Math 225A: Differentiable Manifolds
This is the first quarter of a year-long sequence in geometry
Instructor: Ko Honda
Office: MS 7919
Office Hours: W 3-4pm or by appointment
E-mail: honda at math dot ucla dot edu
TA: Jason Schuchardt; office hours TBA;
jason.sch at math dot ucla dot
Class Meetings: I
plan to record the lectures.
- Lectures: MWF 2pm -
2:50pm on Zoom
- Discussion: Th 2pm - 2:50pm on Zoom
- Review of advanced calculus (calculus on
R^n); inverse and implicit function theorems.
- Differentiable manifolds and their maps.
- Tangent and cotangent bundles, vector bundles.
- Differential forms: tensor and exterior
algebra, exterior differentiation, and Lie derivatives.
- Integration: Stokes' theorem, de Rham
cohomology, and computations using Meyer-Vietoris sequences.
- Vector fields, distributions, Frobenius'
- Knowledge of calculus on R^n, as presented
in the first three chapters of Spivak's Calculus
on Manifolds book.
- This course requires more mathematical
maturity than the average first-year graduate course in the
There will be weekly problem sets; see the class
schedule. Homework is due on Fridays, although there
may be some exceptional weeks. The problem sets count for
a large percentage of your total grade (approximately
70%). You may work with others or consult other textbooks,
but the homework you turn in must be
written by you, in your own words, and you must cite your
sources used and your collaborators!
There will be a take-home
final. This will be approximately 30% of your final grade.
I will follow my Differential Geometry Course Notes. The
main reference is Lee's book, where you can find more details and
Geometry Course Notes
- Lee, Introduction to Smooth Manifolds
- Spivak, A Comprehensive
Introduction to Differential Geometry
- Tu, An Introduction
- Warner, Foundations of Differentiable Manifolds and Lie
WARNING: The course syllabus provides a general plan for
the course; deviations may become necessary.
Last modified: October 1, 2020.