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.

    Growing up in a working-class Long Island family, Massimino catapulted himself to Columbia and then MIT, only to flunk his qualifying exams and be rejected twice by NASA before making it to the final round of astronaut selection—where he was told his poor eyesight meant he’d never make the cut. But even that couldn’t stop him from finally earning his wings, making the jump to training in T-38 Air Force jets and preparing his body—and soul—for the journey to the cosmos.Taking us through the surreal wonder and beauty of his first spacewalk, the tragedy of losing friends in the Columbia shuttle accident, and the development of his enduring love for the Hubble telescope—which he’d be tasked with saving on his final mission— Massimino has written an ode to never giving up and the power of teamwork to make anything possible. Spaceman invites us into a rare, wonderful world where the nerdiest science meets the most thrilling adventure, and pulls back a curtain on just what having “the right stuff” really means.

    Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...Aigner and Ziegler... write: ..". all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999..". the style is clear and entertaining, the level is close to elementary ... and the proofs are brilliant. ..." LMS Newsletter, January 1999This third edition offers two new chapters, on partition identities, and on card shuffling. Three proofs of Euler's most famous infinite series appear in a separate chapter. There is also a number of other improvements, such as an exciting new way to "enumerate the rationals."

    Augustine equate nothingness with the Devil? What tortuous means did 17th-century scientists employ in their attempts to create a vacuum? And why do contemporary quantum physicists believe that the void is actually seething with subatomic activity? You’ll find the answers in this dizzyingly erudite and elegantly explained book by the English cosmologist John D. Barrow.Ranging through mathematics, theology, philosophy, literature, particle physics, and cosmology, The Book of Nothing explores the enduring hold that vacuity has exercised on the human imagination. Combining high-wire speculation with a wealth of reference that takes in Freddy Mercury and Shakespeare alongside Isaac Newton, Albert Einstein, and Stephen Hawking, the result is a fascinating excursion to the vanishing point of our knowledge.

    For even as she sets out to determine how big “really big” may be, Levin gives us an intimate look at the day-to-day life of a globe-trotting physicist, complete with jet lag and romantic disturbances.Nimbly synthesizing geometry, topology, chaos and string theories, Levin shows how the pattern of hot and cold spots left over from the big bang may one day reveal the size and shape of the cosmos. She does so with such originality, lucidity—and even poetry—that How the Universe Got Its Spots becomes a thrilling and deeply personal communication between a scientist and the lay reader.

    Most of the time this math works quietly behind the scenes . . . until it doesn't. All sorts of seemingly innocuous mathematical mistakes can have significant consequences.Math is easy to ignore until a misplaced decimal point upends the stock market, a unit conversion error causes a plane to crash, or someone divides by zero and stalls a battleship in the middle of the ocean.Exploring and explaining a litany of glitches, near misses, and mathematical mishaps involving the internet, big data, elections, street signs, lotteries, the Roman Empire, and an Olympic team, Matt Parker uncovers the bizarre ways math trips us up, and what this reveals about its essential place in our world. Getting it wrong has never been more fun.

    Admittedly real life wasn’t like that. But only, they argued, because we didn’t have enough data to be certain.Then the cracks began to appear. It proved impossible to predict exactly how three planets orbiting each other would move. Meteorologists discovered that the weather was truly chaotic – so dependent on small variations that it could never be predicted for more than a few days out. And the final nail in the coffin was quantum theory, showing that everything in the universe has probability at its heart.That gives human beings a problem. We understand the world through patterns. Randomness and probability will always be alien to us. But it’s time to plunge into this fascinating, shadowy world, because randomness crops up everywhere. Probability and statistics are the only way to get a grip on nature’s workings. They may even seal the fate of free will and predict how the universe will end.Forget Newton’s clockwork universe. Welcome to Dice World.

    You'll find out how to unknot your DNA, how to count like a supercomputer and how to become famous for solving mathematics' most challenging problem.

    Capturing the tone of students exchanging ideas among themselves, this unique guide also explains how calculus is taught, how to get the best teachers, what to study, and what is likely to be on exams—all the tricks of the trade that will make learning the material of first-semester calculus a piece of cake. Funny, irreverent, and flexible, How to Ace Calculus shows why learning calculus can be not only a mind-expanding experience but also fantastic fun.

