Mathematics: Pre Cal Reading List - NF

René Descartes (1596-1650) is one of the towering and central figures in Western philosophy and mathematics. His apothegm "Cogito, ergo sum" marked the birth of the mind-body problem, while his creation of so-called Cartesian coordinates have made our physical and intellectual conquest of physical space possible. But Descartes had a mysterious and mystical side, as well. Almost certainly a member of the occult brotherhood of the Rosicrucians, he kept a secret notebook, now lost, most of which was written in code. After Descartes's death, Gottfried Leibniz, inventor of calculus and one of the greatest mathematicians in history, moved to Paris in search of this notebook--and eventually found it in the possession of Claude Clerselier, a friend of Descartes. Leibniz called on Clerselier and was allowed to copy only a couple of pages--which, though written in code, he amazingly deciphered there on the spot. Leibniz's hastily scribbled notes are all we have today of Descartes's notebook, which has disappeared. Why did Descartes keep a secret notebook, and what were its contents? The answers to these questions lead Amir Aczel and the reader on an exciting, swashbuckling journey, and offer a fascinating look at one of the great figures of Western culture.

The history of pi, says the author, though a small part of the history of mathematics, is nevertheless a mirror of the history of man. Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.

How many socks make a pair? The answer is not always two. And behind this question lies a world of maths that can be surprising, amusing and even beautiful. Using playing cards, a newspaper, the back of an envelope, a Sudoku, some pennies and of course a pair of socks, Rob Eastaway shows how maths can demonstrate its secret beauties in even the most mundane of everyday objects. If you already like maths you'll discover plenty of new surprises. And if you've never picked up a maths book in your life, this one will change your view of the subject forever.

The Hidden Mathematics of Sport takes a novel and intriguing look at sport, by exploring the mathematics behind the action. Discover the best tactics for taking a penalty, the pros and cons of being a consistent golfer, the surprising link between boxing and figure skating, the unusual location of England's earliest 'football' game (in a parish church), and the formula for always winning a game of tennis. Whatever your sporting interests, you will find plenty to absorb and amuse you in this entertaining and unique book - and maybe you will even find some new strategies for beating the odds.

In January 1999, Sarah Flannery, a sports-loving teenager from Blarney in County Cork, Ireland, was awarded Ireland's Young Scientist of the Year for her extraordinary research and discoveries in Internet cryptography. The following day, her story began appearing in Irish papers and soon after was splashed across the front page of the London Times, complete with a photo of Sarah and a caption calling her "brilliant." Just sixteen, she was a mathematician with an international reputation. IN CODE is a heartwarming story that will have readers cheering Sarah on. Originally published in England and cowritten with her mathematician father, David Flannery, IN CODE is "a wonderfully moving story about the thrill of the mathematical chase" (Nature) and "a paean to intellectual adventure" (Times Educational Supplement). A memoir in mathematics, it is all about how a girl next door, nurtured by her family, moved from the simple math puzzles that were the staple of dinnertime conversation to prime numbers, the Sieve of Eratosthenes, Fermat's Little Theorem, googols-and finally into her breathtaking algorithm. Parallel with each step is a modest girl's own self-discovery-her values, her burning curiosity, the joy of persistence, and, above all, her love for her family.

Paul Erdos was an amazing and prolific mathematician whose life as a world-wandering numerical nomad was legendary. He published almost 1500 scholarly papers before his death in 1996, and he probably thought more about math problems than anyone in history. Like a traveling salesman offering his thoughts as wares, Erdos would show up on the doorstep of one mathematician or another and announce, "My brain is open." After working through a problem, he'd move on to the next place, the next solution. Hoffman's book, like Sylvia Nasar's biography of John Nash, A Beautiful Mind, reveals a genius's life that transcended the merely quirky. But Erdos's brand of madness was joyful, unlike Nash's despairing schizophrenia. Erdos never tried to dilute his obsessive passion for numbers with ordinary emotional interactions, thus avoiding hurting the people around him, as Nash did. Oliver Sacks writes of Erdos: "A mathematical genius of the first order, Paul Erdos was totally obsessed with his subject--he thought and wrote mathematics for nineteen hours a day until the day he died. He traveled constantly, living out of a plastic bag, and had no interest in food, sex, companionship, art--all that is usually indispensable to a human life."The Man Who Loved Only Numbers is easy to love, despite his strangeness. It's hard not to have affection for someone who referred to children as "epsilons," from the Greek letter used to represent small quantities in mathematics; a man whose epitaph for himself read, "Finally I am becoming stupider no more"; and whose only really necessary tool to do his work was a quiet and open mind. Hoffman, who followed and spoke with Erdos over the last 10 years of his life, introduces us to an undeniably odd, yet pure and joyful, man who loved numbers more than he loved God--whom he referred to as SF, for Supreme Fascist. He was often misunderstood, and he certainly annoyed people sometimes, but Paul Erdos is no doubt missed. --Therese Littleton

Clear, concise, and superbly written, this book reveals the beauty at the heart of mathematics, and it makes that beauty accessible to everyone. It illustrates the fundamental connection between aesthetics and mathematics by drawing analogies between axioms, applied mathematics, paintings, and symphonies. "Witty, trenchant, and provocative." -- Mathematical Association of America.

