Discrete Mathematics

Learn Combinatorics

Counting cleverly: permutations, combinations, and the binomial theorem.

Free to start · adaptive placement finds your level · reviews timed so it stays learned.

What you'll learn

36 lessons in Combinatorics

Basic countingPermutations & combinationsBinomial theoremInclusion-exclusionPermutations with repetitionGenerating functions introCatalan numbersDerangementsStirling & Bell numbersInteger partitionsRamsey theory introBurnside's lemma & Pólya enumerationYoung tableauxDesign theory & Latin squaresError-correcting codes (intro)Proof of inclusion-exclusionProof: Catalan number formulaBijective proofsCombinatorial game theory (Nim)Probabilistic methodExponential generating functionsThe twelvefold wayLattice paths & the ballot problemPartition generating functions & Euler's pentagonal theoremSperner's & Dilworth's theoremsGaussian binomial coefficientsThe hook length formulaSteiner systems & Fisher's inequalityPosets, lattices & Möbius functionsAnalytic combinatorics & the symbolic methodThe transfer matrix methodExtremal set theoryMatroid theoryThe Combinatorial NullstellensatzThe Lovász local lemmaAdditive combinatorics & sumsets
How Erudia teaches

Built to be understood — and remembered.

Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the moment just before you'd forget it. A short placement check finds what you already know, so you start Combinatorics exactly where it's useful.

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