rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Proofs from THE BOOK
  name:
    name part: Aigner, Martin.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Ziegler, Günter M.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2014
    edition: 5th ed. 2014.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: VIII, 308 p. 255 illus., 9 illus. in color. online resource.
  abstract: 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.
  table of 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.
  note: by Martin Aigner, Günter M. Ziegler.
  subject:
    topic: Mathematics
  subject:
    topic: Computer science
  subject:
    topic: Mathematical analysis
  subject:
    topic: Analysis (Mathematics)
  subject:
    topic: Geometry
  subject:
    topic: Number theory
  subject:
    topic: Combinatorics
  subject:
    topic: Mathematics
  subject:
    topic: Mathematics, general
  subject:
    topic: Number Theory
  subject:
    topic: Geometry
  subject:
    topic: Combinatorics
  subject:
    topic: Analysis
  subject:
    topic: Computer Science, general
  classification: QA1-939
  classification: 510
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783662442050
  identifier: http://dx.doi.org/10.1007/978-3-662-44205-0
  record info:
    record creation date: 140806
    record change date: 20151123194347.0
    record identifier: 978-3-662-44205-0