Algebra
Inequalities, identities, polynomials, functional relationships and structural manipulation.
Olympiads
Develop the habits of an Olympiad problem solver.
Olympiad mathematics rewards depth, originality, proof and persistence. Training should therefore be systematic, long-term and much broader than learning isolated tricks.
Core disciplines
The mathematics behind Olympiad problem solving
Geometry
Euclidean geometry, transformations, configurations, ratios, circles and proof.
Number Theory
Divisibility, congruences, Diophantine equations and arithmetic structure.
Combinatorics
Counting, invariants, graph ideas, extremal reasoning and constructive arguments.
What changes at Olympiad level?
- The problem may not indicate the method.
- Several plausible approaches can fail before one works.
- A correct final answer is not enough: reasoning matters.
- Students must recognise hidden structure.
- Proof becomes a central mathematical skill.
Training philosophy
Learn ideas deeply, attempt hard problems, analyse failed approaches, and write solutions another mathematician can follow.
Pathway
From enrichment to advanced Olympiad work
Foundation enrichmentBuild confidence with non-routine problems.
→AMC-style competition workDevelop breadth, speed and efficient strategies.
→National Olympiad preparationMove into proof and deeper theory.
→Advanced Olympiad trainingWork toward IMO-style mathematical maturity.