**Math 225A: Differentiable Manifolds**
## Fall 2019
Lectures:*
*MWF 2pm - 2:50pm,
Location: MS 6201
Discussion: Tu 2pm - 2:50pm, Location: MS 5233
*Syllabus*
This is the first quarter of a year-long
sequence in geometry and topology.* *
**Instructor:** Ko Honda
**Office:** MS 7919
**Office Hours:** Mon 1-1:50pm, Wed 11am-noon
**E-mail:** honda at math dot ucla dot
edu
**URL: ***http://www.math.ucla.edu/~honda*
**TA: **Austin Christian; office
hours TBA; *archristian at math dot ucla dot edu*
**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 Mondays,
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: September 26,
2019. |