According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
Rezensionen / Stimmen
"...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." - Notices of the AMS
Auflage
1st ed. 1998. Corr. 2nd printing
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Illustrationen
7 colour figures, references, index
Maße
Höhe: 24.2 cm
Breite: 19.3 cm
Gewicht
ISBN-13
978-3-540-63698-4 (9783540636984)
DOI
10.1007/978-3-662-22343-7
Schweitzer Klassifikation
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.
