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E-raamat: Honors Class: Hilbert's Problems and Their Solvers [Taylor & Francis e-raamat]

  • Formaat: 506 pages
  • Ilmumisaeg: 12-Dec-2001
  • Kirjastus: A K Peters
  • ISBN-13: 9780429064296
  • Taylor & Francis e-raamat
  • Hind: 166,18 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
  • Tavahind: 237,40 €
  • Säästad 30%
  • Formaat: 506 pages
  • Ilmumisaeg: 12-Dec-2001
  • Kirjastus: A K Peters
  • ISBN-13: 9780429064296
At the Second International Congress of Mathematicians in 1900, David Hilbert delivered a talk in which he outlined a set of mathematical problems that would define the future of mathematical research in the years to follow. Fellow mathematician Hermann Weyl wrote that by solving one of Hilbert's problems, a mathematician "passed on to the honors class of the mathematical community." Dividing his time between biographical narrative and the mathematics in question, the author explores the progress of the problems, looking at who worked on them, who solved them, how they were solved, and which have not been solved. He argues that the people and ideas involved in the solutions to Hilbert's problems provide an overview of the mathematical culture of the first half of the 20th century. Annotation c. Book News, Inc., Portland, OR (booknews.com)

This eminently readable book focuses on the people of mathematics and draws the reader into their fascinating world. In a monumental address, given to the International Congress of Mathematicians in Paris in 1900, David Hilbert, perhaps the most respected mathematician of his time, developed a blueprint for mathematical research in the new century. Jokingly called a natural introduction to thesis writing with examples, this collection of problems has indeed become a guiding inspiration to many mathematicians, and those who succeeded in solving or advancing their solutions form an Honors Class among research mathematicians of this century. In a remarkable labor of love and with the support of many of the major players in the field, Ben Yandell has written a fascinating account of the achievements of this Honors Class, covering mathematical substance and biographical aspects.
Acknowledgments ix
Introduction: The Origin of the Coordinates
1(22)
Introduction
3(2)
Advice: How to Read This Book
5(2)
The Origin of the Coordinates
7(16)
The Foundation Problems
23(92)
Set Theory, Anyone?
25(12)
I Am Lying (Mathematics Is Consistent)
37(22)
The Perfect Spy: How Many Real Numbers Are There?
59(26)
Can't We Do This with a Computer?
85(30)
The Foundations of Specific Areas
115(48)
In the Original
117(20)
Distance
137(6)
Something for Nothing
143(16)
On Again, Off Again: Physics and Math
159(4)
Number Theory
163(96)
First, State the Tune
165(6)
Transcending Local Conditions
171(32)
The Inordinate Allure of the Prime Numbers
203(10)
Castles of Air
213(46)
Algebra and Geometry: A Miscellany
259(34)
What Is Algebra?
261(8)
Schubert's Variety Show
269(6)
Graph That Curve
275(4)
How Many Kinds of Crystals Are There, and Does the Grocer Know How to Stack Oranges?
279(14)
The Analysis Problems
293(90)
Analysis Takes at Least Seven Years
295(2)
How Famous Can a Function Theorist Be?
297(34)
Schools Amid Turbulence
331(34)
Past Chernaya Rechka, to 61 Savushkina Street
365(8)
Work on It
373(10)
We Come to Our Census
383(4)
Census
385(2)
Appendix 387(2)
Mathematical Problems 389(36)
Notes 425(28)
Selected Bibliography 453(20)
Index 473