This book traces the first faltering steps taken in the mathematical theorisation of infinity which marks the emergence of modern mathematics. It analyses the part played by Indian mathematicians through the Kerala conduit, which is an important but neglected part of the history of mathematics.

Passage to Infinity: Medieval Indian Mathematics from Kerala and its Impact begins with an examination of the social origins of the Kerala School and proceeds to discuss its mathematical genesis as well as its achievements. It presents the techniques employed by the School to derive the series expansions for sine, cosine, arctan, and so on. By using modern notation but remaining close to the methods in the original sources, it enables the reader with some knowledge of trigonometry and elementary algebra to follow the derivations. While delving into the nature of the socio-economic processes that led to the development of scientific knowledge in pre-modern India, the book also probes the validity or otherwise of the conjecture of the transmission of Kerala mathematics to Europe through the Jesuit channel.

The book straddles two domains: science and social sciences. It will appeal to those interested in mathematics, statistics, medieval history, history of science and technology, links between mathematics and culture and the nature of movements of ideas across cultures.

A NEW YORK TIMES BESTSELLER

The official book behind the Academy Award-winning film The Imitation Game, starring Benedict Cumberbatch and Keira Knightley

It is only a slight exaggeration to say that the British mathematician Alan Turing (1912-1954) saved the Allies from the Nazis, invented the computer and artificial intelligence, and anticipated gay liberation by decades--all before his suicide at age forty-one. This New York Times–bestselling biography of the founder of computer science, with a new preface by the author that addresses Turing's royal pardon in 2013, is the definitive account of an extraordinary mind and life.

Capturing both the inner and outer drama of Turing’s life, Andrew Hodges tells how Turing’s revolutionary idea of 1936--the concept of a universal machine--laid the foundation for the modern computer and how Turing brought the idea to practical realization in 1945 with his electronic design. The book also tells how this work was directly related to Turing’s leading role in breaking the German Enigma ciphers during World War II, a scientific triumph that was critical to Allied victory in the Atlantic. At the same time, this is the tragic account of a man who, despite his wartime service, was eventually arrested, stripped of his security clearance, and forced to undergo a humiliating treatment program--all for trying to live honestly in a society that defined homosexuality as a crime.

The inspiration for a major motion picture starring Benedict Cumberbatch and Keira Knightley, Alan Turing: The Enigma is a gripping story of mathematics, computers, cryptography, and homosexual persecution.

Now an HBO® Film starring Oprah Winfrey and Rose Byrne

#1 NEW YORK TIMES BESTSELLER

Her name was Henrietta Lacks, but scientists know her as HeLa. She was a poor black tobacco farmer whose cells—taken without her knowledge in 1951—became one of the most important tools in medicine, vital for developing the polio vaccine, cloning, gene mapping, and more. Henrietta's cells have been bought and sold by the billions, yet she remains virtually unknown, and her family can't afford health insurance. This phenomenal New York Times bestseller tells a riveting story of the collision between ethics, race, and medicine; of scientific discovery and faith healing; and of a daughter consumed with questions about the mother she never knew.

In an unparalleled collaboration, two leading global thinkers in technology and foreign affairs give us their widely anticipated, transformational vision of the future: a world where everyone is connected—a world full of challenges and benefits that are ours to meet and to harness.

Eric Schmidt is one of Silicon Valley’s great leaders, having taken Google from a small startup to one of the world’s most influential companies. Jared Cohen is the director of Google Ideas and a former adviser to secretaries of state Condoleezza Rice and Hillary Clinton. With their combined knowledge and experiences, the authors are uniquely positioned to take on some of the toughest questions about our future: Who will be more powerful in the future, the citizen or the state? Will technology make terrorism easier or harder to carry out? What is the relationship between privacy and security, and how much will we have to give up to be part of the new digital age?

In this groundbreaking book, Schmidt and Cohen combine observation and insight to outline the promise and peril awaiting us in the coming decades. At once pragmatic and inspirational, this is a forward-thinking account of where our world is headed and what this means for people, states and businesses.

With the confidence and clarity of visionaries, Schmidt and Cohen illustrate just how much we have to look forward to—and beware of—as the greatest information and technology revolution in human history continues to evolve. On individual, community and state levels, across every geographical and socioeconomic spectrum, they reveal the dramatic developments—good and bad—that will transform both our everyday lives and our understanding of self and society, as technology advances and our virtual identities become more and more fundamentally real.

As Schmidt and Cohen’s nuanced vision of the near future unfolds, an urban professional takes his driverless car to work, attends meetings via hologram and dispenses housekeeping robots by voice; a Congolese fisherwoman uses her smart phone to monitor market demand and coordinate sales (saving on costly refrigeration and preventing overfishing); the potential arises for “virtual statehood” and “Internet asylum” to liberate political dissidents and oppressed minorities, but also for tech-savvy autocracies (and perhaps democracies) to exploit their citizens’ mobile devices for ever more ubiquitous surveillance. Along the way, we meet a cadre of international figures—including Julian Assange—who explain their own visions of our technology-saturated future.

Inspiring, provocative and absorbing, The New Digital Age is a brilliant analysis of how our hyper-connected world will soon look, from two of our most prescient and informed public thinkers.

For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics. Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics?, Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts. Brought up to date with a new chapter by Ian Stewart, What is Mathematics?, Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved. Formal mathematics is like spelling and grammar--a matter of the correct application of local rules. Meaningful mathematics is like journalism--it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature--it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature--it opens a window onto the world of mathematics for anyone interested to view.

From Freud to Babbitt, from Animal Farm to Sartre to the Great Society, from the Theory of Relativity to counterculture to Kosovo, The Modern Mind is encyclopedic, covering the major writers, artists, scientists, and philosophers who produced the ideas by which we live. Peter Watson has produced a fluent and engaging narrative of the intellectual tradition of the twentieth century, and the men and women who created it.

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.

The author of the bestseller The Disappearing Spoon reveals the secret inner workings of the brain through strange but true stories.

Early studies of the human brain used a simple method: wait for misfortune to strike -- strokes, seizures, infectious diseases, horrendous accidents -- and see how victims coped. In many cases their survival was miraculous, if puzzling. Observers were amazed by the transformations that took place when different parts of the brain were destroyed, altering victims' personalities. Parents suddenly couldn't recognize their own children. Pillars of the community became pathological liars. Some people couldn't speak but could still sing.

In The Tale of the Dueling Neurosurgeons, Sam Kean travels through time with stories of neurological curiosities: phantom limbs, Siamese twin brains, viruses that eat patients' memories, blind people who see through their tongues. He weaves these narratives together with prose that makes the pages fly by, to create a story of discovery that reaches back to the 1500s and the high-profile jousting accident that inspired this book's title.* With the lucid, masterful explanations and razor-sharp wit his fans have come to expect, Kean explores the brain's secret passageways and recounts the forgotten tales of the ordinary people whose struggles, resilience, and deep humanity made neuroscience possible.

