How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics - Tapa dura

9780691127385: How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics
Ver todas las copias de esta edición ISBN.
 
 
Book by Byers William

"Sinopsis" puede pertenecer a otra edición de este libro.

Críticas:

Winner of the 2007 Best Sci-Tech Books in Mathematics, Library Journal

One of Choice's Outstanding Academic Titles for 2007
"Ambitious, accessible and provocative...[In] How Mathematicians Think, William Byers argues that the core ingredients of mathematics are not numbers, structure, patterns or proofs, but ideas...Byers' view springs from the various facets of his career as a researcher and administrator (and, he says, his interest in Zen Buddhism). But it is his experience as a teacher that gives the book some of its extraordinary salience and authority...Good mathematics teaching should not banish ambiguity, but enable students to master it...Everyone should read Byers...His lively and important book establishes a framework and vocabulary to discuss doing, learning, and teaching mathematics, and why it matters."--Donal O'Shea, Nature

"From Byers's book, if you work at it, you will learn some mathematics and, more important, you may begin to see how mathematicians think."--Peter Cameron, Times Higher Education Supplement

"As William Byers points out in this courageous book, mathematics today is obsessed with rigor, and this actually suppresses creativity.... Perfectly formalized ideas are dead, while ambiguous, paradoxical ideas are pregnant with possibilities and lead us in new directions: they guide us to new viewpoints, new truths.... Bravo, Professor Byers, and my compliments to Princeton University Press for publishing this book."--Gregory Chaitin, New Scientist

"Many people assume that mathematicians' thinking processes are strictly methodical and algorithmic. Integrating his experience as a mathematician and as a Buddhist, Byers examines the validity of this assumption. Much of mathematical thought is based on intuition and is in fact outside the realm of black-and-white logic, he asserts. Byers introduces and defines terms such as mathematical ambiguity, contradiction, and paradox and demonstrates how creative ideas emerge out of them. He gives as examples some of the seminal ideas that arose in this manner, such as the resolution of the most famous mathematical problem of all time, the Fermat conjecture. Next, he takes a philosophical look at mathematics, pondering the ambiguity that he believes lies at its heart. Finally, he asks whether the computer accurately models how math is performed. The author provides a concept-laden look at the human face of mathematics."--Science News

"This book is a radically new account of mathematical discourse and mathematical thinking...What Byers's book reveals is that ambiguity is always present...You can't quite say that nobody has said this before. But nobody has said it before in this all-encompassing, coherent way, and in this readable, crystal clear style...This book strikes me as profound, unpretentious, and courageous."--Reuben Hersh, Notices of the AMS

"This is a truly exceptional work. In an almost gripping tour de force, Byers examines the creative impulse of mathematics, which to him is the notion of ambiguity, understood to 'involve a single idea that is perceived in two self-consistent but mutually incompatible frames of reference'...[I]t is a sorely needed complement to often-formulaic textbooks.... An incredible book."--J. Mayer, Choice

"William Byers...has written a passionate defense of the uniquely human aspect of mathematics...Byers [demonstrates] that the insights of mathematicians come about through a discipline that...has something in common with Zen practice. First, there is a positive use of difficulty: 'the paradox has the enormous value of highlighting a fertile area of thought.' Then the breakthrough: 'An idea emerges in response to the tension that results from the conflict inherent in ambiguity.' These sentences from Byers's book apply equally to scientific and spiritual work."--Eliot Fintushel, Tricycle

"After a lifetime of research and teaching, [Byers argues] that mathematical breakthroughs do not come from simply manipulating symbols according to strict rules. Byers writes with verve and clarity about deep and difficult mathematical and philosophical issues such as the relationship between great mathematical ideas and cultural crises. Byers discusses in depth some examples of great ideas and crises...and explains why he is dead against seeing the mind as a computer."--Andrew Robinson, Physics World

"It is a pleasure to read [Byers'] well written, carefully referenced, and clearly illustrated arguments. Byers describes what 'doing math is: a process characterized by the complementary poles of proof and idea, of ambiguity and logic.' Byers' book has given me a greater appreciation for mathematics. I recommend it to anyone interested in, and open-minded about, the attempt to define mathematics."--Lee Kennard, Math Horizons

Reseña del editor:

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.


"Sobre este título" puede pertenecer a otra edición de este libro.

