But a dispute over its discovery sowed the seeds of discontent between two of the greatest scientific giants of all time - Sir Isaac Newton and Gottfried Wilhelm Leibniz." "Today Newton and Leibniz are generally considered the twin independent inventors of calculus. They are both credited with giving mathematics its greatest push forward since the time of the Greeks. Had they known each other under different circumstances, they might have been friends. But in their own lifetimes, the joint glory of calculus was not enough for either and each declared war against the other, openly and in secret." This long and bitter dispute has been swept under the carpet by historians - perhaps because it reveals Newton and Leibniz in their worst light - but The Calculus Wars tells the full story in narrative form for the first time. This history ultimately exposes how these twin mathematical giants were brilliant, proud, at times mad, and in the end completely human.

    This work represents the views of a mathematician on the analogies between computing machines and the living human brain.

    In The Universe and the Teacup, K. C. Cole demystifies mathematics and shows us-with humor and wonderfully accessible stories-why math need not be frightening. Using the O. J. Simpson trial, the bell curve, and Emmy Noether, the nineteenth-century woman scientist whose work was essential for Einstein's theory of relativity, Cole helps us see that more than just being a tool, math is a key to understanding the beauty of everything from rainbows to relativity.

    This work includes differential forms and the elegant forms of Maxwell's equations, and a chapter on probability and statistics. It also illustrates and proves mathematical relations.

    Wolfram lets the world see his work in A New Kind of Science, a gorgeous, 1,280-page tome more than a decade in the making. With patience, insight, and self-confidence to spare, Wolfram outlines a fundamental new way of modeling complex systems. On the frontier of complexity science since he was a boy, Wolfram is a champion of cellular automata--256 "programs" governed by simple nonmathematical rules. He points out that even the most complex equations fail to accurately model biological systems, but the simplest cellular automata can produce results straight out of nature--tree branches, stream eddies, and leopard spots, for instance. The graphics in A New Kind of Science show striking resemblance to the patterns we see in nature every day. Wolfram wrote the book in a distinct style meant to make it easy to read, even for nontechies; a basic familiarity with logic is helpful but not essential. Readers will find themselves swept away by the elegant simplicity of Wolfram's ideas and the accidental artistry of the cellular automaton models. Whether or not Wolfram's revolution ultimately gives us the keys to the universe, his new science is absolutely awe-inspiring. --Therese Littleton

    It's a thinking game. It's also a shifting game. Nowhere is this more evident than in the statistical revolution which has swept through the pastime in recent years, bringing metrics like WAR, OPS, and BABIP into front offices and living rooms alike. So what's on the horizon for a game that is constantly evolving? Positioned at the crossroads of sabermetrics and cognitive science, The Shift alters the trajectory of both traditional and analytics-based baseball thought. With a background in clinical psychology as well as experience in major league front offices, Baseball Prospectus' Russell Carleton illuminates advanced statistics and challenges cultural assumptions, demonstrating along the way that data and logic need not be at odds with the human elements of baseball—in fact, they're inextricably intertwined. Covering topics ranging from infield shifts to paradigm shifts, Carleton writes with verve, honesty, and an engaging style, inviting all those who love the game to examine it deeply and maybe a little differently. Data becomes digestible; intangibles are rendered not only accessible, but quantifiable. Casual fans and statheads alike will not want to miss this compelling meditation on what makes baseball tick.

    This recreational math book takes the reader on a fantastic voyage into the world of natural numbers. From the earliest discoveries of the ancient Greeks to various fundamental characteristics of the natural number sequence, Clawson explains fascinating mathematical mysteries in clear and easy prose. He delves into the heart of number theory to see and understand the exquisite relationships among natural numbers, and ends by exploring the ultimate mystery of mathematics: the Riemann hypothesis, which says that through a point in a plane, no line can be drawn parallel to a given line.While a professional mathematician's treatment of number theory involves the most sophisticated analytical tools, its basic ideas are surprisingly easy to comprehend. By concentrating on the meaning behind various equations and proofs and avoiding technical refinements, Mathematical Mysteries lets the common reader catch a glimpse of this wonderful and exotic world.

    There are deep connections between stars and atoms, between the cosmos and the microworld. Just six numbers, imprinted in the "big bang," determine the essential features of our entire physical world. Moreover, cosmic evolution is astonishingly sensitive to the values of these numbers. If any one of them were "untuned," there could be no stars and no life. This realization offers a radically new perspective on our universe, our place in it, and the nature of physical laws.

