Unit notes
The units below are the teaching spine of the course:
- Week 1 — Sets, functions, and binary operations
- Week 2 — Permutations and the symmetric group
- Week 3 — Divisibility and the division algorithm
- Week 4 — The Euclidean algorithm, primes, and unique factorization
- Week 5 — Equivalence relations, partitions, and congruence classes
- Week 6 — Groups and subgroups
- Week 7 — Cyclic groups and the order of an element
- Week 8 — Cosets and Lagrange’s theorem
- Week 9 — Direct products
- Week 10 — Normal subgroups and quotient groups
- Week 11 — Isomorphisms and structural invariants
- Week 12 — Homomorphisms and the isomorphism theorems
- Week 13 — Cayley’s theorem and permutation representations
- Week 14 — Rings and integral domains
- Week 15 — Fields, characteristic, and the arc of the course