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Discrete Proofs from THE BOOK by Aigner and Ziegler

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  1. Jan 25, 2013 #1

    micromass

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    Table of Contents:
    Code (Text):

    [LIST]
    [*] Number Theory
    [LIST]
    [*] 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
    [*] Some irrational numbers
    [*] Three times \pi^2/6
    [/LIST]
    [*] Geometry
    [LIST]
    [*] 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
    [/LIST]
    [*] Analysis
    [LIST]
    [*] 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
    [/LIST]
    [*] Combinatorics
    [LIST]
    [*] 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
    [*] Completing Latin squares
    [/LIST]
    [*] Graph Theory
    [LIST]
    [*] The Dinitz problem
    [*] 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
    [/LIST]
    [*] About the Illustrations
    [*] Index
    [/LIST]
     
     
    Last edited by a moderator: May 6, 2017
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