*"The Tale of the Dueling Neurosurgeons" refers to the case of French king Henri II, who in 1559 was lanced through the skull during a joust, resulting in one of the most significant cases in neuroscience history. For hundreds of years scientists have gained important lessons from traumatic accidents and illnesses, and such misfortunes still represent their greatest resource for discovery.

A good book may have the power to change the way we see the world, but a great book actually becomes part of our daily consciousness, pervading our thinking to the point that we take it for granted, and we forget how provocative and challenging its ideas once were—and still are. The Structure of Scientific Revolutions is that kind of book. When it was first published in 1962, it was a landmark event in the history and philosophy of science. Fifty years later, it still has many lessons to teach.

With The Structure of Scientific Revolutions, Kuhn challenged long-standing linear notions of scientific progress, arguing that transformative ideas don’t arise from the day-to-day, gradual process of experimentation and data accumulation but that the revolutions in science, those breakthrough moments that disrupt accepted thinking and offer unanticipated ideas, occur outside of “normal science,” as he called it. Though Kuhn was writing when physics ruled the sciences, his ideas on how scientific revolutions bring order to the anomalies that amass over time in research experiments are still instructive in our biotech age.

This new edition of Kuhn’s essential work in the history of science includes an insightful introduction by Ian Hacking, which clarifies terms popularized by Kuhn, including paradigm and incommensurability, and applies Kuhn’s ideas to the science of today. Usefully keyed to the separate sections of the book, Hacking’s introduction provides important background information as well as a contemporary context. Newly designed, with an expanded index, this edition will be eagerly welcomed by the next generation of readers seeking to understand the history of our perspectives on science.

"An engaging tour of vital math for a modern world.... [A] wonderfully accessible book."--Scientific American
Most people are familiar with history's great equations: Newton's Law of Gravity, for instance, or Einstein's theory of relativity. But the way these mathematical breakthroughs have contributed to human progress is seldom appreciated. In In Pursuit of the Unknown, celebrated mathematician Ian Stewart untangles the roots of our most important mathematical statements to show that equations have long been a driving force behind nearly every aspect of our lives.
Using seventeen of our most crucial equations--including the Wave Equation that allowed engineers to measure a building's response to earthquakes, saving countless lives, and the Black-Scholes model, used by bankers to track the price of financial derivatives over time--Stewart illustrates that many of the advances we now take for granted were made possible by mathematical discoveries.
An approachable, lively, and informative guide to the mathematical building blocks of modern life, In Pursuit of the Unknown is a penetrating exploration of how we have also used equations to make sense of, and in turn influence, our world.

From one of the greatest minds in contemporary mathematics, Professor E.T. Bell, comes a witty, accessible, and fascinating look at the beautiful craft and enthralling history of mathematics.

Men of Mathematics provides a rich account of major mathematical milestones, from the geometry of the Greeks through Newton’s calculus, and on to the laws of probability, symbolic logic, and the fourth dimension. Bell breaks down this majestic history of ideas into a series of engrossing biographies of the great mathematicians who made progress possible—and who also led intriguing, complicated, and often surprisingly entertaining lives.

Never pedantic or dense, Bell writes with clarity and simplicity to distill great mathematical concepts into their most understandable forms for the curious everyday reader. Anyone with an interest in math may learn from these rich lessons, an advanced degree or extensive research is never necessary.

A “delightfully astute” and “entertaining” history of the mishaps and meltdowns that have marked the path of scientific progress (Kirkus Reviews, starred review).

Radiation: What could go wrong? In short, plenty. From Marie Curie carrying around a vial of radium salt because she liked the pretty blue glow to the large-scale disasters at Chernobyl and Fukushima, dating back to the late nineteenth century, nuclear science has had a rich history of innovative exploration and discovery, coupled with mistakes, accidents, and downright disasters.

In this lively book, long-time advocate of continued nuclear research and nuclear energy James Mahaffey looks at each incident in turn and analyzes what happened and why, often discovering where scientists went wrong when analyzing past meltdowns. Every incident, while taking its toll, has led to new understanding of the mighty atom—and the fascinating frontier of science that still holds both incredible risk and great promise.
 

From the bestselling author of the acclaimed Chaos and Genius comes a thoughtful and provocative exploration of the big ideas of the modern era: Information, communication, and information theory. 
 
Acclaimed science writer James Gleick presents an eye-opening vision of how our relationship to information has transformed the very nature of human consciousness. A fascinating intellectual journey through the history of communication and information, from the language of Africa’s talking drums to the invention of written alphabets; from the electronic transmission of code to the origins of information theory, into the new information age and the current deluge of news, tweets, images, and blogs. Along the way, Gleick profiles key innovators, including Charles Babbage, Ada Lovelace, Samuel Morse, and Claude Shannon, and reveals how our understanding of information is transforming not only how we look at the world, but how we live.

A New York Times Notable Book
A Los Angeles Times and Cleveland Plain Dealer Best Book of the Year
Winner of the PEN/E. O. Wilson Literary Science Writing Award 

The “highly entertaining” New York Times bestseller, which explains chaos theory and the butterfly effect, from the author of The Information (Chicago Tribune).

For centuries, scientific thought was focused on bringing order to the natural world. But even as relativity and quantum mechanics undermined that rigid certainty in the first half of the twentieth century, the scientific community clung to the idea that any system, no matter how complex, could be reduced to a simple pattern. In the 1960s, a small group of radical thinkers began to take that notion apart, placing new importance on the tiny experimental irregularities that scientists had long learned to ignore. Miniscule differences in data, they said, would eventually produce massive ones—and complex systems like the weather, economics, and human behavior suddenly became clearer and more beautiful than they had ever been before.In this seminal work of scientific writing, James Gleick lays out a cutting edge field of science with enough grace and precision that any reader will be able to grasp the science behind the beautiful complexity of the world around us. With more than a million copies sold, Chaos is “a groundbreaking book about what seems to be the future of physics” by a writer who has been a finalist for both the Pulitzer Prize and the National Book Award, the author of Time Travel: A History and Genius: The Life and Science of Richard Feynman (Publishers Weekly).

In The Secrets of Alchemy, Lawrence M. Principe, one of the world’s leading authorities on the subject, brings alchemy out of the shadows and restores it to its important place in human history and culture. By surveying what alchemy was and how it began, developed, and overlapped with a range of ideas and pursuits, Principe illuminates the practice. He vividly depicts the place of alchemy during its heyday in early modern Europe, and then explores how alchemy has fit into wider views of the cosmos and humanity, touching on its enduring place in literature, fine art, theater, and religion as well as its recent acceptance as a serious subject of study for historians of science. In addition, he introduces the reader to some of the most fascinating alchemists, such as Zosimos and Basil Valentine, whose lives dot alchemy’s long reign from the third century and to the present day. Through his exploration of alchemists and their times, Principe pieces together closely guarded clues from obscure and fragmented texts to reveal alchemy’s secrets, and—most exciting for budding alchemists—uses them to recreate many of the most famous recipes in his lab, including those for the “glass of antimony” and “philosophers’ tree.” This unique approach brings the reader closer to the actual work of alchemy than any other book.

