Konrad Pilch - Olympiad Mathematics
Methods of Proof This should be the first document to read. It details proof
techniques including direct proofs, proofs by contradiction, proof
by contrapositive, induction and a few other interesting proof
techniques.
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Algebra In these documents, you will find basic algebra, polynomials,
functions and their graphs as well as the more difficult concepts
of functional equations and inequalities. This topic is split into
a junior and a senior version where the latter assumes a couple of
years of high school algebra and functions.
Geometry This document covers a large range of material that is likely
to be very new to most readers. Contents include angle chasing,
lengths/areas formulas, triangle centres, circl theorems and
triangle Theorems.
Number Theory This document deals with problems about natural numbers.
Inside you will find divisibility, modulo arithmetic, basics of
elementary number theory including quadratic reciprocity as well
as some standard problem solving techniques.
Combinatorics Last but not least, this document covers topics in
combinatorics including counting methods, game theory, algorithms
and graph theory.
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