Euclid in the Rainforest

Discovering Universal Truth in Logic and Math

Author: Joseph Mazur

Publisher: Dutton Juvenile

ISBN: N.A

Category: Mathematics

Page: 334

View: 7128

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"How does one summarize a book about rainforest adventures, probability, the Cafè Luxembourg, Euclid, and prime numbers? This is an absolutely delightful book, full of insight, suffused with gentle humor-a picaresque novel of mathematics. What do we mean by proof and persuasion in the most symbolic of fields, Mazur asks, and responds with stories that effortlessly guide us to the heartland of reason. This is a fabulous book, in all senses, from beginning to end." Peter Galison, Mallinckrodt Professor of the History of Science and of Physics, Harvard University, author of Einstein''s Clocks, Poincairè''s Maps "Euclid in the Rainforest is beautifully written and packed with insights into how mathemeticians convince themselves they are right. Mazur is a talented teacher who knows his subject inside out, and his delightful stories take his readers to the heart of mathematics-logic and proof. This original and charming book is accessible to anyone, and deserves major success." Ian Stewart, Professor of Mathematics, University of Warwick, author of Math Hysteria, and Flatterland "My chief regret after more than forty years of trying to teach concepts in mathematics and statistics to biology students is that I did not have Mazur''s book available. It should be assigned reading for all undergraduates in science." R. C. Lewontin, Alexander Agassiz Professor, Harvard University "Mazur is an excellent storyteller. Euclid in the Rainforest is a warm and creative masterpiece that reveals the spirit of mathematics." Tadatoshi Akiba, Mayor of the City of Hiroshima "Mazur has a wonderfully engaging writing style, and a marvelous feel for the interface between the physical world as we experience it every day and the mathematical one. This book is a pleasure to read." Joseph Harris, Chair, Department of Mathematics, Harvard University "Mazur''s Euclid in the Rainforest is written with warmth and a lifetime''s attachment to the things of this world and the forms of the world it manifests. Here are the pleasures of sitting with the author, as a young man, learning his craft in a Greenwich Village cafe from an old professor; and later on, teaching the craft in turn to an eight-year-old. Inspiring stuff. By overhearing such conversations as these, the reader too is led to savor the beauties of mathematics." Robert and Ellen Kaplan, co-founders of The Math Circle, and co-authors of The Art of the Infinite: The Pleasures of Mathematics "Delightful, full of insight, suffused with gentle_humor-a picaresque novel of mathematics." Peter Galison How do we know that something is true? How do we know that things really are what they seem? Many people think math and science are the ultimate authorities on reality. Math defines abstract, universal truths; scientific truths are established by experiments in the real world-but underlying both kinds of knowledge is logic. In Euclid in the Rainforest, Joseph Mazur examines the three types of logic that are the basis of our knowledge about the world we live in: the classical logic of the Ancient Greeks, the weird logic of infinity, and the everyday logic of plausible reasoning that guides all science today. Through tales of great moments in the history of math and science, stories of students making discoveries in the classroom, and his own quirky adventures in the Greek Islands, New York, and the jungles of South America, Mazur illuminates how we uncover truth in the tangled web of our experiences-and convince ourselves that we are right. Euclid took the incipient logic of his time to new heights with his magnificent geometry, the whole edifice of which is built on just five assumptions. That logic rigorously defined proof, cleverly avoiding problems with infinity that were introduced when the Pythagoreans discovered that the diagonal of a square could not be measured and Zeno of Elea used infinity to argue that motion is logically impossible. It would be almost two millenia, though, before a good understanding of the logic infinity emerged and made all kinds of technology possible. Plausible reasoning-which is based on the math of probability- lets us assess the general conclusions we derive from specific cases in scientific studies. It gives us the confidence to believe that a conclusion reached today will be true tomorrow, ultimately driving scientific, and human, progress. In lucid, ebullient language, Mazur, a professor of mathematics for over thirty years, makes the fundamentals of the three fundamental types of logic widely accessible for the first time. Deeper questions at the heart of the process of discovery are laid bare: What does it mean to believe a proof? Where does the finite end and the infinite begin? How can we be sure that the statements we make about the material world are accurate? Exposing the surprising roles of intuition, belief and persuasion in logic and math, Mazur tells a real-life detective story that has been going on for millenia: the pursuit of ultimate truth about our world, our universe, and ourselves. © Copyright Pearson Education. All rights reserved.

