Topological Data Analysis — Schedule
Week-by-week schedule of Topological Data Analysis.
The operational schedule for Topological Data Analysis. Per-cohort dates fill in at intake; the structure below is stable across cohorts.
The single source of truth is _data/tda.yml. Edits there flow through this page automatically.
| Week | Title | Pitch | Detail |
|---|---|---|---|
| 01 | Motivations and Overview | Why a topologist's tools — persistent homology, Mapper, stability — turn out to be a working data-science primitive. | week 01 → |
| 02 | Simplicial Complexes and Homology | The combinatorial machinery: simplicial complexes, chain groups, boundary maps, homology as the kernel of a kernel. | week 02 → |
| 03 | Persistent Homology | Tracking the birth and death of topological features across a filtration. The persistence module as the central object. | week 03 → |
| 04 | Barcodes and Persistence Diagrams | Two equivalent visualizations of the same data, each with different statistical and ML affordances. | week 04 → |
| 05 | Stability Theorems | Why TDA features can survive noise: the bottleneck-distance stability of diagrams under Hausdorff perturbations. | week 05 → |
| 06 | Vietoris–Rips, Čech, Alpha, Witness Complexes | The decision that ends up mattering most in practice: which complex to build, and why. | week 06 → |
| 07 | The Mapper Algorithm | TDA's exploratory-analysis cousin: build a topological skeleton of a dataset, label it, look at it. | week 07 → |
| 08 | Distances between Diagrams | How to compare two diagrams, and which comparison is mathematically and statistically defensible. | week 08 → |
| 09 | Machine Learning with TDA | Where TDA features earn their place in a pipeline — and where they don't. | week 09 → |
| 10 | Applications | Three case studies: protein structure, neural-network loss surfaces, and gerrymandering detection. | week 10 → |
| 11 | TDA and Deep Learning | Differentiable persistence, topological loss functions, and the frontier of geometric deep learning. | week 11 → |
| 12 | Final project presentations | Each participant presents a TDA pipeline applied to a dataset of their choice. | week 12 → |
Operational notes
- Default timezone: Africa/Lagos (UTC+1). Per-cohort timing negotiated at intake.
- Lab notebooks and problem-set repos live in the cohort GitHub organization.
- The bilingual lecture notes remain the reference text.