the discovery of pi and calculus, and the butterfly effect. Each topic gets a lavishly illustrated spread with stunning color art, along with formulas and concepts, fascinating facts about scientists’ lives, and real-world applications of the theorems.

    In his provocative new book, Guy Claxton draws on the latest findings in neuroscience and psychology to reveal how our bodies—long dismissed as mere conveyances—actually constitute the core of our intelligent life. From the endocrinal means by which our organs communicate to the instantaneous decision-making prompted by external phenomena, our bodies are able to perform intelligent computations that we either overlook or wrongly attribute to our brains.   Embodied intelligence is one of the most exciting areas in contemporary philosophy and neuropsychology, and Claxton shows how the privilege given to cerebral thinking has taken a toll on modern society, resulting in too much screen time, the diminishment of skilled craftsmanship, and an overvaluing of white-collar over blue-collar labor. Discussing techniques that will help us reconnect with our bodies, Claxton shows how an appreciation of the body’s intelligence will enrich all our lives.

    Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula--long regarded as the gold standard for mathematical beauty--and shows why it still lies at the heart of complex number theory. This book is the sequel to Paul Nahin's An Imaginary Tale: The Story of I [the square root of -1], which chronicled the events leading up to the discovery of one of mathematics' most elusive numbers, the square root of minus one. Unlike the earlier book, which devoted a significant amount of space to the historical development of complex numbers, Dr. Euler begins with discussions of many sophisticated applications of complex numbers in pure and applied mathematics, and to electronic technology. The topics covered span a huge range, from a never-before-told tale of an encounter between the famous mathematician G. H. Hardy and the physicist Arthur Schuster, to a discussion of the theoretical basis for single-sideband AM radio, to the design of chase-and-escape problems. The book is accessible to any reader with the equivalent of the first two years of college mathematics (calculus and differential equations), and it promises to inspire new applications for years to come. Or as Nahin writes in the book's preface: To mathematicians ten thousand years hence, Euler's formula will still be beautiful and stunning and untarnished by time.

    There is no better way to study the big questions in philosophy than to compare how the world's greatest minds have analyzed these questions, defined the terms, and then reasoned out potential solutions. Once you've compared the arguments, the final step is always deciding for yourself whether you find an explanation convincing.This course gives you the tools to follow and create logical arguments while exploring famous philosophers' viewpoints on these important questions. Although progress has been made toward answers, brilliant thinkers have continued to wrestle with many big questions that inspire thoughtful people everywhere. These questions include: What is knowledge? Does God exist? Do humans have free will? What is right and wrong? How should society be organized?Given the complexity of these big questions, it should be no surprise that many controversies are far from settled. In fact, by the end of these 36 lectures, you may be even less sure of the right answers to some of the questions than you were at the beginning. But being a philosopher means constantly testing your views - giving a reasoned defense if you believe you are right and modifying your ideas when you realize you are wrong. You'll discover that great thinkers before you have offered convincing answers to hard questions, philosophers after them have made equally persuasive objections, and then still others have refined the debate even further - causing the issues to come into sharper and sharper focus.Join Plato, St. Anselm, Descartes, Locke, Hume, Kant, Mill, Smith, Marx, Rawls, and many others in an exploration of fundamental questions. Get ready to think big!

    Topics covered in the book include linear equations, ratios, quadratic equations, special factorizations, complex numbers, graphing linear and quadratic equations, linear and quadratic inequalities, functions, polynomials, exponents and logarithms, absolute value, sequences and series, and much more!The text is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, giving the student a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which algebraic techniques are taught. Important facts and powerful problem solving approaches are highlighted throughout the text. In addition to the instructional material, the book contains well over 1000 problems.This book can serve as a complete Algebra I course, and also includes many concepts covered in Algebra II. Middle school students preparing for MATHCOUNTS, high school students preparing for the AMC, and other students seeking to master the fundamentals of algebra will find this book an instrumental part of their mathematics libraries.656About the author: Richard Rusczyk is a co-author of Art of Problem Solving, Volumes 1 and 2, the author of Art of Problem Solving's Introduction to Geometry. He was a national MATHCOUNTS participant, a USA Math Olympiad winner, and is currently director of the USA Mathematical Talent Search.

    Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician.

    It describes how the laws and discoveries of information theory now support controversial revisions to Darwinian evolution, begin to unravel the mysteries of language, memory and dreams, and stimulate provocative ideas in psychology, philosophy, art, music, computers and even the structure of society. Perhaps its most fascinating and unexpected surprise is the suggestion the order and complexity may be as natural as disorder and disorganization. Contrary to the entropy principle, which implies that order is the exception and confusion the rule, information theory asserts that order and sense can indeed prevail against disorder and nonsense. From the simplest forms of organic life to the words used to express our most complex ideas, from our genes to our dreams, from microcomputers to telecommunications, virtually everything around us follows simple rules of information. Life and the material world, like language, remain "grammatical." Grammatical man inhabits a grammatical universe.

    Just how calculus makes these things possible and in doing so finds a correspondence between real numbers and the real world is the subject of this dazzling book by a writer of extraordinary clarity and stylistic brio. Even as he initiates us into the mysteries of real numbers, functions, and limits, Berlinski explores the furthest implications of his subject, revealing how the calculus reconciles the precision of numbers with the fluidity of the changing universe. "An odd and tantalizing book by a writer who takes immense pleasure in this great mathematical tool, and tries to create it in others."--New York Times Book Review

    In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Godel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

    Calculus is not a prerequisite, although examples and exercises using very basic calculus are included (labeled Calculus Required.) The most technology-friendly text on the market, Introductory Linear Algebra is also the most flexible. By omitting certain sections, instructors can cover the essentials of linear algebra (including eigenvalues and eigenvectors), to show how the computer is used, and to introduce applications of linear algebra in a one-semester course.

