Mathematics And The Unexpected

Author : Ivar Ekeland
Publisher : University of Chicago Press
Page : 160 pages
File Size : 52,9 Mb
Release : 1988
Category : Science
ISBN : 0226199894

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Mathematics and the Unexpected by Ivar Ekeland Pdf

"Not the least unexpected thing about Mathematics and the Unexpected is that a real mathematician should write not just a literate work, but a literary one."—Ian Stewart, New Scientist "In this brief, elegant treatise, assessable to anyone who likes to think, Ivar Ekelund explains some philosophical implications of recent mathematics. He examines randomness, the geometry involved in making predictions, and why general trends are easy to project (it will snow in January) but particulars are practically impossible (it will snow from 2 p.m. to 5 p.m. on the 21st)."—Village Voice

Author : Ivar Ekeland
Publisher : University of Chicago Press
Page : 160 pages
File Size : 49,5 Mb
Release : 1990-01-15
Category : Mathematics
ISBN : 9780226199900

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Mathematics and the Unexpected by Ivar Ekeland Pdf

"Not the least unexpected thing about Mathematics and the Unexpected is that a real mathematician should write not just a literate work, but a literary one."—Ian Stewart, New Scientist "In this brief, elegant treatise, assessable to anyone who likes to think, Ivar Ekelund explains some philosophical implications of recent mathematics. He examines randomness, the geometry involved in making predictions, and why general trends are easy to project (it will snow in January) but particulars are practically impossible (it will snow from 2 p.m. to 5 p.m. on the 21st)."—Village Voice

Author : Ivar Ekeland
Publisher : University of Chicago Press
Page : 194 pages
File Size : 55,6 Mb
Release : 1996-06-15
Category : Mathematics
ISBN : 0226199924

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The Broken Dice, and Other Mathematical Tales of Chance by Ivar Ekeland Pdf

Contemplating the randomness of nature, Ekeland extends his consideration of the catastrophe theory of the universe begun in Mathematics and the Unexpected, drawing upon rich literary sources and current topics in math and physics such as chaos theory, information theory, and particle physics. Line drawings.

Author : Martin Gardner
Publisher : Unknown
Page : 268 pages
File Size : 46,6 Mb
Release : 1969
Category : Games
ISBN : UOM:39015017306757

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The Unexpected Hanging by Martin Gardner Pdf

Author : Alfred S. Posamentier,Ingmar Lehmann
Publisher : Prometheus Books
Page : 268 pages
File Size : 47,5 Mb
Release : 2014-08-12
Category : Mathematics
ISBN : 9781616149321

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Mathematical Curiosities by Alfred S. Posamentier,Ingmar Lehmann Pdf

An innovative and appealing way for the layperson to develop math skills--while actually enjoying it Most people agree that math is important, but few would say it's fun. This book will show you that the subject you learned to hate in high school can be as entertaining as a witty remark, as engrossing as the mystery novel you can't put down--in short, fun! As veteran math educators Posamentier and Lehmann demonstrate, when you realize that doing math can be enjoyable, you open a door into a world of unexpected insights while learning an important skill. The authors illustrate the point with many easily understandable examples. One of these is what mathematicians call the "Ruth-Aaron pair" (714 and 715), named after the respective career home runs of Babe Ruth and Hank Aaron. These two consecutive integers contain a host of interesting features, one of which is that their prime factors when added together have the same sum. The authors also explore the unusual aspects of such numbers as 11 and 18, which have intriguing properties usually overlooked by standard math curriculums. And to make you a better all-around problem solver, a variety of problems is presented that appear simple but have surprisingly clever solutions. If math has frustrated you over the years, this delightful approach will teach you many things you thought were beyond your reach, while conveying the key message that math can and should be anything but boring.

Author : Leonard M. Wapner
Publisher : CRC Press
Page : 222 pages
File Size : 50,9 Mb
Release : 2012-06-04
Category : Mathematics
ISBN : 9781568817217

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Unexpected Expectations by Leonard M. Wapner Pdf

Unexpected Expectations: The Curiosities of a Mathematical Crystal Ball explores how paradoxical challenges involving mathematical expectation often necessitate a reexamination of basic premises. The author takes you through mathematical paradoxes associated with seemingly straightforward applications of mathematical expectation and shows how these unexpected contradictions may push you to reconsider the legitimacy of the applications. The book requires only an understanding of basic algebraic operations and includes supplemental mathematical background in chapter appendices. After a history of probability theory, it introduces the basic laws of probability as well as the definition and applications of mathematical expectation/expected value (E). The remainder of the text covers unexpected results related to mathematical expectation, including: The roles of aversion and risk in rational decision making A class of expected value paradoxes referred to as envelope problems Parrondo’s paradox—how negative (losing) expectations can be combined to give a winning result Problems associated with imperfect recall Non-zero-sum games, such as the game of chicken and the prisoner’s dilemma Newcomb’s paradox—a great philosophical paradox of free will Benford’s law and its use in computer design and fraud detection While useful in areas as diverse as game theory, quantum mechanics, and forensic science, mathematical expectation generates paradoxes that frequently leave questions unanswered yet reveal interesting surprises. Encouraging you to embrace the mysteries of mathematics, this book helps you appreciate the applications of mathematical expectation, "a statistical crystal ball." Listen to an interview with the author on NewBooksinMath.com.

