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.
P04 Smooth manifolds
Advanced pathP: Advanced pureplannedabout 180 h (planning estimate)
Draft lectures and exercises are available for this course. They were written by AI and checked by a second AI; no person has reviewed them yet. Use them as a study aid, not as an authority.
Named in: Advanced pure mathematics pathway
Why this course
Calculus on smooth manifolds: charts, forms and Stokes.
Prerequisites
- Required
- U05 Curves, surfaces & differential geometry, B15 Point-set topology, B13 Real analysis II: metric & multivariable analysis
- Recommended
- none
- Can be taken at the same time
- none
- Everything required, transitively (12 courses)
- B01, B02, B03, B04, B06, B08, B09, B13, B15, F01, F02, U05
- Courses that require this one
- P05, E18
Concept-level units
Units follow the syllabus order, as a recommended sequence rather than a gate.
- Charts and smooth structures
- Tangent and cotangent spaces
- Differentials and vector fields
- Differential forms
- Integration and Stokes theorem
- Submanifolds
Assessable outcome
Develop coordinate-independent calculus on smooth manifolds.
Assessment design
- deeper problem sets
- reconstruction of an unfamiliar argument
- advanced source reading
- cumulative examination or substantial project
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.
- Tu · An Introduction to Manifolds
- Lee · Introduction to Smooth Manifolds
Content record
- Version
- 0.0.0
- Review
- no review of any kind
- Provenance
- catalogue imported from the owner brief of 29 Oct 2026; no teaching content authored
- Known issues
- none recorded
- Type
- course
Bridges and laboratories
No bridge or laboratory is attached to this course yet.
You and this course
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