Instructor: Anar Akhmedov
Lectures: MWF 1.25 - 2.15pm in Vincent Hall 2.
E-mail: akhmedov@math.umn.edu
Office Hours: WF 2.30 - 3.30pm. If you have questions, I encourage you to come to my office hours. My office is in room 355 of the Vincent Hall.
Prerequisites: Math 8301 or Instructors permission.
Course Syllabus: Click here to download course syllabus in PDF format.
Textbooks:
Introduction to Smooth Manifolds, by John Lee.
| Title | Author(s), Publ. info | Location |
|---|---|---|
| Differential Forms in Algebraic Topology | R. Bott and L. Tu | On reserve in math library |
| Algebraic Topology | W. Fulton | On reserve in math library |
| Topology from a differential point of view | J. Milnor | On reserve in math library |
Course Outline: This is a second course in topology of manifolds. The spring semester we plan to cover smooth manifolds, tangent spaces, vector fields and vector bundles , embedding/immersion, Sard's theorem, differential forms, integration, de Rham cohomology, duality in manifolds, curvature, Gauss-Bonnet theorem.
Web page: http://www.math.umn.edu/~akhmedov/M8302.html.
Grading: The course grade will be based on homework assignments, in-class midterm and a comprehensive take-home final, with the following weights:
Exams: There will be an in-class midterm on Monday, March 5th and a comprehensive
take-home final examinations. The exams worth 30% + 34% = 64% of the final course grade.
Homework: There will be 8 homeworks in this course, each worth 45 points. Homework will be a fundamental part of this course, and will be worth 360 points (36% of the course grade). The first homework assignment will be due on 01/30. The grader will pick up the homework usually on Mondays (sometimes on Wednesday) after the class. This means that NO LATE HOMEWORK CAN BE ACCEPTED. You may work together on homework, but everyone must turn in their own written solutions. Please staple your homework before handing it in.
If you have questions about the homework, it is best to ask during my office hours.
TAKE HOME FINAL
DUE: by 2.00pm Friday, May 11
Assignment Problems Homework 1
due 01/30
John Lee, Chapter 1, Problems 1.2, 1.5, 1.7, Exercises 1.1, 1.2, 1.3, 1.4
Homework 2
due 02/13
Jonh Lee, Chapter 2, Problems 2.1, 2.5, 2.7, 2.8, 2.10, 2.16
Homework 3
due 02/22
Jonh Lee, Chapter 2, Problems 2.11, 2.12, 2.13,
Chapter 3, 3.1, 3.3, 3.4
Homework 4
due 03/02
Jonh Lee, Chapter 4 Problems 4.1, 4.3, 4.6, 4.11
Homework 5
due 03/23
Jonh Lee,
Chapter 4 Problems 4.13, 4.14, 4.18,
Chapter 5, 5.1, 5.3, 5.6, 5.9, 5.10, 5.11
Homework 6
due 04/06
Jonh Lee, Chapter
Chapter 7, 7.1, 7.3, 7.5, 7.6, 7.8
Homework 7
due 04/20
Jonh Lee, Chapter
Chapter 8, 8.1, 8.2, 8.5, 8.6, 8.13, 8.19, 8.21
Chapter 10, 10.1
Homework 8
due 04/27
Jonh Lee, Chapter
Chapter 11, 11.1, 11.2, 11.8, 11.9,
Chapter 12, 12.1, 12.2, 12.3,
Homework 9 (This homework is optional, and is for extra credit)
due 05/04
Jonh Lee, Chapter
Chapter 13, 13.1, 13.2, 13.3, 13.9, 13.12