An edition of Proofs from the book
(2014)
Proofs from the book
Fifth edition.
by Martin Aigner
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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.
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Book Details
Table of Contents
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
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
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
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
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.
Edition Notes
Includes bibliographical references and index.
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| December 8, 2022 | Edited by MARC Bot | import existing book |
| July 18, 2019 | Created by MARC Bot | import new book |