This epoch-making and monumental work on Vedic Mathematics unfolds a new method of approach. It relates to the truth of numbers and magnitudes equally applicable to all sciences and arts.

WINNER OF THE PULITZER PRIZE • Winner of The New York Public Library’s Helen Bernstein Book Award • “A new classic of science reporting.”—The New York Times

The riveting true story of a small town ravaged by industrial pollution, Toms River melds hard-hitting investigative reporting, a fascinating scientific detective story, and an unforgettable cast of characters into a sweeping narrative in the tradition of A Civil Action, The Emperor of All Maladies, and The Immortal Life of Henrietta Lacks.

One of New Jersey’s seemingly innumerable quiet seaside towns, Toms River became the unlikely setting for a decades-long drama that culminated in 2001 with one of the largest legal settlements in the annals of toxic dumping. A town that would rather have been known for its Little League World Series champions ended up making history for an entirely different reason: a notorious cluster of childhood cancers scientifically linked to local air and water pollution. For years, large chemical companies had been using Toms River as their private dumping ground, burying tens of thousands of leaky drums in open pits and discharging billions of gallons of acid-laced wastewater into the town’s namesake river.

In an astonishing feat of investigative reporting, prize-winning journalist Dan Fagin recounts the sixty-year saga of rampant pollution and inadequate oversight that made Toms River a cautionary example for fast-growing industrial towns from South Jersey to South China. He tells the stories of the pioneering scientists and physicians who first identified pollutants as a cause of cancer, and brings to life the everyday heroes in Toms River who struggled for justice: a young boy whose cherubic smile belied the fast-growing tumors that had decimated his body from birth; a nurse who fought to bring the alarming incidence of childhood cancers to the attention of authorities who didn’t want to listen; and a mother whose love for her stricken child transformed her into a tenacious advocate for change.

A gripping human drama rooted in a centuries-old scientific quest, Toms River is a tale of dumpers at midnight and deceptions in broad daylight, of corporate avarice and government neglect, and of a few brave individuals who refused to keep silent until the truth was exposed.

NAMED ONE OF THE BEST BOOKS OF THE YEAR BY NPR AND KIRKUS REVIEWS

“A thrilling journey full of twists and turns, Toms River is essential reading for our times. Dan Fagin handles topics of great complexity with the dexterity of a scholar, the honesty of a journalist, and the dramatic skill of a novelist.”—Siddhartha Mukherjee, M.D., author of the Pulitzer Prize–winning The Emperor of All Maladies
 
“A complex tale of powerful industry, local politics, water rights, epidemiology, public health and cancer in a gripping, page-turning environmental thriller.”—NPR

“Unstoppable reading.”—The Philadelphia Inquirer
 
“Meticulously researched and compellingly recounted . . . It’s every bit as important—and as well-written—as A Civil Action and The Immortal Life of Henrietta Lacks.”—The Star-Ledger
 
“Fascinating . . . a gripping environmental thriller.”—Kirkus Reviews (starred review)
 
“An honest, thoroughly researched, intelligently written book.”—Slate
 
“[A] hard-hitting account . . . a triumph.”—Nature
 
“Absorbing and thoughtful.”—USA Today


From the Hardcover edition.

Category theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer science, logic, linguistics, cognitive science, philosophy, and any of the other fields in which the ideas are being applied. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of category theory understandable to this broad readership. Although assuming few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided - a must for computer scientists, logicians and linguists! This Second Edition contains numerous revisions to the original text, including expanding the exposition, revising and elaborating the proofs, providing additional diagrams, correcting typographical errors and, finally, adding an entirely new section on monoidal categories. Nearly a hundred new exercises have also been added, many with solutions, to make the book more useful as a course text and for self-study.

New York Times Bestseller: This life story of the quirky physicist is “a thorough and masterful portrait of one of the great minds of the century” (The New York Review of Books). Raised in Depression-era Rockaway Beach, physicist Richard Feynman was irreverent, eccentric, and childishly enthusiastic—a new kind of scientist in a field that was in its infancy. His quick mastery of quantum mechanics earned him a place at Los Alamos working on the Manhattan Project under J. Robert Oppenheimer, where the giddy young man held his own among the nation’s greatest minds. There, Feynman turned theory into practice, culminating in the Trinity test, on July 16, 1945, when the Atomic Age was born. He was only twenty-seven. And he was just getting started. In this sweeping biography, James Gleick captures the forceful personality of a great man, integrating Feynman’s work and life in a way that is accessible to laymen and fascinating for the scientists who follow in his footsteps.

The Age of Wonder is a colorful and utterly absorbing history of the men and women whose discoveries and inventions at the end of the eighteenth century gave birth to the Romantic Age of Science. 

When young Joseph Banks stepped onto a Tahitian beach in 1769, he hoped to discover Paradise. Inspired by the scientific ferment sweeping through Britain, the botanist had sailed with Captain Cook in search of new worlds. Other voyages of discovery—astronomical, chemical, poetical, philosophical—swiftly follow in Richard Holmes's thrilling evocation of the second scientific revolution. Through the lives of William Herschel and his sister Caroline, who forever changed the public conception of the solar system; of Humphry Davy, whose near-suicidal gas experiments revolutionized chemistry; and of the great Romantic writers, from Mary Shelley to Coleridge and Keats, who were inspired by the scientific breakthroughs of their day, Holmes brings to life the era in which we first realized both the awe-inspiring and the frightening possibilities of science—an era whose consequences are with us still.

BONUS MATERIAL: This ebook edition includes an excerpt from Richard Holmes's Falling Upwards.

Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world.

Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us?

Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.

This compact, well-written history — first published in 1948, and now in its fourth revised edition — describes the main trends in the development of all fields of mathematics from the first available records to the middle of the 20th century. Students, researchers, historians, specialists — in short, everyone with an interest in mathematics — will find it engrossing and stimulating.
Beginning with the ancient Near East, the author traces the ideas and techniques developed in Egypt, Babylonia, China, and Arabia, looking into such manuscripts as the Egyptian Papyrus Rhind, the Ten Classics of China, and the Siddhantas of India. He considers Greek and Roman developments from their beginnings in Ionian rationalism to the fall of Constantinople; covers medieval European ideas and Renaissance trends; analyzes 17th- and 18th-century contributions; and offers an illuminating exposition of 19th century concepts. Every important figure in mathematical history is dealt with — Euclid, Archimedes, Diophantus, Omar Khayyam, Boethius, Fermat, Pascal, Newton, Leibniz, Fourier, Gauss, Riemann, Cantor, and many others. For this latest edition, Dr. Struik has both revised and updated the existing text, and also added a new chapter on the mathematics of the first half of the 20th century. Concise coverage is given to set theory, the influence of relativity and quantum theory, tensor calculus, the Lebesgue integral, the calculus of variations, and other important ideas and concepts. The book concludes with the beginnings of the computer era and the seminal work of von Neumann, Turing, Wiener, and others.
"The author's ability as a first-class historian as well as an able mathematician has enabled him to produce a work which is unquestionably one of the best." — Nature Magazine.

