100353 Manifolds and Topology

Course offering details

Instructors: Dr. Keivan Mallahi Karai

Type: Lecture

Org-unit:

Course Name Abbreviation: ManifTopo

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 geometry. Manifolds are among the most fundamental concepts of Mathematics: 1-dimensional manifolds are curves, 2-dimensional manifolds are surfaces, and general manifolds are generalizations of this concept to arbitrary dimensions d.

The course starts with examples of manifolds that arise naturally in various areas of mathematics. Differentiability, tangent spaces and vector fields are then defined. After reviewing the tensor algebra, we formulate and prove Stokes' theorem, which is a natural 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 Poincaré-Hopf theorem will be some of the highlights of the course.

Literature
Primary Text
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 Fri, 3. Sep. 2010 08:15 09:30 East Hall 8 Dr. Keivan Mallahi Karai
2 Wed, 8. Sep. 2010 11:15 12:30 East Hall 8 Dr. Keivan Mallahi Karai
3 Fri, 10. Sep. 2010 08:15 09:30 East Hall 8 Dr. Keivan Mallahi Karai
4 Wed, 15. Sep. 2010 11:15 12:30 East Hall 8 Dr. Keivan Mallahi Karai
5 Fri, 17. Sep. 2010 08:15 09:30 East Hall 8 Dr. Keivan Mallahi Karai
6 Wed, 22. Sep. 2010 11:15 12:30 East Hall 8 Dr. Keivan Mallahi Karai
7 Fri, 24. Sep. 2010 08:15 09:30 East Hall 8 Dr. Keivan Mallahi Karai
8 Wed, 29. Sep. 2010 11:15 12:30 East Hall 8 Dr. Keivan Mallahi Karai
9 Fri, 1. Oct. 2010 08:15 09:30 East Hall 8 Dr. Keivan Mallahi Karai
10 Wed, 6. Oct. 2010 11:15 12:30 East Hall 8 Dr. Keivan Mallahi Karai
11 Fri, 8. Oct. 2010 08:15 09:30 East Hall 8 Dr. Keivan Mallahi Karai
12 Wed, 13. Oct. 2010 11:15 12:30 East Hall 8 Dr. Keivan Mallahi Karai
13 Fri, 15. Oct. 2010 08:15 09:30 East Hall 8 Dr. Keivan Mallahi Karai
14 Wed, 20. Oct. 2010 11:15 12:30 East Hall 8 Dr. Keivan Mallahi Karai
15 Fri, 22. Oct. 2010 08:15 09:30 East Hall 8 Dr. Keivan Mallahi Karai
16 Wed, 27. Oct. 2010 11:15 12:30 East Hall 8 Dr. Keivan Mallahi Karai
17 Fri, 29. Oct. 2010 08:15 09:30 East Hall 8 Dr. Keivan Mallahi Karai
18 Wed, 3. Nov. 2010 11:15 12:30 East Hall 8 Dr. Keivan Mallahi Karai
19 Fri, 5. Nov. 2010 08:15 09:30 East Hall 8 Dr. Keivan Mallahi Karai
20 Wed, 10. Nov. 2010 11:15 12:30 East Hall 8 Dr. Keivan Mallahi Karai
21 Fri, 12. Nov. 2010 08:15 09:30 East Hall 8 Dr. Keivan Mallahi Karai
22 Wed, 17. Nov. 2010 11:15 12:30 East Hall 8 Dr. Keivan Mallahi Karai
23 Fri, 19. Nov. 2010 08:15 09:30 East Hall 8 Dr. Keivan Mallahi Karai
24 Wed, 24. Nov. 2010 11:15 12:30 East Hall 8 Dr. Keivan Mallahi Karai
25 Fri, 26. Nov. 2010 08:15 09:30 East Hall 8 Dr. Keivan Mallahi Karai
26 Wed, 1. Dec. 2010 11:15 12:30 East Hall 8 Dr. Keivan Mallahi Karai
27 Fri, 3. Dec. 2010 08:15 09:30 East Hall 8 Dr. Keivan Mallahi Karai
Course specific exams
Description Date Instructors Mandatory
1. Final Exam Wed, 15. Dec. 2010 16:00-18:00 Dr. Keivan Mallahi Karai Yes
2. Final Exam Time tbd Yes
1. Home Work No Date No
1. Midterm Exam Time tbd No
2. Midterm Exam Time tbd No
Contained in course catalogues
Course catalogue
Course Catalogue > School of Engineering and Science > Undergraduate Programs > Mathematics
Class Session Overview
  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10
  • 11
  • 12
  • 13
  • 14
  • 15
  • 16
  • 17
  • 18
  • 19
  • 20
  • 21
  • 22
  • 23
  • 24
  • 25
  • 26
  • 27
Instructors
Dr. Keivan Mallahi Karai