Under construction. This area is a framework being built: most courses have no teaching material yet, and things may change or break. Private self-study. Not an official programme and not recognised by any ministry or school. No qualification, mark or document is issued, and “years 1 to 3” and “advanced” are names of study paths only.
E34 Topological data analysis
Advanced pathE: Proposed extensionsplannedabout 100 h (planning estimate)
Planned: syllabus only, no teaching material yet. Nothing on this page can be studied; it describes what the course would cover.
Named in: Advanced applied mathematics pathway
Why this course
Persistent homology is the main bridge between topology and data.
Prerequisites
- Required
- B15 Point-set topology, B08 Linear algebra II: abstract structure, U12 Algebraic topology I
- Recommended
- B17 Mathematical statistics I
- Can be taken at the same time
- none
- Everything required, transitively (11 courses)
- B01, B02, B03, B04, B08, B09, B10, B15, F01, F02, U12
- Courses that require this one
- none
Concept-level units
Units follow the syllabus order, as a recommended sequence rather than a gate.
- Simplicial complexes and the nerve theorem
- Homology over a field
- Filtrations and persistent homology
- Barcodes and persistence diagrams, stability theorem
- Mapper
- Statistics of persistence
- Computation and software
- Applications and misuse
Assessable outcome
Compute persistence of a small point cloud by hand and interpret its barcode with its stability guarantee.
Assessment design
- topic exercises
- mixed problem sets
- unseen proof or derivation problems
- cumulative examination
cumulative; uses spaced retrieval
Resources
Every title here is candidate, unverified unless marked verified. Titles were suggested while planning. Nobody has checked that they exist, what they cost or how they are licensed.
- Edelsbrunner and Harer · Computational Topology
- Carlsson · Topology and data (paper)
- Wasserman · Topological data analysis (paper)
Content record
- Version
- 0.0.0
- Review
- no review of any kind
- Provenance
- PROPOSED by the assistant on 4 Nov 2026 so that a person with a mathematics degree can read AI articles fluently; not in the owner's brief; APPROVED by the owner on 4 Nov 2026 as an elective; still needs a curriculum reviewer
- Known issues
- Approved as an elective on 4 Nov 2026; syllabus only, no lessons, candidate resources unverified, needs a curriculum reviewer.
- Type
- course
Bridges and laboratories
No bridge or laboratory is attached to this course yet.
You and this course
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