Art of Problem Solving - Combinatorics
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The Art of Problem Solving wiki's combinatorics hub, linking concise articles on counting principles, permutations, combinations, the binomial theorem, stars and bars, and inclusion-exclusion, with competition problems. Suited to students preparing for contests such as AMC and AIME.
More resources on Combinations
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
Brilliant.org Combinatorics
An interactive Brilliant course on counting, built around short problems with immediate feedback. It covers the rule of product, permutations, combinations, binomial coefficients and casework, so learners can count arrangements and selections without listing them out. Most lessons require a subscription.
Mathematics for Computer Science (MIT 6.042J)
Discrete mathematics for computer science with an emphasis on definitions and proofs: logic, induction, sets and relations, graph theory, modular arithmetic, asymptotics, counting and discrete probability. 25 lecture videos, problem sets and exams with solutions build fluency in writing proofs.
A Course in Combinatorics
Graduate-level textbook covering graph theory, designs, codes, Latin squares, partitions, inclusion-exclusion, generating functions and Ramsey theory in short self-contained chapters. Readers learn standard combinatorial proof techniques and can tackle counting and existence problems beyond introductory discrete mathematics.