# Discrete Proofs from THE BOOK by Aigner and Ziegler

## For those who have used this book

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4. ### Strongly don't Recommend

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1. Jan 25, 2013

### micromass

Staff Emeritus

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]