國立虎尾科技大學 |

Proofs from THE BOOK

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Proofs from THE BOOK/ by Martin Aigner, Gunter M. Ziegler.
Author:	Aigner, Martin.
other author:	Ziegler, Gunter M.
Published:	Berlin, Heidelberg :Springer Berlin Heidelberg : : 2018.,
Description:	viii, 326 p. :digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Mathematics. -
Online resource:	http://dx.doi.org/10.1007/978-3-662-57265-8
ISBN:	9783662572658

Proofs from THE BOOK
Aigner, Martin.

Proofs from THE BOOK[electronic resource] /by Martin Aigner, Gunter M. Ziegler. - 6th ed. - Berlin, Heidelberg :Springer Berlin Heidelberg :2018. - viii, 326 p. :digital ;24 cm.

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 Polya 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. Turan'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.

ISBN: 9783662572658

Standard No.: 10.1007/978-3-662-57265-8doiSubjects--Topical Terms:

527692
Mathematics.

LC Class. No.: QA39.3 / .A346 2018

Dewey Class. No.: 510

Proofs from THE BOOK
LDR:02789nam a2200313 a 4500 001 927244
003 DE-He213
005 20190110103338.0
006 m d
007 cr nn 008maaau
008 190626s2018 gw s 0 eng d
020 $a 9783662572658 $q (electronic bk.)
020 $a 9783662572641 $q (paper)
024 7 $a 10.1007/978-3-662-57265-8 $2 doi
035 $a 978-3-662-57265-8
040 $a GP $c GP
041 0 $a eng
050 4 $a QA39.3 $b .A346 2018
072 7 $a PBH $2 bicssc
072 7 $a MAT022000 $2 bisacsh
082 0 4 $a 510 $2 23
090 $a QA39.3 $b .A289 2018
100 1 $a Aigner, Martin. $3 1077868
245 1 0 $a Proofs from THE BOOK $h [electronic resource] / $c by Martin Aigner, Gunter M. Ziegler.
250 $a 6th ed.
260 $a Berlin, Heidelberg : $c 2018. $b Springer Berlin Heidelberg : $b Imprint: Springer,
300 $a viii, 326 p. : $b digital ; $c 24 cm.
505 0 $a 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 Polya 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. Turan'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.
650 0 $a Mathematics. $3 527692
650 0 $a Computer science $x Mathematics. $3 528496
650 0 $a Mathematical analysis. $3 527926
650 0 $a Geometry. $3 579899
650 0 $a Number theory. $3 527883
650 0 $a Combinatorial analysis. $3 527896
650 0 $a Graph theory. $3 527884
650 2 4 $a Number Theory. $3 672023
650 2 4 $a Analysis. $3 669490
650 2 4 $a Combinatorics. $3 669353
650 2 4 $a Graph Theory. $3 786670
650 2 4 $a Mathematics of Computing. $3 669457
700 1 $a Ziegler, Gunter M. $3 1206409
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-662-57265-8
950 $a Mathematics and Statistics (Springer-11649)