Math 225C: Algebraic Topology

Spring 2017

Instructor: Sucharit Sarkar.
Class: MWF 1-1:50pm, MS 7608.
Office hours: Th 2-2:50pm and F 10-11:50am, MS 6909.

TA: Kevin Carlson.
TA discussion section: Th 1-1:50pm, MS 7608.
TA office hours: By appointment.

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.
Prerequisites: Basic knowledge of algebra and point set topology. Try these problems to check your preparedness.
Useful links: Department page, University page, MyUCLA gradebook.

Homework: Homeworks are due at the beginning of lecture on Monday. Do not submit homework by e-mail. No late homework will be accepted.
HW Due on Problems
1 4/10 0: 1, 2, 3, 13, 1.1: 1, 2, 3, 5, 6.
2 4/17 0: 14, 15, 16, 1.1: 8, 9, 16, 1.2: 3, 6, 7, 8.
3 4/24 1.3: 4, 6, 9, 10, 12, 13, 19, 27, 32.
4 5/1 2.1: 1, 2, 3, 4, 5, 6, 7, 8, 9.
5 5/8 2.1: 10, 11, 12, 13, 14, 15, 16, 18, 30.
6 5/15 2.1: 17, 20, 21, 22, 29, 31, 2.2: 27, 28, 29.
7 5/22 2.2: 2, 3, 4, 5, 7, 8, 9, 10, 12.
8 5/31 2.2: 14, 15, 17, 19, 20, 21, 22, 23, 33, 43.
9 6/5 2.2: 40, 41, 3.1: 5, 6, 8, 9, 3.A: 1, 3, 3.B: 1, 2.
10 6/12 3.2: 1, 3, 5, 7, 8, 11, 12.
You are encouraged to work in groups on your homework; this is generally beneficial to your understanding and helps you learn how to communicate clearly about mathematics. However, you must write up all solutions yourself. Moreover, since crediting your collaborators is an important element of academic ethics, 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: 225C-finals.pdf (Link active 6/9-6/16)
The final take-home final exam due on 6/16. Once again, you are free to collaborate and consult textbooks and notes, but you must write up all the solutions yourself, and you must credit your sources and collaborators. Submitting 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 the MyUCLA gradebook. 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 MyUCLA gradebook, 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 (6/16). 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 MyUCLA.