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.
The style is clear and entertaining and the proofs are brilliant and memorable. … Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems … that would undoubtedly be in the Book of Erdős. … The approach is refreshingly straightforward, all the necessary results from analysis being summarised in boxes, and a short appendix discusses the importance of the zeta-function in number theory. Indeed I have recommended the book to talented undergraduates and to mathematically literate friends. … Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems … that would undoubtedly be in the Book of Erdős. (Gerry Leversha, The Mathematical Gazette, March, 2005)Every finite division ring is a fieldThree famous theorems on finite sets“This book is the fourth edition of Aigner and Ziegler’s attempt to find proofs that Erdos would find appealing. there is enough new material that libraries certainly should do so.
The style is clear and entertaining and the proofs are brilliant and memorable. The theorems are so fundamental … that every mathematician, regardless of speciality, can benefit from reading this book.” (Miklós Bóna, SIGACT News, Vol. During a lecture in 1985, Erdős said, "You don't have to believe in God, but you should believe in The Book." Each chapter is largely independent; some include necessary background as an appendix. Each chapter is largely independent; some include necessary background as an appendix. … I love the fact that the chapters are relatively short and self-contained. He said that there was a book somewhere, possibly in heaven, and that book contained the nicest and most elucidating proof of every theorem in mathematics. … The key to the approachability of Proofs lies not so much in the accessibility of its mathematics, however, as in the rewards it offers: elegant proofs of interesting results, which don’t leave the reader feeling cheated or disappointed."
...The fundamental theorem of algebraA theorem of Pólya on polynomialsOne square and an odd number of trianglesPigeon-hole and double countingProbability makes counting (sometimes) easy“Paul Erdős … had his own way of judging the beauty of various proofs. This revised and enlarged fourth edition of "Proofs from THE BOOK" features five new chapters, which treat classical results such as the "Fundamental Theorem of Algebra", problems about tilings, but also quite recent proofs, for example of the Kneser conjecture in graph theory. 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. 9783662442043 9783662442043 Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required.This revised and enlarged fourth edition of "Proofs from THE BOOK" features five new chapters, which treat classical results such as the "Fundamental Theorem of Algebra", problems about tilings, but also quite recent proofs, for example of the Kneser conjecture in graph theory. 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.
Its thirty chapters, divided into sections on Number Theory, Geometry, Analysis … . … this edition also contains additional material interpolated in the original text, notably the Calkin-Wilf enumeration of the rationals." The book has five parts of roughly equal length.” (Miklόs Bόna, The Book Review Column, 2011) He said that there was a book somewhere, possibly in heaven, and that book contained the nicest and most elucidating proof of every theorem in mathematics. 42. The book has five parts of roughly equal length.” (Miklόs Bόna, The Book Review Column, 2011) “Paul Erdős … had his own way of judging the beauty of various proofs.
Moreover, the exposition makes them transparent. For individuals who do not yet have their own copies, the argument for purchase has just grown stronger.” (Robert Dawson, Zentralblatt MATH, February, 2010)Representing numbers as sums of two squares*immediately available upon purchase as print book shipments may be delayed due to the COVID-19 crisis. there is enough new material that libraries certainly should do so.
Moreover, the exposition makes them transparent. All report that they are captivated by the material and the new view of mathematics it engenders. 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. Moreover, the exposition makes them transparent. ebook access is temporary and does not include ownership of the ebook. From the Reviews...Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, wh This 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. (Zentralblatt für Didaktik de Mathematik, July, 2004){{resources.quantity}}: {{quantity}}This revised and enlarged fourth edition of "Proofs from THE BOOK" features five new chapters, which treat classical results such as the "Fundamental Theorem of Algebra", problems about tilings, but also quite recent proofs, for example of the Kneser conjecture in graph theory.