"Completely fascinating." TIMES EDUCATIONAL SUPLEMENT Journeying through time, THE STORY OF NUMBERS explores the history of mathematics to trace the rise of various number sysems in cultures from Mesopotamia to the modern Computer Era. John McLeish reveals how these number systems in turn have shaped the cultures that devised them. From the secrets and the beauty of the Mayan calendar, to Arabaian algebra, the Chinese counting board, from Pythagoras to Newton to Boole, McLeish uncovers the human side of numbers, who used them and how they have shaped our world.

In this highly readable volume of vignettes of mathematical scandals and gossip, Theoni Pappas assembles 29 fascinating stories of intrigue and the bizarre -- in short, thehuman background of the history of mathematics. Might a haberdasher have changed Einstein's life? Why was the first woman mathematician murdered? How come there's no Nobel Prize in mathematics? Mathematics is principally about numbers, equations, and solutions, all of them precise and timeless. But, behind this arcane matter lies the sometimes sordid world of real people, whose rivalries and deceptions are at odds with the mathematician's reputation for clear thinking and scientific detachment.

Relax: no one understands technical mathematics without lengthy training but we all have an intuitive grasp of the ideas behind the symbols. To celebrate the 50th anniversary of the founding of the Institute of Mathematics and its Applications (IMA), this book is designed to showcase thebeauty of mathematics - including images inspired by mathematical problems - together with its unreasonable effectiveness and applicability, without frying your brain.The book is a collection of 50 original essays contributed by a wide variety of authors. It contains articles by some of the best expositors of the subject (du Sautoy, Singh and Stewart for example) together with entertaining biographical pieces and articles of relevance to our everyday lives (suchas Spiegelhalter on risk and Elwes on medical imaging). The topics covered are deliberately diverse and involve concepts from simple numerology to the very cutting edge of mathematics research. Each article is designed to be read in one sitting and to be accessible to a general audience.There is also other content. There are 50 pictorial "visions of mathematics" which were supplied in response to an open call for contributions from IMA members, Plus readers and the worldwide mathematics community. You'll also find a series of "proofs" of Phythagoras's Theorem - mathematical,literary and comedy - after this, you'll never think of Pythagoras the same way again.

With the same user-friendly, quirky, and perceptive approach that made Innumeracy a bestseller, John Allen Paulos travels though the pages ofthe daily newspaper showing how math and numbers are a key element in many ofthe articles we read every day. From the Senate, SATs, and sex, to crime, celebrities, and cults, he takes stories that may not seem to involvemathematics at all and demonstrates how a lack of mathematical knowledge canhinder our understanding of them.After reading A Mathematician Reads the Newspaper, it will beimpossible to look at the newspaper in the same way.-- PhiladelphiaInquirer It would be great to have John Allen Paulos living next door. Everymorning when you read the paper and come across some story that didn't seemquite right--that had the faint odor of illogic hovering about it-- you couldjust lean out the window and shout, 'John Get the hell over here '. A fun, spunky, wise little book that would be helpful to both the consumers of thenews and its purveyors. -- Washington Post Book World

""A Passion for Mathematics"" is an educational, entertaining trip through the curiosities of the math world, blending an eclectic mix of history, biography, philosophy, number theory, geometry, probability, huge numbers, and mind-bending problems into a delightfully compelling collection that is sure to please math buffs, students, and experienced mathematicians alike. In each chapter, Clifford Pickover provides factoids, anecdotes, definitions, quotations, and captivating challenges that range from fun, quirky puzzles to insanely difficult problems. Readers will encounter mad mathematicians, strange number sequences, obstinate numbers, curious constants, magic squares, fractal geese, monkeys typing Hamlet, infinity, and much, much more. ""A Passion for Mathematics"" will feed readers' fascination while giving them problem-solving skills a great workout!

