Instructor: Anar Akhmedov
Lectures: MWF 1.25 - 2.15pm in Vincent Hall 209.
E-mail: akhmedov@math.umn.edu
Office Hours: MF 11.45am - 12.35pm.
Prerequisites: Math 8301 or Instructors permission.
Textbooks:
Introduction to Smooth Manifolds, by John Lee (2nd edition).
| 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/MATH8302.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 Wednesday, March 8th 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 02/06. The grader will pick up the homework usually on Wednesdays (sometimes on Monday) 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.
| Assignment | Problems |
|---|---|
| Homework 1 due 02/06 |
John Lee (Introduction to Manifolds to Topological Manifolds) Chapter 13, Problems 13.6, 13.7, 13.12 John Lee (main textbook), Chapter 1, Problems 1.2, 1.5, 1.7, Exercises 1.6, 1.7 |
| Homework 2 due 02/15 |
Jonh Lee, Chapter 2, Problems 2.1, 2.5, 2.7, 2.8, 2.10 |
| Homework 3 due 02/27 |
Jonh Lee, Chapter 2, Problems 2.11, 2.12, 2.13, Chapter 3, 3.1, 3.3, 3.4 |
| Homework 4 due 03/06 |
Jonh Lee, Chapter 3 Problems 3.5, 3.6, 3.7, 3.8 |
| Homework 5 due 03/22 |
Jonh Lee, Chapter 4 Problems 4.5, 4.6, 4.7, 4.8 Chapter 8, 8.6, 8.7, 8.10 |
| Homework 6 due 04/05 |
Jonh Lee, Chapter 4, 4.9, 4.10, 4.12, 4.13 Chapter 5, 5.1 5.2, 5.5, 5.7 |
| Homework 7 due 04/28 |
Jonh Lee, Chapter 6 6.2, 6.3, 6.4 Chapter 12 12.1, 12.5, 12.6 |
| Homework 8 due May 05 |
Jonh Lee, Chapter 14 14.1, 14.2, 14.5, 14.7 |