This is an old course webpage
Math 225C: Algebraic Topology
Spring 2023
Instructor: Sucharit Sarkar.
Class: MWF 13:00-13:50, MS 5117.
Office hours: W 11:30-12:30, MS 6909.
TA: Jung Joo Suh.
TA discussion section: Th 13:00-13:50, MS 5127.
TA office hours: W 15:00-16:15, Th 15:30-17:00, MS 3949.
Textbook:
Hatcher,
Algebraic
Topology, Chapters 1-3.
Syllabus: Basic concepts of homotopy theory, fundamental group,
Van Kampen theorem, and covering spaces, singular homology and
cohomology theory, axioms of homology theory, Mayer-Vietoris sequence,
excision, cup products, calculation of homology and cohomology of
standard spaces, cell complexes and cellular homology, Poincare
duality.
Useful
links: Department
page,
Gradescope,
old
Qualifying exams.
Prerequisites: Hatcher Chapter 0, basic knowledge of algebra
(110, 115) and point set topology
(121). Try these
problems to
check your preparedness.
For undergraduates: If you are an undergraduate trying to
enroll in 225C, you will need a PTE from me. You need to meet the
above prerequisites, and in addition, you need to be a Math major with
strong grades (straight A's in all undergraduate Math courses with at
most one B in a non-algebra non-topology undergraduate Math
course). If you meet these requirements, send me an email requesting a
PTE, and attach a copy of your transcript.
Homework: Homeworks are due on Fridays. You must upload your
homeworks (either LaTeX-ed, or handwritten and then scanned) to
Gradescope. Late homeworks will be graded/ungraded based on the TA's
discretion. However, your lowest homework score will be dropped when
computing your grade.
| HW |
Due on |
Problems |
| 1 |
2023-04-14 |
0: 1, 2, 3, 4, 9, 10, 11, 13, 1.1: 1, 2, 3, 5, 6. |
| 2 |
2023-04-21 |
0: 14, 15, 16, 17, 19, 1.1: 8, 9, 16, 17, 20, 1.2: 3, 6, 7, 8, 22. |
| 3 |
2023-04-28 |
1.3: 4, 6, 9, 10, 11, 12, 13, 14, 17, 18, 19, 27, 30, 32. |
| 4 |
2023-05-05 |
2.1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. |
| 5 |
2023-05-12 |
2.1: 11, 12, 13, 14, 15, 16, 18, 23, 24, 30. |
| 6 |
2023-05-19 |
2.1: 17, 19, 20, 21, 22, 26, 27, 29, 31, 2.2: 27, 28, 29. |
| 7 |
2023-05-26 |
2.2: 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 16. |
| 8 |
2023-06-02 |
2.2: 14, 15, 17, 19, 20, 21, 22, 23, 32, 33, 41, 43. |
| 9 |
2023-06-09 |
3.2: 1, 3, 7, 8, 11, 3.A: 1, 3, 3.B: 1, 2. |
You should write down with whom
you worked at the top of each assignment. You should also cite any
sources (other than lectures and the textbook) that you use.
Exams: The final is take-home; you must upload your exam
(either LaTeX-ed, or handwritten and then scanned) to Gradescope by
2023-06-14. There will be no make-up exams. Taking the final exam is
mandatory. In particular, note that university policy requires that a
student who misses the finals be automatically given F, unless it is
due to extreme and documented circumstances, in which case, if the
performance in the course is otherwise satisfactory, the grade might
be I.
Grading: Numerical grades will be recorded in Gradescope. The composite numerical grade will be computed as 70% HW +
30% Final, and the final letter grades will be assigned based on that.
If you believe a problem on a homework or an exam has been graded
incorrectly, or that your score was not correctly recorded in the
Gradescope, you must bring this to the attention of the
instructor within 10 calendar days of the due date of the assignment
in question, or the date of the exam, and before the end of the
quarter. Grading complaints not initiated within this period of
time will not be considered. Please verify in a timely manner that
your scores are correctly recorded on Gradescope.