Author	Aigner, Martin. author
Title	Proofs from THE BOOK [electronic resource] / by Martin Aigner, Gรผnter M. Ziegler
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004
Edition	Third Edition
Connect to	http://dx.doi.org/10.1007/978-3-662-05412-3
Descript	VIII, 239 p. online resource

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 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures, and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately, and the proofs are brilliant. Moreover, the exposition makes them transparent. ..." 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 an exciting new way to "enumerate the rationals."

Number Theory -- 1. Six proofs of the infinity of primes -- 2. Bertrandโs postulate -- 3. Binomial coefficients are (almost) never powers -- 4. Representing numbers as sums of two squares -- 5. Every finite division ring is a field -- 6. Some irrational numbers -- 7. Three times ?2/6 -- Geometry -- 8. Hilbertโs third problem: decomposing polyhedra -- 9. Lines in the plane and decompositions of graphs -- 10. The slope problem -- 11. Three applications of Eulerโs formula -- 12. Cauchyโs rigidity theorem -- 13. Touching simplices -- 14. Every large point set has an obtuse angle -- 15. Borsukโs conjecture -- Analysis -- 16. Sets, functions, and the continuum hypothesis -- 17. In praise of inequalities -- 18. A theorem of Pรณlya on polynomials -- 19. On a lemma of Littlewood and Offord -- 20. Cotangent and the Herglotz trick -- 21. Buffonโs needle problem -- Combinatorics -- 22. Pigeon-hole and double counting -- 23. Three famous theorems on finite sets -- 24. Shuffling cards -- 25. Lattice paths and determinants -- 26. Cayleyโs formula for the number of trees -- 27. Completing Latin squares -- 28. The Dinitz problem -- 29. Identities versus bijections -- Graph Theory -- 30. Five-coloring plane graphs -- 31. How to guard a museum -- 32. Turรกnโs graph theorem -- 33. Communicating without errors -- 34. Of friends and politicians -- 35. Probability makes counting (sometimes) easy -- About the Illustrations

1. Mathematics
2. Computer science
3. Mathematical analysis
4. Analysis (Mathematics)
5. Geometry
6. Number theory
7. Combinatorics
8. Mathematics
9. Mathematics
10. general
11. Number Theory
12. Geometry
13. Combinatorics
14. Analysis
15. Computer Science
16. general