Napoleon's Buttons is the fascinating account of seventeen groups of molecules that have greatly influenced the course of history. These molecules provided the impetus for early exploration, and made possible the voyages of discovery that ensued. The molecules resulted in grand feats of engineering and spurred advances in medicine and law; they determined what we now eat, drink, and wear. A change as small as the position of an atom can lead to enormous alterations in the properties of a substance-which, in turn, can result in great historical shifts.

With lively prose and an eye for colorful and unusual details, Le Couteur and Burreson offer a novel way to understand the shaping of civilization and the workings of our contemporary world.

The never-before-told account of the intersection of some of the most insightful minds of the 20th century, and a fascinating look at how war, resistance, and friendship can catalyze genius.
 
In the spring of 1940, the aspiring but unknown writer Albert Camus and budding scientist Jacques Monod were quietly pursuing ordinary, separate lives in Paris. After the German invasion and occupation of France, each joined the Resistance to help liberate the country from the Nazis and ascended to prominent, dangerous roles. After the war and through twists of circumstance, they became friends, and through their passionate determination and rare talent they emerged as leading voices of modern literature and biology, each receiving the Nobel Prize in their respective fields.
 
Drawing upon a wealth of previously unpublished and unknown material gathered over several years of research, Brave Genius tells the story of how each man endured the most terrible episode of the twentieth century and then blossomed into extraordinarily creative and engaged individuals. It is a story of the transformation of ordinary lives into exceptional lives by extraordinary events--of courage in the face of overwhelming adversity, the flowering of creative genius, deep friendship, and of profound concern for and insight into the human condition.

“Bryson is as amusing as ever….As a celebration of 350 years of modern science, [Seeing Further] it is a worthy tribute.”
—The Economist

In Seeing Further, New York Times bestseller Bill Bryson takes readers on a guided tour through the great discoveries, feuds, and personalities of modern science. Already a major bestseller in the UK, Seeing Further tells the fascinating story of science and the Royal Society with Bill Bryson’s trademark wit and intelligence, and contributions from a host of well known scientists and science fiction writers, including Richard Dawkins, Neal Stephenson, James Gleick, and Margret Atwood. It is a delightful literary treat from the acclaimed author who previous explored the current state of scientific knowledge in his phenomenally popular book, A Short History of Nearly Everything.

This exceptional graphic novel recounts the spiritual odyssey of philosopher Bertrand Russell. In his agonized search for absolute truth, Russell crosses paths with legendary thinkers like Gottlob Frege, David Hilbert, and Kurt Gödel, and finds a passionate student in the great Ludwig Wittgenstein. But his most ambitious goal-to establish unshakable logical foundations of mathematics-continues to loom before him. Through love and hate, peace and war, Russell persists in the dogged mission that threatens to claim both his career and his personal happiness, finally driving him to the brink of insanity.

This story is at the same time a historical novel and an accessible explication of some of the biggest ideas of mathematics and modern philosophy. With rich characterizations and expressive, atmospheric artwork, the book spins the pursuit of these ideas into a highly satisfying tale.

Probing and ingeniously layered, the book throws light on Russell's inner struggles while setting them in the context of the timeless questions he spent his life trying to answer. At its heart, Logicomix is a story about the conflict between an ideal rationality and the unchanging, flawed fabric of reality.

When Robert Louis Stevenson wrote his gothic horror story of Dr. Jekyll and Mr. Hyde, he based the house of the genial doctor-turned-fiend on the home of John Hunter. The choice was understandable, for Hunter was both widely acclaimed and greatly feared.
 
From humble origins, John Hunter rose to become the most famous anatomist and surgeon of the eighteenth century. In an age when operations were crude, extremely painful, and often fatal, he rejected medieval traditions to forge a revolution in surgery founded on pioneering scientific experiments. Using the knowledge he gained from countless human dissections, Hunter worked to improve medical care for both the poorest and the best-known figures of the era—including Sir Joshua Reynolds and the young Lord Byron.
 
An insatiable student of all life-forms, Hunter was also an expert naturalist. He kept exotic creatures in his country menagerie and dissected the first animals brought back by Captain Cook from Australia. Ultimately his research led him to expound highly controversial views on the age of the earth, as well as equally heretical beliefs on the origins of life more than sixty years before Darwin published his famous theory.
 
Although a central figure of the Enlightenment, Hunter’s tireless quest for human corpses immersed him deep in the sinister world of body snatching. He paid exorbitant sums for stolen cadavers and even plotted successfully to steal the body of Charles Byrne, famous in his day as the “Irish giant.”
 
In The Knife Man, Wendy Moore unveils John Hunter’s murky and macabre world—a world characterized by public hangings, secret expeditions to dank churchyards, and gruesome human dissections in pungent attic rooms. This is a fascinating portrait of a remarkable pioneer and his determined struggle to haul surgery out of the realms of meaningless superstitious ritual and into the dawn of modern medicine.

The dramatic human story of an epic scientific quest and of one man's forty-year obsession to find a solution to the thorniest scientific dilemma of the day--"the longitude problem."

Anyone alive in the eighteenth century would have known that "the longitude problem" was the thorniest scientific dilemma of the day-and had been for centuries. Lacking the ability to measure their longitude, sailors throughout the great ages of exploration had been literally lost at sea as soon as they lost sight of land. Thousands of lives and the increasing fortunes of nations hung on a resolution. One man, John Harrison, in complete opposition to the scientific community, dared to imagine a mechanical solution-a clock that would keep precise time at sea, something no clock had ever been able to do on land.

Longitude is the dramatic human story of an epic scientific quest and of Harrison's forty-year obsession with building his perfect timekeeper, known today as the chronometer. Full of heroism and chicanery, it is also a fascinating brief history of astronomy, navigation, and clockmaking, and opens a new window on our world.

Fifty years ago, James D. Watson, then just twentyfour, helped launch the greatest ongoing scientific quest of our time. Now, with unique authority and sweeping vision, he gives us the first full account of the genetic revolution—from Mendel’s garden to the double helix to the sequencing of the human genome and beyond.
Watson’s lively, panoramic narrative begins with the fanciful speculations of the ancients as to why “like begets like” before skipping ahead to 1866, when an Austrian monk named Gregor Mendel first deduced the basic laws of inheritance. But genetics as we recognize it today—with its capacity, both thrilling and sobering, to manipulate the very essence of living things—came into being only with the rise of molecular investigations culminating in the breakthrough discovery of the structure of DNA, for which Watson shared a Nobel prize in 1962. In the DNA molecule’s graceful curves was the key to a whole new science.

