Number Theory |
Six proofs of the infinity of primes / 1: |
Bertrand's postulate / 2: |
Binomial coefficients are (almost) never powers / 3: |
Representing numbers as sums of two squares / 4: |
Every finite division ring is a field / 5: |
Some irrational numbers / 6: |
Geometry |
Hilbert's third problem: decomposing polyhedra / 7: |
Lines in the plane and decompositions of graphs / 8: |
The slope problem / 9: |
Three applications of Euler's formula / 10: |
Cauchy's rigidity theorem / 11: |
The problem of the thirteen spheres / 12: |
Touching simplices / 13: |
Every large point set has an obtuse angle / 14: |
Borsuk's conjecture / 15: |
Analysis |
Sets, functions, and the continuum hypothesis / 16: |
In praise of inequalities / 17: |
A theorem of Pólya on polynomials / 18: |
On a lemma of Littlewood and Offord / 19: |
Combinatorics |
Pigeon-hole and double counting / 20: |
Three famous theorems on finite sets / 21: |
Cayley's formula for the number of trees / 22: |
Completing Latin squares / 23: |
The Dinitz problem |
Graph Theory |
Five-coloring plane graphs / 25: |
How to guard a museum / 26: |
Turan's graph theorem / 27: |
Communicating without errors / 28: |
Of friends and politicians / 29: |
Probability makes counting (sometimes) easy / 30: |
About the Illustrations |
Index |
Number Theory |
Six proofs of the infinity of primes / 1: |
Bertrand's postulate / 2: |
Binomial coefficients are (almost) never powers / 3: |
Representing numbers as sums of two squares / 4: |
Every finite division ring is a field / 5: |