MATH 480
Geometry and Topology
Fall 2025
Topics
- Surfaces in three dimensions
- First and second fundamental forms
- Principal, Gaussian and mean curvature
- Geodesics
- Gauss’ Theorema Egregium
- Gauss–Bonnet theorem
- Graduate independent study in Riemannian geometry on manifolds
Readings
- A. Presley. Elementary Differential Geometry, 2nd edition. Springer. ISBN 978-1-84882-890-2 / 978-1-84882-891-9.
- Directed parallel course notes for interested undergraduates and graduate students taking their first graduate geometry course: Sigmundur Gudmundsson. An Introduction to Riemannian Geometry. AMS Open Math Notes. https://www.ams.org/open-math-notes/omn-view-listing?listingId=110709
- Graduate directed reading: Wolfgang Kühnel. Differential Geometry: Curves – Surfaces – Manifolds, 2nd edition.
- Graduate directed reading: V. Muñoz et al. Geometry and Topology of Manifolds: Surfaces and Beyond.
- Other material (not labelled required): M. P. do Carmo. Differential Geometry of Curves and Surfaces.
- Other material (not labelled required): Kristopher Tapp. Differential Geometry of Curves and Surfaces.
- Other material (not labelled required): Theodore Shifrin. Differential Geometry (electronic resource).
- Other material for MSc/PhD students (not labelled required): M. P. do Carmo. Riemannian Geometry.
- Other material for MSc/PhD students (not labelled required): John M. Lee. Riemannian Manifolds.
Fall 2023 · MATH 480
Readings
- Wolfgang Kühnel, Differential Geometry: Curves – Surfaces – Manifolds, 2nd edition (for graduate students).
- M. P. do Carmo, Differential Geometry of Curves and Surfaces.
- Kristopher Tapp, Differential Geometry of Curves and Surfaces.
- Theodore Shifrin, Differential Geometry (electronic resource).
- M. P. do Carmo, Riemannian Geometry (for MSc/PhD students).
- John M. Lee, Riemannian Manifolds (for MSc/PhD students).
Winter 2022 · MATH 480
Readings
- Wolfgang Kühnel, Differential Geometry: Curves – Surfaces – Manifolds, 2nd edition (for graduate students).
- M. P. do Carmo, Differential Geometry of Curves and Surfaces.
- Kristopher Tapp, Differential Geometry of Curves and Surfaces.
- Theodore Shifrin, Differential Geometry (electronic resource).
- M. P. do Carmo, Riemannian Geometry (for MSc/PhD students).
- John M. Lee, Riemannian Manifolds (for MSc/PhD students).
Sources
- Course catalogue ↗2026–2027
- Syllabus or course outline ↗Fall 2025
- Historical course outline ↗Fall 2023
- Historical course outline ↗Winter 2022
- Fall 2025 outline. Course header explicitly lists MATH 480, MAST 657, MAST 857. Only Presley is under the explicit required-textbook designation. Subsequent directed readings and the “Other material” list retain their separate status.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. The Kühnel text is specifically for graduate students. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. The Kühnel text is specifically for graduate students. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.