Having shown that the secret of life is chemical, modern genetics has set mankind off on a journey unimaginable just a few decades ago. Watson provides the general reader with clear explanations of molecular processes and emerging technologies. He shows us how DNA continues to alter our understanding of human origins, and of our identities as groups and as individuals. And with the insight of one who has remained close to every advance in research since the double helix, he reveals how genetics has unleashed a wealth of possibilities to alter the human condition—from genetically modified foods to genetically modified babies—and transformed itself from a domain of pure research into one of big business as well. It is a sometimes topsy-turvy world full of great minds and great egos, driven by ambitions to improve the human condition as well as to improve investment portfolios, a world vividly captured in these pages.

Facing a future of choices and social and ethical implications of which we dare not remain uninformed, we could have no better guide than James Watson, who leads us with the same bravura storytelling that made The Double Helix one of the most successful books on science ever published. Infused with a scientist’s awe at nature’s marvels and a humanist’s profound sympathies, DNA is destined to become the classic telling of the defining scientific saga of our age.

A masterful commentary on the history of science from the Greeks to modern times, by Nobel Prize-winning physicist Steven Weinberg—a thought-provoking and important book by one of the most distinguished scientists and intellectuals of our time.

In this rich, irreverent, and compelling history, Nobel Prize-winning physicist Steven Weinberg takes us across centuries from ancient Miletus to medieval Baghdad and Oxford, from Plato’s Academy and the Museum of Alexandria to the cathedral school of Chartres and the Royal Society of London. He shows that the scientists of ancient and medieval times not only did not understand what we understand about the world—they did not understand what there is to understand, or how to understand it. Yet over the centuries, through the struggle to solve such mysteries as the curious backward movement of the planets and the rise and fall of the tides, the modern discipline of science eventually emerged. Along the way, Weinberg examines historic clashes and collaborations between science and the competing spheres of religion, technology, poetry, mathematics, and philosophy.

An illuminating exploration of the way we consider and analyze the world around us, To Explain the World is a sweeping, ambitious account of how difficult it was to discover the goals and methods of modern science, and the impact of this discovery on human knowledge and development.

A Chicago Tribune "Best Books of 2014" • A Slate "Best Books 2014: Staff Picks" • A St. Louis Post-Dispatch "Best Books of 2014"

The fascinating story of one of the most important scientific discoveries of the twentieth century.

We know it simply as "the pill," yet its genesis was anything but simple. Jonathan Eig's masterful narrative revolves around four principal characters: the fiery feminist Margaret Sanger, who was a champion of birth control in her campaign for the rights of women but neglected her own children in pursuit of free love; the beautiful Katharine McCormick, who owed her fortune to her wealthy husband, the son of the founder of International Harvester and a schizophrenic; the visionary scientist Gregory Pincus, who was dismissed by Harvard in the 1930s as a result of his experimentation with in vitro fertilization but who, after he was approached by Sanger and McCormick, grew obsessed with the idea of inventing a drug that could stop ovulation; and the telegenic John Rock, a Catholic doctor from Boston who battled his own church to become an enormously effective advocate in the effort to win public approval for the drug that would be marketed by Searle as Enovid.

Spanning the years from Sanger’s heady Greenwich Village days in the early twentieth century to trial tests in Puerto Rico in the 1950s to the cusp of the sexual revolution in the 1960s, this is a grand story of radical feminist politics, scientific ingenuity, establishment opposition, and, ultimately, a sea change in social attitudes. Brilliantly researched and briskly written, The Birth of the Pill is gripping social, cultural, and scientific history.

This engaging book presents the essential mathematics needed to describe, simulate, and render a 3D world. Reflecting both academic and in-the-trenches practical experience, the authors teach you how to describe objects and their positions, orientations, and trajectories in 3D using mathematics. The text provides an introduction to mathematics for game designers, including the fundamentals of coordinate spaces, vectors, and matrices. It also covers orientation in three dimensions, calculus and dynamics, graphics, and parametric curves.

A thrilling nonfiction tour of the cosmos that brings the universe down to Earth, from one of the all-time masters of science fiction.
 
No one makes sense out of science like Isaac Asimov. Are you puzzled by pulsars? Baffled by black holes? Bewildered by the big bang? If so, here are succinct, crystal-clear answers to more than one hundred of the most significant questions about the essential nature of the universe—questions that have fired the imagination since the beginning of history.
 
Over the course of this fantastic voyage, the origins, the discoveries, and the stunning achievements of astronomy will unfold before your eyes. You will experience close encounters with giant planets, exploding stars, distant galaxies, and more. For anyone who has ever asked the ultimate questions, who has ever looked up at the sky and asked What in heaven is going on?, Isaac Asimov’s unique vision, skill, and authority will bring the big picture into focus.
 
“A fine introduction to modern astronomical theory.”—Library Journal

In 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. Gödel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.

At a summer tea party in Cambridge, England, a lady states that tea poured into milk tastes differently than that of milk poured into tea. Her notion is shouted down by the scientific minds of the group. But one guest, by the name Ronald Aylmer Fisher, proposes to scientifically test the lady's hypothesis. There was no better person to conduct such a test. For Fisher had brought to the field of statistics an emphasis on controlling the methods for obtaining data and the importance of interpretation. He knew that how the data was gathered and applied was as important as the data themselves.

In The Lady Tasting Tea, readers will encounter not only Ronald Fisher's theories (and their repercussions), but the ideas of dozens of men and women whose revolutionary work affects our everyday lives. Writing with verve and wit, author David Salsburg traces the rise and fall of Karl Pearson's theories, explores W. Edwards Deming's statistical methods of quality control (which rebuilt postwar Japan's economy), and relates the story of Stella Cunliff's early work on the capacity of small beer casks at the Guinness brewing factory.

The Lady Tasting Tea is not a book of dry facts and figures, but the history of great individuals who dared to look at the world in a new way.

Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.

This book, for the first time, provides laymen and mathematicians alike with a detailed picture of the historical development of one of the most momentous achievements of the human intellect ― the calculus. It describes with accuracy and perspective the long development of both the integral and the differential calculus from their early beginnings in antiquity to their final emancipation in the 19th century from both physical and metaphysical ideas alike and their final elaboration as mathematical abstractions, as we know them today, defined in terms of formal logic by means of the idea of a limit of an infinite sequence.
But while the importance of the calculus and mathematical analysis ― the core of modern mathematics ― cannot be overemphasized, the value of this first comprehensive critical history of the calculus goes far beyond the subject matter. This book will fully counteract the impression of laymen, and of many mathematicians, that the great achievements of mathematics were formulated from the beginning in final form. It will give readers a sense of mathematics not as a technique, but as a habit of mind, and serve to bridge the gap between the sciences and the humanities. It will also make abundantly clear the modern understanding of mathematics by showing in detail how the concepts of the calculus gradually changed from the Greek view of the reality and immanence of mathematics to the revised concept of mathematical rigor developed by the great 19th century mathematicians, which held that any premises were valid so long as they were consistent with one another. It will make clear the ideas contributed by Zeno, Plato, Pythagoras, Eudoxus, the Arabic and Scholastic mathematicians, Newton, Leibnitz, Taylor, Descartes, Euler, Lagrange, Cantor, Weierstrass, and many others in the long passage from the Greek "method of exhaustion" and Zeno's paradoxes to the modern concept of the limit independent of sense experience; and illuminate not only the methods of mathematical discovery, but the foundations of mathematical thought as well.

