The Moment of Proof

Mathematical Epiphanies

Author: Donald C. Benson

Publisher: Oxford University Press

ISBN: 0198027745

Category: Mathematics

Page: 352

View: 6135

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When Archimedes, while bathing, suddenly hit upon the principle of buoyancy, he ran wildly through the streets of Syracuse, stark naked, crying "eureka!" In The Moment of Proof, Donald Benson attempts to convey to general readers the feeling of eureka--the joy of discovery--that mathematicians feel when they first encounter an elegant proof. This is not an introduction to mathematics so much as an introduction to the pleasures of mathematical thinking. And indeed the delights of this book are many and varied. The book is packed with intriguing conundrums--Loyd's Fifteen Puzzle, the Petersburg Paradox, the Chaos Game, the Monty Hall Problem, the Prisoners' Dilemma--as well as many mathematical curiosities. We learn how to perform the arithmetical proof called "casting out nines" and are introduced to Russian peasant multiplication, a bizarre way to multiply numbers that actually works. The book shows us how to calculate the number of ways a chef can combine ten or fewer spices to flavor his soup (1,024) and how many people we would have to gather in a room to have a 50-50 chance of two having the same birthday (23 people). But most important, Benson takes us step by step through these many mathematical wonders, so that we arrive at the solution much the way a working scientist would--and with much the same feeling of surprise. Every fan of mathematical puzzles will be enthralled by The Moment of Proof. Indeed, anyone interested in mathematics or in scientific discovery in general will want to own this book.

Geschichte der Mathematik kompakt

Das Wichtigste aus Analysis, Wahrscheinlichkeitstheorie, angewandter Mathematik, Topologie und Mengenlehre

Author: Franka Miriam Brückler

Publisher: Springer-Verlag

ISBN: 3662555743

Category: Mathematics

Page: 159

View: 6876

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Dieses Buch gibt einen kompakten Überblick über die historische Entwicklung und Ideengeschichte derjenigen mathematischen Gebiete, die sich erst in der Neuzeit zu eigenständigen Teildisziplinen entwickelt haben: Analysis, Wahrscheinlichkeitstheorie, angewandte Mathematik, Topologie und Mengenlehre. Die Darstellung verzichtet auf Vollständigkeit und konzentriert sich stattdessen ganz bewusst auf wesentliche oder besonders interessante Aspekte: Einzelne Persönlichkeiten und Ideen werden exemplarisch herausgegriffen und detaillierter dargestellt als andere – es entsteht jedoch insgesamt ein stimmiges, ausgewogenes und dennoch übersichtliches Gesamtbild. Dabei wird insbesondere begreifbar, dass die historische Entwicklung der Mathematik von zahlreichen Einflüssen angetrieben wurde, dass zahlreiche theoretische Resultate aus ganz praktischen Gründen gefunden wurden (und umgekehrt), und dass es zu den wenigsten mathematischen Problemen nur einen (richtigen) Lösungsweg gibt. Auch Querverbindungen zwischen den verschiedenen Disziplinen werden deutlich. Das Buch wendet sich an all jene, die eine übersichtliche, kurze Darstellung der zentralen Momente in der Geschichte der Mathematik suchen – vor allem Professoren, (zukünftige) Lehrer und Studierende.

CRC Concise Encyclopedia of Mathematics, Second Edition

Author: Eric W. Weisstein

Publisher: CRC Press

ISBN: 1420035223

Category: Mathematics

Page: 3252

View: 6228

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Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the dedication of author Eric Weisstein to collecting, cataloging, and referencing mathematical facts, formulas, and definitions. He has now updated most of the original entries and expanded the Encyclopedia to include 1000 additional pages of illustrated entries. The accessibility of the Encyclopedia along with its broad coverage and economical price make it attractive to the widest possible range of readers and certainly a must for libraries, from the secondary to the professional and research levels. For mathematical definitions, formulas, figures, tabulations, and references, this is simply the most impressive compendium available.

A Smoother Pebble

Mathematical Explorations

Author: Donald C. Benson

Publisher: Oxford University Press

ISBN: 9780198032977

Category: Mathematics

Page: 280

View: 1844

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This book takes a novel look at the topics of school mathematics--arithmetic, geometry, algebra, and calculus. In this stroll on the mathematical seashore we hope to find, quoting Newton, "...a smoother pebble or a prettier shell than ordinary..." This book assembles a collection of mathematical pebbles that are important as well as beautiful.

The Ballet of the Planets

A Mathematician's Musings on the Elegance of Planetary Motion

Author: Donald Benson

Publisher: Oxford University Press

ISBN: 0199939292

Category: Mathematics

Page: 192

View: 5675

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The Ballet of the Planets unravels the beautiful mystery of planetary motion, revealing how our understanding of astronomy evolved from Archimedes and Ptolemy to Copernicus, Kepler, and Newton. Mathematician Donald Benson shows that ancient theories of planetary motion were based on the assumptions that the Earth was the center of the universe and the planets moved in a uniform circular motion. Since ancient astronomers noted that occasionally a planet would exhibit retrograde motion--would seem to reverse its direction and move briefly westward--they concluded that the planets moved in epicyclic curves, circles with smaller interior loops, similar to the patterns of a child's Spirograph. With the coming of the Copernican revolution, the retrograde motion was seen to be apparent rather than real, leading to the idea that the planets moved in ellipses. This laid the ground for Newton's great achievement--integrating the concepts of astronomy and mechanics--which revealed not only how the planets moved, but also why. Throughout, Benson focuses on naked-eye astronomy, which makes it easy for the novice to grasp the work of these pioneers of astronomy.