The #1 New York Times bestseller The phenomenal true story of the black female mathematicians at NASA whose calculations helped fuel some of America's greatest achievements in space--a powerful, revelatory history essential to our understanding of race, discrimination, and achievement in modern America. The basis for the smash Academy Award-nominated film starring Taraji P. Henson, Octavia Spencer, Janelle Monae, Kirsten Dunst, and Kevin Costner. Before John Glenn orbited the earth, or Neil Armstrong walked on the moon, a group of dedicated female mathematicians known as "human computers" used pencils, slide rules and adding machines to calculate the numbers that would launch rockets, and astronauts, into space. Among these problem-solvers were a group of exceptionally talented African American women, some of the brightest minds of their generation. Originally relegated to teaching math in the South's segregated public schools, they were called into service during the labor shortages of World War II, when America's aeronautics industry was in dire need of anyone who had the right stuff. Suddenly, these overlooked math whizzes had a shot at jobs worthy of their skills, and they answered Uncle Sam's call, moving to Hampton, Virginia and the fascinating, high-energy world of the Langley Memorial Aeronautical Laboratory. Even as Virginia's Jim Crow laws required them to be segregated from their white counterparts, the women of Langley's all-black "West Computing" group helped America achieve one of the things it desired most: a decisive victory over the Soviet Union in the Cold War, and complete domination of the heavens. Starting in World War II and moving through to the Cold War, the Civil Rights Movement and the Space Race, Hidden Figures follows the interwoven accounts of Dorothy Vaughan, Mary Jackson, Katherine Johnson and Christine Darden, four African American women who participated in some of NASA's greatest successes. It chronicles their careers over nearly three decades they faced challenges, forged alliances and used their intellect to change their own lives, and their country's future.

Knowing that the most exciting math is not taught in school, Professor Ian Stewart has spent years filling his cabinet with intriguing mathematical games, puzzles, stories, and factoids intended for the adventurous mind. This book reveals the most exhilarating oddities from Professor Stewart's legendary cabinet. Inside, you will find hidden gems of logic, geometry, and probability-like how to extract a cherry from a cocktail glass (harder than you think), a pop-up dodecahedron, and the real reason why you can't divide anything by zero. Scattered among these are keys to Fermat's last theorem, the Poincaréonjecture, chaos theory, and the P=NP problem (you'll win a million dollars if you solve it). You never know what enigmas you'll find in the Stewart cabinet, but they're sure to be clever, mind-expanding, and delightfully fun.

Mathematics has the power to open our eyes to new and unsuspected regularities in nature - the secret structure of a cloud or the hidden rhythms of the weather. This book aims to equip the reader with a mathematician's eye, changing the way we view the world.

Alan Turing (1912-54) was a British mathematician who made history. His breaking of the German U-boat Enigma cipher in World War II ensured Allied-American control of the Atlantic. But Turing's vision went far beyond the desperate wartime struggle. Already in the 1930s he had defined the concept of the universal machine, which underpins the computer revolution. In 1945 he was a pioneer of electronic computer design. But Turing's true goal was the scientific understanding of the mind, brought out in the drama and wit of the famous "Turing test" for machine intelligence and in his prophecy for the twenty-first century.
Drawn in to the cockpit of world events and the forefront of technological innovation, Alan Turing was also an innocent and unpretentious gay man trying to live in a society that criminalized him. In 1952 he revealed his homosexuality and was forced to participate in a humiliating treatment program, and was ever after regarded as a security risk. His suicide in 1954 remains one of the many enigmas in an astonishing life story.

Popular math at its most entertaining and enlightening. "Zero is really something"-Washington Post A New York Times Notable Book. The Babylonians invented it, the Greeks banned it, the Hindus worshiped it, and the Church used it to fend off heretics. Now it threatens the foundations of modern physics. For centuries the power of zero savored of the demonic; once harnessed, it became the most important tool in mathematics. For zero, infinity's twin, is not like other numbers. It is both nothing and everything. In Zero, Science Journalist Charles Seife follows this innocent-looking number from its birth as an Eastern philosophical concept to its struggle for acceptance in Europe, its rise and transcendence in the West, and its ever-present threat to modern physics. Here are the legendary thinkers--from Pythagoras to Newton to Heisenberg, from the Kabalists to today's astrophysicists--who have tried to understand it and whose clashes shook the foundations of philosophy, science, mathematics, and religion. Zero has pitted East against West and faith against reason, and its intransigence persists in the dark core of a black hole and the brilliant flash of the Big Bang. Today, zero lies at the heart of one of the biggest scientific controversies of all time: the quest for a theory of everything.

How can we be sure that Pythagoras's theorem is really true? Why is the "angle in a semicircle" always 90 degrees? And how can tangents help determine the speed of a bullet?David Acheson takes the reader on a highly illustrated tour through the history of geometry, from ancient Greece to the present day. He emphasizes throughout elegant deduction and practical applications, and argues that geometry can offer the quickest route to the whole spirit of mathematics at itsbest. Along the way, we encounter the quirky and the unexpected, meet the great personalities involved, and uncover some of the loveliest surprises in mathematics.

