Number Theory
1.Six proofs of the infinity of primes
2.Bertrand''s postulate
3.Binomialcoefficients are almost never powers
4.Representing numbers as sums of two squares
5.The law of quadratic reciprocity
6.Every firute division ring is afield
7.Some irrational numbers
8.Three times ∏26
Geometry
9.Hilbert''s tlurd problem: decomposing polyhedra
10.Lines in the plane and decompositions of graphs
11.The slopeproblem
12.Three applications of Euler''s formula
13.Cauchy''s rigidity theorem
14.Touching simplices
15.Every large point set has an obtuse angle
16.Borsuk''s conjecture
Analysis
17.In praise ofinequalities
19.The fundamental theorem of algebra
20.One square and an odd number of triangles
21.A theorem of Polya on polynomials
22.On alemma of Littlewood and Offord
23.Cotangent and the Herglotz trick
24.Buffon''s needle problem
Combinatorics
25.Pigeon-hole and double counting
26.Tiling rectangles
27.Three famous theorems on finite sets
28.Shuffling cards
29.Lattice paths and determinants
30.Cayley''s formula for the number of trees
31.IdenMes versus bijections
32.Completing Latin squares
Graph Theory
33.The Dinitz problem
34.Five-coloring plane graphs
35.How to guard a museum
36.Turan''s graph theorem
37.Communicating without errors
38.The chromatic number of Kneser graphs
39.Of friends and politicians
40.Probability makes counting sometimes easy
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