Instructor: Ko Honda
Office: MS 7901
Office Hours: Wed 10-12 noon
E-mail: honda at math dot ucla dot edu.
Telephone: 310-825-2143
URL: http://www.math.ucla.edu/~honda

TA: Michael Miller; office hours TBA; smmiller at ucla dot edu

Topics

1. Review of advanced calculus (calculus on R^n); inverse and implicit function theorems.
2. Differentiable manifolds and their maps.
3. Tangent and cotangent bundles, vector bundles.
4. Differential forms: tensor and exterior algebra, exterior differentiation, and Lie derivatives.
5. Integration: Stokes' theorem, de Rham cohomology, and computations using Meyer-Vietoris sequences.
6. 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. 
  

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

1. Differential Geometry Course Notes
2. Lee, Introduction to Smooth Manifolds
   
3. Spivak, A Comprehensive Introduction to Differential Geometry
4. Tu, An Introduction to Manifolds
   
5. Warner, Foundations of Differentiable Manifolds and Lie Groups
6. Peter Petersen's notes