Proofs from the Book

ISBN-10: 3540404600
ISBN-13: 9783540404606
Edition: 3rd 2004 (Revised)
List price: $49.95
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Description: 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.  More...

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Book details

List price: $49.95
Edition: 3rd
Copyright year: 2004
Publisher: Springer
Publication date: 11/13/2003
Binding: Hardcover
Pages: 240
Size: 8.25" wide x 9.75" long x 0.75" tall
Weight: 1.892
Language: English

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. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...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 "... the style is clear and entertaining, the level is close to elementary ... and the proofs are brilliant. ..." LMS Newsletter, January 1999 This third edition offers two new chapters, on partition identities, and on card shuffling. Three proofs of Euler's most famous infinite series appear in a separate chapter. There is also a number of other improvements, such as an exciting new way to "enumerate the rationals".

Number Theory
Six proofs of the infinity of primes
Bertrand's postulate
Binomial coefficients are (almost) never powers
Representing numbers as sums of two squares
Every finite division ring is a field
Some irrational numbers
Geometry
Hilbert's third problem: decomposing polyhedra
Lines in the plane and decompositions of graphs
The slope problem
Three applications of Euler's formula
Cauchy's rigidity theorem
Touching simplices
Every large point set has an obtuse angle
Borsuk's conjecture
Analysis
Sets, functions, and the continuum hypothesis
In praise of inequalities
A theorem of Polya on polynomials
On a lemma of Littlewood and Offord
Cotangent and the Herglotz trick
Buffon's needle problem
Combinatorics
Pigeon-hole and double counting
Three famous theorems on finite sets
Lattice paths and determinants
Cayley's formula for the number of trees
Completing Latin squares
The Dinitz problem
Graph Theory
Five-coloring plane graphs
How to guard a museum
Turan's graph theorem
Communicating without errors
Of friends and politicians
Probability makes counting (sometimes) easy
About the Illustrations
Index

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