Week 1: Permutation groups, group axioms, order and conjugacy, subgroups
Week 2: Group actions, homomorphisms, isomorphisms, quotient groups, products
Week 3: Orbit counting theorem, fixed points, Sylow's theorems
Week 4: Sylow's theorems (continued), free groups
Week 5: Generators and relations
Week 6: Rings, Euclidean domains, ideals and factorization
Week 7: Examples of commutative and non-commutative rings, quotients by ideals
Week 8: Tensor and exterior algebras, modules
Week 9: Sums, quotients and homomorphisms of modules
Week 10: Free modules, determinants, primary decomposition
Week 11:Finitely generated modules and the Noetherian condition
Week 12: Smith form, structure theorem for finitely generated modules over a PID, Jordan canonical form
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