عنوان

Proofs from THE BOOK /

شابک

3662572648

شابک

3662572656

شابک

9783662572641

شابک

9783662572658

شماره

b624291

عنوان اصلي

Proofs from THE BOOK /

نام عام مواد

[Book]

نام نخستين پديدآور

by Martin Aigner, Günter M. Ziegler ; including illustrations by Karl H. Hofmann.

وضعيت ويراست

Sixth edition.

نام خاص و کميت اثر

1 online resource (viii, 326 pages) :

ساير جزييات

illustrations

متن يادداشت

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.

بدون عنوان

0

متن يادداشت

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.

عنوان

Proofs from the book.

شماره استاندارد بين المللي کتاب و موسيقي

3662572648

موضوع مستند نشده

Combinatorial analysis.

موضوع مستند نشده

Computer science-- Mathematics.

موضوع مستند نشده

Geometry.

موضوع مستند نشده

Graph theory.

موضوع مستند نشده

Mathematical analysis.

موضوع مستند نشده

Mathematics.

موضوع مستند نشده

Number theory.

موضوع مستند نشده

Analysis.

موضوع مستند نشده

Combinatorics.

موضوع مستند نشده

Geometry.

موضوع مستند نشده

Graph Theory.

موضوع مستند نشده

Mathematics of Computing.

موضوع مستند نشده

Mathematics.

موضوع مستند نشده

Number Theory.

موضوع مستند نشده

Combinatorial analysis.

موضوع مستند نشده

Computer science-- Mathematics.

موضوع مستند نشده

Geometry.

موضوع مستند نشده

Graph theory.

موضوع مستند نشده

Mathematical analysis.

موضوع مستند نشده

Mathematics.

موضوع مستند نشده

Number theory.

موضوع مستند نشده

MAT022000

موضوع مستند نشده

PBH

شماره

ويراست

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Aigner, Martin,1942-

مستند نام اشخاص تاييد نشده

Ziegler, Günter M.

تاريخ عمليات

20200617083442.0

قواعد فهرست نويسي ( بخش توصيفي )

pn

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y