A National Bestseller, a New York Times Notable Book, and an Entertainment Weekly Best Book of the Year

From Steven Johnson, the dynamic thinker routinely compared to James Gleick, Dava Sobel, and Malcolm Gladwell, The Ghost Map is a riveting page-turner about a real-life historical hero, Dr. John Snow. It's the summer of 1854, and London is just emerging as one of the first modern cities in the world. But lacking the infrastructure -- garbage removal, clean water, sewers -- necessary to support its rapidly expanding population, the city has become the perfect breeding ground for a terrifying disease no one knows how to cure. As the cholera outbreak takes hold, a physician and a local curate are spurred to action-and ultimately solve the most pressing medical riddle of their time.

In a triumph of multidisciplinary thinking, Johnson illuminates the intertwined histories and interconnectedness of the spread of disease, contagion theory, the rise of cities, and the nature of scientific inquiry, offering both a riveting history and a powerful explanation of how it has shaped the world we live in.

In 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. Gödel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book - extensively rewritten for its second edition - will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.

Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. This 2007 fifth edition has been thoroughly revised by John Burgess. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems. This updated edition is also accompanied by a website as well as an instructor's manual.

The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In The Irrationals, the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational numbers are surprisingly difficult to define—and why so many questions still surround them. Fascinating and illuminating, this is a book for everyone who loves math and the history behind it.

Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th–16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. This brought about the crucial change in the concept of number that made possible modern science — in which the symbolic "form" of a mathematical statement is completely inseparable from its "content" of physical meaning. Includes a translation of Vieta's Introduction to the Analytical Art. 1968 edition. Bibliography.

The fascinating autobiography of the legendary inventor behind the radio, wireless energy, robotics, and much more.

Famous for his pioneering contributions to the electronic age, his lifelong feud with Thomas Edison, and his erratic behavior, Nikola Tesla was one of the most brilliant and daring inventors and visionaries of his time. My Inventions is Tesla's autobiography, with meditations on his major discoveries and innovations, including the rotating magnetic field, the magnifying transmitter, and the Tesla coil. This volume also includes three articles by Tesla, as well as an enlightening introduction that discredits many of the myths surrounding the thinker's eccentric life. This rare window into the industrial age's most tragic genius will fascinate historians, scientists, aspiring inventors, and curious fans alike.

For more than seventy years, Penguin has been the leading publisher of classic literature in the English-speaking world. With more than 1,700 titles, Penguin Classics represents a global bookshelf of the best works throughout history and across genres and disciplines. Readers trust the series to provide authoritative texts enhanced by introductions and notes by distinguished scholars and contemporary authors, as well as up-to-date translations by award-winning translators.

John Napier (1550–1617) is celebrated today as the man who invented logarithms—an enormous intellectual achievement that would soon lead to the development of their mechanical equivalent in the slide rule: the two would serve humanity as the principal means of calculation until the mid-1970s. Yet, despite Napier's pioneering efforts, his life and work have not attracted detailed modern scrutiny. John Napier is the first contemporary biography to take an in-depth look at the multiple facets of Napier’s story: his privileged position as the eighth Laird of Merchiston and the son of influential Scottish landowners; his reputation as a magician who dabbled in alchemy; his interest in agriculture; his involvement with a notorious outlaw; his staunch anti-Catholic beliefs; his interactions with such peers as Henry Briggs, Johannes Kepler, and Tycho Brahe; and, most notably, his estimable mathematical legacy.

Julian Havil explores Napier’s original development of logarithms, the motivations for his approach, and the reasons behind certain adjustments to them. Napier’s inventive mathematical ideas also include formulas for solving spherical triangles, "Napier’s Bones" (a more basic but extremely popular alternative device for calculation), and the use of decimal notation for fractions and binary arithmetic. Havil also considers Napier’s study of the Book of Revelation, which led to his prediction of the Apocalypse in his first book, A Plaine Discovery of the Whole Revelation of St. John—the work for which Napier believed he would be most remembered.

John Napier assesses one man’s life and the lasting influence of his advancements on the mathematical sciences and beyond.

A symbol for what is not there, an emptiness that increases any number it's added to, an inexhaustible and indispensable paradox. As we enter the year 2000, zero is once again making its presence felt. Nothing itself, it makes possible a myriad of calculations. Indeed, without zero mathematics as we know it would not exist. And without mathematics our understanding of the universe would be vastly impoverished. But where did this nothing, this hollow circle, come from? Who created it? And what, exactly, does it mean? Robert Kaplan's The Nothing That Is: A Natural History of Zero begins as a mystery story, taking us back to Sumerian times, and then to Greece and India, piecing together the way the idea of a symbol for nothing evolved. Kaplan shows us just how handicapped our ancestors were in trying to figure large sums without the aid of the zero. (Try multiplying CLXIV by XXIV). Remarkably, even the Greeks, mathematically brilliant as they were, didn't have a zero--or did they? We follow the trail to the East where, a millennium or two ago, Indian mathematicians took another crucial step. By treating zero for the first time like any other number, instead of a unique symbol, they allowed huge new leaps forward in computation, and also in our understanding of how mathematics itself works. In the Middle Ages, this mathematical knowledge swept across western Europe via Arab traders. At first it was called "dangerous Saracen magic" and considered the Devil's work, but it wasn't long before merchants and bankers saw how handy this magic was, and used it to develop tools like double-entry bookkeeping. Zero quickly became an essential part of increasingly sophisticated equations, and with the invention of calculus, one could say it was a linchpin of the scientific revolution. And now even deeper layers of this thing that is nothing are coming to light: our computers speak only in zeros and ones, and modern mathematics shows that zero alone can be made to generate everything. Robert Kaplan serves up all this history with immense zest and humor; his writing is full of anecdotes and asides, and quotations from Shakespeare to Wallace Stevens extend the book's context far beyond the scope of scientific specialists. For Kaplan, the history of zero is a lens for looking not only into the evolution of mathematics but into very nature of human thought. He points out how the history of mathematics is a process of recursive abstraction: how once a symbol is created to represent an idea, that symbol itself gives rise to new operations that in turn lead to new ideas. The beauty of mathematics is that even though we invent it, we seem to be discovering something that already exists. The joy of that discovery shines from Kaplan's pages, as he ranges from Archimedes to Einstein, making fascinating connections between mathematical insights from every age and culture. A tour de force of science history, The Nothing That Is takes us through the hollow circle that leads to infinity.

A few million years ago, our ancestors came down from the trees and began to stand upright, freeing our hands to create tools and our minds to grapple with the world around us.
 
Leonard Mlodinow takes us on a passionate and inspiring tour through the exciting history of human progress and the key events in the development of science. In the process, he presents a fascinating new look at the unique characteristics of our species and our society that helped propel us from stone tools to written language and through the birth of chemistry, biology, and modern physics to today’s technological world.
 
