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
Resource Information
The item Proofs from the book, Martin Aigner, Günter M. Ziegler ; illustrations by Karl H. Hofmann represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Proofs from the book, Martin Aigner, Günter M. Ziegler ; illustrations by Karl H. Hofmann represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 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 nonexistence 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
 Language
 eng
 Edition
 Fifth edition.
 Extent
 1 online resource (viii, 308 pages)
 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. Pigeonhole 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. Fivecoloring 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
 Isbn
 9783662442050
 Label
 Proofs from the book
 Title
 Proofs from the book
 Statement of responsibility
 Martin Aigner, Günter M. Ziegler ; illustrations by Karl H. Hofmann
 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 nonexistence 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
 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. Pigeonhole 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. Fivecoloring 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
 10.1007/9783662442050
 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
 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. Pigeonhole 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. Fivecoloring 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
 10.1007/9783662442050
 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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