## Math 131, Topology

### Course Outline:

An introduction to point-set, geometric, and algebraic topology. For point-set topology, topics covered include set theory, topological spaces, connectedness, compactness, and metric spaces. For geometric/algebraic topology we will discuss the fundamental group, homotopy type, covering spaces, and the classification of closed surfaces.

### Textbook:

J. Munkres, Topology, 2nd ed.Pentice-Hall 2000.

### Prerequisites:

Acquaintance with metric spaces (e.g. Math 23, 25, 55, 101, 112) and elementary group theory (e.g. Math 101, 122). This should not be your first proof-based math course.

### Exams:

There will one in-class midterm exam on Thursday, March 13. Subject to approval of the registrar, the final exam will be a take-home exam. It will be posted on the web on Saturday, May 3 and due in my office on Thursday, May 8 at 3:00 pm. You should expect that the exam will take about 2.5 days of that period. Makeup exams will only be given in extreme circumstances.

### Homework:

There will be one HW assignment per week, which will be assigned on Tuesday and due the next Tuesday. Homework assignments must be turned in on time; no late homework will be accepted. However, your lowest homework grade will be dropped. Homework assignments will be posted on the course web page.

You are allowed, nay encouraged, to work together on homework problems. However, you must write up your solutions individually, and give credit to your collaborators.

Homework will be worth 30% of the final grade, the midterm 30%, and the final 40%.

### Office Hours:

In addition to the times above, I am available by appointment. For an appointment, just talk to me before/after class or send me e-mail.

### First HW assignment

Due Thursday Feb 6.
• Read the following sections of Munkres Chapter 1: 1,2,3,5,7. You can skip equivalence relations in section 3 for now.
• Problems from Munkres:
1.1: 2(p,q), 5(b,c), 7, 10(c,d).
1.2: 1,5.
1.3: 6, 9, 13, 15(b).
1.7: 3, 5(e,h), 6.