. . Nothing less than a major contribution to the scientific culture of this world." — The New York Times Book ReviewThis major survey of mathematics, featuring the work of 18 outstanding Russian mathematicians and including material on both elementary and advanced levels, encompasses 20 prime subject areas in mathematics in terms of their simple origins and their subsequent sophisticated developement. As Professor Morris Kline of New York University noted, "This unique work presents the amazing panorama of mathematics proper. It is the best answer in print to what mathematics contains both on the elementary and advanced levels."Beginning with an overview and analysis of mathematics, the first of three major divisions of the book progresses to an exploration of analytic geometry, algebra, and ordinary differential equations. The second part introduces partial differential equations, along with theories of curves and surfaces, the calculus of variations, and functions of a complex variable. It furthur examines prime numbers, the theory of probability, approximations, and the role of computers in mathematics. The theory of functions of a real variable opens the final section, followed by discussions of linear algebra and nonEuclidian geometry, topology, functional analysis, and groups and other algebraic systems.Thorough, coherent explanations of each topic are further augumented by numerous illustrative figures, and every chapter concludes with a suggested reading list. Formerly issued as a three-volume set, this mathematical masterpiece is now available in a convenient and modestly priced one-volume edition, perfect for study or reference."This is a masterful English translation of a stupendous and formidable mathematical masterpiece . . ." — Social Science

    Full of insights, arguments and philosophical perspectives, the book covers an amazing array of topics. Beginning in antiquity with Democritus, it progresses through logic and set theory, computability and complexity theory, quantum computing, cryptography, the information content of quantum states and the interpretation of quantum mechanics. There are also extended discussions about time travel, Newcomb's Paradox, the anthropic principle and the views of Roger Penrose. Aaronson's informal style makes this fascinating book accessible to readers with scientific backgrounds, as well as students and researchers working in physics, computer science, mathematics and philosophy.

    Even after more than three centuries and the revolutions of Einsteinian relativity and quantum mechanics, Newtonian physics continues to account for many of the phenomena of the observed world, and Newtonian celestial dynamics is used to determine the orbits of our space vehicles.This completely new translation, the first in 270 years, is based on the third (1726) edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms. Newton's principles describe acceleration, deceleration, and inertial movement; fluid dynamics; and the motions of the earth, moon, planets, and comets. A great work in itself, the Principia also revolutionized the methods of scientific investigation. It set forth the fundamental three laws of motion and the law of universal gravity, the physical principles that account for the Copernican system of the world as emended by Kepler, thus effectively ending controversy concerning the Copernican planetary system.The illuminating Guide to the Principia by I. Bernard Cohen, along with his and Anne Whitman's translation, will make this preeminent work truly accessible for today's scientists, scholars, and students.

    Len Fisher turns his attention to the science of cooperation in his lively and thought-provoking book. Fisher shows how the modern science of game theory has helped biologists to understand the evolution of cooperation in nature, and investigates how we might apply those lessons to our own society. In a series of experiments that take him from the polite confines of an English dinner party to crowded supermarkets, congested Indian roads, and the wilds of outback Australia, not to mention baseball strategies and the intricacies of quantum mechanics, Fisher sheds light on the problem of global cooperation. The outcomes are sometimes hilarious, sometimes alarming, but always revealing. A witty romp through a serious science, Rock, Paper, Scissors will both teach and delight anyone interested in what it what it takes to get people to work together.

    But now, astonishing new research is revealing patterns in human behavior previously thought to be purely random. Precise, orderly, predictable patterns... Albert Laszlo Barabasi, already the world's preeminent researcher on the science of networks, describes his work on this profound mystery in Bursts, a stunningly original investigation into human nature. His approach relies on the digital reality of our world, from mobile phones to the Internet and email, because it has turned society into a huge research laboratory. All those electronic trails of time stamped texts, voicemails, and internet searches add up to a previously unavailable massive data set of statistics that track our movements, our decisions, our lives. Analysis of these trails is offering deep insights into the rhythm of how we do everything. His finding? We work and fight and play in short flourishes of activity followed by next to nothing. The pattern isn't random, it's "bursty." Randomness does not rule our lives in the way scientists have assumed up until now. Illustrating this revolutionary science, Barabasi artfully weaves together the story of a 16th century burst of human activity-a bloody medieval crusade launched in his homeland, Transylvania-with the modern tale of a contemporary artist hunted by the FBI through our post 9/11 surveillance society. These narratives illustrate how predicting human behavior has long been the obsession, sometimes the duty, of those in power. Barabási's astonishingly wide range of examples from seemingly unrelated areas include how dollar bills move around the U.S., the pattern everyone follows in writing email, the spread of epidemics, and even the flight patterns of albatross. In all these phenomena a virtually identical, mathematically described bursty pattern emerges.Bursts reveals what this amazing new research is showing us about where individual spontaneity ends and predictability in human behavior begins. The way you think about your own potential to do something truly extraordinary will never be the same.

