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.
U05 Curves, surfaces & differential geometry
Years 1 to 3 pathU: Years 1 to 3 electivesplannedabout 120 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: Years 1 to 3 pathway
Why this course
Curvature and surfaces: the concrete road to manifolds.
Prerequisites
Concept-level units
Units follow the syllabus order, as a recommended sequence rather than a gate.
- Curves and curvature
- Surfaces and parametrization
- Tangent spaces
- First and second fundamental forms
- Geodesics
- Curvature and intrinsic geometry
Assessable outcome
Compute geometric quantities and distinguish intrinsic from extrinsic structure.
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.
- do Carmo · Differential Geometry of Curves and Surfaces
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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