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Aigner, Martinauthor

6th ed. 2018.

1 online resource (VIII, 326 pages)

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 [pi]2/6 -- 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 P�olya 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. Tur�an'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.

Ziegler, G�unter M