Spring 2027

Differentiable Manifolds

Differentiable manifolds, vector bundles, implicit function theorem, submersions and immersions, vector fields and flows, foliations and Frobenius theorem, differential forms and exterior calculus, integration and Stokes' theorem, De Rham theory, Riemannian metrics. Familiarity with basic undergraduate analysis coursesMATH 521and522orMATH 621) is strongly recommended.

no offering record for this termCredits unavailable
Recorded instructors · Spring 2027 No instructors listed

Summary

1 / 6

Past student reviews · Sean Paul, Alex Waldron

Lectures and homework were difficult. Homework required long periods of thinking and step-by-step writing, while grading was described as harsh.

Grade history

↗
average GPA
letter grades
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AB
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All recorded terms · compare terms & instructors

Prerequisites

Course map

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

    • Graduate/professional standing
    • member of the Pre-Masters Mathematics (Visiting International) Program
    take one
MATH 761

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

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

Professors

Spring 2027

No instructors recorded for this selection.

Historical instructors & teaching patterns

ALEX WALDRON is recorded teaching in Fall 2024. Recorded history may be incomplete and does not establish a future schedule.

SEAN PAUL is recorded teaching in Fall 2013, Spring 2019, Spring 2022. 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

Spring 2027

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SectionModeEnrolled / capacityWaitlist

Times are Central. Select a meeting for details; export includes recorded dates for the selected sections.

Meeting source records
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Student experience

the class

Past student reviews · Alex Waldron

Students described the course as demanding but responsible, noting that harsh grading helped diagnose problems and correct imperfect intuition.

Recent recorded grades — Spring 2024: 3.96 GPA, 100.0% A/AB (n=24 letter grades); Fall 2024: 3.71 GPA, 85.7% A/AB (n=14 letter grades); Fall 2025: 3.69 GPA, 79.3% A/AB (n=29 letter grades).

difficulty & workload

Past student reviews · Sean Paul, Alex Waldron

Lectures and homework were difficult. Homework required long periods of thinking and step-by-step writing, while grading was described as harsh.

Past student reviews · Alex Waldron

One student found the teaching decent and standard but noted that the professor was difficult to get along with.

Grades

Latest available · Fall 2025— not enough history to project Spring 2027.

average GPA
A / AB grades
letter grades
Instructor

Grade distribution · % of letter grades

A
AB
B
BC
C
D
F

Grades over time

Through Fall 2025

More grade details Grade mix, volume & source data

Not enough comparable courses for Spring 2027 in UW–Madison.

Sources & history

UW–Madison

Catalog & offerings

Descriptions, prerequisites, and recorded course offerings.

Catalog observation history

Observations at scan time; dates do not imply when a catalog change took effect.

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Selected offering source records

No offering records for the selected term.

Raw records 
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Student reviews

Original comments behind the course and instructor summaries.

Read original reviews
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Madgrades

Grade history

Recorded grade distributions by term, section, and instructor.

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Dataset & model

Recorded 2026-10-14

View the dataset on Hugging Face
Model outputs & technical records
Qwen/Qwen3.8-27B
LLM outputs across runs
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Full model traces

Recorded model configuration, reasoning, and tool conversations.

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Model & dataset provenance 
{
  "model": "Qwen/Qwen3.8-27B",
  "model_revision": "1d4bf0f2ff6012fd82039f2fa52739d0dd7c60c0",
  "task_version": "17",
  "output_id": "5defed5b26671088e4557b8cd58e4351f9c48d54115a98048bdff7915974ed21",
  "requirements_status": "needs_review",
  "dataset_revision": "fc1811fa52e581ea57a35c0cf3343f8740a8ffbf",
  "observed_at": "2026-10-14 17:50:09.728220+00:00"
}