  • EditorialPrinceton University Press
  • Año de publicación2007
  • ISBN 10 0691127387
  • ISBN 13 9780691127385
  • EncuadernaciónTapa dura
  • Número de páginas424
  • Valoración
Comprar nuevo Ver este artículo

Gastos de envío: EUR 28,21
De Estados Unidos de America a España

Destinos, gastos y plazos de envío

Añadir al carrito

Otras ediciones populares con el mismo título

9780691145990: How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics

Edición Destacada

ISBN 10:  ISBN 13:  9780691145990
Editorial: Princeton University Press, 2010
Tapa blanda

Los mejores resultados en AbeBooks

Imagen de archivo

Byers, William
Publicado por Princeton University Press (2007)
ISBN 10: 0691127387 ISBN 13: 9780691127385
Nuevo Tapa dura Cantidad disponible: 1
Librería:
Wizard Books
(Long Beach, CA, Estados Unidos de America)

Descripción Hardcover. Condición: new. New. Nº de ref. del artículo: Wizard0691127387

Más información sobre este vendedor | Contactar al vendedor

Comprar nuevo
EUR 23,28
Convertir moneda

Añadir al carrito

Gastos de envío: EUR 28,21
De Estados Unidos de America a España
Destinos, gastos y plazos de envío
Imagen de archivo

Byers, William
Publicado por Princeton University Press (2007)
ISBN 10: 0691127387 ISBN 13: 9780691127385
Nuevo Tapa dura Cantidad disponible: 1
Librería:
GoldBooks
(Austin, TX, Estados Unidos de America)

Descripción Hardcover. Condición: new. New Copy. Customer Service Guaranteed. Nº de ref. del artículo: think0691127387

Más información sobre este vendedor | Contactar al vendedor

Comprar nuevo
EUR 25,73
Convertir moneda

Añadir al carrito

Gastos de envío: EUR 29,13
De Estados Unidos de America a España
Destinos, gastos y plazos de envío
Imagen de archivo

Byers, William
Publicado por Princeton University Press (2007)
ISBN 10: 0691127387 ISBN 13: 9780691127385
Nuevo Tapa dura Cantidad disponible: 1
Librería:
Front Cover Books
(Denver, CO, Estados Unidos de America)

Descripción Condición: new. Nº de ref. del artículo: FrontCover0691127387

Más información sobre este vendedor | Contactar al vendedor

Comprar nuevo
EUR 27,33
Convertir moneda

Añadir al carrito

Gastos de envío: EUR 28,21
De Estados Unidos de America a España
Destinos, gastos y plazos de envío
Imagen de archivo

Byers, William
Publicado por Princeton University Press (2007)
ISBN 10: 0691127387 ISBN 13: 9780691127385
Nuevo Tapa dura Cantidad disponible: 1
Librería:
GoldenWavesOfBooks
(Fayetteville, TX, Estados Unidos de America)

Descripción Hardcover. Condición: new. New. Fast Shipping and good customer service. Nº de ref. del artículo: Holz_New_0691127387

Más información sobre este vendedor | Contactar al vendedor

Comprar nuevo
EUR 22,45
Convertir moneda

Añadir al carrito

Gastos de envío: EUR 38,38
De Estados Unidos de America a España
Destinos, gastos y plazos de envío
Imagen de archivo

Byers, William
ISBN 10: 0691127387 ISBN 13: 9780691127385
Nuevo Tapa dura Original o primera edición Cantidad disponible: 1
Librería:
Theoria Books
(Andover, MA, Estados Unidos de America)

Descripción Hardcover. Condición: New. Estado de la sobrecubierta: New. 1st Edition. 415 pp., vii. '1' in number line. Contents in three SECTIONS and nine chapters, following Introduction, "Turning on the Light": I: THE LIGHT OF AMBIGUITY 1. "Ambiguity in Mathematics"; 2. "The Contradictory in Mathematics"; 3. "Paradoxes and Mathematics: Infinity and the Real Numbers"; 4. "More Paradoxes of Infinity: Geometry, Cardinality and Beyond"; II. THE LIGHT AS IDEA 5. "The Idea as an Organizing Principle"; 6. "Ideas, Logic and Paradoxes"; 7. "Great Ideas"; III. THE LIGHT AND THE EYE OF THE BEHOLDER 8. "The Truth of Mathematics"; 9. "Conclusion: Is Mathematics Algorithmic or Creative?"; Notes, pp. 389-397; Bibliography, pp. 399-405; Index, pp. 407-415. Black cloth with brilliant gilt lettering on spine. Dustwrapper not price-clipped ($35.00), illustrated with green chalice-shape on most of front cover, with title lettering in black, edged in yellow, across middle front cover, above subtitle in smaller white letters, all superimposed upon chalice, on lower half front over; author name lettering in thin, smaller maroon letters across top front cover. (NO previous owner names; NO remainder marks.) Absolutely FLAWLESS artifact and dustwrapper. Gift-Giving Quality. Laid in news clipping (NO offsetting): 6 Letters to the Editor of the New York Times, 7 31 2012, prompted by Andrew Hacker's Sunday Review piece, "Is Algebra Necessary?". Nº de ref. del artículo: 002284

