Euclid in the Rainforest

Discovering Universal Truth in Logic and Math

Author: Joseph Mazur

Publisher: Penguin

ISBN: 1101664878

Category: Mathematics

Page: 352

View: 2421

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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: Medical

Page: 343

View: 3846

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Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.

The Motion Paradox

The 2,500-Year Old Puzzle Behind All the Mysteries of Time and Space

Author: Joseph Mazur

Publisher: Penguin

ISBN: 1440649650

Category: Science

Page: 272

View: 9616

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The epic tale of an ancient, unsolved puzzle and how it relates to all scientific attempts to explain the basic structure of the universe At the dawn of science the ancient Greek philosopher Zeno formulated his paradox of motion, and amazingly, it is still on the cutting edge of all investigations into the fabric of reality. Zeno used logic to argue that motion is impossible, and at the heart of his maddening puzzle is the nature of space and time. Is space-time continuous or broken up like a string of beads? Over the past two millennia, many of our greatest minds—including Aristotle, Galileo, Newton, Einstein, Stephen Hawking, and other current theoreticians—have been gripped by the mystery this puzzle represents. Joseph Mazur, acclaimed author of Euclid in the Rainforest, shows how historic breakthroughs in our understanding of motion shed light on Zeno’s paradox. The orbits of the planets were explained, the laws of motion were revealed, the theory of relativity was discovered—but the basic structure of time and space remained elusive. In the tradition of Fermat’s Enigma and Zero, The Motion Paradox is a lively history of this apparently simple puzzle whose solution—if indeed it can be solved—will reveal nothing less than the fundamental nature of reality.

A Tour of the Calculus

Author: David Berlinski

Publisher: Vintage

ISBN: 9780307789730

Category: Mathematics

Page: 352

View: 5560

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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.

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: 5824

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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.

Games of Life

Explorations in Ecology, Evolution and Behavior

Author: Karl Sigmund

Publisher: Courier Dover Publications

ISBN: 0486812898

Category: Science

Page: 272

View: 9022

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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 Parrot's Theorem

A Novel

Author: Denis Guedj

Publisher: Macmillan

ISBN: 1466851678

Category: Fiction

Page: 352

View: 3701

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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.

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: 1790

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Enlightening Symbols

A Short History of Mathematical Notation and Its Hidden Powers

Author: Joseph Mazur

Publisher: Princeton University Press

ISBN: 1400850118

Category: Mathematics

Page: 312

View: 4114

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While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted. Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics. From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.

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: 757

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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.

The Universe and the Teacup

The Mathematics of Truth and Beauty

Author: K. C. Cole

Publisher: Houghton Mifflin Harcourt

ISBN: 9780156006569

Category: Mathematics

Page: 214

View: 1706

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A noted science writer explores how mathematics can explain such events as the O. J. Simpson verdict and the errors undermining the infamous Bell Curve, and introduces a little-known woman without whom the theory of relativity never would have worked. Reprint. 35,000 first printing.

The Tiger That Isn't

Seeing Through a World of Numbers

Author: Andrew Dilnot,Michael Blastland

Publisher: Profile Books

ISBN: 1847650791

Category: Mathematics

Page: 192

View: 6775

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Mathematics scares and depresses most of us, but politicians, journalists and everyone in power use numbers all the time to bamboozle us. Most maths is really simple - as easy as 2+2 in fact. Better still it can be understood without any jargon, any formulas - and in fact not even many numbers. Most of it is commonsense, and by using a few really simple principles one can quickly see when maths, statistics and numbers are being abused to play tricks - or create policies - which can waste millions of pounds. It is liberating to understand when numbers are telling the truth or being used to lie, whether it is health scares, the costs of government policies, the supposed risks of certain activities or the real burden of taxes.

Archimedes

The Father of Mathematics

Author: Heather Hasan

Publisher: The Rosen Publishing Group, Inc

ISBN: 9781404207745

Category: Juvenile Nonfiction

Page: 112

View: 1971

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

Death's Acre

Inside the Legendary Forensic Lab the Body Farm Where the Dead Do Tell Tales

Author: William Bass,Jon Jefferson

Publisher: Penguin

ISBN: 9781101204726

Category: True Crime

Page: 320

View: 8234

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Dr. Bill Bass, one of the world's leading forensic anthropologists, gained international attention when he built a forensic lab like no other: The Body Farm. Now, this master scientist unlocks the gates of his lab to reveal his most intriguing cases-and to revisit the Lindbergh kidnapping and murder, fifty years after the fact.

The Science of Vampires

Author: Katherine M. Ramsland

Publisher: Penguin

ISBN: 9780425186169

Category: Body, Mind & Spirit

Page: 276

View: 5147

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Sheds new light on the myths, facts, and fallacies of the vampire, drawing on forensic experts, artists, and real-life bloodsuckers to answer questions about the Vampire Personality Disorder, the forensics of vampirism, the vampire polysexual world, and facts about vampire legends. Original.

Mathematics in Ancient Greece

Author: Tobias Dantzig

Publisher: Courier Corporation

ISBN: 0486149986

Category: Mathematics

Page: 192

View: 3713

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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.

Kiss My Math

Showing Pre-algebra Who's Boss

Author: Danica McKellar

Publisher: Penguin

ISBN: 9781594630491

Category: Juvenile Nonfiction

Page: 335

View: 5961

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The television actress and mathematics guru author of Math Doesn't Suck presents a pre-algebra primer for seventh- to ninth-graders, in an accessible reference that shares time-saving tricks, real-world examples, and detailed practice problems. 100,000 first printing.

One Two Three . . . Infinity

Facts and Speculations of Science

Author: George Gamow

Publisher: Courier Corporation

ISBN: 0486135179

Category: Science

Page: 384

View: 1695

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Over 120 delightful pen-and-ink illustrations by the author add another dimension of good-natured charm to these wide-ranging explorations. A mind-expanding volume for the layman and the science-minded.

The Poincare Conjecture

In Search of the Shape of the Universe

Author: Donal O'Shea

Publisher: Bloomsbury Publishing USA

ISBN: 9780802718945

Category: Mathematics

Page: 304

View: 9690

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Henri Poincaré was one of the greatest mathematicians of the late nineteenth and early twentieth century. He revolutionized the field of topology, which studies properties of geometric configurations that are unchanged by stretching or twisting. The Poincaré conjecture lies at the heart of modern geometry and topology, and even pertains to the possible shape of the universe. The conjecture states that there is only one shape possible for a finite universe in which every loop can be contracted to a single point. Poincaré's conjecture is one of the seven "millennium problems" that bring a one-million-dollar award for a solution. Grigory Perelman, a Russian mathematician, has offered a proof that is likely to win the Fields Medal, the mathematical equivalent of a Nobel prize, in August 2006. He also will almost certainly share a Clay Institute millennium award. In telling the vibrant story of The Poincaré Conjecture, Donal O'Shea makes accessible to general readers for the first time the meaning of the conjecture, and brings alive the field of mathematics and the achievements of generations of mathematicians whose work have led to Perelman's proof of this famous conjecture.