## Olympiad training handouts

I have taught classes at various math olympiad training programs. Here are some of my handouts and training material.

### Algebra

- 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

### Combinatorics

- Bijections
- Algebraic Techniques
in Combinatorics - MOP 2007 Black Group

Applications of linear algebra and posets to olympiad-style combinatorics problems. - Tiling - MOP 2007
Blue group

Discussion of tiling boxes with bricks. Contains many coloring and tiling problems. - Counting
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

### Geometry

- Lemmas in Euclidean Geometry - Canadian 2007 Summer Training

A collection of commonly occuring configurations in geometry problems.

- Cyclic
Quadrilaterals – The Big Picture - Canadian 2009 Winter
Training

Explores many properties of the complete cyclic quadrilateral and its Miquel point, and also discusses several useful geometric techniques. - Three
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.

### Number theory

*a*± 1 (Solutions) - UK Trinity Training 2011^{n}

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

## IMO 2008

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

### My competition records as a participant

- Putnam: 2006 Fellow; 2007 Seventh place; 2008 Fellow; 2009 Fellow
- IMO: 2004 Bronze; 2005 Gold; 2006 Silver
- USAMO: 2004 HM; 2005 Third Place; 2006 Third Place
- Canadian MO: 2004 First Place; 2005 Third Place; 2006 Second Place