### MATH 525
Algebraic topology I, Spring 2019.

**Class time and place:** MWF 3.00-3.50pm, 347 Altgeld Hall.

**Professor:** Igor Mineyev, 243 Illini Hall. It is better to talk to me during and after the class
and to come to office hours rather than to send email. Discussions are more efficient that way.

**Office hours:** Monday and Wednesday, 2.00-2.50pm.

Course description.

**Textbook:**
Allen Hatcher. Algebraic topology.
Freely
available online.
We will follow the numbering of the problems on that page, in case it is different from the book.

**Prerequisites:**
Math 417 (Introduction to Abstract Algebra) and Math 448 (Complex Variables), or equivalent.
The following background is expected for the course:

- The standard concepts of point-set topology
(metric spaces, open and closed sets, topological spaces, ...) Math 432 is a good sourse for this, or learn these
notions from any standard textbook on general topology, for example,
*James Munkres, Topology* or
*John Kelley, General Topology*.
- The standard concepts of abstract algebra (groups, group actions, fields, vector spaces,
classification of finitely generated abelian groups, free groups ...) Math 417 is a source for some of this, or use any of the many textbooks on abstract algebra, for example,
*Derek Robinson, An introduction to Abstract algebra*.

**Homework and exams.**
Homework will appear here.
If a newer version does not show up, restart your browser.
It is important to learn the material **after each class**.
Two lowest homework assignments will be dropped at the end of the course
to allow for personal emergency situations when there is a strong reason for missing a class.
Do not miss exams, quizzes and regular classes.
**It is important to attend the class.**
If you absolutely must miss a class, learn the material from your friends' notes.

- The first midterm exam: Friday, February 22, 2019. Before the curve, the median for this exam was 91, mean 89.5, standard deviation 4.1.
- The second midterm exam: Friday, April 5, 2019.
- The final exam: at 8:00-11:00 a.m., Thursday, May 9, 2019, in the regular classroom,
as required by the final exam schedule.

**Grades and grading policy.**
The current grades for the course will be posted (though not immediately).
To see your current grade for the class, click on the "Score Reports" link on the left in
www.math.illinois.edu/Classes/,
then enter your password.
The line "hw3:86<88/100" means that your score for homework 3 was 86 out of 100, and it was rescaled to 88 because of the curve used.
88 corresponds to B+ in the standard overall curve (90 is the highest lower bound for A-, 80 for B-, etc). The scores marked with "*'' are dropped. (This will show up only at the very end of the semester.) Let me know if there are any errors in the scores.
The average of the two midterms will count as 30% of the grade, the homework
40%, and the final exam 30%.

Interesting links related to topology.