Best resources to learnMath Competitions & Olympiads

Euclidean Geometry in Mathematical Olympiads (EGMO)

The standard modern olympiad geometry text: cyclic quadrilaterals, power of a point, homothety, then complex numbers, barycentric coordinates, inversion and projective methods. Over three hundred contest problems, with the author's errata and reader notes hosted free. Olympiad geometry is the one subject where general problem-solving texts are insufficient - it has its own toolkit (complex numbers, barycentrics, inversion) that Zeitz and Engel barely touch. This is the acknowledged modern treatment, and the specialist slot in the set.

Problem-Solving Strategies

Thirteen hundred competition problems organized by strategy - invariance, coloring, extremal principle, pigeonhole, functional equations - with full solutions. Less a textbook than a drill bank for grinding technique after you know what proofs are.

The Art and Craft of Problem Solving (3rd Edition)

Teaches problem-solving as a discipline rather than a topic list: investigation, wishful thinking, invariants, extremal arguments, then the four standard olympiad subjects. Where Engel drills and Evan Chen goes deep on technique, Zeitz explains the meta-level habits - how to open a problem you have no idea how to start, when to look for an invariant, why extremal arguments work. It is the one book here that a motivated learner with no proof background can start cold. Written by a 1974 IMO gold medallist and long-time olympiad coach.

intermediate🇬🇧

How to Solve It: A New Aspect of Mathematical Method

George Pólya's classic guide to mathematical problem solving, built around a four-step method of understanding, planning, carrying out and looking back, plus a dictionary of heuristics such as working backwards, auxiliary problems and generalization. Readers learn to attack unfamiliar problems and proofs systematically.

beginner🇬🇧

🌐Websites(4)

IMO Official Problem Archive (1959-present)

Official papers from every International Mathematical Olympiad since 1959, in the original languages and English, alongside country results and medal thresholds. The primary source for what IMO problems actually look like. Also useful beyond the problems themselves: the results tables show what score actually earns a medal, which calibrates expectations better than any commentary.

AoPS Wiki: AMC, AIME and USAMO Problems and Solutions

Complete archive of AMC 8, AMC 10, AMC 12, AIME, USAMO and USAJMO papers, every problem with multiple community-written solutions. The standard practice ground for working up the American competition ladder. Practice against real past papers is the non-negotiable core of olympiad training, and this is the free, complete, solution-annotated archive for the AMC-to-USAMO ladder.

intermediate🇬🇧

Math Olympiad Beginner's Page

A coach's blunt roadmap for entering proof-based competition math: which contests to enter first, why USAMTS suits beginners, how much to read versus solve, and which books are worth buying at each stage.

intermediate🇬🇧

Evan Chen's Olympiad Handouts

Free LaTeX handouts from a 2014 IMO gold medallist covering olympiad inequalities, functional equations, projective geometry, proof-writing style, and an unofficial olympiad syllabus. The working technique notes MOP and OTIS students actually train from.