Konrad Pilch - Olympiad Mathematics

Me  In 2005 and 2006, I was a member of the Australian International Mathematical Olympiad team. See the official IMO website for my results! I have been involved as a live-in staff member with the Australian International Mathematical Olympiad Program from 2007 - 2015 and I have also mentored two students Yanning Xu and Alex Chua who also represented Australia. Below are some of the material I have collected together to help students learn some of the theory and skills to solve problems. The below documents are aimed at high school students aiming to get into olympiad mathematics (although it may also be useful to students in the system already).

Most recent edits: 7th April, 2016



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.


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.
  • Coming soon.