Fall 2026

Introduction to Manifolds

Introduction to manifolds covering integration, differential forms, Stokes theorem, and Cauchy integral theorem.

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

Summary

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Recent recorded grades — Fall 2012: 3.15 GPA, 50.0% A/AB (n=10 letter grades); Fall 2022: 3.83 GPA, 88.9% A/AB (n=9 letter grades); Fall 2023: 3.82 GPA, 85.7% A/AB (n=14 letter grades).

Grade history

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average GPA
letter grades
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Prerequisites

Course map

MATH 522, (MATH 521 and 561), graduate/professional standing, or declared in Mathematics VISP

MATH 621

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Prerequisite text tree

Professors

Fall 2026

No instructors recorded for this selection.

Historical instructors & teaching patterns

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Calendar & sections

Fall 2026

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Student experience

the class

Recent recorded grades — Fall 2012: 3.15 GPA, 50.0% A/AB (n=10 letter grades); Fall 2022: 3.83 GPA, 88.9% A/AB (n=9 letter grades); Fall 2023: 3.82 GPA, 85.7% A/AB (n=14 letter grades).

difficulty & workload

No workload feedback recorded.

Topics

  • Integration in Euclidean spaces and change of variables
  • Multilinear algebra and differential forms
  • Manifolds, tangent spaces, and Stokes theorem
  • Classical vector analysis and Cauchy integral theorem

Skills

  • Integration in Euclidean spaces and change of variables
  • Multilinear algebra and differential forms
  • Manifolds, tangent spaces, and Stokes theorem
  • Classical vector analysis and Cauchy integral theorem

Grades

Latest available · Fall 2023— 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 Fall 2023

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Sources & history

UW–Madison

Catalog & offerings

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Dataset & model

Recorded 2026-09-07

View the dataset on Hugging Face
Model outputs & technical records
nvidia/Qwen3.6-35B-A3B-NVFP4
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": "nvidia/Qwen3.6-35B-A3B-NVFP4",
  "model_revision": "1355db6a052410cfd62085d94b58866fd0f2c3c5",
  "task_version": "14",
  "output_id": "a4c2c1acc6170287252392d064fd3fbcde2923ab1a9f8c6fbe3113c9508aa91d",
  "requirements_status": "valid",
  "dataset_revision": "e243353dcb7d79b7247ced91d69443ef4c2a6349",
  "observed_at": "2026-09-07 15:55:43.033547+00:00"
}