100353 Manifolds and Topology

Course offering details

Instructors: Dr. Keivan Mallahi Karai

Type: Lecture

Org-unit:

Course Name Abbreviation: ManifoldsTop

Credits: 7.50

Min. | Max. participants: - | -

Partial Grades:
Final Exam (40%, Mandatory)
Home Work (30%)
Midterm Exam (30%)

Official Course Description:
This course is an introduction to the language and some of the fundamental
concepts of modern geometry. Manifolds are among the most fundamental concepts of mathematics:
curves and surfaces are important special cases that have historical significance.
The course starts with introducing the notion of a manifold, followed by examples that naturally
arise in various areas of mathematics. Differentiability, tangent spaces and vector fields
are then defined. This will be followed by establishing the notion of integration on manifolds.
We will then formulate and prove Stokes’ theorem, which is the higher-dimensional generalization
of the fundamental theorem of calculus. Among the further topics that are discussed in
the course are: orientation, degree of a map, Lie groups and their actions. The classification
of one- and two-dimensional manifolds and the Poincar´e-Hopf theorem will be some of the
highlights of the course.

Literature
Primary Text
  • Introduction to smooth manifolds
Required Reading (To view a list click a category.)
Recommended Reading (To view a list click a category.)
Appointments
Date From To Room Instructors
1 Tue, 4. Feb. 2014 11:15 12:30 East Hall 3 Dr. Keivan Mallahi Karai
2 Th, 6. Feb. 2014 09:45 11:00 East Hall 3 Dr. Keivan Mallahi Karai
3 Tue, 11. Feb. 2014 11:15 12:30 East Hall 3 Dr. Keivan Mallahi Karai
4 Th, 13. Feb. 2014 09:45 11:00 East Hall 3 Dr. Keivan Mallahi Karai
5 Tue, 18. Feb. 2014 11:15 12:30 East Hall 3 Dr. Keivan Mallahi Karai
6 Th, 20. Feb. 2014 09:45 11:00 East Hall 3 Dr. Keivan Mallahi Karai
7 Tue, 25. Feb. 2014 11:15 12:30 East Hall 3 Dr. Keivan Mallahi Karai
8 Th, 27. Feb. 2014 09:45 11:00 East Hall 3 Dr. Keivan Mallahi Karai
9 Tue, 4. Mar. 2014 11:15 12:30 East Hall 3 Dr. Keivan Mallahi Karai
10 Th, 6. Mar. 2014 09:45 11:00 East Hall 3 Dr. Keivan Mallahi Karai
11 Tue, 11. Mar. 2014 11:15 12:30 East Hall 3 Dr. Keivan Mallahi Karai
12 Th, 13. Mar. 2014 09:45 11:00 East Hall 3 Dr. Keivan Mallahi Karai
13 Tue, 18. Mar. 2014 11:15 12:30 East Hall 3 Dr. Keivan Mallahi Karai
14 Th, 20. Mar. 2014 09:45 11:00 East Hall 3 Dr. Keivan Mallahi Karai
15 Tue, 25. Mar. 2014 11:15 12:30 East Hall 3 Dr. Keivan Mallahi Karai
16 Th, 27. Mar. 2014 09:45 11:00 East Hall 3 Dr. Keivan Mallahi Karai
17 Tue, 1. Apr. 2014 11:15 12:30 East Hall 3 Dr. Keivan Mallahi Karai
18 Th, 3. Apr. 2014 09:45 11:00 East Hall 3 Dr. Keivan Mallahi Karai
19 Tue, 8. Apr. 2014 11:15 12:30 East Hall 3 Dr. Keivan Mallahi Karai
20 Th, 10. Apr. 2014 09:45 11:00 East Hall 3 Dr. Keivan Mallahi Karai
21 Tue, 22. Apr. 2014 11:15 12:30 East Hall 3 Dr. Keivan Mallahi Karai
22 Th, 24. Apr. 2014 09:45 11:00 East Hall 3 Dr. Keivan Mallahi Karai
23 Tue, 29. Apr. 2014 11:15 12:30 East Hall 3 Dr. Keivan Mallahi Karai
24 Tue, 6. May 2014 11:15 12:30 East Hall 3 Dr. Keivan Mallahi Karai
25 Th, 8. May 2014 09:45 11:00 East Hall 3 Dr. Keivan Mallahi Karai
26 Tue, 13. May 2014 11:15 12:30 East Hall 3 Dr. Keivan Mallahi Karai
27 Th, 15. May 2014 09:45 11:00 East Hall 3 Dr. Keivan Mallahi Karai
Course specific exams
Description Date Instructors Mandatory
1. Final Exam Sat, 24. May 2014 09:00-11:00 Dr. Keivan Mallahi Karai Yes
2. Final Exam Time tbd Yes
1. Home Work No Date No
1. Midterm Exam Time tbd No
Contained in course catalogues
Course catalogue
Course Catalogue > School of Engineering and Science > Mathematical Sciences > Undergraduate Level Courses
Class Session Overview
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Instructors
Dr. Keivan Mallahi Karai