000 06094nam a22005775i 4500
001 978-3-662-57265-8
003 DE-He213
005 20200712170937.0
007 cr nn 008mamaa
008 180614s2018 gw | s |||| 0|eng d
020 _a9783662572658
_9978-3-662-57265-8
024 7 _a10.1007/978-3-662-57265-8
_2doi
050 4 _aQA241-247.5
072 7 _aPBH
_2bicssc
072 7 _aMAT022000
_2bisacsh
072 7 _aPBH
_2thema
082 0 4 _a512.7
_223
100 1 _aAigner, Martin.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aProofs from THE BOOK
_h[electronic resource] /
_cby Martin Aigner, Günter M. Ziegler.
250 _a6th ed. 2018.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2018.
300 _aVIII, 326 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aNumber 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.
520 _aThis 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.
650 0 _aNumber theory.
650 0 _aGeometry.
650 0 _aMathematical analysis.
650 0 _aAnalysis (Mathematics).
650 0 _aCombinatorics.
650 0 _aGraph theory.
650 0 _aComputer science—Mathematics.
650 1 4 _aNumber Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M25001
650 2 4 _aGeometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21006
650 2 4 _aAnalysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12007
650 2 4 _aCombinatorics.
_0http://scigraph.springernature.com/things/product-market-codes/M29010
650 2 4 _aGraph Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M29020
650 2 4 _aMathematics of Computing.
_0http://scigraph.springernature.com/things/product-market-codes/I17001
700 1 _aZiegler, Günter M.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662572641
776 0 8 _iPrinted edition:
_z9783662572665
856 4 0 _uhttps://doi.org/10.1007/978-3-662-57265-8
912 _aZDB-2-SMA
999 _c17923
_d17923
942 _cebook