Euclid in the Rainforest

Discovering Universal Truth in Logic and Math

Author: Joseph Mazur

Publisher: Penguin

ISBN: 1101664878

Category: Mathematics

Page: 352

View: 6343

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Like Douglas Hofstadter’s Gödel, Escher, Bach, and David Berlinski’s A Tour of the Calculus, Euclid in the Rainforest combines the literary with the mathematical to explore logic—the one indispensable tool in man’s quest to understand the world. Underpinning both math and science, it is the foundation of every major advancement in knowledge since the time of the ancient Greeks. Through adventure stories and historical narratives populated with a rich and quirky cast of characters, Mazur artfully reveals the less-than-airtight nature of logic and the muddled relationship between math and the real world. Ultimately, Mazur argues, logical reasoning is not purely robotic. At its most basic level, it is a creative process guided by our intuitions and beliefs about the world.

What is Mathematics, Really?

Author: Reuben Hersh

Publisher: Oxford University Press, USA

ISBN: 9780195130874

Category: Mathematics

Page: 343

View: 2515

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Reflecting an insider's view of mathematical life, the author argues that mathematics must be historically evolved, and intelligible only in a social context.

What's Luck Got to Do with It?

The History, Mathematics, and Psychology of the Gambler's Illusion

Author: Joseph Mazur

Publisher: Princeton University Press

ISBN: 9781400834457

Category: Mathematics

Page: 296

View: 5992

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Why do so many gamblers risk it all when they know the odds of winning are against them? Why do they believe dice are "hot" in a winning streak? Why do we expect heads on a coin toss after several flips have turned up tails? What's Luck Got to Do with It? takes a lively and eye-opening look at the mathematics, history, and psychology of gambling to reveal the most widely held misconceptions about luck. It exposes the hazards of feeling lucky, and uses the mathematics of predictable outcomes to show when our chances of winning are actually good. Mathematician Joseph Mazur traces the history of gambling from the earliest known archaeological evidence of dice playing among Neolithic peoples to the first systematic mathematical studies of games of chance during the Renaissance, from government-administered lotteries to the glittering seductions of grand casinos, and on to the global economic crisis brought on by financiers' trillion-dollar bets. Using plenty of engaging anecdotes, Mazur explains the mathematics behind gambling--including the laws of probability, statistics, betting against expectations, and the law of large numbers--and describes the psychological and emotional factors that entice people to put their faith in winning that ever-elusive jackpot despite its mathematical improbability. As entertaining as it is informative, What's Luck Got to Do with It? demonstrates the pervasive nature of our belief in luck and the deceptive psychology of winning and losing. Some images inside the book are unavailable due to digital copyright restrictions.

A Tour of the Calculus

Author: David Berlinski

Publisher: Vintage

ISBN: 9780307789730

Category: Mathematics

Page: 352

View: 5543

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Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall. Just how calculus makes these things possible and in doing so finds a correspondence between real numbers and the real world is the subject of this dazzling book by a writer of extraordinary clarity and stylistic brio. Even as he initiates us into the mysteries of real numbers, functions, and limits, Berlinski explores the furthest implications of his subject, revealing how the calculus reconciles the precision of numbers with the fluidity of the changing universe. "An odd and tantalizing book by a writer who takes immense pleasure in this great mathematical tool, and tries to create it in others."--New York Times Book Review From the Trade Paperback edition.

Fluke

Author: Joseph Mazur

Publisher: Oneworld Publications

ISBN: 1780749015

Category: Mathematics

Page: 256

View: 7795

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What are the chances?! This exclamation greets the scarcely believable coincidence – you’re picked up by the same taxi driver several years and thousands of miles apart or, in a second-hand bookshop far from home, you find your own childhood copy of Winnie-the-Pooh on the shelf. But the unlikely is more probable than you think. Against every fibre of common sense, the fact is that it’s quite likely that some squirrel, somewhere, will be struck by lightning as it crosses the road. The chaos and unpredictability of our lives is an illusion. There is a rational order to the universe, and it’s called mathematics. Fluke is a fascinating investigation into the true nature of chance, a must-read for maths enthusiasts and avid storytellers alike, it tears down the veil of improbability to reveal the wonderfully possible.