    They'll also find the related analytic geometry much easier. The clear review of algebra and geometry in this edition will make calculus easier for students who wish to strengthen their knowledge in these areas. Updated to meet the emphasis in current courses, this new edition of a popular guide--more than 104,000 copies were bought of the prior edition--includes problems and examples using graphing calculators..

    It was a time of backward-seeming notions, when almost everyone still accepted the biblical account of creation as the literal truth and authoritarianism as the most natural and viable social order. But by the time both men died, the world had changed: ordinary people understood that life on earth was a story of continuous evolution, and the Civil War had proved that a democracy could fight for principles and endure. And with these signal insights much else had changed besides. Together, Darwin and Lincoln had become midwives to the spirit of a new world, a new kind of hope and faith.""Searching for the men behind the icons of emancipation and evolution, Adam Gopnik shows us, in this captivating double life, Lincoln and Darwin as they really were: family men and social climbers; ambitious manipulators and courageous adventurers; the living husband, father, son, and student behind each myth. How do we reconcile Lincoln, the supremely good man we know, with the hardened commander who wittingly sent tens of thousands of young soldiers to certain death? Why did the relentlessly rational Darwin delay publishing his "Great Idea" for almost twenty years? How did inconsolable grief at the loss of a beloved child change each man? And what comfort could either find - for himself or for a society now possessed of a sadder, if wiser, understanding of our existence? Such human questions and their answers are the stuff of this book."Above all, we see Lincoln and Darwin as thinkers and writers - as makers and witnesses of the great change in thought that marks truly modern times: a hundred years after the Enlightenment, the old rule of faith and fear finally yielding to one of reason, argument, and observation not merely as intellectual ideals but as a way of life; the judgment of divinity at last submitting to the verdicts of history and time. Lincoln considering human history, Darwin reflecting on deep time - both reshaped our understanding of what life is and how it attains meaning. And they invented a new language to express that understanding.Angels and Ages is an original and personal account of the creation of the liberal voice - of the way we live now and the way we talk at home and in public. Showing that literary eloquence is essential to liberal civilization, Adam Gopnik reveals why our heroes should be possessed by the urgency of utterance, obsessed by the need to see for themselves, and endowed with the gift to speak for us all.

    The era covered by this book, 1950 to 1990, was surely one of the golden ages of science as well as the American university.Cherished myths are debunked along the way as Gian-Carlo Rota takes pleasure in portraying, warts and all, some of the great scientific personalities of the period Stanislav Ulam (who, together with Edward Teller, signed the patent application for the hydrogen bomb), Solomon Lefschetz (Chairman in the 50s of the Princeton mathematics department), William Feller (one of the founders of modern probability theory), Jack Schwartz (one of the founders of computer science), and many others.Rota is not afraid of controversy. Some readers may even consider these essays indiscreet. After the publication of the essay "The Pernicious Influence of Mathematics upon Philosophy" (reprinted six times in five languages) the author was blacklisted in analytical philosophy circles. Indiscrete Thoughts should become an instant classic and the subject of debate for decades to come."Read Indiscrete Thoughts for its account of the way we were and what we have become; for its sensible advice and its exuberant rhetoric."--The Mathematical Intelligencer"Learned, thought-provoking, politically incorrect, delighting in paradox, and likely to offend but everywhere readable and entertaining."--The American Mathematical Monthly"It is about mathematicians, the way they think, and the world in which the live. It is 260 pages of Rota calling it like he sees it... Readers are bound to find his observations amusing if not insightful. Gian-Carlo Rota has written the sort of book that few mathematicians could write. What will appeal immediately to anyone with an interest in research mathematics are the stories he tells about the practice of modern mathematics."--MAA Reviews"

    Michael Guillen, known to millions as the science editor of ABC's Good Morning America, tells the fascinating stories behind five mathematical equations. As a regular contributor to daytime's most popular morning news show and an instructor at Harvard University, Dr. Michael Guillen has earned the respect of millions as a clear and entertaining guide to the exhilarating world of science and mathematics. Now Dr. Guillen unravels the equations that have led to the inventions and events that characterize the modern world, one of which -- Albert Einstein's famous energy equation, E=mc2 -- enabled the creation of the nuclear bomb. Also revealed are the mathematical foundations for the moon landing, airplane travel, the electric generator -- and even life itself. Praised by Publishers Weekly as "a wholly accessible, beautifully written exploration of the potent mathematical imagination," and named a Best Nonfiction Book of 1995, the stories behind The Five Equations That Changed the World, as told by Dr. Guillen, are not only chronicles of science, but also gripping dramas of jealousy, fame, war, and discovery. Dr. Michael Guillen is Instructor of Physics and Mathematics in the Core Curriculum Program at Harvard University.

     This top-selling, theorem-proof text presents a careful treatment of the principal topics of linear algebra, and illustrates the power of the subject through a variety of applications. It emphasizes the symbiotic relationship between linear transformations and matrices, but states theorems in the more general infinite-dimensional case where appropriate.