Más información sobre este vendedor | Contactar al vendedor

Comprar nuevo
EUR 25,72
Convertir moneda

Añadir al carrito

Gastos de envío: EUR 43,51
De Estados Unidos de America a España
Destinos, gastos y plazos de envío
Imagen de archivo

Byers, William
Publicado por Princeton University Press (2007)
ISBN 10: 0691127387 ISBN 13: 9780691127385
Nuevo Tapa dura Cantidad disponible: 1
Librería:
GF Books, Inc.
(Hawthorne, CA, Estados Unidos de America)

Descripción Condición: New. Book is in NEW condition. Nº de ref. del artículo: 0691127387-2-1

Más información sobre este vendedor | Contactar al vendedor

Comprar nuevo
EUR 59,80
Convertir moneda

Añadir al carrito

Gastos de envío: EUR 18,49
De Estados Unidos de America a España
Destinos, gastos y plazos de envío
Imagen de archivo

Byers, William
Publicado por Princeton University Press (2007)
ISBN 10: 0691127387 ISBN 13: 9780691127385
Nuevo Tapa dura Cantidad disponible: 1
Librería:
Book Deals
(Tucson, AZ, Estados Unidos de America)

Descripción Condición: New. New! This book is in the same immaculate condition as when it was published. Nº de ref. del artículo: 353-0691127387-new

Más información sobre este vendedor | Contactar al vendedor

Comprar nuevo
EUR 59,81
Convertir moneda

Añadir al carrito

Gastos de envío: EUR 19,42
De Estados Unidos de America a España
Destinos, gastos y plazos de envío
Imagen de archivo

Byers, William
Publicado por Princeton University Press (2007)
ISBN 10: 0691127387 ISBN 13: 9780691127385
Nuevo Tapa dura Cantidad disponible: 1
Librería:
Save With Sam
(North Miami, FL, Estados Unidos de America)

Descripción Hardcover. Condición: New. Brand New!. Nº de ref. del artículo: VIB0691127387

Más información sobre este vendedor | Contactar al vendedor

Comprar nuevo
EUR 63,14
Convertir moneda

Añadir al carrito

Gastos de envío: EUR 30,06
De Estados Unidos de America a España
Destinos, gastos y plazos de envío
Imagen de archivo

Byers, William
Publicado por Princeton University Press (2007)
ISBN 10: 0691127387 ISBN 13: 9780691127385
Nuevo Tapa dura Cantidad disponible: 1
Librería:
BennettBooksLtd
(LOS ANGELES, CA, Estados Unidos de America)

Descripción Condición: New. New. In shrink wrap. Looks like an interesting title! 1.47. Nº de ref. del artículo: Q-0691127387

Más información sobre este vendedor | Contactar al vendedor

Comprar nuevo
EUR 54,87
Convertir moneda

Añadir al carrito

Gastos de envío: EUR 40,69
De Estados Unidos de America a España
Destinos, gastos y plazos de envío
Imagen de archivo

Byers, William
Publicado por Princeton University Press (2007)
ISBN 10: 0691127387 ISBN 13: 9780691127385
Nuevo Tapa dura Cantidad disponible: 1
Librería:
The Book Spot
(Sioux Falls, SD, Estados Unidos de America)

Descripción Hardcover. Condición: New. Nº de ref. del artículo: Abebooks180731

Más información sobre este vendedor | Contactar al vendedor

Comprar nuevo
EUR 60,96
Convertir moneda

Añadir al carrito

Gastos de envío: EUR 41,62
De Estados Unidos de America a España
Destinos, gastos y plazos de envío

Existen otras copia(s) de este libro

Ver todos los resultados de su búsqueda