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© LIBERO v6.4.1sp220816
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Catalogue Information
Field name
Details
Dewey Class
512.7
Title
Proofs from THE BOOK ([EBook]) / by Martin Aigner, Günter M. Ziegler
Author
Aigner, Martin , 1942-
Added Personal Name
Ziegler, Günter M. , 1963-
Other name(s)
SpringerLink (Online service)
Edition statement
Second Edition
Publication
Berlin, Heidelberg : Springer , 2001
Physical Details
VIII, 215 pages: 198 illus., 6 illus. in color. : online resource.
ISBN
9783662043158
Summary Note
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. For this revised and expanded second edition several chapters have been revised and expanded, and three new chapters have been added.:
Contents note
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. Touching simplices -- 13. Every large point set has an obtuse angle -- 14. Borsuk’s conjecture -- Analysis -- 15. Sets, functions, and the continuum hypothesis -- 16. In praise of inequalities -- 17. A theorem of Pólya on polynomials -- 18. On a lemma of Littlewood and Offord -- 19. Cotangent and the Herglotz trick -- 20. Buffon’s needle problem -- Combinatorics -- 21. Pigeon-hole and double counting -- 22. Three famous theorems on finite sets -- 23. Lattice paths and determinants -- 24. Cayley’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. Turán’s graph theorem -- 30. Communicating without errors -- 31. Of friends and politicians -- 32. Probability makes counting (sometimes) easy -- About the Illustrations.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-3-662-04315-8
Links to Related Works
Subject References:
Analysis (Mathematics)
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Combinatorics
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Computer Science
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Geometry
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Mathematical analysis
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Mathematics
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Number Theory
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Authors:
Aigner, Martin 1942-
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author
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Ziegler, Günter M. 1963-
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Corporate Authors:
SpringerLink (Online service)
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Classification:
512.7
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