Through Euclid's Window Leonard Mlodinow brilliantly and delightfully leads us on a journey through five revolutions in geometry, from the Greek concept of parallel lines to the latest notions of hyperspace. Here is an altogether new, refreshing, alternative history of math revealing how simple questions anyone might ask about space -- in the living room or in some other galaxy -- have been the hidden engine of the highest achievements in science and technology. Based on Mlodinow's extensive historical research; his studies alongside colleagues such as Richard Feynman and Kip Thorne; and interviews with leading physicists and mathematicians such as Murray Gell-Mann, Edward Witten, and Brian Greene, Euclid's Window is an extraordinary blend of rigorous, authoritative investigation and accessible, good-humored storytelling that makes a stunningly original argument asserting the primacy of geometry. For those who have looked through Euclid's Window, no space, no thing, and no time will ever be quite the same.

Simply put, an algorithm is a set of instructions-it's the code that makes computers run. A basic idea that proved elusive for hundreds of years and bent the minds of the greatest thinkers in the world, the algorithm is what made the modern world possible. Without the algorithm, there would have been no computer, no Internet, no virtual reality, no e-mail, or any other technological advance that we rely on every day. In The Advent of the Algorithm, David Berlinski combines science, history, and math to explain and explore the intriguing story of how the algorithm was finally discovered by a succession of mathematicians and logicians, and how this paved the way for the digital age. Beginning with Leibniz and culminating in the middle of the twentieth century with the groundbreaking work of Gödel and Turing, The Advent of the Algorithm is an epic tale told with clarity and imaginative brilliance.

With the born storyteller's command of narrative and imaginative approach, Leonard Mlodinow vividly demonstrates how our lives are profoundly informed by chance and randomness and how everything from wine ratings and corporate success to school grades and political polls are less reliable than we believe. By showing us the true nature of chance and revealing the psychological illusions that cause us to misjudge the world around us, Mlodinow gives us the tools we need to make more informed decisions. 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.

E=mc². Just about everyone has at least heard of Albert Einstein's formulation of 1905, which came into the world as something of an afterthought. But far fewer can explain his insightful linkage of energy to mass. David Bodanis offers an easily grasped gloss on the equation. Mass, he writes, "is simply the ultimate type of condensed or concentrated energy," whereas energy "is what billows out as an alternate form of mass under the right circumstances."
Just what those circumstances are occupies much of Bodanis's book, which pays homage to Einstein and, just as important, to predecessors such as Maxwell, Faraday, and Lavoisier, who are not as well known as Einstein today. Balancing writerly energy and scholarly weight, Bodanis offers a primer in modern physics and cosmology, explaining that the universe today is an expression of mass that will, in some vastly distant future, one day slide back to the energy side of the equation, replacing the "dominion of matter" with "a great stillness"--a vision that is at once lovely and profoundly frightening.
Without sliding into easy psychobiography, Bodanis explores other circumstances as well; namely, Einstein's background and character, which combined with a sterling intelligence to afford him an idiosyncratic view of the way things work--a view that would change the world.

Physicist and popular science writer Barry Parker speaks to the broadest possible audience in bringing Einstein's theories to life. Given the fervent renewed appreciation for the contributions Albert Einstein has bestowed on humanity, Parker thinks it only right to dedicate a book to explaining in the clearest possible terms the meaning and beauty of Einstein's theories. While tracing the story of Einstein's life, Parker seizes on the crucial groundbreaking theories that Einstein envisioned. Not since Isaac Newton had anyone conceived the universe in such a revolutionary, startling new way. Through Parker's eloquence, eye for detail, and clever use of Einsteinian cartoons and vivid illustrations, he enables the reader to see and appreciate for perhaps the first time the full meaning and scope of Einstein's Special Theory of Relativity and General Theory of Relativity. Parker then guides the reader to the next step in Einstein's revelations: the possibility of time travel. In exploring the fascinating implications of Einstein's thought, Parker treats us to the experience of discovering a black hole, traversing curved spacetime, and greeting our much younger twin who has just returned from a long and arduous spaceflight. Parker's incomparable gift for language captures Einstein's uniqueness, singular brilliance, and stunning theories. The clarity of the writing coupled with the many illustrations will drive home the point why so many consider Einstein to be the greatest scientist who ever lived and Time magazine named Albert Einstein "Person of the Century."

