MATH 6230, Differential Geometry 1, Spring 2022


Dr. Markus Pflaum

Course Contents:

This course is an introduction to topological and smooth manifolds, smooth maps between manifolds, tangent and cotangent bundles, submanifolds, vector fields, flows, differential forms and integration on manifolds. This is one of the pillar courses required of Mathematics PhD students.


Lecture Hours and Venue:

MWF 11:15 am - 12:05 pm, MATH 220.

Office Hours:

Monday 12:05 pm - 1.05 pm, Tuesday 2:00 pm - 3:00 pm, and by appointment


Assignments will be given online on a regular basis on the course homepage. Homework is usually due two weeks after the assignment. It is the student's responsibility to get these assignments submitted even in the event of an absence from class. Show all your work. Homework will be graded.

Homework   Due Date    Homework   Due Date    Homework   Due Date   
Set 1 01/26/2022 Set 2 02/14/2022 Set 3 03/04/2022
Set 4 03/18/2022 Set 5 04/11/2022 Set 6 04/22/2022

Course Project:

In addition to the homework, each student has to write a short paper (around 5 pages) on a particular topic from Differential Geometry. The papers are due April 28, 2022. A selection of possible topics is provided here, but you can propose your own project theme.


May 1st, 7:30pm to 10:00pm in MATH 220

Course Grading:

Your grade will be determined from the graded homework (50 %), the course project (25%) and the final (25%).


Lee, Introduction to Smooth Manifolds, Springer

Last modified: Monday Jan 10, 2022, 12:25:18