Coverart for item
The Resource Proofs from the book, Martin Aigner, Günter M. Ziegler ; illustrations by Karl H. Hofmann

Proofs from the book, Martin Aigner, Günter M. Ziegler ; illustrations by Karl H. Hofmann

Label
Proofs from the book
Title
Proofs from the book
Statement of responsibility
Martin Aigner, Günter M. Ziegler ; illustrations by Karl H. Hofmann
Creator
Contributor
Author
Illustrator
Subject
Language
eng
Summary
This revised and enlarged fifth editionfeatures 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 mathematician, regardless of speciality, can benefit from reading this book. ..." SIGACT News, December 2011
Cataloging source
GW5XE
http://library.link/vocab/creatorDate
1942-
http://library.link/vocab/creatorName
Aigner, Martin
Dewey number
510
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA39.2
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
  • Ziegler, Günter M.
  • Hofmann, Karl Heinrich
http://library.link/vocab/subjectName
  • Mathematics
  • Mathematics
  • Physical Sciences & Mathematics
  • Mathematical Theory
  • Mathematics
  • Mathematics, general
  • Number Theory
  • Geometry
  • Combinatorics
  • Analysis
  • Computer Science, general
  • Mathématiques
  • Mathematics
Label
Proofs from the book, Martin Aigner, Günter M. Ziegler ; illustrations by Karl H. Hofmann
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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 [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 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 power 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
Control code
886904540
Dimensions
unknown
Edition
Fifth edition.
Extent
1 online resource (viii, 308 pages)
File format
unknown
Form of item
online
Isbn
9783662442050
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-662-44205-0
Other physical details
illustrations (some color)
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)886904540
Label
Proofs from the book, Martin Aigner, Günter M. Ziegler ; illustrations by Karl H. Hofmann
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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 [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 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 power 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
Control code
886904540
Dimensions
unknown
Edition
Fifth edition.
Extent
1 online resource (viii, 308 pages)
File format
unknown
Form of item
online
Isbn
9783662442050
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-662-44205-0
Other physical details
illustrations (some color)
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)886904540

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      38.944491 -92.326012
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