Reality, today's physicists tell us, is created by the vibrations of exquisitely tiny superstrings in ten spatial dimensions. Ten dimensions? Most of us have barely gotten used to the idea that there are four. Using simple geometry and an easygoing writing style, author Rob Bryanton starts with the lower dimensions that we are all familiar with, then uses those concepts to build one layer upon another, ultimately arriving at a way of imagining the tenth dimension. Part scientific exploration, part philosophy, this unique book touches upon such diverse topics as dark matter, Feynman's sum over paths, the quantum observer, and the soul. It is aimed at anyone interested in leading-edge theories about cosmology and the nature of reality, but it is not about mainstream physics. Rather, Imagining the Tenth Dimension is a mind-expanding exercise that could change the way you view this incredible universe in which we live

Malba Tahan is the creation of a celebrated Brazilian mathematician who was looking for a way to bring some of the mysteries and delights of mathematics to a wider public. He turned out to be a born storyteller.The adventures of Beremiz Samir, The Man Who Counted, take the reader on an exotic journey in which, time and again, he summons his extraordinary mathematical powers to settle disputes, give wise advice, overcome dangerous enemies, and win for himself fame and fortune. as we accompany him, we learn much of the history of famous mathematicisns who preceded him; we undergo a series of trials at the hands of the wise men of the day; and we come to admire the warm wisdom and patience that earn him the respect and affection of those whose problems he resolves so astutely. In the grace of their telling, these stories hold unusual delights for the reader.

Calculus is the key to much of modern science and engineering. It is the mathematical method for the analysis of things that change, and since in the natural world we are surrounded by change, the development of calculus was a huge breakthrough in the history of mathematics. But it is alsosomething of a mathematical adventure, largely because of the way infinity enters at virtually every twist and turn...In The Calculus Story David Acheson presents a wide-ranging picture of calculus and its applications, from ancient Greece right up to the present day. Drawing on their original writings, he introduces the people who helped to build our understanding of calculus. With a step by step treatment, hedemonstrates how to start doing calculus, from the very beginning.

From New York Times bestselling author Edward Dolnick, the true story of a pivotal moment in modern history when a group of strange, tormented geniuses--Isaac Newton chief among them--invented science and remade our understanding of the world. At a time when the world was falling apart-- in an age of religious wars, plague, and the Great Fire of London--a group of men looked around them and saw a world of perfect order. Chaotic as it looked, these earliest scientists declared, the universe was in fact an intricate and perfectly regulated clockwork. This was the tail-end of Shakespeare's century, and these were brilliant, ambitious, confused, conflicted men. They believed in angels and alchemy and the devil, and they believed that the universe followed precise, mathematical laws. This is the story of the bewildered geniuses who made the modern world.

Professor John D. Barrow has all the answers. In 100 Essential Things You Didn't Know You Didn't Know About Maths and the Arts, he shows us that mathematics and the arts are not so far removed from each other. He takes us on a 100-step tour, guiding us through art forms as various as sculpture, literature, architecture and dance, and reveals what maths can tell us about the mysteries of the worlds of art and design.
We find out why diamonds sparkle, how many words Shakespeare knew and why the shower is the best place to sing. We discover why an egg is egg-shaped, why Charles Dickens crusaded against maths and how a soprano can shatter a wine glass without touching it...
Enlivening the everyday with a new way of looking at the world, this book will enrich your understanding of the maths and art that surround us in our day-to-day lives.

The world of maths can seem mind-boggling, irrelevant and, let's face it, boring. This groundbreaking book reclaims maths from the geeks.
Mathematical ideas underpin just about everything in our lives: from the surprising geometry of the 50p piece to how probability can help you win in any casino. In search of weird and wonderful mathematical phenomena, Alex Bellos travels across the globe and meets the world's fastest mental calculators in Germany and a startlingly numerate chimpanzee in Japan.
Packed with fascinating, eye-opening anecdotes, Alex's Adventures in Numberland is an exhilarating cocktail of history, reportage and mathematical proofs that will leave you awestruck.

With a foreword by Tim Rice, this book will change the way you see the world. Why is it better to buy a lottery ticket on a Friday? Why are showers always too hot or too cold? And what's the connection between a rugby player taking a conversion and a tourist trying to get the best photograph of Nelson's Column? These and many other fascinating questions are answered in this entertaining and highly informative book, which is ideal for anyone wanting to remind themselves - or discover for the first time - that maths is relevant to almost everything we do.   Dating, cooking, travelling by car, gambling and even life-saving techniques have links with intriguing mathematical problems, as you will find explained here. Whether you have a PhD in astrophysics or haven't touched a maths problem since your school days, this book will give you a fresh understanding of the world around you.

"Witty, compelling, and just plain fun to read . . ." --Evelyn Lamb, Scientific American The Freakonomics of math--a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn't confined to abstract incidents that never occur in real life, but rather touches everything we do--the whole world is shot through with it. Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It's a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does "public opinion" really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer? How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician's method of analyzing life and exposing the hard-won insights of the academic community to the layman--minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia's views on crime and punishment, the psychology of slime molds, what Facebook can and can't figure out about you, and the existence of God. Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is "an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength." With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.

