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Other Useful Resources

This page collects strong external resources for specific contest math topics. Use it as a companion to USAMO Guide when you want extra explanations, alternate problem sets, or deeper dives.

Combinatorics

Counting, casework, generating functions, and olympiad combinatorics training.

Notebook with counting notes and a pen on a desk.
Combinatorics

AoPS Intermediate Counting Course

Structured lessons and practice for permutations, combinations, and bijections.

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Open book and notes representing advanced combinatorics study.
Combinatorics

Yufei Zhao - Enumerative Combinatorics Notes

High-quality olympiad notes with clear combinatorial arguments and examples.

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Handwritten combinatorics formulas and symbols on paper.
Combinatorics

Brilliant - Combinatorics Wiki

Quick refreshers and concept overviews for counting fundamentals and beyond.

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Algebra and Functional Equations

Polynomials, identities, inequalities, and functional equation techniques.

Math notebook with algebraic expressions.
Algebra and Functional Equations

AoPS Intermediate Algebra Course

Strong foundation for transformations, equations, and contest-level manipulations.

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Close-up of algebra equations written on a chalkboard.
Algebra and Functional Equations

Cut-the-Knot Algebra Collection

A deep archive of algebra techniques, identities, and problem discussions.

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Equation-filled page highlighting functional equation work.
Algebra and Functional Equations

IMOmath - Functional Equations

Olympiad-style functional equation problems sorted for focused practice.

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Geometry

Synthetic geometry, coordinate methods, and olympiad geometry problem solving.

Geometric diagram sketches and study notes.
Geometry

Evan Chen - Euclidean Geometry in Mathematical Olympiads

One of the best references for olympiad geometry with modern techniques.

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Student materials for geometry practice on a desk.
Geometry

AoPS Intro/Intermediate Geometry

Progressive geometry curriculum from foundational theorems to hard problems.

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Classic textbook and notebook used for geometry learning.
Geometry

Geometry Revisited (Coxeter-Greitzer)

Classic book that builds geometric intuition and proof-writing habits.

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Number Theory

Divisibility, modular arithmetic, diophantine equations, and prime techniques.

Notebook with number sequences and arithmetic notes.
Number Theory

AoPS Number Theory Course

A systematic path through foundational and advanced contest number theory.

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Printed handouts and annotated number theory solutions.
Number Theory

Paul Zeitz - Number Theory Handouts

Excellent olympiad-focused problems and classic methods in one place.

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Study setup with number theory references and notes.
Number Theory

Brilliant - Number Theory Wiki

Useful concept summaries for quick recall and revision.

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General Olympiad Training

Past papers, solution archives, strategy references, and broad practice sources.

Organized contest prep notes and planning documents.
General Olympiad Training

AoPS Wiki - AMC/AIME/USAMO Archives

Official statements, community solutions, and historical contest collections.

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Calendar and notebook for competition scheduling.
General Olympiad Training

MAA Competitions

Contest logistics, dates, and official pages for US competition programs.

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Olympiad-style problem sheets laid out for training.
General Olympiad Training

IMO Official Site - Problem Archive

International Olympiad problems for stretching proof and strategy skills.

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