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 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. ...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.
All report that they are captivated by the material and the new view of mathematics it engenders. (3), September, 2011)To get the free app, enter your mobile phone number.“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 Erdős.
Indeed I have recommended the book to talented undergraduates and to mathematically literate friends. Thirty beautiful examples are presented here.
… 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 style is inviting and it is very hard to stop part way through a chapter.
The mathematical heroes of this book are "perfect proofs": brilliant ideas, clever connections and wonderful observations that bring new insight and surprising perspectives on basic and challenging problems from Number Theory, Geometry, Analysis, Combinatorics, and Graph Theory. … The book has five parts of roughly equal length.” (Miklόs Bόna, The Book Review Column, 2011) ...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. Proofs from THE BOOK (Summer 2020, Session II) is about extremely elegant proofs from many areas of mathematics.
… The authors have tried, in homage to Erdős, to approximate this tome; successive editions appear to be achieving uniform convergence.
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.
Thirty beautiful examples are presented here. Proofs from THE BOOK By admin123 | September 26, 2019. 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.
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Proofs from the Book