In this book, you'll learn why Florence Nightingale introduced pie charts, how Lewis Carroll regarded Pythagoras, and why some infinities are larger than others. You'll also meet the mathematician who knew eight languages by the time he was eleven, the one who was sent to jail for gambling, and the one who published a lot yet never existed.

A moving and enlightening look at the unbelievable true story of how gifted prodigy Ramanujan stunned the scholars of Cambridge University and revolutionized mathematics. In 1913, a young unschooled Indian clerk wrote a letter to G H Hardy, begging the preeminent English mathematician's opinion on several ideas he had about numbers. Realizing the letter was the work of a genius, Hardy arranged for Srinivasa Ramanujan to come to England. Thus began one of the most improbable and productive collaborations ever chronicled. With a passion for rich and evocative detail, Robert Kanigel takes us from the temples and slums of Madras to the courts and chapels of Cambridge University, where the devout Hindu Ramanujan, "the Prince of Intuition," tested his brilliant theories alongside the sophisticated and eccentric Hardy, "the Apostle of Proof." In time, Ramanujan's creative intensity took its toll: he died at the age of thirty-two, but left behind a magical and inspired legacy that is still being plumbed for its secrets today.

"What can I do with a degree in math?" You've worked hard for that math degree. Now what? Sometimes, the choice of careers can seem endless. The most difficult part of a job search is starting it. This is where Great Jobs for Math Majors comes in. Designed to help you put your major to work, this handy guide covers the basics of a job search and provides detailed profiles of careers in math. From the worlds of finance and science to manufacturing and education, you'll explore a variety of job options for math majors and determine the best fit for your personal, professional, and practical needs. Do you want to be an actuary? Work in the banking industry? Program computers? In this updated edition, you'll find: Job-search basics such as crafting résumés and writing cover letters Self-assessment exercises to help determine your professional fit Investigative tools to help you find the perfect job Networking tips to get your foot in the door before your résumé is even sent True tales from practicing professionals about everyday life on the job Current statistics on earnings, advancement, and the future of the profession Resources for further information, including journals, professional associations, and online resources

Stories of famously eccentric Princetonians abound—such as that of chemist Hubert Alyea, the model for The Absent-Minded Professor, or Ralph Nader, said to have had his own key to the library as an undergraduate. Or the "Phantom of Fine Hall," a figure many students had seen shuffling around the corridors of the math and physics building wearing purple sneakers and writing numerology treatises on the blackboards. The Phantom was John Nash, one of the most brilliant mathematicians of his generation, who had spiraled into schizophrenia in the 1950s. His most important work had been in game theory, which by the 1980s was underpinning a large part of economics. When the Nobel Prize committee began debating a prize for game theory, Nash's name inevitably came up—only to be dismissed, since the prize clearly could not go to a madman. But in 1994 Nash, in remission from schizophrenia, shared the Nobel Prize in economics for work done some 45 years previously.
Sylvia Nasar has written a biography of Nash that looks at all sides of his life. She gives an intelligent, understandable exposition of his mathematical ideas and a picture of schizophrenia that is evocative but decidedly unromantic. Her story of the machinations behind Nash's Nobel is fascinating and one of very few such accounts available in print (the CIA could learn a thing or two from the Nobel committees).

Why do even well-educated people understand so little about mathematics? And what are the costs of our innumeracy? John Allen Paulos, in his celebrated bestseller first published in 1988, argues that our inability to deal rationally with very large numbers and the probabilities associated with them results in misinformed governmental policies, confused personal decisions, and an increased susceptibility to pseudoscience of all kinds. Innumeracy lets us know what we're missing, and how we cando something about it. Sprinkling his discussion of numbers and probabilities with quirky stories and anecdotes, Paulos ranges freely over many aspects of modern life, from contested elections to sports stats, from stock scams and newspaper psychics to diet and medical claims, sex discrimination, insurance, lotteries, and drug testing. Readers ofInnumeracywill be rewarded with scores of astonishing facts, a fistful of powerful ideas, and, most important, a clearer, more quantitative way of looking at their world.

Part of the joy of mathematics is that it is everywhere-in soap bubbles, electricity, da Vinci's masterpieces, even in an ocean wave. Written by the well-known mathematics teacher consultant, this volume's collection of over 200 clearly illustrated mathematical ideas, concepts, puzzles, and games shows where they turn up in the "real" world. You'll find out what a googol is, visit hotel infinity, read a thorny logic problem that was stumping them back in the 8th century. THE JOY OF MATHEMATICS is designed to be opened at random...it's mini essays are self-contained providing the reader with an enjoyable way to explore and experience mathematics at its best.

