**Author**: Ivar Ekeland

**Publisher:**University of Chicago Press

**ISBN:**9780226199900

**Category:**Mathematics

**Page:**146

**View:**5049

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# Search Results for: mathematics-and-the-unexpected

**Author**: Ivar Ekeland

**Publisher:** University of Chicago Press

**ISBN:** 9780226199900

**Category:** Mathematics

**Page:** 146

**View:** 5049

"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
*Mathematics and Destiny*

**Author**: Ivar Ekeland

**Publisher:** University of Chicago Press

**ISBN:** 0226199959

**Category:** Mathematics

**Page:** 207

**View:** 1894

Optimists believe this is the best of all possible worlds. And pessimists fear that might really be the case. But what is the best of all possible worlds? How do we define it? Is it the world that operates the most efficiently? Or the one in which most people are comfortable and content? Questions such as these have preoccupied philosophers and theologians for ages, but there was a time, during the seventeenth and eighteenth centuries, when scientists and mathematicians felt they could provide the answer. This book is their story. Ivar Ekeland here takes the reader on a journey through scientific attempts to envision the best of all possible worlds. He begins with the French physicist Maupertuis, whose least action principle asserted that everything in nature occurs in the way that requires the least possible action. This idea, Ekeland shows, was a pivotal breakthrough in mathematics, because it was the first expression of the concept of optimization, or the creation of systems that are the most efficient or functional. Although the least action principle was later elaborated on and overshadowed by the theories of Leonhard Euler and Gottfried Leibniz, the concept of optimization that emerged from it is an important one that touches virtually every scientific discipline today. Tracing the profound impact of optimization and the unexpected ways in which it has influenced the study of mathematics, biology, economics, and even politics, Ekeland reveals throughout how the idea of optimization has driven some of our greatest intellectual breakthroughs. The result is a dazzling display of erudition—one that will be essential reading for popular-science buffs and historians of science alike.

**Author**: Ivar Ekeland

**Publisher:** University of Chicago Press

**ISBN:** 9780226199924

**Category:** Mathematics

**Page:** 190

**View:** 5714

Ivar Ekeland extends his consideration of the catastrophe theory of the universe begun in his widely acclaimed Mathematics and the Unexpected, by drawing on rich literary sources, particularly the Norse saga of Saint Olaf, and such current topics as chaos theory, information theory, and particle physics. "Ivar Ekeland gained a large and enthusiastic following with Mathematics and the Unexpected, a brilliant and charming exposition of fundamental new discoveries in the theory of dynamical systems. The Broken Dice continues the same theme, and in the same elegant, seemingly effortless style, but focuses more closely on the implications of those discoveries for the rest of human culture. What are chance and probability? How has our thinking about them been changed by the discovery of chaos? What are all of these concepts good for? . . . Ah, but, I mustn't give the game away, any more than I should if I were reviewing a detective novel. And this is just as gripping a tale. . . . Beg, borrow, or preferably buy a copy. . . . I guarantee you won't be disappointed."—Ian Stewart, Science
*A Study of the Logic of Humor*

**Author**: John Allen Paulos

**Publisher:** University of Chicago Press

**ISBN:** 9780226650234

**Category:** Mathematics

**Page:** 124

**View:** 2476

John Allen Paulos cleverly scrutinizes the mathematical structures of jokes, puns, paradoxes, spoonerisms, riddles, and other forms of humor, drawing examples from such sources as Rabelais, Shakespeare, James Beattie, René Thom, Lewis Carroll, Arthur Koestler, W. C. Fields, and Woody Allen. "Jokes, paradoxes, riddles, and the art of non-sequitur are revealed with great perception and insight in this illuminating account of the relationship between humor and mathematics."—Joseph Williams, New York Times "'Leave your mind alone,' said a Thurber cartoon, and a really complete and convincing analysis of what humour is might spoil all jokes forever. This book avoids that danger. What it does. . .is describe broadly several kinds of mathematical theory and apply them to throw sidelights on how many kinds of jokes work."—New Scientist "Many scholars nowadays write seriously about the ludicrous. Some merely manage to be dull. A few—like Paulos—are brilliant in an odd endeavor."—Los Angeles Times Book Review
*With a New Afterword and Expanded Bibliography*

