LEADER 06297nam 22008535 450 001 9910299988603321 005 20201109120111.0 010 $a3-662-44205-1 024 7 $a10.1007/978-3-662-44205-0 035 $a(CKB)3710000000219533 035 $a(SSID)ssj0001338828 035 $a(PQKBManifestationID)11796894 035 $a(PQKBTitleCode)TC0001338828 035 $a(PQKBWorkID)11345403 035 $a(PQKB)10352099 035 $a(DE-He213)978-3-662-44205-0 035 $a(MiAaPQ)EBC6315828 035 $a(MiAaPQ)EBC1802928 035 $a(MiAaPQ)EBC5590820 035 $a(Au-PeEL)EBL1802928 035 $a(OCoLC)886904540 035 $a(Au-PeEL)EBL5590820 035 $a(PPN)180623079 035 $a(EXLCZ)993710000000219533 100 $a20140806d2014 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aProofs from THE BOOK /$fby Martin Aigner, Günter M. Ziegler 205 $a5th ed. 2014. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2014. 215 $a1 online resource (VIII, 308 p. 255 illus., 9 illus. in color.) 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-662-44204-3 327 $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 ?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. Pigeon-hole 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 po wer of entropy -- 38. Five-coloring 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. 330 $aThis revised and enlarged fifth edition features 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 non-existence 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 ma thematician, regardless of speciality, can benefit from reading this book. ... " SIGACT News, December 2011. 606 $aMathematics 606 $aNumber theory 606 $aGeometry 606 $aCombinatorics 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aComputer science 606 $aMathematics, general$3https://scigraph.springernature.com/ontologies/product-market-codes/M00009 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 606 $aGeometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21006 606 $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 606 $aComputer Science, general$3https://scigraph.springernature.com/ontologies/product-market-codes/I00001 615 0$aMathematics. 615 0$aNumber theory. 615 0$aGeometry. 615 0$aCombinatorics. 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 0$aComputer science. 615 14$aMathematics, general. 615 24$aNumber Theory. 615 24$aGeometry. 615 24$aCombinatorics. 615 24$aAnalysis. 615 24$aComputer Science, general. 676 $a510 700 $aAigner$b Martin$4aut$4http://id.loc.gov/vocabulary/relators/aut$0281930 702 $aZiegler$b Günter M$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299988603321 996 $aProofs from The Book$9924243 997 $aUNINA