Wouldn't it be great if all school teachers (from kindergarten through high school) would share the joy of mathematics with their students, rather than focus only on the prescribed curriculum that will subsequently be tested? aThis book promises to help teachers and all readers do just that by revealing some wonders of mathematics often missing from classrooms. Here's your chance to catch up with the math gems you may have missed in your school years. aaaa Using jargon-free language and many illustrations, the authors--all veteran math educators--explore five areas--arithmetic, algebra, geometry, probability, and the ways in which mathematics can reinforce common sense. Among other things, you'll learn "the rule of 72," which enables you to quickly determine how long it will take your bank account to double its value at a specific interest rate. Other handy techniques include an automatic algorithm for multiplying numbers mentally and a clever application that will allow you to convert from miles to kilometers (or the reverse) mentally. A delightful presentation of geometric novelties reveals relationships that could have made your study of geometry more fun and enlightening. In the area of probability there is a host of interesting examples- from the famous Monty-Hall problem to the counterintuitive probability of two people having the same birthday in a crowded room. aaaa Finally, the authors demonstrate how math will make you a better thinker by improving your organizing abilities and providing useful and surprising solutions to common mathematics problems. You'll come away with a grasp of math you never thought possible and a true appreciation for this "queen of the sciences."

You may have watched hundreds of episodes ofThe Simpsons (and its sister showFuturama) without ever realizing that cleverly embedded in many plots are subtle references to mathematics, ranging from well-known equations to cutting-edge theorems and conjectures. That they exist, Simon Singh reveals, underscores the brilliance of the shows' writers, many of whom have advanced degrees in mathematics in addition to their unparalleled sense of humor. While recounting memorable episodes such as "Bart the Genius" and "Homer3," Singh weaves in mathematical stories that explore everything from p to Mersenne primes, Euler's equation to the unsolved riddle of P v. NP; from perfect numbers to narcissistic numbers, infinity to even bigger infinities, and much more. Along the way, Singh meets members ofThe Simpsons' brilliant writing team-among them David X. Cohen, Al Jean, Jeff Westbrook, and Mike Reiss-whose love of arcane mathematics becomes clear as they reveal the stories behind the episodes. With wit and clarity, displaying a true fan's zeal, and replete with images from the shows, photographs of the writers, and diagrams and proofs,The Simpsons and Their Mathematical Secrets offers an entirely new insight into the most successful show in television history.

Mathematician Ian Stewart tells readers what he wishes he had known when he was a student. He takes up subjects ranging from the philosophical to the practical-what mathematics is and why it's worth doing, the relationship between logic and proof, the role of beauty in mathematical thinking, the future of mathematics, how to deal with the peculiarities of the mathematical community, and many others.

Too often math gets a bad rap, characterized as dry and difficult. But, Alex Bellos says, "math can be inspiring and brilliantly creative. Mathematical thought is one of the great achievements of the human race, and arguably the foundation of all human progress. The world of mathematics is a remarkable place." Bellos has traveled all around the globe and has plunged into history to uncover fascinating stories of mathematical achievement, from the breakthroughs of Euclid, the greatest mathematician of all time, to the creations of the Zen master of origami, one of the hottest areas of mathematical work today. Taking us into the wilds of the Amazon, he tells the story of a tribe there who can count only to five and reports on the latest findings about the math instinct--including the revelation that ants can actually count how many steps they've taken. Journeying to the Bay of Bengal, he interviews a Hindu sage about the brilliant mathematical insights of the Buddha, while in Japan he visits the godfather of Sudoku and introduces the brainteasing delights of mathematical games. Exploring the mysteries of randomness, he explains why it is impossible for our iPods to truly randomly select songs. In probing the many intrigues of that most beloved of numbers, pi, he visits with two brothers so obsessed with the elusive number that they built a supercomputer in their Manhattan apartment to study it. Throughout, the journey is enhanced with a wealth of intriguing illustrations, such as of the clever puzzles known as tangrams and the crochet creation of an American math professor who suddenly realized one day that she could knit a representation of higher dimensional space that no one had been able to visualize. Whether writing about how algebra solved Swedish traffic problems, visiting the Mental Calculation World Cup to disclose the secrets of lightning calculation, or exploring the links between pineapples and beautiful teeth, Bellos is a wonderfully engaging guide who never fails to delight even as he edifies. Here's Looking at Euclid is a rare gem that brings the beauty of math to life.

It Must Be Beautiful is a collection of 12 essays on the power and beauty of modern scientific equations by some of the world's foremost scientists and historians.

