Proofs from THE BOOK

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Springer Science & Business Media, 2013 M03 14 - 239 páginas

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".

 

Páginas seleccionadas

Contenido

Number Theory
2
Six proofs of the infinity of primes
3
Bertrands postulate
7
Binomial coefficients are almost never powers
13
Representing numbers as sums of two squares
17
Every finite division ring is a field
23
Some irrational numbers
27
Three times π²6 35
34
On a lemma of Littlewood and Offord
123
Cotangent and the Herglotz trick
127
Buffons needle problem
133
Combinatorics
137
Pigeonhole and double counting
139
Three famous theorems on finite sets 151
150
Shuffling cards
157
Lattice paths and determinants
167

Geometry
43
decomposing polyhedra
45
Lines in the plane and decompositions of graphs 53
52
The slope problem
59
Three applications of Eulers formula 65
64
Cauchys rigidity theorem
71
Touching simplices
75
Every large point set has an obtuse angle
79
Borsuks conjecture
85
Analysis
91
Sets functions and the continuum hypothesis
93
In praise of inequalities
109
A theorem of Pólya on polynomials 117
116
Cayleys formula for the number of trees
173
Completing Latin squares
179
The Dinitz problem
185
Identities versus bijections
191
Graph Theory
197
How to guard a museum
203
Turáns graph theorem
207
Communicating without errors
213
Of friends and politicians
223
Probability makes counting sometimes easy 227
226
About the Illustrations
236
Index
237
Derechos de autor

Otras ediciones - Ver todas

Proofs from THE BOOK
Martin Aigner,Günter M. Ziegler
Vista previa limitada - 2004
Proofs from THE BOOK
Martin Aigner,Günter M. Ziegler
Sin vista previa disponible - 2012

Términos y frases comunes

Amer angles assume Bertrand's postulate bijection binomial coefficients bipartite graph Book Proof Borsuk's conjecture cardinal cards cells Chapter chromatic number color column combinatorial compute configuration congruent conjecture consider contains convex corresponding countable deck denote diagonal distinct dual graph eigenvalues elements equal Euler's formula exactly example finite set function graph G graph theory hence Hilbert's third problem implies induction inequality infinite integers intersect Latin square lemma length linear Math Mathematical matrix multiple n-set natural number number of edges obtain ordinal number P₁ pairs partial Latin square partition path Paul Erdős permutations plane graph points polygon polyhedra polynomial polytopes precisely prime number probability prove random representation result riffle shuffles roots sequence subgraph subset summands Suppose Sylvester-Gallai theorem theorem tree triangle Turán values vectors vertex set vertices yields

Información bibliográfica

TítuloProofs from THE BOOK
AutoresMartin Aigner, Günter M. Ziegler
Ilustrado porKarl H. Hofmann
Edición3, ilustrada
EditorSpringer Science & Business Media, 2013
ISBN3662054124, 9783662054123
Largo239 páginas
  
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