Author : Kit Yates
Publisher : Simon and Schuster
Page : 288 pages
File Size : 55,8 Mb
Release : 2021-04-27
Category : MATHEMATICS
ISBN : 9781982111885

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The Math of Life and Death by Kit Yates Pdf

"Few of us really appreciate the full power of math--the extent to which its influence is not only in every office and every home, but also in every courtroom and hospital ward. In this ... book, Kit Yates explores the true stories of life-changing events in which the application--or misapplication--of mathematics has played a critical role: patients crippled by faulty genes and entrepreneurs bankrupted by faulty algorithms; innocent victims of miscarriages of justice; and the unwitting victims of software glitches"--Publisher marketing.

Author : Leonard M. Wapner
Publisher : CRC Press
Page : 220 pages
File Size : 45,5 Mb
Release : 2012-06-04
Category : Mathematics
ISBN : 9781439867679

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Unexpected Expectations by Leonard M. Wapner Pdf

Unexpected Expectations: The Curiosities of a Mathematical Crystal Ball explores how paradoxical challenges involving mathematical expectation often necessitate a reexamination of basic premises. The author takes you through mathematical paradoxes associated with seemingly straightforward applications of mathematical expectation and shows how these unexpected contradictions may push you to reconsider the legitimacy of the applications. The book requires only an understanding of basic algebraic operations and includes supplemental mathematical background in chapter appendices. After a history of probability theory, it introduces the basic laws of probability as well as the definition and applications of mathematical expectation/expected value (E). The remainder of the text covers unexpected results related to mathematical expectation, including: The roles of aversion and risk in rational decision making A class of expected value paradoxes referred to as envelope problems Parrondo’s paradox—how negative (losing) expectations can be combined to give a winning result Problems associated with imperfect recall Non-zero-sum games, such as the game of chicken and the prisoner’s dilemma Newcomb’s paradox—a great philosophical paradox of free will Benford’s law and its use in computer design and fraud detection While useful in areas as diverse as game theory, quantum mechanics, and forensic science, mathematical expectation generates paradoxes that frequently leave questions unanswered yet reveal interesting surprises. Encouraging you to embrace the mysteries of mathematics, this book helps you appreciate the applications of mathematical expectation, "a statistical crystal ball." Listen to an interview with the author on NewBooksinMath.com.

Author : David Lindsay Roberts
Publisher : Johns Hopkins University Press
Page : 255 pages
File Size : 48,8 Mb
Release : 2019-10-08
Category : Mathematics
ISBN : 9781421433080

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Republic of Numbers by David Lindsay Roberts Pdf

Republic of Numbers will appeal to anyone who is interested in learning how mathematics has intertwined with American history.

Author : Kit Yates
Publisher : Basic Books
Page : 371 pages
File Size : 41,6 Mb
Release : 2023-10-31
Category : Mathematics
ISBN : 9781541604940

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How to Expect the Unexpected by Kit Yates Pdf

A “vivid, wide-ranging, and delightful guide” (bestselling author Tim Harford) for understanding how and why predictions go wrong, with practical tips to give you a better chance of getting them right How can you be 100 percent sure you will win a bet? Why did so many Pompeians stay put while Mount Vesuvius was erupting? Are you more likely to work in a kitchen if your last name is Baker? Ever since the dawn of human civilization, we have been trying to make predictions about what the world has in store for us. For just as long, we have been getting it wrong. In How to Expect the Unexpected, mathematician Kit Yates uncovers the surprising science that undergirds our predictions—and how we can use it to our advantage. From religious oracles to weather forecasters, and from politicians to economists, we are subjected to poor predictions all the time. Synthesizing results from math, biology, psychology, sociology, medicine, economic theory, and physics, Yates provides tools for readers to understand uncertainty and to recognize the cognitive biases that make accurate predictions so hard to come by. This book will teach you how and why predictions go wrong, help you to spot phony forecasts, and give you a better chance of getting your own predictions correct.

Author : J”ran Friberg
Publisher : World Scientific
Page : 308 pages
File Size : 51,7 Mb
Release : 2005
Category : Mathematics
ISBN : 9789812701121

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Unexpected Links Between Egyptian and Babylonian Mathematics by J”ran Friberg Pdf

Mesopotamian mathematics is known from a great number of cuneiform texts, most of them Old Babylonian, some Late Babylonian or pre-Old-Babylonian, and has been intensively studied during the last couple of decades. In contrast to this Egyptian mathematics is known from only a small number of papyrus texts, and the few books and papers that have been written about Egyptian mathematical papyri have mostly reiterated the same old presentations and interpretations of the texts. In this book, it is shown that the methods developed by the author for the close study of mathematical cuneiform texts can also be successfully applied to all kinds of Egyptian mathematical texts, hieratic, demotic, or Greek-Egyptian. At the same time, comparisons of a large number of individual Egyptian mathematical exercises with Babylonian parallels yield many new insights into the nature of Egyptian mathematics and show that Egyptian and Babylonian mathematics display greater similarities than expected.

