What you'll learn

46 lessons in Abstract Algebra

What is a group?Subgroups & Lagrange's theoremRingsFields & Galois previewNormal subgroupsQuotient groupsGroup homomorphismsPolynomial ringsVector spaces as modulesGroup actions & orbit-stabilizerFree groups & presentationsIdeals & quotient ringsPIDs, UFDs, Euclidean domainsSimple groups & classificationSolvable & nilpotent groupsGalois correspondenceGroup representations introProof of Lagrange's theoremProof of orbit-stabilizerProof of first isomorphism theoremTensor products of modulesField extensions & finite fieldsThe isomorphism theoremsSemidirect productsPermutations & the symmetric groupParity, sign & the alternating groupConjugacy classes & the class equationCauchy's theorem & p-groupsSylow's theoremsTransitivity & primitivitySimplicity of the alternating groupComposition series & Jordan–HölderBurnside's counting lemmaCharacter theory & Schur orthogonalityStructure of finitely generated abelian groupsSolvability by radicals & Abel–RuffiniModules over a PID & canonical formsSemisimple rings & Wedderburn–ArtinGroup extensions & the Schur multiplierReflection & Coxeter groupsFree products & amalgamationQuaternions, octonions & the division-algebra towerClifford algebras & the geometric productSmith normal formWreath productsCayley graphs

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 day its model predicts you would forget it. A short placement check finds what you already know, so you start Abstract Algebra exactly where it's useful.

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