Resources
The books, videos, tools, and free PDFs our team actually uses — not a generic list. Every item here was chosen because it genuinely works.
Free Downloads
9 PDFsLegitimate free PDFs — no piracy, no sketchy sites. Most are freely released by the authors themselves. Direct download links where available.
Competition Prep
AMC · AIME · MATHCOUNTSWhere to find past problems, official archives, and the people who actually coach olympiad teams.
Every AMC 8, 10, 12, and AIME problem with community solutions going back to 1950. Free, searchable, and the single best source for competition practice.
VisitLast year's school, chapter, and state competitions are always available for free. Purchase past years for deeper practice.
VisitHandouts on inequalities, summation, probability, CRT, proof-writing, and more — all freely downloadable. Used at MOP and international training programs.
VisitFree past AMC 8 and AMC 10 problems with solutions, from the former USA IMO team coach. Clean interface, mobile-friendly, with real-time solve sessions.
VisitBooks Worth Buying
4 picksNot an exhaustive list — a deliberate short one. These are the books our team returns to.
The best single book for getting into mathematical olympiad thinking. Covers strategy, tactics, and mindset across all competition topics.
A guided tour through mathematics — connecting calculus, number theory, and topology to everyday life. Written for a general audience but deeply insightful.
The 358-year story of Fermat's Last Theorem — the most dramatic mathematical problem ever posed. Reads like a thriller while teaching real mathematics.
A Pulitzer-winning exploration of self-reference, logic, consciousness, and meaning. Connects mathematical logic to music, art, and the nature of thought.
YouTube Channels
4 channelsAll free. All genuinely good. Each comes with a suggested starting video because it's easy to land on the wrong one first.
Animated visualizations of calculus, linear algebra, probability, and number theory. Build the kind of geometric intuition that no textbook can.
Research mathematicians talking about the numbers, theorems, and results they personally love. Genuine enthusiasm, no watered-down explanations.
Applied math and comedy. Matt finds real-world problems — license plates, spreadsheet errors, brick patterns — and does proper mathematics on them.
Deep, rigorous dives into beautiful theorems with actual proofs. Covers material most channels are afraid to touch — Q-series, generating functions, Ramanujan.
Interactive Tools
6 toolsUse these to explore, visualize, and practice. Most are completely free.
Free adaptive problem practice from Art of Problem Solving. Adjusts difficulty in real time. The best free competition math trainer that exists.
The best free graphing calculator. Plots functions, handles implicit curves, and lets you animate variables. Cleaner than TI-84, faster than Wolfram.
Dynamic geometry construction tool — draw, drag, and explore theorems interactively. Better than any textbook for building geometric intuition.
120+ geometric construction puzzles using only compass and straightedge. Builds proof intuition through elegant, progressively harder puzzles.
600+ math problems that require both mathematical insight and some programming to solve. Perfect for the intersection of math and CS.
Guided interactive courses in math, science, and CS. Their guided-discovery approach is genuinely effective for building intuition before drilling problems.
Websites
Reference sites, problem archives, and community hubs worth bookmarking.
Found something we should include?
We'd love your recommendations. Send us a book, PDF, or site that changed how you think about math.