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#

• English (pdf) (git)
  Notes on proof-writing style. These were used at MOP in 2016, later updated March 2020 and December 2023.

• From the Author’s Side: Thoughts on Problem Writing (pdf) (git)
  A short philosophical blurb about writing problems for math olympiads.

• Intro to Proofs for the Morbidly Curious (pdf) (git)
  An excessively long description of how mathematical proofs work in theory and in practice.

• Unofficial syllabus for math olympiads (pdf) (git)
  Rough informal guidance on what topics appear on math olympiads, for people who are new to the scene.

Journals#

• IMO 2014 Journal (pdf) (git)
  This describes my experiences competing as TWN2 at the 55th IMO 2014. (You can download full-resolution photos from the trip.)

• Taiwan TST 2014 Reflection (pdf) (git)
  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) (git)
  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) (git)
  An introduction to functional equations for olympiad students. An updated version appears as Chapter 3 of OTIS Excerpts.

• Lagrange Multipliers Done Correctly (pdf) (git)
  This is a description of the conditions necessary to execute a Lagrange Multipliers solution on an olympiad.

• Monsters (pdf) (git)
  A handout discussing pathological functional equations. An updated version appears as Chapter 4 of OTIS Excerpts.

• Olympiad Inequalities (pdf) (git)
  English translation of my original notes in Chinese. Describes some “standard strategies” for handling olympiad inequalities.
  Original Chinese version: (pdf) (git)
  An updated version appears as Chapter 3 of OTIS Excerpts.

• SOS: A Dumbass’s Perspective (pdf) (git)
  Describes the SOS method for solving inequalities.

• Summation (pdf) (git)
  General discussion of sums and products, and how to deal with them. Includes generating functions.

Combinatorics (Gryffindor)#

• Expected Uses of Probability (pdf) (git)
  Inspired by Po-Shen Loh’s talk at the 55th IMO 2014 on 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) (git)
  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) (git)
  English translation of my original notes in Chinese. Describes the classic method of complex numbers.
  Original Chinese version: (pdf) (git)
  

• Constructing Diagrams (pdf) (git)
  A handout on advice for drawing diagrams on geometry problems.

• How to Use Directed Angles (pdf) (git)
  A short note on the use of directed angles in olympiad solutions. See also FAQ C-11.

• Lemmas in AoPS Geometry (pdf) (git)
  A sardonically named handout that lists some silly names in olympiad geometry popular culture on the Internet.

• The Incenter/Excenter Lemma (pdf) (git)
  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) (git)
  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) (git)
  Article on orders and primitive roots, in particular featuring the sum of squares lemma and its generalization to arbitrary cyclotomic polynomials. An updated version appears as Chapter 13 of OTIS Excerpts.

• The Chinese Remainder Theorem (pdf) (git)
  An article on the Chinese Remainder “Theorem”.

Miscellaneous#

• Chinese Terminology Sheet (pdf) (git)
  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. I use traditional characters, but you can also find a version with simplified characters too.

• EXCL 2023: Thoughts and Q/A on math olympiad coaching (pdf) (git)
  Slides from a talk I gave in November 2023 about experiences with coaching students for math olympiads.

• How to annoy Evan with LaTeX (pdf) (git)
  A list of pet peeves in LaTeX. See also Evan’s LaTeX style guide.

• LaTeX Example File (pdf) (git)
  A short document which shows what a “typical” LaTeX file looks like. It was written for beginners.

• 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.