About the course
You can download a single PDF containing the latest versions of all eight chapters here, and this playlist contains pre-recorded lecture videos.
The first part of the course, spanning Weeks 1–5, is an introduction to the fundamentals of algebraic topology. The second part, spanning Weeks 5–8, centres on material pertaining to topological data analysis.
Syllabus: simplicial complexes, geometric realisations and simplicial maps; homotopy equivalence, carriers, nerves and fibres; homology and its computation; exact sequences and the snake lemma; cohomology, cup and cap products, Poincaré duality; persistent homology; cellular sheaves and their cohomology; discrete Morse theory.
Important: the course is graded via a final miniproject which covers the above material.
Lectures
Here is the latest version of the lecture notes (Weeks 1–8) in a single PDF, and here is a YouTube playlist of pre-recorded videos of this course from a few years ago. The notes and videos by week:
| Week | Topic | Materials |
|---|---|---|
| 01 | Complexes | notes videos |
| 02 | Homotopy | notes videos |
| 03 | Homology | notes videos |
| 04 | Sequences | notes videos |
| 05 | Cohomology | notes videos |
| 06 | Persistence | notes videos |
| 07 | Sheaves | notes videos |
| 08 | Gradients | notes videos |
Hand-written lecture notes from 2020 are under Antiques.
Exercises
Here are the problem sheets for the course. If you are seeking more thrills, consult the exercises at the end of every chapter of the lecture notes.
Antiques
The hand-written, scanned lecture notes from Hilary 2020.