Seduced by Logic

Émilie Du Châtelet, Mary Somerville and the Newtonian Revolution

Author: Robyn Arianrhod

Publisher: Oxford University Press

ISBN: 0199931615

Category: Mathematics

Page: 338

View: 6895

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Newton's explanations of natural laws shattered the way mankind perceived the universe, and hence were not immediately embraced. How can anyone warm to a force that could not be seen or touched? But for two women, separated by time and space but joined in their passion for Newtonian physics,that force drove them to great achievements. Brilliant, determined, and almost entirely self-taught, they dedicated their lives to explaining and disseminating Newton's discoveries.Robyn Arianrhod's Seduced by Logic tells the dual biography of Emilie du Chatelet and Mary Somerville, who, despite living a century apart, were connected by their love for mathematics and their places at the heart of the most advanced scientific society of their age. When Newton published hisrevolutionary theory of gravity in 1687, most of his Continental peers rejected it for its reliance on physical observation and mathematical insight and its lack of religious or metaphysical hypotheses. But the brilliant French aristocrat and intellectual Emilie du Chatelet and some of her earlyeighteenth-century Enlightenment colleagues - including her lover, Voltaire - realized the Principia Mathematica had changed everything, marking the beginning of theoretical science as a predictive, quantitative, and secular discipline. Emilie devoted herself to furthering Newton's ideas in France,and her translation of the Principia became the accepted French version of his work. Almost a century later, in Scotland, Mary Somerville taught herself mathematics and rose from genteel poverty to become a world authority on Newtonian physics. Living in France, she became acquainted with the workof one of Newton's proteges, Pierre Simon Laplace, and translated his six-volume Celestial Mechanics into English. It remained the standard astronomy text for the next century, and was considered the most influential work since Principia. Combining biography and history of science, Seduced by Logic not only reveals the fascinating story of two incredibly talented women, but also brings to life a period of dramatic political and scientific change. With lucidity and skill, Arianrhod reveals the intimate links between the unfoldingNewtonian revolution and the origins of intellectual and political liberty.

The Parrot's Theorem

A Novel

Author: Denis Guedj

Publisher: Macmillan

ISBN: 1466851678

Category: Fiction

Page: 352

View: 8225

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Mr. Ruche, a Parisian bookseller, receives a bequest from a long lost friend in the Amazon of a vast library of math books, which propels him into a great exploration of the story of mathematics. Meanwhile Max, whose family lives with Mr. Ruche, takes in a voluble parrot who will discuss math with anyone. When Mr. Ruche learns of his friend's mysterious death in a Brazilian rainforest, he decides that with the parrot's help he will use these books to teach Max and his brother and sister the mysteries of Euclid's Elements, Pythagoras's Theorem and the countless other mathematical wonders. But soon it becomes clear that Mr. Ruche has inherited the library for reasons other than enlightenment, and before he knows it the household is racing to prevent the parrot and vital, new theorems from falling into the wrong hands. An immediate bestseller when first published in France, The Parrot's Theorem charmingly combines a straightforward history of mathematics and a first-rate murder mystery.

Euclid's Window

The Story of Geometry from Parallel Lines to Hyperspace

Author: Leonard Mlodinow

Publisher: Simon and Schuster

ISBN: 9781439135372

Category: Science

Page: 320

View: 1703

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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.

Magical Mathematics

The Mathematical Ideas that Animate Great Magic Tricks

Author: Persi Diaconis,Ron Graham,Ronald L. Graham

Publisher: Princeton University Press

ISBN: 0691151644

Category: Crafts & Hobbies

Page: 244

View: 9754

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Magical Mathematics reveals the secrets of fun-to-perform card tricks—and the profound mathematical ideas behind them—that will astound even the most accomplished magician. Persi Diaconis and Ron Graham provide easy, step-by-step instructions for each trick, explaining how to set up the effect and offering tips on what to say and do while performing it. Each card trick introduces a new mathematical idea, and varying the tricks in turn takes readers to the very threshold of today’s mathematical knowledge. Diaconis and Graham tell the stories—and reveal the best tricks—of the eccentric and brilliant inventors of mathematical magic. The book exposes old gambling secrets through the mathematics of shuffling cards, explains the classic street-gambling scam of three-card Monte, traces the history of mathematical magic back to the oldest mathematical trick—and much more.

Mapping Decline

St. Louis and the Fate of the American City

Author: Colin Gordon

Publisher: University of Pennsylvania Press

ISBN: 0812291506

Category: History

Page: 304

View: 3475

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Once a thriving metropolis on the banks of the Mississippi, St. Louis, Missouri, is now a ghostly landscape of vacant houses, boarded-up storefronts, and abandoned factories. The Gateway City is, by any measure, one of the most depopulated, deindustrialized, and deeply segregated examples of American urban decay. "Not a typical city," as one observer noted in the late 1970s, "but, like a Eugene O'Neill play, it shows a general condition in a stark and dramatic form." Mapping Decline examines the causes and consequences of St. Louis's urban crisis. It traces the complicity of private real estate restrictions, local planning and zoning, and federal housing policies in the "white flight" of people and wealth from the central city. And it traces the inadequacy—and often sheer folly—of a generation of urban renewal, in which even programs and resources aimed at eradicating blight in the city ended up encouraging flight to the suburbs. The urban crisis, as this study of St. Louis makes clear, is not just a consequence of economic and demographic change; it is also the most profound political failure of our recent history. Mapping Decline is the first history of a modern American city to combine extensive local archival research with the latest geographic information system (GIS) digital mapping techniques. More than 75 full-color maps—rendered from census data, archival sources, case law, and local planning and property records—illustrate, in often stark and dramatic ways, the still-unfolding political history of our neglected cities.

