MATH 4540 — Introduction to Differential Geometry
General Information
Differential geometry involves using calculus to study geometric concepts such as curvature and geodesics. This introductory course focuses on the differential geometry of curves and surfaces. It may also touch upon the higher-dimensional generalizations, Riemannian manifolds, which underlie the study of general relativity. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course.
Full Cornell course description (SP26)
Credits: 4
Prerequisites and Enrollment
Prerequisites: a semester of linear algebra (MATH 2210, MATH 2230, MATH 2310, or MATH 2940) and a semester of multivariable calculus (MATH 2220, MATH 2240, or MATH 1920), or equivalent.
Recorded Offerings
| Semester | Listed instructors | Course details |
|---|---|---|
| Spring 2026 | Xiaodong Cao | Roster / syllabus |
Workload and General Advice
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Course information checked against Cornell’s Spring and Fall 2026 rosters on September 18, 2026. The listed semesters are verified examples, not a complete offering history.