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, 2001 |

Edition | Second Edition |

Connect to | http://dx.doi.org/10.1007/978-3-662-04315-8 |

Descript | VIII, 215 p. 198 illus., 6 illus. in color. online resource |

SUMMARY

The (mathematical) heroes of this book are "perfect proofs": brilliant ideas, clever connections and wonderful observations that bring new insight and surprising perspectives on basic and challenging problems from Number Theory, Geometry, Analysis, Combinatorics, and Graph Theory. Thirty beautiful examples are presented here. They are candidates for The Book in which God records the perfect proofs - according to the late Paul Erdรถs, who himself suggested many of the topics in this collection. The result is a book which will be fun for everybody with an interest in mathematics, requiring only a very modest (undergraduate) mathematical background. For this revised and expanded second edition several chapters have been revised and expanded, and three new chapters have been added

CONTENT

Number Theory -- 1. Six proofs of the infinity of primes -- 2. Bertrandโ{128}{153}s 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 -- Geometry -- 7. Hilbertโ{128}{153}s third problem: decomposing polyhedra -- 8. Lines in the plane and decompositions of graphs -- 9. The slope problem -- 10. Three applications of Eulerโ{128}{153}s formula -- 11. Cauchyโ{128}{153}s rigidity theorem -- 12. Touching simplices -- 13. Every large point set has an obtuse angle -- 14. Borsukโ{128}{153}s conjecture -- Analysis -- 15. Sets, functions, and the continuum hypothesis -- 16. In praise of inequalities -- 17. A theorem of Pรณlya on polynomials -- 18. On a lemma of Littlewood and Offord -- 19. Cotangent and the Herglotz trick -- 20. Buffonโ{128}{153}s needle problem -- Combinatorics -- 21. Pigeon-hole and double counting -- 22. Three famous theorems on finite sets -- 23. Lattice paths and determinants -- 24. Cayleyโ{128}{153}s formula for the number of trees -- 25. Completing Latin squares -- 26. The Dinitz problem -- Graph Theory -- 27. Five-coloring plane graphs -- 28. How to guard a museum -- 29. Turรกnโ{128}{153}s graph theorem -- 30. Communicating without errors -- 31. Of friends and politicians -- 32. Probability makes counting (sometimes) easy -- About the Illustrations

Mathematics
Computer science
Mathematical analysis
Analysis (Mathematics)
Geometry
Number theory
Combinatorics
Mathematics
Number Theory
Geometry
Analysis
Combinatorics
Computer Science general