MATH 225ASmooth Manifolds
Mathematics · 4 units · Graduate courses (200-299)
Smooth manifolds and smooth maps; inverse and implicit function theorems, submersions, immersions, submanifolds; tangent and cotangent bundles, vector bundles; differential forms, exterior differentiation, and Lie derivatives; integration, Stokes’ theorem, de Rham cohomology, and computations using the Mayer-Vietoris sequences; vector fields, integral curves, distributions, Frobenius’ theorem.
S/U or letter grading.
When it runs
- Fall 2025
- Fall 2026
Scheduled, not typical — from UCLA’s Schedule of Classes, which publishes Fall 2025 through Spring 2027 and nothing before it.
Requisites
UCLA lists no requisites for this course.
Requires
Everything that has to come before this course, not just the courses named in the requisite above.
Nothing — this is an entry point.
Unlocks
What this course is a requisite for, and what those courses lead to in turn.
MATH 225A
- MATH 226ADifferential Geometry
- MATH 233Partial Differential Equations on Manifolds
- MATH 226BDifferential Geometry
- MATH 234Topics in Differential Geometry
- MATH 226CDifferential Geometry
- MATH 235Topics in Manifold Theory
- MATH 236Topics in Geometric Topology
5 courses list this as a requisite. The whole downstream is here — 8 courses over 2 levels. Every course here opens its own tree.