Mathematics in Ancient Greece

Author: Tobias Dantzig

Publisher: Courier Corporation

ISBN: 0486149986

Category: Mathematics

Page: 192

View: 6903

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Written by a specialist in interpreting science for lay readers, this lively book recounts the human story behind mathematics, including the insights of such thinkers as Euclid and Hippocrates. 1955 edition.

Archimedes

The Father of Mathematics

Author: Heather Hasan

Publisher: The Rosen Publishing Group, Inc

ISBN: 9781404207745

Category: Juvenile Nonfiction

Page: 112

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Describes the life and ideas of the Greek philosopher whose principles greatly influenced mathematics and physics.

Number

The Language of Science; a Critical Survey Written for the Cultured Non-mathematician

Author: Tobias Dantzig

Publisher: N.A

ISBN: N.A

Category: Arithmetic

Page: 262

View: 5763

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The Universe and the Teacup

The Mathematics of Truth and Beauty

Author: K. C. Cole

Publisher: HMH

ISBN: 0547546149

Category: Mathematics

Page: 224

View: 5741

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From the acclaimed Los Angeles Times science writer, a wise, witty, and elegant study of how math provides practical solutions to everyday problems. Are the secrets of the universe written in words—or is it all about the digits? K.C. Cole follows up her paean to the power of physics, Sympathetic Vibrations, with this engaging and accessible guide to the might and majesty of mathematics. The Universe and the Teacup uses relatable examples, humorous prose, and whimsical line drawings to demonstrate math’s ability to “translate the complexity of the world into manageable patterns.” Cole shows how mathematical concepts illuminate everything from human risk-taking behavior to astronomical investigation, game theory to logic problems—not to mention the very structure of the universe itself. Brimming with trivia stressing the importance of math throughout history, this is a book both math nerds and the “innumerate” everyday person can enjoy in equal measure. “Cole writes clearly, simply and vividly,” noted The New York Times. “She so obviously likes mathematics, the reader can't help liking it too.” Filled with “a thousand fascinating facts and shrewd observations (Martin Gardner, Los Angeles Times), this book demonstrates how the truth and beauty of everything, from relativity to rainbows, is all in the numbers.

Games of Life

Explorations in Ecology, Evolution and Behavior

Author: Karl Sigmund

Publisher: Courier Dover Publications

ISBN: 0486812898

Category: Science

Page: 272

View: 1419

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Accessible, informative, and enjoyable treatment discusses the application of the ideas and methods of game theory and mathematical modeling to such areas as evolution, sex, animal behavior, and aggression. "Excellent." — Nature

The Art of the Infinite

The Pleasures of Mathematics

Author: Robert Kaplan,Ellen Kaplan

Publisher: Bloomsbury Publishing USA

ISBN: 1608198693

Category: Mathematics

Page: 416

View: 3259

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Traces the development of mathematical thinking and describes the characteristics of the "republic of numbers" in terms of humankind's fascination with, and growing knowledge of, infinity.

Absolute Zero and the Conquest of Cold

Author: Tom Shachtman

Publisher: HMH

ISBN: 9780547525952

Category: Science

Page: 272

View: 5598

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“A lovely, fascinating book, which brings science to life.” —Alan Lightman Combining science, history, and adventure, Tom Shachtman “holds the reader’s attention with the skill of a novelist” as he chronicles the story of humans’ four-centuries-long quest to master the secrets of cold (Scientific American). “A disarming portrait of an exquisite, ferocious, world-ending extreme,” Absolute Zero and the Conquest of Cold demonstrates how temperature science produced astonishing scientific insights and applications that have revolutionized civilization (Kirkus Reviews). It also illustrates how scientific advancement, fueled by fortuitous discoveries and the efforts of determined individuals, has allowed people to adapt to—and change—the environments in which they live and work, shaping man’s very understanding of, and relationship, with the world. This “truly wonderful book” was adapted into an acclaimed documentary underwritten by the National Science Foundation and the Alfred P. Sloan Foundation, directed by British Emmy Award winner David Dugan, and aired on the BBC and PBS’s Nova in 2008 (Library Journal). “An absorbing account to chill out with.” —Booklist