In the tradition of A Beautiful Mind, here is an engaging biography of a world-famous Canadian geometry genius, Donald Coxeter, whose work has slowly and steadily become the air we breathe, with everyday applications in telecommunication and e-commerce, among other fields. King of Infinite Space combines two bestselling categories, popular science and biography. It makes geometry accessible through the fascinating life of the 20th century's greatest classical geometer -- a man who also happens to be a Canadian. Coxeter's story weaves together several rich and surprising threads, from the idiosyncratic nature of his personal life to the geopolitical fabric of his times -- what he calls the wild wicked world -- and illuminates the importance of mathematics therein. Indeed, Coxeter is credited with saving classical geometry from near extinction: for over fifty years, he fought a quiet war of attrition against disdain for his unfashionable geometry, stoically retaining his passion for the beauty of shapes.

Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market! The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.

Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them. In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics.

In the bestselling literary tradition of Lewis Thomas's Lives of a Cell and James Watson's The Double Helix, Poetry of the Universe is a delightful and compelling narrative charting the evolution of mathematical ideas that have helped to illuminate the nature of the observable universe. In a richly anecdotal fashion, the book explores the leaps of imagination and vision in mathematics that have helped pioneer our understanding of the world around us.

A Publishers Weekly best book of 1995! Dr. 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.

The scientist, philosopher, and man portrayed through his own words. A classic collection now back in print!

In a work of awesome scope, Amir Aczel investigates what powers the stars on their journey to the edge of the universe. Using Einstein and his theories to explain the latest developments in cosmology, Aczel outlines the links between relativity and cosmology via Einstein's "cosmological constant." In the author's view, Einstein served as God's mouthpiece, revealing the most fundamental truths about our larger environment, truths contemporary scientists are just now confirming. This book is the first to discuss certain letters of Einstein that put a new spin on his relationship with other scientists and on his early efforts to prove his revolutionary theories.

There are two kinds of math: the hard kind and the easy kind. The easy kind, practiced by ants, shrimp, Welsh corgis -- and us -- is innate. What innate calculating skills do we humans have? Leaving aside built-in mathematics, such as the visual system, ordinary people do just fine when faced with mathematical tasks in the course of the day. Yet when they are confronted with the same tasks presented as "math," their accuracy often drops. But if we have innate mathematical ability, why do we have to teach math and why do most of us find it so hard to learn? Are there tricks or strategies that the ordinary person can do to improve mathematical ability? Can we improve our math skills by learning from dogs, cats, and other creatures that "do math"? The answer to each of these questions is a qualified yes. All these examples of animal math suggest that if we want to do better in the formal kind of math, we should see how it arises from natural mathematics. From NPR's "Math Guy" -- The Math Instinct will provide even the most number-phobic among us with confidence in our own mathematical abilities.

What are the odds of two people at a party having the same birthday? Or that you'll draw a fourth queen for your poker hand? Or that Earthlings are alone in the universe? Or that the cute girl in accounting will go out with you on a date? If you're the kind of person who spends a lot of time pondering such dilemmas, you'll probably enjoy Jeffrey Rosenthal's entertaining book Struck by Lightning. Rosenthal, a Harvard math PhD and a professor of statistics at the University of Toronto, makes statistics come alive with colourful writing and everyday examples of how uncertainty affects our lives. He notes that people have a love-hate relationship with randomness. "We are inexplicably delighted by strange coincidences and striking similarities," he writes. But we also hate the dark side of uncertainty--the possibility of disease, plane crashes, collapsing bridges. Rosenthal's goal is to help teach readers to worry less and appreciate the randomness of life. "Uncertainty is here to stay," he writes. "We have two options: we can let uncertainty get the better of us or we can learn to understand randomness."
Rosenthal shows how readers can use probability theory for everything from improving their luck at poker or Monopoly to assessing whether they might be attacked by terrorists while traveling. It can be used to devise a better computer password or to analyze studies of a drug recommended by your doctor. And yes, readers can figure out the odds they'll be hit by lightning and how a certain Cuban farmer happened to be struck five times. There are even clues about whether life exists on other planets. In a world where events often seem to be spinning out of control, Rosenthal makes a convincing case that we should embrace randomness, and his book is a great primer for how to do it.

Biologists have long dismissed mathematics as being unable to meaningfully contribute to our understanding of living beings. Within the past ten years, however, mathematicians have proven that they hold the key to unlocking the mysteries of our world--and ourselves. InThe Mathematics of Life, Ian Stewart provides a fascinating overview of the vital but little-recognized role mathematics has played in pulling back the curtain on the hidden complexities of the natural world--and how its contribution will be even more vital in the years ahead. In his characteristically clear and entertaining fashion, Stewart explains how mathematicians and biologists have come to work together on some of the most difficult scientific problems that the human race has ever tackled, including the nature and origin of life itself.