Proofs from THE BOOK
This revised and enlarged fifth edition features four new chapters, which contain highly original and delightful proofs for classics such as the spectral theorem from linear algebra, some more recent jewels like the non-existence of the Borromean rings and other surprises. From the Reviews "......
| Autor principal: | |
|---|---|
| Autor Corporativo: | |
| Otros Autores: | |
| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
2014.
|
| Edición: | 5th ed |
| Colección: | Springer eBooks.
|
| Acceso en línea: | Conectar con la versión electrónica |
| Ver en Universidad de Navarra: | https://innopac.unav.es/record=b32929699*spi |
Tabla de Contenidos:
- 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 s2/6
- 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. On a lemma of Littlewood and Offord
- 25. Cotangent and the Herglotz trick
- 26. Buffon’s needle problem
- Combinatorics: 27. Pigeon-hole and double counting
- 28. Tiling rectangles
- 29. Three famous theorems on finite sets
- 30. Shuffling cards
- 31. Lattice paths and determinants
- 32. Cayley’s formula for the number of trees
- 33. Identities versus bijections
- 34. The finite Kakeya problem
- 35. Completing Latin squares
- Graph Theory: 36. The Dinitz problem
- 37. Permanents and the po wer of entropy
- 38. Five-coloring plane graphs
- 39. How to guard a museum
- 40. Turán’s graph theorem
- 41. Communicating without errors
- 42. The chromatic number of Kneser graphs
- 43. Of friends and politicians
- 44. Probability makes counting (sometimes) easy
- About the Illustrations
- Index.