**Author**: Martin Gardner

**Publisher:** N.A

**ISBN:** 9780226282565

**Category:** Mathematics

**Page:** 263

**View:** 7666

Gathers paradoxes, logic puzzles, number problems, geometric problems, gambling puzzles, optical illusions, string, word, and chess problems featured in Scientific American
*The Curiosities of a Mathematical Crystal Ball*

**Author**: Leonard M. Wapner

**Publisher:** CRC Press

**ISBN:** 1568817215

**Category:** Mathematics

**Page:** 220

**View:** 5514

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

**Author**: Joseph Mazur

**Publisher:** Princeton University Press

**ISBN:** 9781400834457

**Category:** Mathematics

**Page:** 296

**View:** 537

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.
*The Math and Myth of Coincidence*

**Author**: Joseph Mazur

**Publisher:** Basic Books

**ISBN:** 0465040004

**Category:** Mathematics

**Page:** 288

**View:** 5896

A mathematical guide to understanding why life can seem to be one big coincidence—and why the odds of just about everything are better than we would think
*Heroes, Martyrs, and the Rise of Modern Mathematics*

**Author**: Amir R. Alexander

**Publisher:** Harvard University Press

**ISBN:** 9780674046610

**Category:** Mathematics

**Page:** 307

**View:** 3819

Argues that the death of Evariste Galois, the founder of modern algebra, following a duel in 1832 marked the end of an era in mathematics.
*How Mathematics Unveils the Universe*

**Author**: Ian Stewart

**Publisher:** Basic Books

**ISBN:** 0465096115

**Category:** Mathematics

**Page:** 360

**View:** 515

A prize-winning popular science writer uses mathematical modeling to explain the cosmos. In Calculating the Cosmos, Ian Stewart presents an exhilarating guide to the cosmos, from our solar system to the entire universe. He describes the architecture of space and time, dark matter and dark energy, how galaxies form, why stars implode, how everything began, and how it's all going to end. He considers parallel universes, the fine-tuning of the cosmos for life, what forms extraterrestrial life might take, and the likelihood of life on Earth being snuffed out by an asteroid. Beginning with the Babylonian integration of mathematics into the study of astronomy and cosmology, Stewart traces the evolution of our understanding of the cosmos: How Kepler's laws of planetary motion led Newton to formulate his theory of gravity. How, two centuries later, tiny irregularities in the motion of Mars inspired Einstein to devise his general theory of relativity. How, eighty years ago, the discovery that the universe is expanding led to the development of the Big Bang theory of its origins. How single-point origin and expansion led cosmologists to theorize new components of the universe, such as inflation, dark matter, and dark energy. But does inflation explain the structure of today's universe? Does dark matter actually exist? Could a scientific revolution that will challenge the long-held scientific orthodoxy and once again transform our understanding of the universe be on the way? In an exciting and engaging style, Calculating the Cosmos is a mathematical quest through the intricate realms of astronomy and cosmology.
*The Art and Science of Leonardo da Vinci*

**Author**: Bulent Atalay

**Publisher:** Smithsonian Institution

**ISBN:** 1588343537

**Category:** Art

**Page:** 352

**View:** 4488

Leonardo da Vinci was one of history's true geniuses, equally brilliant as an artist, scientist, and mathematician. Readers of The Da Vinci Code were given a glimpse of the mysterious connections between math, science, and Leonardo's art. Math and the Mona Lisa picks up where The Da Vinci Code left off, illuminating Leonardo's life and work to uncover connections that, until now, have been known only to scholars. Bülent Atalay, a distinguished scientist and artist, examines the science and mathematics that underlie Leonardo's work, paying special attention to the proportions, patterns, shapes, and symmetries that scientists and mathematicians have also identified in nature. Following Leonardo's own unique model, Atalay searches for the internal dynamics of art and science, revealing to us the deep unity of the two cultures. He provides a broad overview of the development of science from the dawn of civilization to today's quantum mechanics. From this base of information, Atalay offers a fascinating view into Leonardo's restless intellect and modus operandi, allowing us to see the source of his ideas and to appreciate his art from a new perspective.

