# Olympiad Articles

These are some handouts I’ve written over the years. The Math and Problem-Solving sections of my personal blog might also be of interest. See also Recommendations for other authors I like, and my geometry book for a comprehensive textbook in Euclidean geometry. See also Problems for contest papers.

*If you notice any errors, please let me know!*

**LaTeX notes**:
I provided the LaTeX source for most of these files as an example here.
But note to compile these documents in LaTeX, you will need
my personal style file evan.sty.
Because this style file evolves over time,
your output might look a little different from the PDF’s attached here.

## Beginners#

I suggest reading through the beginner’s page first.

## General#

**Unofficial syllabus for math olympiads**(pdf) (tex)

Rough informal guidance on what topics appear on math olympiads, for people who are new to the scene.

**English**(pdf) (tex)

Notes on proof-writing style. These were used at MOP in 2016, later updated March 2020.

**Intro to Proofs for the Morbidly Curious**(pdf) (tex)

An excessively long description of how mathematical proofs work in theory and in practice.

**From the Author’s Side: Thoughts on Problem Writing**(pdf) (tex)

A short philosophical blurb about writing problems for math olympiads.

## Journals#

**Taiwan TST 2014 Reflection**(pdf) (tex)

This describes my experiences competing for a position on the Taiwan IMO 2014 team. It also contains an extensive commentary on each of the Team Selection Tests and Quizzes, which together covered most of the 2013 IMO Shortlist.

**USAMO 2014 Contest Analysis**(pdf) (tex)

This describes in detail the thought process behind each of my solutions to the USAMO 2014. I also scanned the solutions I submitted.

## Algebra (Hufflepuff)#

**Introduction to Functional Equations**(pdf) (tex)

An introduction to functional equations for olympiad students.

**Summation**(pdf) (tex)

General discussion of sums and products, and how to deal with them. Includes generating functions.

**Lagrange Multipliers Done Correctly**(pdf) (tex)

This is a description of the conditions necessary to execute a Lagrange Multipliers solution on an olympiad.

**Olympiad Inequalities**(pdf) (tex)

English translation of my original notes in Chinese. Describes some “standard strategies” for handling olympiad inequalities.

Original Chinese version: (pdf) (tex)

## Combinatorics (Gryffindor)#

**Expected Uses of Probability**(pdf) (tex)

Inspired by Po-Shen Loh’s talk at the 55th IMO 2014 or Problem 6. Talks about expected value and the probabilistic method. This article was included in Mathematical Reflections, Issue 6 of 2014.

## Geometry (Slytherin)#

**A Guessing Game: Mixtilinear Incircles**(pdf) (tex)

A quick description of some nice properties of mixtilinear incircles. Presented as a “guessing game” where one has to guess collinear points, cyclic quadrilaterals, and so on beforehand.

**Barycentric Coordinates in Olympiad Geometry**(full) (abridged)

One of my most famous handouts from 2012. Introduces from scratch the method of barycentric coordinates. This was the basis of chapter 7 of my geometry textbook.

**Bashing Geometry with Complex Numbers**(pdf) (tex)

English translation of my original notes in Chinese. Describes the classic method of complex numbers.

Original Chinese version: (pdf) (tex)

**How to Use Directed Angles**(pdf) (tex)

A short note on the use of directed angles in olympiad solutions. Why didn’t anyone beat me to writing this?

**The Incenter/Excenter Lemma**(pdf) (tex)

A collection of problems which exhibit the first olympiad configuration I got to know well, the famous “incenter/excenter lemma”.

**Writing Olympiad Geometry Problems**(pdf) (tex)

For students who are interested in writing their own olympiad geometry problems! Or more generally, anyone who is curious how my geometry problems get created.

Also: chapter 2 (on power of point) or chapter 8 (on inversion) of my textbook.

## Number theory (Ravenclaw)#

**Orders Modulo a Prime**(pdf) (tex)

Article on orders and primitive roots, in particular featuring the sum of squares lemma and its generalization to arbitrary cyclotomic polynomials.

## Miscellaneous#

**Chinese Terminology Sheet**(pdf) (tex)

These are the notes that I took when I was studying traditional Chinese in preparation for the Taiwan IMO selection and training camps. It is updated occasionally as I add entries. Needs extra preamble file.

**LaTeX Example File**(pdf) (tex)

A short document which shows what a “typical” LaTeX file looks like. It was written for beginners.

**How to annoy Evan with LaTeX**(pdf) (tex)

A list of pet peeves in LaTeX. See also Evan’s LaTeX style guide.

**OMO Spring 2014 Executive Report**(pdf) (tex)

A short report on running the Online Math Open for Spring 2014. This is mostly for the sake of those who will be running the future installments of the contest, as one of us is graduating.

**USAMO 2003 Rubric**(pdf)

The grading rubric for USAMO 2003.