    This book marks the first substantial and authoritative effort to close this gap. Colin Camerer, one of the field's leading figures, uses psychological principles and hundreds of experiments to develop mathematical theories of reciprocity, limited strategizing, and learning, which help predict what real people and companies do in strategic situations. Unifying a wealth of information from ongoing studies in strategic behavior, he takes the experimental science of behavioral economics a major step forward. He does so in lucid, friendly prose.Behavioral game theory has three ingredients that come clearly into focus in this book: mathematical theories of how moral obligation and vengeance affect the way people bargain and trust each other; a theory of how limits in the brain constrain the number of steps of I think he thinks . . . reasoning people naturally do; and a theory of how people learn from experience to make better strategic decisions. Strategic interactions that can be explained by behavioral game theory include bargaining, games of bluffing as in sports and poker, strikes, how conventions help coordinate a joint activity, price competition and patent races, and building up reputations for trustworthiness or ruthlessness in business or life.While there are many books on standard game theory that address the way ideally rational actors operate, Behavioral Game Theory stands alone in blending experimental evidence and psychology in a mathematical theory of normal strategic behavior. It is must reading for anyone who seeks a more complete understanding of strategic thinking, from professional economists to scholars and students of economics, management studies, psychology, political science, anthropology, and biology.

    Rather than a "how to" for hands-on techies, the book entices lay-readers and experts alike by covering new case studies and the latest state-of-the-art techniques.You have been predicted — by companies, governments, law enforcement, hospitals, and universities. Their computers say, "I knew you were going to do that!" These institutions are seizing upon the power to predict whether you're going to click, buy, lie, or die.Why? For good reason: predicting human behavior combats financial risk, fortifies healthcare, conquers spam, toughens crime fighting, and boosts sales.How? Prediction is powered by the world's most potent, booming unnatural resource: data. Accumulated in large part as the by-product of routine tasks, data is the unsalted, flavorless residue deposited en masse as organizations churn away. Surprise! This heap of refuse is a gold mine. Big data embodies an extraordinary wealth of experience from which to learn.Predictive analytics unleashes the power of data. With this technology, the computer literally learns from data how to predict the future behavior of individuals. Perfect prediction is not possible, but putting odds on the future — lifting a bit of the fog off our hazy view of tomorrow — means pay dirt.In this rich, entertaining primer, former Columbia University professor and Predictive Analytics World founder Eric Siegel reveals the power and perils of prediction: -What type of mortgage risk Chase Bank predicted before the recession. -Predicting which people will drop out of school, cancel a subscription, or get divorced before they are even aware of it themselves. -Why early retirement decreases life expectancy and vegetarians miss fewer flights. -Five reasons why organizations predict death, including one health insurance company. -How U.S. Bank, European wireless carrier Telenor, and Obama's 2012 campaign calculated the way to most strongly influence each individual. -How IBM's Watson computer used predictive modeling to answer questions and beat the human champs on TV's Jeopardy! -How companies ascertain untold, private truths — how Target figures out you're pregnant and Hewlett-Packard deduces you're about to quit your job. -How judges and parole boards rely on crime-predicting computers to decide who stays in prison and who goes free. -What's predicted by the BBC, Citibank, ConEd, Facebook, Ford, Google, IBM, the IRS, Match.com, MTV, Netflix, Pandora, PayPal, Pfizer, and Wikipedia. A truly omnipresent science, predictive analytics affects everyone, every day. Although largely unseen, it drives millions of decisions, determining whom to call, mail, investigate, incarcerate, set up on a date, or medicate.Predictive analytics transcends human perception. This book's final chapter answers the riddle: What often happens to you that cannot be witnessed, and that you can't even be sure has happened afterward — but that can be predicted in advance?Whether you are a consumer of it — or consumed by it — get a handle on the power of Predictive Analytics.

    The book's patient explanations are written in an informal, non-intimidating style. To underscore the relevance of mathematics to economics, the author allows the economist's analytical needs to motivate the study of related mathematical techniques; he then illustrates these techniques with appropriate economics models. Graphic illustrations often visually reinforce algebraic results. Many exercise problems serve as drills and help bolster student confidence. These major types of economic analysis are covered: statics, comparative statics, optimization problems, dynamics, and mathematical programming. These mathematical methods are introduced: matrix algebra, differential and integral calculus, differential equations, difference equations, and convex sets.