    Deciding whether to build another power generation plant in the next five years requires forecasts of future demand. Scheduling staff in a call centre next week requires forecasts of call volumes. Stocking an inventory requires forecasts of stock requirements. Telecommunication routing requires traffic forecasts a few minutes ahead. Whatever the circumstances or time horizons involved, forecasting is an important aid in effective and efficient planning. This textbook provides a comprehensive introduction to forecasting methods and presents enough information about each method for readers to use them sensibly. Examples use R with many data sets taken from the authors' own consulting experience.

    With metaprogramming, you can produce elegant, clean, and beautiful programs. Once the domain of expert Rubyists, metaprogramming is now accessible to programmers of all levels. This thoroughly revised and updated second edition of the bestselling Metaprogramming Ruby explains metaprogramming in a down-to-earth style and arms you with a practical toolbox that will help you write your best Ruby code ever.Dig under the surface and explore Ruby's most advanced feature: a collection of techniques and tricks known as metaprogramming. In this book, you'll learn metaprogramming as an essential component of Ruby and discover the deep, non-obvious details of the language. Once you understand the tenets of Ruby, including the object model, scopes, and singleton classes, you're on your way to applying metaprogramming both in your daily work assignments and in your fun, after-hours projects.Metaprogramming Ruby, Second Edition makes mastering the language enjoyable. The book is packed with: Pragmatic examples of metaprogramming in action, many of which come straight from real-life gems such as Rails.Programming challenges that let you experiment and play with some of the most out-there metaprogramming concepts.Metaprogramming spells--33 practical recipes and idioms that you can study and apply right now, to write code that is sure to impress.This completely revised new edition covers the new features in Ruby 2.0 and 2.1, and contains code from the latest Ruby libraries, including Rails 4. Most examples are new, from the wild, with more recent libraries. And the book reflects current ideas of when and how much metaprogramming you should use.Whether you're a Ruby apprentice on the path to mastering the language or a Ruby wiz in search of new tips, this book is for you.What You Need: Ruby 2.x, Ruby 1.9, or a recent version of JRuby.

    In The Master Algorithm, Pedro Domingos lifts the veil to give us a peek inside the learning machines that power Google, Amazon, and your smartphone. He assembles a blueprint for the future universal learner--the Master Algorithm--and discusses what it will mean for business, science, and society. If data-ism is today's philosophy, this book is its bible.

    If you're a reasonably proficient programmer who can think logically, you have all the background you'll need. Stepanov and Rose introduce the relevant abstract algebra and number theory with exceptional clarity. They carefully explain the problems mathematicians first needed to solve, and then show how these mathematical solutions translate to generic programming and the creation of more effective and elegant code. To demonstrate the crucial role these mathematical principles play in many modern applications, the authors show how to use these results and generalized algorithms to implement a real-world public-key cryptosystem. As you read this book, you'll master the thought processes necessary for effective programming and learn how to generalize narrowly conceived algorithms to widen their usefulness without losing efficiency. You'll also gain deep insight into the value of mathematics to programming--insight that will prove invaluable no matter what programming languages and paradigms you use. You will learn aboutHow to generalize a four thousand-year-old algorithm, demonstrating indispensable lessons about clarity and efficiencyAncient paradoxes, beautiful theorems, and the productive tension between continuous and discreteA simple algorithm for finding greatest common divisor (GCD) and modern abstractions that build on itPowerful mathematical approaches to abstractionHow abstract algebra provides the idea at the heart of generic programmingAxioms, proofs, theories, and models: using mathematical techniques to organize knowledge about your algorithms and data structuresSurprising subtleties of simple programming tasks and what you can learn from themHow practical implementations can exploit theoretical knowledge

    A prize of one million dollars was offered to anyone who could unravel it, but Perelman declined the winnings, and in doing so inspired journalist Masha Gessen to tell his story. Drawing on interviews with Perelman’s teachers, classmates, coaches, teammates, and colleagues in Russia and the United States—and informed by her own background as a math whiz raised in Russia—Gessen uncovered a mind of unrivaled computational power, one that enabled Perelman to pursue mathematical concepts to their logical (sometimes distant) end. But she also discovered that this very strength turned out to be Perelman's undoing and the reason for his withdrawal, first from the world of mathematics and then, increasingly, from the world in general.

    

    Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world.