math 583b: topological data analysis
- Instructor: Kyle Ormsby
- Syllabus
- Course meetings: MW 9-10:20 in CLK 120
- Drop-in hours: MW 10:30-11:30 in PDL C-524
- Course notes (updated 22 April)
- Demos / code
week 1
Monday 25 March: Welcome & warmup — code
Wednesday 27 March: Topology, simplicial complexes, and homology review
week 2
Monday 1 April: Homology review and classifying persistence modules
Wednesday 3 April: Čech and Vietoris–Rips complexes
week 3
Monday 8 April: Distance and stability for persistence diagrams — code
Wednesday 10 April: Morse theory and zigzag persistence — project info
week 4
Monday 15 April: Topological analysis of weighted graphs — code
Wednesday 17 April: Poset-filtered objects and generalized persistence
week 5
Monday 22 April: Structure and invariants for generalized persistence modules
Wednesday 24 April: NO CLASS (traveling for lecture)
week 6
Monday 29 April: NO CLASS (serving on Reed thesis committee)
Wednesday 1 May: Hierarchical clustering and ultrametric spaces
week 7
Monday 6 May: CAT(0) cubical complexes, the geodesic treepath problem, and Fréchet means
Wednesday 8 May: Case study: Topological network analysis of beta-amyloid and tau in Alzheimer’s disease using PET imaging data
week 8
Monday 13 May: flex / additional case studies
Wednesday 15 May: student presentations
week 9
Monday 20 May: student presentations
Wednesday 22 May: student presentations
week 10
Monday 27 May: NO CLASS (Memorial Day)
Wednesday 29 May: student presentations