100341 Introductory Topology

Course offering details

Instructors: Dr. Pavel Tumarkin

Type:

Org-unit:

Course Name Abbreviation: IntroTopology

Hours per week: 3

Credits: 7.50

Min. | Max. participants: - | -

Partial Grades:
Final Grade

Official Course Description:
This course is an introduction to some basic concepts and techniques in topology. The first part of the course builds on material in 100211 Analysis I on the topology of metric spaces; we introduce topological spaces and continuous maps and proceed to discuss properties of spaces including connectedness, compactness and the Hausdorff property. Basic constructions such as the product and quotient of spaces are also treated.

The second part of the course concerns a higher notion of connectedness. We define the notion of homotopy, construct the fundamental group of a space and prove the Seifert-van Kampen theorem, a key tool for computing fundamental groups. We discuss in some detail covering spaces and their relation with the fundamental group, including the construction of the universal covering space.

The course concludes with a brief treatment of higher homotopy groups
and a sketch of the classification of closed surfaces.

Literature
Primary Text
  • Elementary Topology: Problem Textbook
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 Th, 3. Sep. 2009 14:15 15:30 East Hall 4 Dr. Pavel Tumarkin
2 Fri, 4. Sep. 2009 14:15 15:30 East Hall 4 Dr. Pavel Tumarkin
3 Th, 10. Sep. 2009 14:15 15:30 East Hall 4 Dr. Pavel Tumarkin
4 Fri, 11. Sep. 2009 14:15 15:30 East Hall 4 Dr. Pavel Tumarkin
5 Th, 17. Sep. 2009 14:15 15:30 East Hall 4 Dr. Pavel Tumarkin
6 Fri, 18. Sep. 2009 14:15 15:30 East Hall 4 Dr. Pavel Tumarkin
7 Th, 24. Sep. 2009 14:15 15:30 East Hall 4 Dr. Pavel Tumarkin
8 Wed, 30. Sep. 2009 17:15 18:30 East Hall 3 Dr. Pavel Tumarkin
9 Th, 1. Oct. 2009 14:15 15:30 East Hall 4 Dr. Pavel Tumarkin
10 Wed, 7. Oct. 2009 17:15 18:30 East Hall 3 Dr. Pavel Tumarkin
11 Th, 8. Oct. 2009 14:15 15:30 East Hall 4 Dr. Pavel Tumarkin
12 Wed, 14. Oct. 2009 17:15 18:30 East Hall 3 Dr. Pavel Tumarkin
13 Th, 15. Oct. 2009 14:15 15:30 East Hall 4 Dr. Pavel Tumarkin
14 Wed, 21. Oct. 2009 17:15 18:30 East Hall 3 Dr. Pavel Tumarkin
15 Th, 22. Oct. 2009 14:15 15:30 East Hall 4 Dr. Pavel Tumarkin
16 Wed, 28. Oct. 2009 17:15 18:30 East Hall 3 Dr. Pavel Tumarkin
17 Th, 29. Oct. 2009 14:15 15:30 East Hall 4 Dr. Pavel Tumarkin
18 Wed, 4. Nov. 2009 17:15 18:30 East Hall 3 Dr. Pavel Tumarkin
19 Th, 5. Nov. 2009 14:15 15:30 East Hall 4 Dr. Pavel Tumarkin
20 Th, 12. Nov. 2009 14:15 15:30 East Hall 4 Dr. Pavel Tumarkin
21 Wed, 18. Nov. 2009 17:15 18:30 East Hall 3 Dr. Pavel Tumarkin
22 Th, 19. Nov. 2009 14:15 15:30 East Hall 4 Dr. Pavel Tumarkin
23 Wed, 25. Nov. 2009 17:15 18:30 East Hall 3 Dr. Pavel Tumarkin
24 Th, 26. Nov. 2009 14:15 15:30 East Hall 4 Dr. Pavel Tumarkin
25 Wed, 2. Dec. 2009 17:15 18:30 East Hall 3 Dr. Pavel Tumarkin
26 Th, 3. Dec. 2009 14:15 15:30 East Hall 4 Dr. Pavel Tumarkin
27 Th, 17. Dec. 2009 10:15 15:45 East Hall 4 Dr. Pavel Tumarkin
Course specific exams
Description Date Instructors Mandatory
1. Final Grade No Date Yes
2. Final Grade No Date Yes
Contained in course catalogues
Course catalogue
Course Catalogue > School of Engineering and Science > Undergraduate Programs > Mathematics
Class Session Overview
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Instructors
Dr. Pavel Tumarkin