Differential Geometry covers the theory of curves and surfaces using differential methods in n-dimensional real space, including manifolds, Riemannian metrics, curvature, and geodesics.
Past student reviews · Ruobing Zhang
Students reported the material felt graduate-level and the final exam was extremely difficult and toughly graded.
Recall and state the formal definitions of the mathematical objects and their properties used in differential geometry in n-dimensional real space (e.g., vector spaces and inner product spaces, manifolds, Riemannian metric on a manifold, arc length, curvature, torsion, geodesic curves, etc.).
Recall and state the standard theorems of differential geometry (e.g., Frenet-Serret equations, Hopf winding number theorem, four vertex theorem for convex curves, etc.), and recall the arguments for these theorems and the underlying logic of their proofs.
Compute various quantities related to curves and surfaces in the n-dimensional real space using the definitions and theorems (e.g., the fundamental forms, arc length, curvature, total derivative, etc.).
Use the covered theorems in the context of longer arguments by examining their premises (e.g., arguing paths are geodesics, applying the inverse function theorem to show a level set is a manifold, etc. ).
Prove or disprove statements related to the above definitions, properties, and theorems using techniques of mathematical argument (direct methods, indirect methods, constructing examples and counterexamples, induction, etc.).
Convey arguments using English and appropriate mathematical terminology, notation and grammar.
Identify applications of course content in current areas of research.
Source: UW Guide
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(MATH 320, 340, 341, 345, or 375) and (MATH 322, 341, 376, 421, 467, or 521), graduate/professional standing, or declared in Mathematics VISP (undergraduate or graduate)
“Used by” includes alternatives; linked courses may have other requirements. This is a best-effort interpretation; check the catalog requirements above.
Raw average: 4.86/5 from 29 quality ratings. The adjusted rating blends this with the UW review average (3.66/5), weighted as 20 additional ratings. Smaller samples stay closer to that average. Each captured review is counted once in the prior; this does not correct who chooses to leave a review.
RMP profile ↗ · All captured review dates; profile matched by name.
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MUSTAFA KALAFAT is recorded teaching in Spring 2010. Recorded history may be incomplete and does not establish a future schedule.
RUIFANG SONG is recorded teaching in Spring 2014. Recorded history may be incomplete and does not establish a future schedule.
RUOBING ZHANG is recorded teaching in Spring 2025. Recorded history may be incomplete and does not establish a future schedule.
Recorded history may be incomplete and does not establish a future schedule.
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| Section | Mode | Enrolled / capacity | Waitlist |
|---|---|---|---|
| LEC 001 | Classroom Instruction | 0 / 30 | 0 |
Times are Central. Select a meeting for details; export includes recorded dates for the selected sections. Enrollment reflects scan time.
Past student reviews · Mustafa Kalafat
Past students described the course as thoughtful, with lectures that connected calculus topics to differential geometry rather than simply reproducing the textbook.
Recent recorded grades — Spring 2024: 3.23 GPA, 61.5% A/AB (n=13 letter grades); Spring 2025: 3.45 GPA, 71.4% A/AB (n=21 letter grades); Spring 2026: 3.50 GPA, 76.2% A/AB (n=21 letter grades).
Past student reviews · Ruobing Zhang
Students reported the material felt graduate-level and the final exam was extremely difficult and toughly graded.
Past student reviews · Chenxi Wu
One student found the instructor helpful, noting that homeworks and exams were straightforward if they attended lectures and studied the material.
Latest available · Spring 2026— not enough history to project Spring 2027.
Through Spring 2026
Not enough comparable courses for Spring 2027 in UW–Madison.
Descriptions, prerequisites, and recorded course offerings.
Observations at scan time; dates do not imply when a catalog change took effect.
Differential Geometry
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]Original comments behind the course and instructor summaries.
Recorded grade distributions by term, section, and instructor.
Explore recorded gradesRecorded 2026-10-14
Recorded model configuration, reasoning, and tool conversations.
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