Author : Ivar Ekeland
Publisher : University of Chicago Press
Page : 214 pages
File Size : 51,5 Mb
Release : 2007-10-31
Category : Mathematics
ISBN : 9780226199955

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The Best of All Possible Worlds by Ivar Ekeland Pdf

Optimists believe this is the best of all possible worlds, and pessimists fear that might really be the case. There was a time, during the 17th and 18th centuries, when scientists and mathematicians felt they could provide the answer. This book is their story.

Author : John D. Beasley
Publisher : Courier Corporation
Page : 228 pages
File Size : 49,7 Mb
Release : 2013-01-18
Category : Mathematics
ISBN : 9780486151625

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The Mathematics of Games by John D. Beasley Pdf

"Mind-exercising and thought-provoking."—New Scientist If playing games is natural for humans, analyzing games is equally natural for mathematicians. Even the simplest of games involves the fundamentals of mathematics, such as figuring out the best move or the odds of a certain chance event. This entertaining and wide-ranging guide demonstrates how simple mathematical analysis can throw unexpected light on games of every type—games of chance, games of skill, games of chance and skill, and automatic games. Just how random is a card shuffle or a throw of the dice? Is bluffing a valid poker strategy? How can you tell if a puzzle is unsolvable? How large a role does luck play in games like golf and soccer? This book examines each of these issues and many others, along with the general principles behind such classic puzzles as peg solitaire and Rubik's cube. Lucid, instructive, and full of surprises, it will fascinate mathematicians and gamesters alike.

Author : Richard Hoshino
Publisher : FriesenPress
Page : 165 pages
File Size : 48,6 Mb
Release : 2015-01-26
Category : International Mathematical Olympiad
ISBN : 9781460258736

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The Math Olympian by Richard Hoshino Pdf

BETHANY MACDONALD HAS TRAINED SIX LONG YEARS FOR THIS MOMENT. SHE'LL TRY TO SOLVE FIVE QUESTIONS IN THREE HOURS, FOR ONE IMPROBABLE DREAM. THE DREAM OF REPRESENTING HER COUNTRY, AND BECOMING A MATH OLYMPIAN. As a small-town girl in Nova Scotia bullied for liking numbers more than boys, and lacking the encouragement of her unsupportive single mother who frowns at her daughter's unrealistic ambition, Bethany's road to the International Math Olympiad has been marked by numerous challenges. Through persistence, perseverance, and the support of innovative mentors who inspire her with a love of learning, Bethany confronts these challenges and develops the creativity and confidence to reach her potential. In training to become a world-champion "mathlete", Bethany discovers the heart of mathematics - a subject that's not about memorizing formulas, but rather about problem-solving and detecting patterns to uncover truth, as well as learning how to apply the deep and unexpected connections of mathematics to every aspect of her life, including athletics, spirituality, and environmental sustainability. As Bethany reflects on her long journey and envisions her exciting future, she realizes that she has shattered the misguided stereotype that only boys can excel in math, and discovers a sense of purpose that through mathematics, she can and she will make an extraordinary contribution to society.

Author : Barry Cipra
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 47,8 Mb
Release : 2024-06-14
Category : Science
ISBN : 0821890433

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What's Happening in the Mathematical Sciences by Barry Cipra Pdf

Mathematicians like to point out that mathematics is universal. In spite of this, most people continue to view it as either mundane (balancing a checkbook) or mysterious (cryptography). This fifth volume of the What's Happening series contradicts that view by showing that mathematics is indeed found everywhere-in science, art, history, and our everyday lives. Here is some of what you'll find in this volume: Mathematics and Science Mathematical biology: Mathematics was key tocracking the genetic code. Now, new mathematics is needed to understand the three-dimensional structure of the proteins produced from that code. Celestial mechanics and cosmology: New methods have revealed a multitude of solutions to the three-body problem. And other new work may answer one of cosmology'smost fundamental questions: What is the size and shape of the universe? Mathematics and Everyday Life Traffic jams: New models are helping researchers understand where traffic jams come from-and maybe what to do about them! Small worlds: Researchers have found a short distance from theory to applications in the study of small world networks. Elegance in Mathematics Beyond Fermat's Last Theorem: Number theorists are reaching higher ground after Wiles' astounding 1994 proof: new developments inthe elegant world of elliptic curves and modular functions. The Millennium Prize Problems: The Clay Mathematics Institute has offered a million dollars for solutions to seven important and difficult unsolved problems. These are just some of the topics of current interest that are covered in thislatest volume of What's Happening in the Mathematical Sciences. The book has broad appeal for a wide spectrum of mathematicians and scientists, from high school students through advanced-level graduates and researchers.