Along the way he explores the cultural conditions that influenced scientific thought through the ages and the colorful personalities of some of the great philosophers, scientists, and thinkers: Galileo, who preferred painting and poetry to medicine and dropped out of university; Isaac Newton, who stuck needlelike bodkins into his eyes to better understand changes in light and color; and Antoine Lavoisier, who drank nothing but milk for two weeks to examine its effects on his body. Charles Darwin, Albert Einstein, Werner Heisenberg, and many lesser-known but equally brilliant minds also populate these pages, each of their stories showing how much of human achievement can be attributed to the stubborn pursuit of simple questions (why? how?), bravely asked.
 
The Upright Thinkers is a book for science lovers and for anyone interested in creative thinking and in our ongoing quest to understand our world. At once deeply informed, accessible, and infused with the author’s trademark wit, this insightful work is a stunning tribute to humanity’s intellectual curiosity.
 
(With black-and-white illustrations throughout.)


From the Hardcover edition.

What enables individually simple insects like ants to act with such precision and purpose as a group? How do trillions of neurons produce something as extraordinarily complex as consciousness? In this remarkably clear and companionable book, leading complex systems scientist Melanie Mitchell provides an intimate tour of the sciences of complexity, a broad set of efforts that seek to explain how large-scale complex, organized, and adaptive behavior can emerge from simple interactions among myriad individuals. Based on her work at the Santa Fe Institute and drawing on its interdisciplinary strategies, Mitchell brings clarity to the workings of complexity across a broad range of biological, technological, and social phenomena, seeking out the general principles or laws that apply to all of them. Richly illustrated, Complexity: A Guided Tour--winner of the 2010 Phi Beta Kappa Book Award in Science--offers a wide-ranging overview of the ideas underlying complex systems science, the current research at the forefront of this field, and the prospects for its contribution to solving some of the most important scientific questions of our time.

The popular features from Volume 1 are all here. The field-tested probes are short, easy to administer, and ready to reproduce. Teacher materials explain science content and suggest grade-appropriate ways to present information. But Volume 2 covers more life science and Earth and space science probes. Volume 2 also suggests ways to embed the probes throughout your instruction, not just when starting a unit or topic.

In this sweeping and richly illustrated history, S. Frederick Starr tells the fascinating but largely unknown story of Central Asia's medieval enlightenment through the eventful lives and astonishing accomplishments of its greatest minds--remarkable figures who built a bridge to the modern world. Because nearly all of these figures wrote in Arabic, they were long assumed to have been Arabs. In fact, they were from Central Asia--drawn from the Persianate and Turkic peoples of a region that today extends from Kazakhstan southward through Afghanistan, and from the easternmost province of Iran through Xinjiang, China.

Lost Enlightenment recounts how, between the years 800 and 1200, Central Asia led the world in trade and economic development, the size and sophistication of its cities, the refinement of its arts, and, above all, in the advancement of knowledge in many fields. Central Asians achieved signal breakthroughs in astronomy, mathematics, geology, medicine, chemistry, music, social science, philosophy, and theology, among other subjects. They gave algebra its name, calculated the earth's diameter with unprecedented precision, wrote the books that later defined European medicine, and penned some of the world's greatest poetry. One scholar, working in Afghanistan, even predicted the existence of North and South America--five centuries before Columbus. Rarely in history has a more impressive group of polymaths appeared at one place and time. No wonder that their writings influenced European culture from the time of St. Thomas Aquinas down to the scientific revolution, and had a similarly deep impact in India and much of Asia.

Lost Enlightenment chronicles this forgotten age of achievement, seeks to explain its rise, and explores the competing theories about the cause of its eventual demise. Informed by the latest scholarship yet written in a lively and accessible style, this is a book that will surprise general readers and specialists alike.

Some images inside the book are unavailable due to digital copyright restrictions.

In August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: "On the Number of Prime Numbers Less Than a Given Quantity." In the middle of that paper, Riemann made an incidental remark â€" a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false?

Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic â€" defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark â€" the Riemann Hypothesis â€" that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows â€" subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age.

It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many â€" the veritable "great white whale" of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution.

Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, the Riemann Hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof â€" and those who have been consumed by it.

The History and Practice of Ancient Astronomy combines new scholarship with hands-on science to bring readers into direct contact with the work of ancient astronomers. While tracing ideas from ancient Babylon to sixteenth-century Europe, the book places its greatest emphasis on the Greek period, when astronomers developed the geometric and philosophical ideas that have determined the subsequent character of Western astronomy. The author approaches this history through the concrete details of ancient astronomical practice. Carefully organized and generously illustrated, the book can teach readers how to do real astronomy using the methods of ancient astronomers. For example, readers will learn to predict the next retrograde motion of Jupiter using either the arithmetical methods of the Babylonians or the geometric methods of Ptolemy. They will learn how to use an astrolabe and how to design sundials using Greek and Roman techniques. The book also contains supplementary exercises and patterns for making some working astronomical instruments, including an astrolabe and an equatorium. More than a presentation of astronomical methods, the book provides a critical look at the evidence used to reconstruct ancient astronomy. It includes extensive excerpts from ancient texts, meticulous documentation, and lively discussions of the role of astronomy in the various cultures. Accessible to a wide audience, this book will appeal to anyone interested in how our understanding of our place in the universe has changed and developed, from ancient times through the Renaissance.

Longlisted for the 2015 PEN/E.O. Wilson Literary Science Writing Award
Short-listed for Physics World's Book of the Year
The Sunday Times (UK) Best Science Book of 2014
A Publishers Weekly Top 10 Science Book of Fall 2014
An NBC News Top Science and Tech Book of 2014
A Politics & Prose 2014 Staff Pick

In the sixteenth century, Nicolaus Copernicus dared to go against the establishment by proposing that Earth rotates around the Sun. Having demoted Earth from its unique position in the cosmos to one of mediocrity, Copernicus set in motion a revolution in scientific thought. This perspective has influenced our thinking for centuries. However, recent evidence challenges the Copernican Principle, hinting that we do in fact live in a special place, at a special time, as the product of a chain of unlikely events. But can we be significant if the Sun is still just one of a billion trillion stars in the observable universe? And what if our universe is just one of a multitude of others-a single slice of an infinity of parallel realities?

In The Copernicus Complex, the renowned astrophysicist Caleb Scharf takes us on a scientific adventure, from tiny microbes within the Earth to distant exoplanets, probability theory, and beyond, arguing that there is a solution to this contradiction, a third way of viewing our place in the cosmos, if we weigh the evidence properly. As Scharf explains, we do occupy an unusual time in a 14-billion-year-old universe, in a somewhat unusual type of solar system surrounded by an ocean of unimaginable planetary diversity: hot Jupiters with orbits of less than a day, planet-size rocks spinning around dead stars, and a wealth of alien super-Earths. Yet life here is built from the most common chemistry in the universe, and we are a snapshot taken from billions of years of biological evolution. Bringing us to the cutting edge of scientific discovery, Scharf shows how the answers to fundamental questions of existence will come from embracing the peculiarity of our circumstance without denying the Copernican vision.

