## Algebraic Topology I (Autumn 2017)

This will be an introductory course in algebraic topology, intended for upper-level undergraduates and beginning graduate students.

Topics covered include:

- the fundamental group,
- singular homology,
- cell complexes and cellular homology,
- universal coefficients and the Eilenberg-Steenrod axioms.

Along the way we will introduce the basics of homological algebra and category theory.

## Algebraic Topology II (Spring 2018)

This is a continuation course to Algebraic Topology I.

Topics covered include:

- products in homology (the Eilenberg-Zilber Theorem and the Künneth Formula),
- cohomology (the ring structure and Poincaré duality),
- topics in homotopy theory (including the classical theorems of Serre, Hurewicz, Blakers-Massey and Whitehead.)

I will again produce full lecture notes.