Proofs from THE BOOK

• Κύριοι συγγραφείς: Aigner, Martin (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut), Ziegler, Günter M. (http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2018.
• Έκδοση: 6th ed. 2018.
• Θέματα: Number theory.; Geometry.; Mathematical analysis.; Analysis (Mathematics).; Combinatorics.; Graph theory.; Computer science-Mathematics.; Number Theory.; Analysis.; Graph Theory.; Mathematics of Computing.

This revised and enlarged sixth edition of Proofs from THE BOOK features an entirely new chapter on Van der Waerden's permanent conjecture, as well as additional, highly original and delightful proofs in other chapters. From the citation on the occasion of the 2018 "Steele Prize for Mathem...

Πίνακας περιεχομένων:

• 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 π2/6
• 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. Van der Waerden's permanent conjecture
• 25. On a lemma of Littlewood and Offord
• 26. Cotangent and the Herglotz trick
• 27. Buffon's needle problem
• Combinatorics: 28. Pigeon-hole and double counting
• 29. Tiling rectangles
• 30. Three famous theorems on finite sets
• 31. Shuffling cards
• 32. Lattice paths and determinants
• 33. Cayley's formula for the number of trees
• 34. Identities versus bijections
• 35. The finite Kakeya problem
• 36. Completing Latin squares
• Graph Theory: 37. Permanents and the power of entropy
• 38. The Dinitz problem
• 39. Five-coloring plane graphs
• 40. How to guard a museum
• 41. Turán's graph theorem
• 42. Communicating without errors
• 43. The chromatic number of Kneser graphs
• 44. Of friends and politicians
• 45. Probability makes counting (sometimes) easy
• About the Illustrations
• Index.