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＜電子ブック＞
Proofs from THE BOOK / by Martin Aigner, Günter M. Ziegler

版	1st ed. 1998.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1998
本文言語	英語
大きさ	VIII, 199 p : online resource
著者標目	*Aigner, Martin author Ziegler, Günter M author SpringerLink (Online service)
件　名	LCSH:Number theory LCSH:Geometry LCSH:Mathematical analysis LCSH:Discrete mathematics FREE:Number Theory FREE:Geometry FREE:Analysis FREE:Discrete Mathematics
一般注記	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. Every finite division ring is a field -- 6. Some irrational numbers -- Geometry -- 7. Hilbert’s third problem: decomposing polyhedra -- 8. Lines in the plane and decompositions of graphs -- 9. The slope problem -- 10. Three applications of Euler’s formula -- 11. Cauchy’s rigidity theorem -- 12. The problem of the thirteen spheres -- 13. Touching simplices -- 14. Every large point set has an obtuse angle -- 15. Borsuk’s conjecture -- Analysis -- 16. Sets, functions, and the continuum hypothesis -- 17. In praise of inequalities -- 18. A theorem of Pólya on polynomials -- 19. On a lemma of Littlewood and Offord -- Combinatorics -- 20. Pigeon-hole and double counting -- 21. Three famous theorems on finite sets -- 22. Cayley’s formula for the number of trees -- 23. Completing Latin squares -- 23. The Dinitz problem -- Graph Theory -- 25. Five-coloring plane graphs -- 26. How to guard a museum -- 27. Turán’s graph theorem -- 28. Communicating without errors -- 29. Of friends and politicians -- 30. Probability makes counting (sometimes) easy -- About the Illustrations 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 Erdös, 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 HTTP:URL=https://doi.org/10.1007/978-3-662-22343-7

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