Fall 2026

Differential Geometry

Covers the metric properties of Riemannian manifolds, including geodesics, comparison theorems, and Hodge-de Rham theory.

no offering record for this termCredits unavailable
Recorded instructors · Fall 2026 No instructors listed

Summary

1 / 5

Historical reviews of Sean Paul: Reviewers characterize the difficulty as high, citing a lack of clear grading standards. One student rated the difficulty at 5, noting that grades seemed based on personal satisfaction rather than objective performance.

Grade history

average GPA
letter grades
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Prerequisites

Course map

Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program

  • Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program
MATH 765

This is a best-effort interpretation; check the catalog requirements above.

Prerequisite text tree
  • Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program

Professors

Fall 2026

No instructors recorded for this selection.

Historical instructors & teaching patterns

Historical reviews of Sean Paul: Sean Paul is described as irresponsible and unorganized, with lectures that fail to cover core topics like Jacobi fields. Reviewers criticize his lack of clear grading criteria and his tendency to blame students for their struggles.

SEAN PAUL is recorded teaching in Spring 2008, Spring 2010, Spring 2012, Spring 2016, Spring 2018, Spring 2019, Fall 2022, 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.

Calendar & sections

Fall 2026

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No records available.

Student experience

the class

Sean Paul's historical reviews describe a frustrating experience with unorganized lectures and unclear grading criteria. Students report that course content often diverged from expected topics, leading to significant dissatisfaction with the instruction quality.

Recent recorded grades — Fall 2023: 4.00 GPA, 100.0% A/AB (n=11 letter grades); Spring 2025: 3.62 GPA, 91.7% A/AB (n=12 letter grades); Spring 2026: 4.00 GPA, 100.0% A/AB (n=19 letter grades).

difficulty & workload

Historical reviews of Sean Paul: Reviewers characterize the difficulty as high, citing a lack of clear grading standards. One student rated the difficulty at 5, noting that grades seemed based on personal satisfaction rather than objective performance.

Historical reviews of Sean Paul: Students found lectures unhelpful, with content focusing on the instructor's specific interests rather than core course material. Reviewers also noted a lack of support, with the instructor attributing student struggles entirely to their own faults.

Topics

  • Vector bundles, connections, and submanifolds.
  • Geodesics and the Hopf-Rinow theorem.
  • Second variation of arc length and Jacobi fields.
  • Comparison theorems and spaces of constant curvature.
  • Hodge-de Rham theory.

Skills

  • Analyze metric properties of Riemannian manifolds.
  • Apply vector bundle theory and connections to Riemannian geometry.
  • Study geodesics and variational properties of arc length.
  • Utilize comparison theorems and Hodge-de Rham theory.

Grades

Latest available · Spring 2026— not enough history to project Fall 2026.

average GPA
A / AB grades
letter grades
Instructor

Grade distribution · % of letter grades

A
AB
B
BC
C
D
F

Grades over time

Through Spring 2026

More grade details Grade mix, volume & source data

Not enough comparable courses for Fall 2026 in UW–Madison.

Sources & history

UW–Madison

Catalog & offerings

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Student reviews

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Model outputs & technical records
nvidia/Qwen3.6-35B-A3B-NVFP4
LLM outputs across runs
Full model traces

Recorded model configuration, reasoning, and tool conversations.

Model & dataset provenance
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  "task_version": "14",
  "output_id": "7940d059b7ddfc9eeae447a9e1d2d7d8d57cb5248126b16f4198d1fc14469470",
  "requirements_status": "valid",
  "dataset_revision": "e243353dcb7d79b7247ced91d69443ef4c2a6349",
  "observed_at": "2026-09-07 15:55:43.033547+00:00"
}