Proofs from the book

Martin Aigner, Gunter M. Ziegler

246 pages, parution le 16/12/2003 (3^eme édition)

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Résumé

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
- Three times π²/6
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
- Shuffling cards
- Lattice paths and determinants
- Cayley's formula for the number of trees
- Completing Latin squares
- The Dinitz problem
- Identities versus bijections
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

L'auteur - Martin Aigner

Freie Universität Berlin, Germany.

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L'auteur - Gunter M. Ziegler

Technische Universität Berlin, Germany.

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Martin Aigner, Gunter M. Ziegler
Parution	16/12/2003
Édition	3^eme édition
Nb. de pages	246
Format	19,5 x 24,5
Couverture	Relié
Poids	850g
Intérieur	Noir et Blanc
EAN13	9783540404606