With characteristic verve, Scharf uses the latest scientific findings to reconsider where we stand in the balance between cosmic significance and mediocrity, order and chaos. Presenting a compelling and bold view of our true status, The Copernicus Complex proposes a way forward in the ultimate quest: determining life's abundance, not just across this universe but across all realities.

The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest mathematical background, this biography brings out the central importance of e to mathematics and illuminates a golden era in the age of science.

From the reviews of the second edition:

"This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here."

(David Parrott, Australian Mathematical Society)

"The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community."

(European Mathematical Society)

"Since Stillwell treats many topics, most mathematicians will learn a lot from this book as well as they will find pleasant and rather clear expositions of custom materials. The book is accessible to students that have already experienced calculus, algebra and geometry and will give them a good account of how the different branches of mathematics interact."

(Denis Bonheure, Bulletin of the Belgian Society)

This third edition includes new chapters on simple groups and combinatorics, and new sections on several topics, including the Poincare conjecture. The book has also been enriched by added exercises.

In this age of DNA computers and artificial intelligence, information is becoming disembodied even as the "bodies" that once carried it vanish into virtuality. While some marvel at these changes, envisioning consciousness downloaded into a computer or humans "beamed" Star Trek-style, others view them with horror, seeing monsters brooding in the machines. In How We Became Posthuman, N. Katherine Hayles separates hype from fact, investigating the fate of embodiment in an information age.

Hayles relates three interwoven stories: how information lost its body, that is, how it came to be conceptualized as an entity separate from the material forms that carry it; the cultural and technological construction of the cyborg; and the dismantling of the liberal humanist "subject" in cybernetic discourse, along with the emergence of the "posthuman."

Ranging widely across the history of technology, cultural studies, and literary criticism, Hayles shows what had to be erased, forgotten, and elided to conceive of information as a disembodied entity. Thus she moves from the post-World War II Macy Conferences on cybernetics to the 1952 novel Limbo by cybernetics aficionado Bernard Wolfe; from the concept of self-making to Philip K. Dick's literary explorations of hallucination and reality; and from artificial life to postmodern novels exploring the implications of seeing humans as cybernetic systems.

Although becoming posthuman can be nightmarish, Hayles shows how it can also be liberating. From the birth of cybernetics to artificial life, How We Became Posthuman provides an indispensable account of how we arrived in our virtual age, and of where we might go from here.

Practical, scientific, philosophical, and artistic problems have caused men to investigate mathematics. But there is one other motive which is as strong as any of these—the search for beauty. Mathematics is an art, and as such affords the pleasures which all the arts afford." In this erudite, entertaining college-level text, Morris Kline, Professor Emeritus of Mathematics at New York University, provides the liberal arts student with a detailed treatment of mathematics in a cultural and historical context. The book can also act as a self-study vehicle for advanced high school students and laymen.
Professor Kline begins with an overview, tracing the development of mathematics to the ancient Greeks, and following its evolution through the Middle Ages and the Renaissance to the present day. Subsequent chapters focus on specific subject areas, such as "Logic and Mathematics," "Number: The Fundamental Concept," "Parametric Equations and Curvilinear Motion," "The Differential Calculus," and "The Theory of Probability." Each of these sections offers a step-by-step explanation of concepts and then tests the student's understanding with exercises and problems. At the same time, these concepts are linked to pure and applied science, engineering, philosophy, the social sciences or even the arts.
In one section, Professor Kline discusses non-Euclidean geometry, ranking it with evolution as one of the "two concepts which have most profoundly revolutionized our intellectual development since the nineteenth century." His lucid treatment of this difficult subject starts in the 1800s with the pioneering work of Gauss, Lobachevsky, Bolyai and Riemann, and moves forward to the theory of relativity, explaining the mathematical, scientific and philosophical aspects of this pivotal breakthrough. Mathematics for the Nonmathematician exemplifies Morris Kline's rare ability to simplify complex subjects for the nonspecialist.

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.

A Nobel Prize-winning physicist, a loving husband and father, an enthusiastic teacher, a surprisingly accomplished bongo player, and a genius of the highest caliber---Richard P. Feynman was all these and more. Perfectly Reasonable Deviations From the Beaten Track--collecting over forty years' worth of Feynman's letters--offers an unprecedented look at the writer and thinker whose scientific mind and lust for life made him a legend in his own time. Containing missives to and from such scientific luminaries as Victor Weisskopf, Stephen Wolfram, James Watson, and Edward Teller, as well as a remarkable selection of letters to and from fans, students, family, and people from around the world eager for Feynman's advice and counsel, Perfectly Reasonable Deviations From the Beaten Track not only illuminates the personal relationships that underwrote the key developments in modern science, but also forms the most intimate look at Feynman yet available. Feynman was a man many felt close to but few really knew, and this collection reveals the full wisdom and private passion of a personality that captivated everyone it touched. Perfectly Reasonable Deviations From the Beaten Track is an eloquent testimony to the virtue of approaching the world with an inquiring eye; it demonstrates the full extent of the Feynman legacy like never before. Edited and with additional commentary by his daughter Michelle, it's a must-read for Feynman fans everywhere, and for anyone seeking to better understand one of the towering figures--and defining personalities--of the twentieth century.

Among the many constants that appear in mathematics, π, e, and i are the most familiar. Following closely behind is y, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery.

In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics.

Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + . . . Up to 1/n, minus the natural logarithm of n--the numerical value being 0.5772156. . . . But unlike its more celebrated colleagues π and e, the exact nature of gamma remains a mystery--we don't even know if gamma can be expressed as a fraction.

Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics today--the Riemann Hypothesis (though no proof of either is offered!).

Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians.

The Magic of Math is the math book you wish you had in school. Using a delightful assortment of examples—from ice cream scoops and poker hands to measuring mountains and making magic squares—this book empowers you to see the beauty, simplicity, and truly magical properties behind those formulas and equations that once left your head spinning. You'll learn the key ideas of classic areas of mathematics like arithmetic, algebra, geometry, trigonometry, and calculus, but you'll also have fun fooling around with Fibonacci numbers, investigating infinity, and marveling over mathematical magic tricks that will make you look like a math genius!

A mathematician who is known throughout the world as the “mathemagician,” Arthur Benjamin mixes mathematics and magic to make the subject fun, attractive, and easy to understand. In The Magic of Math, Benjamin does more than just teach skills: with a tip of his magic hat, he takes you on as his apprentice to teach you how to appreciate math the way he does. He motivates you to learn something new about how to solve for x, because there is real pleasure to be found in the solution to a challenging problem or in using numbers to do something useful. But what he really wants you to do is be able to figure out why, for that's where you'll find the real beauty, power, and magic of math.

If you are already someone who likes math, this book will dazzle and amuse you. If you never particularly liked or understood math, Benjamin will enlighten you and—with a wave of his magic wand—turn you into a math lover.