Olympiads

This page lists the books, handouts, and references I used during my Math Olympiad preparation. Alongside that, I’d like to share a piece of advice I learned the hard way, i.e., by making the mistake myself.

• Never be afraid to try hard problems; don’t give up on them too easily.
  I realized this during the final months of my prep, when my problem-solving ability seemed to hit a ceiling. Trying harder problems exposes you to new ideas, unexpected tools, and alternate ways of thinking even if you don’t solve them. Configuration geometry is a great example since struggling with difficult setups teaches you what kinds of perturbations or tricks are worth exploring later.

  It’s worth mentioning that if you’re in OTIS, try starting directly with the D-version of a unit instead of going through the B-version first. Even if you can’t solve the problems initially, analyze the solutions carefully and go through the examples thoroughly. After all, we humans are nothing but machine-learning models with an additional parameter for emotions added in. The more you see, the more you learn, and the more you can deliver.

In case any of of the links break, a remote Google Drive copy of the articles can be found here.

Geometry

1. Euclidean Geometry in Mathematical Olympiads, by Evan Chen
2. A Beautiful Journey Through Olympiad Geometry, by Stefan Lozanovski
   • Selected results from the book — link.
3. Lemmas in Olympiad Geometry, by Cosmin Pohoata and Titu Andreescu
   • Selected results from the book — link (incomplete).
4. Power of Point:
   • POP handout, by Kagebaka
5. Isogonal Conjugates:
   • Isogonal Conjugates handout, by WizardMath
   • Advanced Lemmas in Geometry handout, by Fedir Yudin
6. Anti-Steiner Point:
   • Anti-Steiner Point handout, by Nguyen Duc Toan
7. Config Geo:
   • Murica, by i3435
     • Selected results from the handout — link.
8. Poncelet Porism:
   • Poncelet Porism handout, by Swapnaneel Da
9. DDIT:
   • DDIT handout, by MarkBcc168
10. Polar Duality:
    • Polar Duality handout, by riadok
11. Method of Moving Points:
    • Moving Points tutorial, by yayups
    • MMP handout, by zacchro, yayups, and anantmudgal09
    • MMP handout, by Vlados021
    • $\mathbb{RP}^2$ handout, by Flash_Sloth
12. Conic Geo:
    • Geometry of Conics, by Alexey A. Zaslavsky and Arseniy Akopyan
    • Conic Geo handout, by DGO team
    • Poncelet Conic handout, by Ivan Zelich
13. Neuberg Cubic:
    • Neuberg Cubic handout, by Ivan Zelich and Xuming Liang
14. For problem practice, try solving problems from OTIS units.
15. Additional Resources:
    • Kimberling’s Encyclopedia of Triangle Centers (ETC)
    • Catalog of Triangle Cubics
    • Properties of the Sharky-Devil Point
    • Parallelogram Isogonality Lemma
    • Isogonal Line Lemma
    • Circumcevian Ping-Pong Lemma
    • A few Geo blogs:
      • amar_04’s blog
      • AlastorMoody’s blog
      • math_pi_rate’s blog
      • TelvCohl’s blog
      • Functional_equation’s blog
      • Darij Grinberg’s contribution to Wolfram MathWorld
      To learn even more, you can check out their posts. You can learn a lot of advanced tools by reading solutions by people like Luis González, TelvCohl, etc. (Let’s hope I’m not missing out names$\dots$ 💀)

Number Theory

1. Modern Olympiad Number Theory, by Aditya Khurmi
2. For problem practice, try solving problems from OTIS units.

Combinatorics

1. An Exploration of Olympiad Combinatorics, by Rushil Mathur
   • I haven’t personally gone through this book, but I’ve heard that it’s extremely well-written for beginners.
2. Problem Solving Tactics, by A. Di Pasquale, N. Do, and D. Mathews
3. Problem-Solving Methods in Combinatorics, by Pablo Soberón
4. For problem practice, try solving problems from OTIS units.
5. Olympiad Combinatorics, by Pranav A. Sriram
   • Readers interested in exploring more can check out this book. (It’s quite challenging for beginners as the learning curve is quite steep.)

Algebra

1. Introduction to Functional Equations, by Evan Chen
2. Introduction to Olympiad Inequalities, by Evan Chen
3. OTIS Excerpts, by Evan Chen
4. For problem practice, try solving problems from OTIS units.
   • I used to main Geometry, but D-wrapfn remains my favorite unit to this day.