440-2 - Geometry/Topology: Differentiable Manifolds
Monday, Wednesday, Friday 10:00am - 10:50am, Lunt 102
Course website: www.math.northwestern.edu/~tosatti/dg.html
Office: Lunt 225
Wednesdays, 2:00pm - 3:00pm
or by appointment
Yajnaseni Dutta - firstname.lastname@example.org
This course is an introduction to smooth manifolds and basic differential geometry. See the syllabus below for more detailed content information.
J.M.Lee - Introduction to Smooth Manifolds (Second edition), Springer 2012.
There will be weekly written assignments which can be found below along with the due date and time. Problem sets are due on Mondays in class,
except as marked below. The solutions will be posted below.
Grading and Final:
The class grades will be based on the weekly homework and on the final exam.
The projected final exam date is Thursday, March 19
from 3:00pm to 5:00pm in Lunt 102.
This is a tentative syllabus and it is likely to change as the course progresses.
|| Topics Covered
| Jan. 5, 7, 9
|| Multilinear algebra
Due January 12 in class
| Jan. 12, 14, 16
|| Differentiable manifolds
Due January 21 in class
| Jan. 19
|| MLK day, no class
| Jan. 21, 23
|| Tangent vectors
Due January 26 in class
| Jan. 26, 28, 30
|| Sumbanifolds, vector fields
Due February 2 in class
| Feb. 2, 4, 6
|| Flows, Lie derivative
Due February 9 in class
| Feb. 9, 11, 13
||Frobenius theorem, Lie groups and Lie algebras
Due February 16 in class
|Feb. 16, 18, 20
Due February 25 in class
|Feb. 23, 25, 27
Due March 2 in class
|Mar. 2, 4, 6
||Orientation, integration, Stokes' theorem
Due March 9 in class
|Mar. 9, 11, 13
||Riemannian metrics, geodesics
||Practice problems for the final exam
Final exam with solutions