**Author**: Emmanuel Tsukerman

**Publisher:** Createspace Independent Publishing Platform

**ISBN:** 9781532704970

**Category:**

**Page:** 84

**View:** 2352

Wild roses have 5 petals, Bloodroots have 8, black-eyed Susans have 13, Chicories 21, Gaillardias 34, daisies 55 and sunflowers 89. Each number of petals is the sum of the preceding two. Rainbows appear always at 42 degrees above the horizon. Water droplets as we all know conform to a spherical shape. Curious to find out why? In Math and Nature you will find mathematical explanations to all these marvels and many more, such as why kittens roll up into little balls, and why cicadas have 13- and 17-year life-cycles, in language accessible to a wide audience. Math and Nature contains more than 100 color illustrations to make reading fun and exciting.

**Author**: Steven R. Finch

**Publisher:** Cambridge University Press

**ISBN:** 9780521818056

**Category:** Mathematics

**Page:** 602

**View:** 5203

Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This work represents an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
*The Power of Mathematical Thinking*

**Author**: Jordan Ellenberg

**Publisher:** Penguin

**ISBN:** 0143127535

**Category:** Business & Economics

**Page:** 480

**View:** 3881

"Using the mathematician's method of analyzing life and exposing the hard-won insights of the academic community to the layman, minus the jargon ... Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need"--
*From Pythagoras to Schoenberg*

**Author**: Eli Maor

**Publisher:** Princeton University Press

**ISBN:** 1400889898

**Category:** Mathematics

**Page:** 176

**View:** 7004

How music has influenced mathematics, physics, and astronomy from ancient Greece to the twentieth century Music is filled with mathematical elements, the works of Bach are often said to possess a math-like logic, and Igor Stravinsky said "musical form is close to mathematics," while Arnold Schoenberg, Iannis Xenakis, and Karlheinz Stockhausen went further, writing music explicitly based on mathematical principles. Yet Eli Maor argues that music has influenced math at least as much as math has influenced music. Starting with Pythagoras, proceeding through the work of Schoenberg, and ending with contemporary string theory, Music by the Numbers tells a fascinating story of composers, scientists, inventors, and eccentrics who played a role in the age-old relationship between music, mathematics, and the sciences, especially physics and astronomy. Music by the Numbers explores key moments in this history, particularly how problems originating in music have inspired mathematicians for centuries. Perhaps the most famous of these problems is the vibrating string, which pitted some of the greatest mathematicians of the eighteenth century against each other in a debate that lasted more than fifty years and that eventually led to the development of post-calculus mathematics. Other highlights in the book include a comparison between meter in music and metric in geometry, complete with examples of rhythmic patterns from Bach to Stravinsky, and an exploration of a suggestive twentieth-century development: the nearly simultaneous emergence of Einstein's theory of relativity and Schoenberg's twelve-tone system. Weaving these compelling historical episodes with Maor's personal reflections as a mathematician and lover of classical music, Music by the Numbers will delight anyone who loves mathematics and music.

**Author**: Martin Aigner,Günter M. Ziegler

**Publisher:** Springer

**ISBN:** 3662442051

**Category:** Mathematics

**Page:** 308

**View:** 1131

This revised and enlarged fifth edition features four new chapters, which contain highly original and delightful proofs for classics such as the spectral theorem from linear algebra, some more recent jewels like the non-existence of the Borromean rings and other surprises. From the Reviews "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..." LMS Newsletter, January 1999 "Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant and the remaining open questio ns so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ... " SIGACT News, December 2011.
*A Mathematical Paradox*

**Author**: Leonard M. Wapner

**Publisher:** A K Peters/CRC Press

**ISBN:** 9781568813271

**Category:** Mathematics

**Page:** 232

**View:** 6737

Take an apple and cut it into five pieces. Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician.
*A Mathematical Journey*

**Author**: Sarah Flannery

**Publisher:** Algonquin Books

**ISBN:** 9781565123779

**Category:** Biography & Autobiography

**Page:** 341

**View:** 621

Originally published in England and cowritten with her father, "In Code" is "a wonderfully moving story about the thrill of the mathematical chase" ("Nature") and "a paean to intellectual adventure" ("Times Educational Supplement"). A memoir in mathematics, it is all about how a girl next door became an award-winning mathematician. photo insert.
*‘Moving mathematics teaching into the age of quantum mechanics and relativity.’*

**Author**: Malcolm Cameron

**Publisher:** Malcolm Cameron

**ISBN:** 1925635783

**Category:** Mathematics

**Page:** 168

**View:** 6473

Malcolm McDonald, FEDFA Union, State President, 1992-96

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