Proofs from the book
By: Martin Aigner, Günter M. Ziegler ; including illustrations by Karl H. Hofmann
Contributors: Ziegler, Günter M.
Edition: Fifth edition.
Publisher: Springer
Published: 2014
Language: eng
Number of pages: 308
ISBN-13: 9783662442043
Subjects: Mathematics
Description: The mathematical heroes of this book are 'perfect proofs': brilliant ideas, clever connections & wonderful observations that bring new insight & surprising perspectives on basic & challenging problems from number theory, geometry, analysis, combinatorics & graph theory. 30 examples are presented.
Notes: Includes bibliographical references and index.
Table of contents: title: 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 ; The law of quadratic reciprocity ; Every finite division ring is a field ; The spectral theorem and Hadamard's determinant problem ; Some irrational numbers ; Three times [pi squared]/6; title: 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 ; The Borromean rings don't exist ; Touching simplices ; Every large point set has an obtuse angle ; Borsuk's conjecture; title: Analysis: Sets, functions, and the continuum hypothesis ; In praise of inequalities ; The fundamental theorem of algebra ; One square and an odd number of triangles ; A theorem of Pólya on polynomials ; On a lemma of Littlewood and Offord ; Cotangent and the Herglotz trick ; Buffon's needle problem; title: Combinatorics: Pigeon-hole and double counting ; Tiling rectangles ; Three famous theorems on finite sets ; Shuffling cards ; Lattice paths and determinants ; Cayley's formula for the number of trees ; Identities versus bijections ; The finite Kakeya problem ; Completing Latin squares; title: Graph theory: The Dinitz problem ; Permanents and the power of entropy ;  Five-coloring plane graphs ; How to guard a museum ; Turán's graph theorem ; Communicating without errors ; The chromatic number of Kneser graphs ; Of friends and politicians ; Probability makes counting (sometimes) easy.