    He was referring to battlefield tactics, but the same can be said about any strategic situation. Even seemingly certain defeat can be turned into victory--whether in battle, business, or life--by those with the strategic vision to recognize how to "change the game" to their own advantage.The aim of David McAdams's Game-Changer is nothing less than to empower you with this wisdom--not just to win in every strategic situation (or "game") you face but to change those games and the ecosystems in which they reside to transform your life and our lives together for the better.Game-Changer develops six basic ways to change games--commitment, regulation, cartelization, retaliation, trust, and relationships--enlivened by countless colorful characters and unforgettable examples from the worlds of business, medicine, finance, military history, crime, sports, and more.The book then digs into several real-world strategic challenges, such as how to keep prices low on the Internet, how to restore the public's lost trust in for-charity telemarketers, and even how to save mankind from looming and seemingly unstoppable drug-resistant disease. In each case, McAdams uses the game-theory approach developed in the book to identify the strategic crux of the problem and then leverages that "game-awareness" to brainstorm ways to change the game to solve or at least mitigate the underlying problem.So get ready for a fascinating journey. You'll emerge a deeper strategic thinker, poised to change and win all the games you play. In doing so, you can also make the world a better place. "Just one Game-Changer [is] enough to seed and transform an entire organization into a more productive, happier, and altogether better place," McAdams writes. Just imagine what we can do together.

    But as risk expert Gerd Gigerenzer shows, the surprising truth is that in the real world, we often get better results by using simple rules and considering less information. In Risk Savvy, Gigerenzer reveals that most of us, including doctors, lawyers, financial advisers, and elected officials, misunderstand statistics much more often than we think, leaving us not only misinformed, but vulnerable to exploitation. Yet there is hope. Anyone can learn to make better decisions for their health, finances, family, and business without needing to consult an expert or a super computer, and Gigerenzer shows us how.Risk Savvy is an insightful and easy-to-understand remedy to our collective information overload and an essential guide to making smart, confident decisions in the face of uncertainty.

    Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation.In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge--from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool--the general principle--from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems.Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.

    In this unconventional introduction, physicist Leonard Susskind and hacker-scientist George Hrabovsky offer a first course in physics and associated math for the ardent amateur. Unlike most popular physics books—which give readers a taste of what physicists know but shy away from equations or math—Susskind and Hrabovsky actually teach the skills you need to do physics, beginning with classical mechanics, yourself. Based on Susskind's enormously popular Stanford University-based (and YouTube-featured) continuing-education course, the authors cover the minimum—the theoretical minimum of the title—that readers need to master to study more advanced topics.An alternative to the conventional go-to-college method, The Theoretical Minimum provides a tool kit for amateur scientists to learn physics at their own pace.

    Topics covered include matrix multiplication, row reduction, matrix inverse, orthogonality and computation. The self-teaching book is loaded with examples and graphics and provides a wide array of probing problems, accompanying solutions, and a glossary. Chapter 1: Introduction to Vectors; Chapter 2: Solving Linear Equations; Chapter 3: Vector Spaces and Subspaces; Chapter 4: Orthogonality; Chapter 5: Determinants; Chapter 6: Eigenvalues and Eigenvectors; Chapter 7: Linear Transformations; Chapter 8: Applications; Chapter 9: Numerical Linear Algebra; Chapter 10: Complex Vectors and Matrices; Solutions to Selected Exercises; Final Exam. Matrix Factorizations. Conceptual Questions for Review. Glossary: A Dictionary for Linear Algebra Index Teaching Codes Linear Algebra in a Nutshell.

    From the classroom to the courtroom and from financial markets to supermarkets, Mlodinow's intriguing and illuminating look at how randomness, chance, and probability affect our daily lives will intrigue, awe, and inspire.

    Thorp invented card counting, proving the seemingly impossible: that you could beat the dealer at the blackjack table. As a result he launched a gambling renaissance. His remarkable success--and mathematically unassailable method--caused such an uproar that casinos altered the rules of the game to thwart him and the legions he inspired. They barred him from their premises, even put his life in jeopardy. Nonetheless, gambling was forever changed.Thereafter, Thorp shifted his sights to "the biggest casino in the world" Wall Street. Devising and then deploying mathematical formulas to beat the market, Thorp ushered in the era of quantitative finance we live in today. Along the way, the so-called godfather of the quants played bridge with Warren Buffett, crossed swords with a young Rudy Giuliani, detected the Bernie Madoff scheme, and, to beat the game of roulette, invented, with Claude Shannon, the world's first wearable computer.Here, for the first time, Thorp tells the story of what he did, how he did it, his passions and motivations, and the curiosity that has always driven him to disregard conventional wisdom and devise game-changing solutions to seemingly insoluble problems. An intellectual thrill ride, replete with practical wisdom that can guide us all in uncertain financial waters, A Man for All Markets is an instant classic--a book that challenges its readers to think logically about a seemingly irrational world.Praise for A Man for All Markets"In A Man for All Markets, [Thorp] delightfully recounts his progress (if that is the word) from college teacher to gambler to hedge-fund manager. Along the way we learn important lessons about the functioning of markets and the logic of investment."--The Wall Street Journal"[Thorp] gives a biological summation (think Richard Feynman's Surely You're Joking, Mr. Feynman!) of his quest to prove the aphorism 'the house always wins' is flawed. . . . Illuminating for the mathematically inclined, and cautionary for would-be gamblers and day traders"-- Library Journal