How Mathematicians Think

How Mathematicians Think

Author: William Byers

Publisher: Princeton University Press

Published: 2010-05-02

Total Pages: 424

ISBN-13: 0691145997

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To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.


Goin' Crazy with Sam Peckinpah and All Our Friends

Goin' Crazy with Sam Peckinpah and All Our Friends

Author: Max Evans

Publisher: UNM Press

Published: 2014-10-15

Total Pages: 355

ISBN-13: 0826335888

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Almost as famous for the legendary excesses of his personal life as for his films, Sam Peckinpah (1925–1984) cemented his reputation as one of the great American directors with movies such as The Wild Bunch and Pat Garrett and Billy the Kid. Max Evans, one of Peckinpah’s best friends, experienced the director’s mercurial character and personal demons firsthand. In this enthralling memoir we follow Evans and Peckinpah through conversations in bars, family gatherings, binges on drugs and alcohol, struggles with film producers and executives, and Peckinpah’s abusive behavior—sometimes directed at Evans himself. Evans’s stories—most previously unpublished—provide a uniquely intimate look at Peckinpah, their famous friends (including Lee Marvin, Brian Keith, Joel McCrea, and James Coburn), and the business of Hollywood in the 1960s and 1970s.


A History of Abstract Algebra

A History of Abstract Algebra

Author: Israel Kleiner

Publisher: Springer Science & Business Media

Published: 2007-09-20

Total Pages: 175

ISBN-13: 081764685X

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This book does nothing less than provide an account of the intellectual lineage of abstract algebra. The development of abstract algebra was propelled by the need for new tools to address certain classical problems that appeared insoluble by classical means. A major theme of the book is to show how abstract algebra has arisen in attempting to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved. Mathematics instructors, algebraists, and historians of science will find the work a valuable reference.


Frobenius Splitting Methods in Geometry and Representation Theory

Frobenius Splitting Methods in Geometry and Representation Theory

Author: Michel Brion

Publisher: Springer Science & Business Media

Published: 2007-08-08

Total Pages: 259

ISBN-13: 0817644059

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Systematically develops the theory of Frobenius splittings and covers all its major developments. Concise, efficient exposition unfolds from basic introductory material on Frobenius splittings—definitions, properties and examples—to cutting edge research.


Lie Theory

Lie Theory

Author: Jean-Philippe Anker

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 341

ISBN-13: 0817681922

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* First of three independent, self-contained volumes under the general title, "Lie Theory," featuring original results and survey work from renowned mathematicians. * Contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations." * Comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations. * Should benefit graduate students and researchers in mathematics and mathematical physics.


Encyclopaedia Britannica Almanac 2010

Encyclopaedia Britannica Almanac 2010

Author: Encyclopaedia Britannica, Inc.

Publisher: Encyclopaedia Britannica, Inc.

Published: 2010-01-01

Total Pages: 882

ISBN-13: 1615353291

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The Encyclopaedia Britannica 2010 Almanac, is the complete source for fast facts. Published in association with Time Magazine, the Encyclopaedia Britannica Almanac 2010 includes more coverage of key subjects such as the arts, business, people, science, and the world than other leading almanacs. Read about the ongoing humanitarian crisis in Darfur, the rise of global food prices and the accompanying political and financial effects, the growing military operation in Afghanistan, the lives of influential political leaders, athletes, authors, heroes and much more !


Yvain

Yvain

Author: Chretien de Troyes

Publisher: Yale University Press

Published: 1987-09-10

Total Pages: 244

ISBN-13: 0300038380

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A twelfth-century poem by the creator of the Arthurian romance describes the courageous exploits and triumphs of a brave lord who tries to win back his deserted wife's love