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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
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
Martin Aigner received his Ph.D. in Mathematics in 1965 from the University of Vienna. He then spent five years in the United States, the last two at the University of North Carolina at Chapel Hill where he was introduced to the combinatorial world (which he has never left since) by G. C. Rota and the late R. C. Bose. After extensive travels he returned to Europe and spent three years at the University of Tübingen with a senior fellowship of the German Science Foundation. Since 1974 he has been a Professor of Mathematics at the Free University of Berlin.
Martin Aigner has published in various fields of combinatorics and graph theory and is the author of several monographs on discrete mathematics, graph theory and the theory of search.
Revised and enlarged sixth edition
New chapter on Van der Waerden's permanent conjecture
New sections on the asymptotics for the number of Latin squares
New proof for the Basel problem
Geometric explanation for the involution proof for Fermat's two squares theorem
Presents some recent jewels and surprises
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 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. 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.
| Erscheinungsjahr: | 2018 |
|---|---|
| Fachbereich: | Populäre Darstellungen |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Inhalt: |
VIII
326 S. |
| ISBN-13: | 9783662572641 |
| ISBN-10: | 3662572648 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-662-57264-1 |
| Einband: | Gebunden |
| Autor: |
Aigner, Martin
Ziegler, Günter M. |
| Illustrator: | Hofmann, Karl H. |
| Auflage: | 6th ed. 2018 |
| Hersteller: | Springer |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Abbildungen: | 278 schwarz-weiße und 6 farbige Abbildungen, Bibliographie |
| Maße: | 248 x 198 x 23 mm |
| Von/Mit: | Martin Aigner (u. a.) |
| Erscheinungsdatum: | 06.07.2018 |
| Gewicht: | 0,936 kg |
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