Instructor Info

Name: Nathan Broaddus
Email: broaddus@math.ohio-state.edu
Office: MW (Math Tower) 650
Office Phone: 292 0605

Office Hours

Mondays 11:30am-12:30pm and Wednesdays 10:30am-11:30pm or by appointment

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