Kisacanin B. Mathematical Problems and Proofs: Combinatorics, Number Theory, and Geometry

Kluwer Academic Publishers, 2002. - 220 pages.
Key to Symbols.
Set Theory.
Sets and Elementary Set Operations.
Cartesian Product and Relations.
Functions and Operations.
Cardinality.
Problems.
Combinatorics.
Four Enumeration Principles.
Introductory Problems.
Basic Definitions.
Generating Functions.
Problems.
Number Theory.
Divisibility of Numbers.
Important Functions in Number Theory.
Congruences.
Diophantine Equations.
Problems.
Geometry.
Properties of Triangles.
Analogies in Geometry.
Two Geometric Tricks.
Problems.
Appendixes.
Mathematical Induction.
Overview.
Examples.
Problems.
Hints and Notes.
Important Mathematical Constants.
Great Mathematicians.
Greek Alphabet.