What you'll learn

27 lessons in Algebraic Number Theory

Number fields & rings of integersFailure of unique factorizationUnique factorization of idealsRamificationThe ideal class groupMinkowski's geometry of numbersDirichlet's unit theoremCyclotomic fieldsDirichlet L-functions & primes in APQuadratic reciprocity revisitedp-adic numbersThe discriminant & the differentDecomposition, inertia & FrobeniusLocal fields & completionsHensel's lemmaDedekind zeta & the class number formulaThe Hasse–Minkowski local-global principleClass field theory & Artin reciprocityAdeles & idelesGalois cohomology & Hilbert 90Central simple algebras & the Brauer groupLocal class field theoryElliptic curves & Mordell–WeilGalois representationsModularity & the proof of FermatIwasawa theoryThe Weil conjectures & étale cohomology

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 Number Theory exactly where it's useful.

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Related Discrete Mathematics subjects

Combinatorics Graph theory Boolean algebra & logic Diophantine Approximation Discrete Math Number Theory