### Lecture Notes

- Week 1 — Axioms for homology, category theory, singular simplicial homology
- Week 2 — Snake lemma, homotopy axiom, reduced homology, excision axiom
- Week 3 — Excision axiom
- Week 4 — Additivity axiom, naturality of the connecting homomorphism, cellular homology
- Week 5 — Degree (for spheres), cellular boundary map
- Week 6 — Homology and the fundamental group
- Week 7 — Tensor products, Tor, homology with coefficients, Universal coefficient theorem
- Week 8 — Künneth formula, Künneth formula for chain complexes, Acyclic model theorem
- Week 9 — Review of homotopy groups, Hurewicz homomorphism, Hurewicz theorem
- Week 10 — Proof of Hurewicz Isomorphism Theorem