Introduction to Manifolds
Covers integration in Euclidean spaces, multilinear algebra, differential forms, manifolds, Stokes theorem, classical vector analysis, and the Cauchy integral theorem.
Summary
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).
What you’ll be able to do
Use the techniques of multilinear algebra and apply them to differential forms in Euclidean space and on abstract differentiable manifolds. This includes being able to compute with the exterior derivative.
Identify and/or construct differentiable manifolds. This includes being able to identify spaces as differentiable manifolds and to endow abstract topological spaces with differentiable manifold structures.
Extend calculus concepts from Euclidean space in order to apply them to abstract differentiable manifolds. This includes being able to identify and work with differentiable maps between differentiable manifolds in computations and proofs
Use the essential definitions and theorems from calculus on manifolds in the context of computations and proofs. This includes taking Lie derivatives of vector fields on differentiable manifolds, computing integrals of curves, integrating differential forms, and Stokes’ theorem.
Identify applications of course content in current areas of research.
Source: UW Guide
Grade history
↗All recorded terms · compare terms & instructors
Prerequisites
Course mapMATH 522, (MATH 521 and 561), graduate/professional standing, or declared in Mathematics VISP
This is a best-effort interpretation; check the catalog requirements above.
Professors
Spring 2027No instructors recorded for this selection.
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Spring 2027Schedule loads here as you scroll.
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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, vector fields, and differential forms
- Manifolds, tangent spaces, integration on manifolds, and Stokes theorem
- Classical vector analysis and the Cauchy integral theorem
Skills
- Apply multilinear algebra techniques to differential forms and compute exterior derivatives.
- Identify or construct differentiable manifolds and endow topological spaces with manifold structures.
- Compute Lie derivatives, integrate curves and differential forms, and apply Stokes' theorem.
Grades
Latest available · Fall 2023— not enough history to project Spring 2027.
Grade distribution · % of letter grades
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Through Fall 2023
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Explore recorded gradesRecorded 2026-10-14
Model outputs & technical records
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Model & dataset provenance
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