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: Point-set topology and algebra.
Course Syllabus: Click here to download course syllabus in PDF format
Textbooks:
Algebraic Topology, by Allen Hatcher
and
Introduction to Topological Manifolds,
Second Edition by John Lee.
Hatcher's book is also available free online, at http://www.math.cornell.edu/~hatcher/AT/ATpage.html
| Title | Author(s), Publ. info | Location |
|---|---|---|
| Topology and Geometry | G. Bredon | 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 first course in topology of manifolds. The fall semester we plan to cover the classification of compact surfaces, the fundamental group and covering spaces, homology, basic cohomology.
Web page: http://www.math.umn.edu/~akhmedov/M8301.html.
Grading: The course grade will be based on homework assignments, in-class midterm and a comprehensive take-home final, with the following weights:
The grader for this course is Nur Saglam. You can reach her via email at sagla004@math.umn.edu
Exams: There will be an in-class midterm on Wednesday, November 2nd and a comprehensive take-home final examinations. The exams worth 30% + 35% = 65% of the final course grade.
Homework: There will be 8 homeworks in this course, each worth 100 points. Homework will be a fundamental part of this course, and will be worth 800 points (35% of the course grade). The first homework assignment will be due on 09/19. 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.
Useful Links:
MIDTERM
TAKE HOME FINAL
DUE: by 2.00pm Friday, December 16
Assignment Problems Homework 1
due 09/19
Allen Hatcher, Chapter 0, Problems 2, 9, 10
Jonh Lee, Chapter 2, Problems 11, 16, 17, 23, 25
Homework 2
due 09/28
Allen Hatcher, Chapter 0, Problems 14, 16, 18, 19, 20
Jonh Lee, Chapter 3, Problems 14, 16
Homework 3
due 10/10
Allen Hatcher, Chapter 1, Section 1.1, Problems 1, 3, 5, 8,
Jonh Lee, Chapter 7, Problems 1, 11, 12, 14
Homework 4
due 10/19
Allen Hatcher, Chapter 1, Section 1.1, Problems 10, 12, 15, 16 b-f, 17, 18
Jonh Lee, Chapter 7, Problems 5, 13, 15
Homework 5
due 10/28
Allen Hatcher, Chapter 1, Section 1.2, Problems 2, 3, 4, 6, 9, 14, 21
Jonh Lee, Chapter 10, Problems 5, 7, 9, 11
Homework 6
due 11/14
Allen Hatcher, Chapter 1, Section 1.3, Problems 2, 9, 10, 14, 20, 30
Jonh Lee, Chapter 11, Problems 6, 11
Homework 7
due 11/21
Jonh Lee, Chapter 12, Problems 2, 4, 6, 11
Homework 8
due 12/05
Jonh Lee, Chapter 13, Problems 1, 2, 3, 6, 10
Homework 9 (Extra Credit)
due 12/12
Allen Hatcher, Chapter 2, Section 2.1, Problems 4, 8, 9, 12, 13, 14, 15, 29
Codes
HW 1 Scores
HW 2 Scores
HW 3 Scores
HW 4 Scores
HW 5 Scores
HW 6 Scores
HW 7 Scores
HW 8 Scores
MIDTERM
FINAL
135
100
98
100
100
94
92
100
98
48
69
940
90
82
95
84
80
94
70
75
14
65
945
91
88
86
96
80
0
70
98
23
38.5
538
97
98
98
93
90
86
95
90
38
66.5
971
94
88
96
100
93
98
95
98
35
65
800
94
100
98
100
100
100
100
100
50
67
538
97
100
100
100
93
99
97
91
48
66
311
100
100
100
100
100
97
100
100
46
70
564
99
95
100
100
100
100
100
98
37
70
895
95
95
100
100
91
100
100
100
32
67
274
96
88
85
90
93
97
100
98
50
68
087
100
99
100
100
95
100
100
100
42
70
936
93
83
87
90
96
100
97
98
31
69
053
93
100
98
100
100
100
100
100
50
67
251
86
98
100
100
97
99
87
84
20
62
163
33
0
86
80
91
93
80
98
21
57
993
96
92
100
88
86
94
96
98
31
68.5
015
83
88
100
88
92
94
93
100
19
66
Introduction to Topology from Wikipedia
Gluing a Sphere
Gluing a Torus
Gluing a Mobius Band
The Adventures of the Klein Bottle
Cutting a Mobius band
Visualizing real projective plane
Space-Filling Curves
Use the Java applet in above link to draw the sequences of curves that define the 2-dimensional space-filling curves.
The fundamental Group of the Torus is abelian