Since then, Sylvia Nasar's celebrated biography A Beautiful Mind, the basis of a new major motion picture, has revealed the man. The Essential John Nash reveals his work--in his own words. This book presents, for the first time, the full range of Nash's diverse contributions not only to game theory, for which he received the Nobel, but to pure mathematics--from Riemannian geometry and partial differential equations--in which he commands even greater acclaim among academics. Included are nine of Nash's most influential papers, most of them written over the decade beginning in 1949.From 1959 until his astonishing remission three decades later, the man behind the concepts "Nash equilibrium" and "Nash bargaining"--concepts that today pervade not only economics but nuclear strategy and contract talks in major league sports--had lived in the shadow of a condition diagnosed as paranoid schizophrenia. In the introduction to this book, Nasar recounts how Nash had, by the age of thirty, gone from being a wunderkind at Princeton and a rising mathematical star at MIT to the depths of mental illness.In his preface, Harold Kuhn offers personal insights on his longtime friend and colleague; and in introductions to several of Nash's papers, he provides scholarly context. In an afterword, Nash describes his current work, and he discusses an error in one of his papers. A photo essay chronicles Nash's career from his student days in Princeton to the present. Also included are Nash's Nobel citation and autobiography.The Essential John Nash makes it plain why one of Nash's colleagues termed his style of intellectual inquiry as "like lightning striking." All those inspired by Nash's dazzling ideas will welcome this unprecedented opportunity to trace these ideas back to the exceptional mind they came from.

    Accordingly, he once derided as "spooky action at a distance" the notion that two elementary particles far removed from each other could nonetheless influence each other's properties—a hypothetical phenomenon his fellow theorist Erwin Schrödinger termed "quantum entanglement."In a series of ingenious experiments conducted in various locations—from a dank sewage tunnel under the Danube River to the balmy air between a pair of mountain peaks in the Canary Islands—the author and his colleagues have demonstrated the reality of such entanglement using photons, or light quanta, created by laser beams. In principle the lessons learned may be applicable in other areas, including the eventual development of quantum computers.

    This introductory text is suitable for use in a course on the subject or for self-study, featuring broad coverage and a readable exposition, with many examples and exercises. The four main chapters present the basics: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature is the inclusion of many optional topics not usually part of a first course due to time constraints: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and Steenrod squares and powers.

    Includes such gems as:? There are 42 eyes in a deck of cards, and 42 dots on a pair of dice ? In order to fill in a map so that neighboring regions never get the same color, one never needs more than four colors ? Hells Angels use the number 81 in their insignia because the initials H and A are the eighth and first numbers in the alphabet respectively

    Carroll at his very best.--Bill Bryson, author of The Body: A Guide for Occupants From acclaimed writer and biologist Sean B. Carroll, a rollicking, awe-inspiring story of the surprising power of chance in our lives and the worldWhy is the world the way it is? How did we get here? Does everything happen for a reason or are some things left to chance? Philosophers and theologians have pondered these questions for millennia, but startling scientific discoveries over the past half century are revealing that we live in a world driven by chance. A Series of Fortunate Events tells the story of the awesome power of chance and how it is the surprising source of all the beauty and diversity in the living world.Like every other species, we humans are here by accident. But it is shocking just how many things--any of which might never have occurred--had to happen in certain ways for any of us to exist. From an extremely improbable asteroid impact, to the wild gyrations of the Ice Age, to invisible accidents in our parents' gonads, we are all here through an astonishing series of fortunate events. And chance continues to reign every day over the razor-thin line between our life and death.This is a relatively small book about a really big idea. It is also a spirited tale. Drawing inspiration from Monty Python, Kurt Vonnegut, and other great thinkers, and crafted by one of today's most accomplished science storytellers, A Series of Fortunate Events is an irresistibly entertaining and thought-provoking account of one of the most important but least appreciated facts of life.

    

    It covers areas such as fundamentals, logic, counting, relations and digraphs, trees, topics in graph theory, languages and finite-state machines, and groups and coding.