Olympiad training handouts
I have taught at various math olympiad training programs. Here are some of my handouts.
- Integer Polynomials - MOP 2007 Black group
Integer polynomials, including various irreducibility criteria.
- Inequalities - Canadian
2008 Winter Training
Contains a short essay discussing the IMO 2001 inequality.
- Polynomials - Canadian 2008 Summer Training
Advanced techniques in polynomials. Roots of unity, integer divisibility, intermediate value theorem, Lagrange interpolation, Chebyshev polynomials, irreducibility criteria, and Rouché's theorem.
- Determinants: Evaluation and Manipulation - MIT UMA Putnam Talk
- Linear algebra tricks for the Putnam - MIT UMA Putnam Talk
- Algebraic Techniques
in Combinatorics - MOP 2007 Black Group
Applications of linear algebra and posets to olympiad-style combinatorics problems.
- Tiling - MOP 2007
Discussion of tiling boxes with bricks. Contains many coloring and tiling problems.
in Two Ways - MOP 2007 Blue and Black group
- Combinatorics: bijections, catalan numbers, counting in two ways - Canadian 2008 Winter Training
- Combinatorics: pigeonhole principle, coloring, binomial coefficients, bijections - AwesomeMath 2007
- Combinatorics: counting in two ways, generating functions, algebraic combinatorics - AwesomeMath 2007
- Lemmas in Euclidean Geometry - Canadian 2007 Summer Training
A collection of commonly occuring configurations in geometry problems.
Quadrilaterals – The Big Picture - Canadian 2009 Winter
Explores many properties of the complete cyclic quadrilateral and its Miquel point, and also discusses several useful geometric techniques.
Lemmas in Geometry (Solutions) -
Canadian 2010 Winter Training
- Power of a Point (Solutions) - UK Trinity Training 2011 (Mint group)
- Circles -
Canadian 2008 Summer Training
Contains a section on a particular tangent circle configuration, and another section on projective geometry, poles and polars. Here's some additional food for thought.
- Similarity - Canadian 2007 Summer Training
Applications of similar triangles and spiral similarity.
- an ± 1 (Solutions) - UK
Trinity Training 2011
Working with expression of the form \(a^n \pm 1\) and the exponent lifting lemma.
- Modular arithmetic: Divisibility, Fermat, Euler, Wilson, residue classes, order - AwesomeMath 2007
In 2008, I was the deputy leader of the Canadian team for the 49th International Mathematical Olympiad (IMO) in Madrid, Spain. Here are the webpages for the training camps and the team that year:
- Winter Camp: the week-long training camp at York University in January, 2008.
- Summer Camp: the two-week long training camp prior to the IMO.
- IMO Team: dedicated to the Canadian IMO 2008 team.
Canadian IMO Training website — Training camps from other years