The Resource Proofs from THE BOOK, by Martin Aigner, Günter M. Ziegler, (electronic resource)

Proofs from THE BOOK, by Martin Aigner, Günter M. Ziegler, (electronic resource)

Label
Proofs from THE BOOK
Title
Proofs from THE BOOK
Statement of responsibility
by Martin Aigner, Günter M. Ziegler
Creator
Contributor
Author
Author
Subject
Language
eng
Summary
This revised and enlarged sixth edition of Proofs from THE BOOK features an entirely new chapter on Van der Waerden’s permanent conjecture, as well as additional, highly original and delightful proofs in other chapters. From the citation on the occasion of the 2018 "Steele Prize for Mathematical Exposition" “... It is almost impossible to write a mathematics book that can be read and enjoyed by people of all levels and backgrounds, yet Aigner and Ziegler accomplish this feat of exposition with virtuoso style. [...] This book does an invaluable service to mathematics, by illustrating for non-mathematicians what it is that mathematicians mean when they speak about beauty.” 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
http://library.link/vocab/creatorName
Aigner, Martin
Dewey number
512.7
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • XSuTo4yXZwA
  • bdTfrOeUgOs
Image bit depth
0
LC call number
QA241-247.5
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
Ziegler, Günter M.
http://library.link/vocab/subjectName
  • Number theory
  • Geometry
  • Global analysis (Mathematics)
  • Combinatorics
  • Computer science
  • Number Theory
  • Geometry
  • Analysis
  • Combinatorics
  • Graph Theory
  • Mathematics of Computing
Label
Proofs from THE BOOK, by Martin Aigner, Günter M. Ziegler, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
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 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. 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. Turán’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
Dimensions
unknown
Edition
6th ed. 2018.
Extent
1 online resource (VIII, 326 p.)
File format
multiple file formats
Form of item
online
Isbn
9783662572658
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-662-57265-8
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3810000000358851
  • (DE-He213)978-3-662-57265-8
  • (EXLCZ)993810000000358851
Label
Proofs from THE BOOK, by Martin Aigner, Günter M. Ziegler, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
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 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. 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. Turán’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
Dimensions
unknown
Edition
6th ed. 2018.
Extent
1 online resource (VIII, 326 p.)
File format
multiple file formats
Form of item
online
Isbn
9783662572658
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-662-57265-8
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3810000000358851
  • (DE-He213)978-3-662-57265-8
  • (EXLCZ)993810000000358851

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