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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Aigner, Martin. Proofs from the book. [S.l.] : Springer, 2014 (OCoLC)884616897 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Martin Aigner; Günter M Ziegler; Karl Heinrich Hofmann |

ISBN: | 9783662442050 3662442051 3662442043 9783662442043 |

OCLC Number: | 886904540 |

Description: | 1 online resource (viii, 308 pages) : illustrations (some color) |

Contents: | Number Theory: 1. Six proofs of the infinity of primes -- 2. Bertrand's postulate -- 3. Binomial coefficients are (almost) never powers -- 4. Representing numbers as sums of two squares -- 5. The law of quadratic reciprocity -- 6. Every finite division ring is a field -- 7. The spectral theorem and Hadamard's determinant problem -- 8. Some irrational numbers -- 9. Three times [pi]2/6 -- Geometry: 10. Hilbert's third problem: decomposing polyhedral -- 11. Lines in the plane and decompositions of graphs -- 12. The slope problem -- 13. Three applications of Euler's formula -- 14. Cauchy's rigidity theorem -- 15. The Borromean rings don't exist -- 16. Touching simplices -- 17. Every large point set has an obtuse angle -- 18. Borsuk's conjecture -- Analysis: 19. Sets, functions, and the continuum hypothesis -- 20. In praise of inequalities -- 21. The fundamental theorem of algebra -- 22. One square and an odd number of triangles -- 23. A theorem of Pólya on polynomials -- 24. On a lemma of Littlewood and Offord -- 25. Cotangent and the Herglotz trick -- 26. Buffon's needle problem -- Combinatorics: 27. Pigeon-hole and double counting -- 28. Tiling rectangles -- 29. Three famous theorems on finite sets -- 30. Shuffling cards -- 31. Lattice paths and determinants -- 32. Cayley's formula for the number of trees -- 33. Identities versus bijections -- 34. The finite Kakeya problem -- 35. Completing Latin squares -- Graph Theory: 36. The Dinitz problem -- 37. Permanents and the power of entropy -- 38. Five-coloring plane graphs -- 39. How to guard a museum -- 40. Turán's graph theorem -- 41. Communicating without errors -- 42. The chromatic number of Kneser graphs -- 43. Of friends and politicians -- 44. Probability makes counting (sometimes) easy -- About the Illustrations -- Index. |

Responsibility: | Martin Aigner, Günter M. Ziegler ; illustrations by Karl H. Hofmann. |

### Abstract:

## Reviews

*Editorial reviews*

Publisher Synopsis

"This book by Aigner and Ziegler, now in its fifth edition, seeks to pay homage to the late Paul Erdos by attempting to provide an approximation of `The Book.' ... Throughout, illustrations and figures are used to support the arguments in the main text; these can greatly help the readability of the proofs, especially for novices like me. ... the book is a marvelous project and this new edition provides a good amount of fresh material." (Harry Strange, Computing Reviews, March, 2015) Read more...

*User-contributed reviews*