Proofs from THE BOOK,9783540404606

Proofs from THE BOOK

by ;
Edition: 3rd
ISBN13: 9783540404606
ISBN10: 3540404600
Format: Hardcover
Pub. Date: 2003-12-01
Publisher(s): Springer Verlag
List Price: $53.45

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Summary

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. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...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 "... the style is clear and entertaining, the level is close to elementary ... and the proofs are brilliant. ..." LMS Newsletter, January 1999 This third edition offers two new chapters, on partition identities, and on card shuffling. Three proofs of Euler's most famous infinite series appear in a separate chapter. There is also a number of other improvements, such as an exciting new way to "enumerate the rationals".

Table of Contents

Number Theory 1(42)
1. Six proofs of the infinity of primes
3(4)
2. Bertrand's postulate
7(6)
3. Binomial coefficients are (almost) never powers
13(4)
4. Representing numbers as sums of two squares
17(6)
5. Every finite division ring is a field
23(4)
6. Some irrational numbers
27(8)
7. Three times π2/6
35(8)
Geometry 43(48)
8. Hilbert's third problem: decomposing polyhedra
45(8)
9. Lines in the plane and decompositions of graphs
53(6)
10. The slope problem
59(6)
11. Three applications of Euler's formula
65(6)
12. Cauchy's rigidity theorem
71(4)
13. Touching simplices
75(4)
14. Every large point set has an obtuse angle
79(6)
15. Borsuk's conjecture
85(6)
Analysis 91(46)
16. Sets, functions, and the continuum hypothesis
93(16)
17. In praise of inequalities
109(8)
18. A theorem of Pólya on polynomials
117(6)
19. On a lemma of Littlewood and Offord
123(4)
20. Cotangent and the Herglotz trick
127(6)
21. Buffon's needle problem
133(4)
Combinatorics 137(60)
22. Pigeon-hole and double counting
139(12)
29. Three famous theorems on finite set
151(6)
24. Shuffling cards
157(10)
25. Lattice path and determinants
167(6)
26. Cayley's formula for the number of trees
173(6)
27. Completing Latin squares
179(6)
28. The Dinitz problem
185(6)
29. Identities versus bijections
191(6)
Graph Theory 197(39)
30. Five-coloring plane graphs
199(4)
31. How to guard a museum
203(4)
32. Turán's graph theory
207(6)
33. Communicating without errors
213(10)
34. Of friends and politicians
223(4)
35. Probability makes counting (sometimes) easy
227(9)
About the Illustrations 236(1)
Index 237

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