**Math 225A: Differentiable Manifolds**
## Fall 2020
*Syllabus*
This is the first quarter of a year-long sequence in geometry
and topology.* *
**Instructor:** Ko Honda
**Office:** MS 7919
**Office Hours:** W 3-4pm or by appointment
**E-mail:** honda at math dot ucla dot edu
**URL: ***http://www.math.ucla.edu/~honda*
**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
**Topics**
- 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'
theorem.
**Prerequisites**
- 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
mathematics department.
**Homework**
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!**
**Final examination**
There will be a take-home
final. This will be approximately 30% of your final grade.
**References**
I will follow my Differential Geometry Course Notes. The
main reference is Lee's book, where you can find more details and
examples.
- Differential
Geometry Course Notes
- Lee,
*Introduction to Smooth Manifolds*
- Spivak,
* A **C**ompreh**ensive
Introducti**on to Differential Geometry*
- Tu,
*An **In**t**roduction
to **Manifolds*
- Warner, Foundations of Differentiable Manifolds and Lie
Groups
- Peter
Petersen's notes
WARNING: The course syllabus provides a general plan for
the course; deviations may become necessary.
Last modified: October 1, 2020. |