Das lebendige Theorem

Author: Cédric Villani

Publisher: S. Fischer Verlag

ISBN: 3104025665

Category: Mathematics

Page: 304

View: 3144

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Im Kopf eines Genies – der Bericht von einem mathematischen Abenteuer und der Roman eines sehr erfolgreichen Forschers Cédric Villani gilt als Kandidat für die begehrte Fields-Medaille, eine Art Nobelpreis für Mathematiker. Sie wird aber nur alle vier Jahre vergeben, und man muss unter 40 sein. Er hat also nur eine Chance. Unmöglich! Unmöglich? Fieberhaft macht er sich an die Arbeit. Jetzt erzählt er seine Geschichte, und ihm gelingt das Unglaubliche: Wir werden direkte Zeugen der Denkprozesse eines Mathematikers, und das, ohne die dazugehörigen Formeln verstehen zu müssen. Ein Buch, so einzigartig wie sein Autor.

The Liar Paradox and the Towers of Hanoi

the 10 greatest math puzzles of all time

Author: Marcel Danesi

Publisher: John Wiley & Sons Inc

ISBN: N.A

Category: Mathematics

Page: 248

View: 3997

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A walk through history's most mind-boggling puzzles Ever since the Sphinx asked his legendary riddle of Oedipus, riddles, conundrums, and puzzles of all sizes have kept humankind perplexed and amused. The Liar Paradox and the Towers of Hanoi takes die-hard puzzle mavens on a tour of the world's most enduringly intriguing braintwisters, from Königsberg's Bridges and the Hanoi Towers to Fibonacci's Rabbits, the Four Color Problem, and the Magic Square. Each chapter introduces the basic puzzle, discusses the mathematics behind it, and includes exercises and answers plus additional puzzles similar to the one under discussion. Here is a veritable kaleidoscope of puzzling labyrinths, maps, bridges, and optical illusions that will keep aficionados entertained for hours. Marcel Danesi (Etobicoke, ON, Canada) is the author of Increase Your Puzzle IQ

Mathematics

Author: Barry Max Brandenberger

Publisher: MacMillan Reference Library

ISBN: N.A

Category: Juvenile Nonfiction

Page: 4

View: 3755

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This new series offers the most comprehensive views of key areas in the world of science. Each set explores all facets of the topic, offering not only descriptive and analytical information, but also cultural and ethical issues, and career opportunities in many fields of science.

The Saga of Mathematics

A Brief History

Author: Marty Lewinter,William Widulski

Publisher: Pearson College Division

ISBN: N.A

Category: Mathematics

Page: 302

View: 4052

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This inexpensive paperback uses lively language to put mathematics in an interesting, historical context and points out the many links to art, philosophy, music, computers, navigation, science, and technology. The arithmetic, algebra, and geometry are presented in a way that makes them relevant to daily life as well as larger issues. Topics include: Oh So Mysterious Egyptian Mathematics; Mesopotamia Here We Come; Those Incredible Greeks; Greeks Bearing Gifts; Must All Good Things Come to an End?; Europe Smells the Coffee; Mathematics Marches On; A Few Good Men; A Most Amazing Century of Mathematical Marvels!; The Age of Euler; A Century of Surprises; Ones and Zeros; Some More Math Before You Go.

The Puzzle Instinct

The Meaning of Puzzles in Human Life

Author: Marcel Danesi

Publisher: Bloomington : Indiana University Press

ISBN: N.A

Category: Language Arts & Disciplines

Page: 269

View: 4399

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Publisher Fact Sheet Recalling Stephen Pinker's The Language Instinct, the author argues that humans are born with an "instinct for puzzles" that betrays a larger search for the meaning of life. This "instinct" has led to discoveries in mathematics and science, as well as revolutions in philosophical thought.

Versus

Author: Umberto Eco

Publisher: N.A

ISBN: N.A

Category: Semantics

Page: N.A

View: 7364

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ERA

Author: Gale Group

Publisher: N.A

ISBN: 9780787634513

Category: Universities and colleges

Page: 950

View: 5005

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This up-to-date resource presents 3,500 national, regional, local and international lists and rankings compiled from hundreds of sources. Entries typically include a description of the ranking; background information on criteria for establishing the hierarchy; additional remarks about the ranking; the complete or partial (if extensive) ranking; and a complete source citation for locating additional information if necessary.

Blink!

Die Macht des Moments

Author: Malcolm Gladwell

Publisher: Campus Verlag

ISBN: 3593405008

Category: Science

Page: 264

View: 1499

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Jeder kennt sie: Momente, in denen wir denken, ohne zu denken.Wir nennen sie Intuition oder Bauchgefühl. Aber sie sind viel mehr: Unser Gehirn arbeitet dann auf Hochtouren, um uns die richtigen Entscheidungen zu liefern. Malcolm Gladwell erklärt die Macht dieses Augenblicks und zeigt, wie wir unsere verborgene Intelligenz trainieren und besser nutzen können.