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Title: Proofs from the Book by Martin Aigner, Gunter M. Ziegler ISBN: 3-540-40460-0 Publisher: Springer Verlag Pub. Date: December, 2003 Format: Hardcover Volumes: 1 List Price(USD): $34.95 |
Average Customer Rating: 4.75 (4 reviews)
Rating: 5
Summary: A fitting tribute to the great Paul Erdos
Comment: Paul Erdos once remarked that you need not believe in God, but you certainly have to believe in the book in which God maintains the "perfect" mathematical proofs. Martin Aigner and Gunter Ziegler have certainly done a great job with this book, a fitting tribute to the great Erdos himself.
I had purchased a copy of the 1st edition of this book and was plesantly surprised that the authors had come up with a 2nd edition, with a few more "perfect" proofs.
My personal favorites are "The Shannon capacity of a graph". where the Lovasz theta number would eventually lead to semidefinite programming, Erdos' probabilistic method where probability makes counting sometimes easy, computing the number of trees in a graph, how many guards it takes to guard a museum, and the section on Turan's theorem.
This book deserves to be on the bookshelves of both amateur and professional mathematicians.
Rating: 5
Summary: Proofs from THE book!!!!!!!
Comment: An excellent book which looks at all branches of mathematics - graph theory, combinatorics, even logic. Contains some of the most spectacular proofs to math's most interesting conjectures. I highly recommend this book for any student interested in pursuing mathematics beyond high school. -I am sorry for my broken english, I speak French.
Rating: 4
Summary: original
Comment: This book was conceived as a tribute to Paul Erdos for his 85th birthday. It is clearly inspired by his aestetics and research interests. The proofs are from number theory, combinatorial geometry, inequalities, combinatorics and graph theory. The statements are very often easy to understand; for example "there always exists a prime number between n and 2n", "every set of more than 2^d points in R^d determines at least one obtuse angle". Theorems and proofs are chosen because of their simplicity and elegance, not their relevance to modern or past mathematics. The book is, graphically and stilistically, a gem.
Overall, this is great reading for mathematicians and mathematically literate readers alike. It's also a bit odd, since the book is neither a reference nor a textbook. The only criticism I have is not directed to the book itself. It would be much appreciated to have similar books, but focused on different topics. For example "probabilistic proofs from the book", or "topological proofs from the book".
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Title: Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by John Derbyshire ISBN: 0309085497 Publisher: Joseph Henry Press Pub. Date: 23 April, 2003 List Price(USD): $27.95 |
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Title: Gamma : Exploring Euler's Constant by Julian Havil ISBN: 0691099839 Publisher: Princeton Univ Pr Pub. Date: 17 March, 2003 List Price(USD): $29.95 |
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Title: Riemann's Zeta Function by Harold M. Edwards ISBN: 0486417409 Publisher: Dover Pubns Pub. Date: 13 June, 2001 List Price(USD): $14.95 |
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Title: Abel's Proof : An Essay on the Sources and Meaning of Mathematical Unsolvability by Peter Pesic ISBN: 0262162164 Publisher: MIT Press Pub. Date: 01 May, 2003 List Price(USD): $24.95 |
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Title: Combinatorics of Finite Sets by Ian Anderson ISBN: 0486422577 Publisher: Dover Pubns Pub. Date: 03 May, 2002 List Price(USD): $12.95 |
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