Abstract & Pure

Learn Algebraic K-Theory

One invariant built twice: complete a monoid of projective modules into a group, and a ring's arithmetic, a manifold's topology and a field's Galois theory all turn out to be recorded in the same place. Covers K_0 through K_2, Whitehead torsion, Quillen's higher theory and the finite-field computation.

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

What you'll learn

18 lessons in Algebraic K-Theory

Group completion$K_0$ of a ringSerre-Swan$K_0$ of a Dedekind domainIdempotents and rank$K_1$ and the Whitehead lemmaDeterminants and $SK_1$Whitehead torsion$K_2$ and the Steinberg groupMilnor K-theory and symbolsRelative $K$-theory and excisionLocalization and devissageNegative $K$-theoryQuillen's plus constructionThe Q-construction$K$-theory of finite fieldsWall's finiteness obstructionWhere $K$-theory goes next
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 Algebraic K-Theory exactly where it's useful.

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