Proofs from THE BOOK / by Martin Aigner, Günter M. Ziegler.

Format:

Book

Author/Creator:

Aigner, Martin., Author.

Ziegler, Günter M., Author.

Language:

English

Subjects (All):

Mathematics.

Number theory.

Geometry.

Combinatorial analysis.

Mathematical analysis.

Analysis (Mathematics).

Computer science.

Mathematics, general.

Number Theory.

Combinatorics.

Analysis.

Computer Science, general.

Local Subjects:

Mathematics, general.

Number Theory.

Geometry.

Combinatorics.

Analysis.

Computer Science, general.

Physical Description:

1 online resource (VIII, 308 p. 255 illus., 9 illus. in color.)

Edition:

5th ed. 2014.

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2014.

Language Note:

English

Summary:

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 "... Inside PFTB (Proofs from The Book) is indeed 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. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures, and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately, and the proofs are brilliant. ..." LMS Newsletter, January 1999 "Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant, and the remaining open questions so intriguing that every ma thematician, regardless of speciality, can benefit from reading this book. ... " SIGACT News, December 2011.

Contents:

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. 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.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Description based on publisher supplied metadata and other sources.

ISBN:

3-662-44205-1

OCLC:

886904540