    For some of us, the word conjures up memories of ten-pound textbooks and visions of tedious abstract equations. And yet, in reality, calculus is fun, accessible, and surrounds us everywhere we go. In Everyday Calculus, Oscar Fernandez shows us how to see the math in our coffee, on the highway, and even in the night sky.Fernandez uses our everyday experiences to skillfully reveal the hidden calculus behind a typical day's events. He guides us through how math naturally emerges from simple observations-how hot coffee cools down, for example-and in discussions of over fifty familiar events and activities. Fernandez demonstrates that calculus can be used to explore practically any aspect of our lives, including the most effective number of hours to sleep and the fastest route to get to work. He also shows that calculus can be both useful-determining which seat at the theater leads to the best viewing experience, for instance-and fascinating-exploring topics such as time travel and the age of the universe. Throughout, Fernandez presents straightforward concepts, and no prior mathematical knowledge is required. For advanced math fans, the mathematical derivations are included in the appendixes.Whether you're new to mathematics or already a curious math enthusiast, Everyday Calculus invites you to spend a day discovering the calculus all around you. The book will convince even die-hard skeptics to view this area of math in a whole new way.

    Among them would be history makers, including the first American woman and the first African American in space. This assembly of astronauts would carry NASA through the most tumultuous years of the space shuttle program. Four would die on Challenger. USAF Colonel Mike Mullane was a member of this astronaut class, and Riding Rockets is his story -- told with a candor never before seen in an astronaut's memoir. Mullane strips the heroic veneer from the astronaut corps and paints them as they are -- human. His tales of arrested development among military flyboys working with feminist pioneers and post-doc scientists are sometimes bawdy, often hilarious, and always entertaining. Mullane vividly portrays every aspect of the astronaut experience -- from telling a female technician which urine-collection condom size is a fit; to walking along a Florida beach in a last, tearful goodbye with a spouse; to a wild, intoxicating, terrifying ride into space; to hearing "Taps" played over a friend's grave. Mullane is brutally honest in his criticism of a NASA leadership whose bungling would precipitate the Challenger disaster. Riding Rockets is a story of life in all its fateful uncertainty, of the impact of a family tragedy on a nine-year-old boy, of the revelatory effect of a machine called Sputnik, and of the life-steering powers of lust, love, and marriage. It is a story of the human experience that will resonate long after the call of "Wheel stop."

    According to revolutionary new research, some birds rival primates and even humans in their remarkable forms of intelligence. In The Genius of Birds, acclaimed author Jennifer Ackerman explores their newly discovered brilliance and how it came about. As she travels around the world to the most cutting-edge frontiers of research, Ackerman not only tells the story of the recently uncovered genius of birds but also delves deeply into the latest findings about the bird brain itself that are shifting our view of what it means to be intelligent. At once personal yet scientific, richly informative and beautifully written, The Genius of Birds celebrates the triumphs of these surprising and fiercely intelligent creatures.

    Almost a decade earlier, Dr. Sacks had published his masterpiece Awakenings but the book had hardly been an immediate success, and the rumpled clinician was still largely unknown. Over the ensuing four years, the two men worked closely together until Sacks asked Weschler to abandon the profile, a request to which Weschler acceded. The two remained close friends, however, across the next thirty years and then, just as Sacks was dying, he urged Weschler to take up the project once again. This book is the result of that entreaty.Weschler sets Sacks's brilliant table talk and extravagant personality in vivid relief. We see Sacks rowing and ranting and caring deeply; composing the essays that would form The Man Who Mistook His Wife for a Hat ; recalling his turbulent drug-fueled younger days; helping his patients and exhausting his friends; and waging intellectual war against a medical and scientific establishment that failed to address his greatest concern: the spontaneous specificity of the individual human soul. And all the while he is pouring out a stream of glorious, ribald, hilarious, and often profound conversation that establishes him as one of the great talkers of the age.

    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.

    presents some of the most famous mathematical proofs in a charming book that will appeal to nonmathematicians and math experts alike. Grasp in an instant why Pythagoras's theorem must be correct. Follow the ancient Chinese proof of the volume formula for the frustrating frustum, and Archimedes' method for finding the volume of a sphere. Discover the secrets of pi and why, contrary to popular belief, squaring the circle really is possible. Study the subtle art of mathematical domino tumbling, and find out how slicing cones helped save a city and put a man on the moon.