MATH 535 - General Topology

Fall 2014

Fall 2014

A printable syllabus can be found here. A note regarding emergency procedures in the case of fire, tornado, or an active threat can be found here. (It can also be found on the syllabus.)

Course Information

- Section: MATH 535 Section P1
- Time: TR 11:00-12:20pm
- Location: 443 Altgeld Hall
- Instructor: Jordan Watts
- Email: jawatts at illinois
- Office Hours: T 2-3, or by appointment
- Office: 238 Illini Hall

Course Description

Point-Set Topology is a language developed for the purpose of describing arrangements of points by how they are separated from one another. Motivated by properties enjoyed by open and closed sets studied in real analysis, we will develop the notion of a topology, and attempt to generalise many of these well-known properties to more general spaces. In particular, we will study metric spaces, subspaces, quotient spaces, products, and function spaces. We also will discuss more classical algebraic topology from a more modern perspective. We shall see that interesting algebraic structures arise from considering paths in a space. Indeed, via the language of categories, functors, groupoids, and natural transformations, we will develop a theory that will allow us to obtain global properties of a space, using paths.

Prerequisites and Restrictions

4 credit hours. MATH 447 or equivalent, 417 or equivalent, or consent of instructor.

Texts

There will be no required text for MATH 535. The recommended text will be *Topology and Groupoids* by Robert Brown, 2006 edition, BookSurge Publishing. There is a webpage for the book here, and a cheaper digital version can be found here.

Other potentially useful books include:

*Topology*by Munkres*Topology and Geometry*by Bredon

Grading

There will be a final exam worth 30% of the course grade. The remaining 70% will be based on homework assignments. There will be 7 homework assignments, due roughly every two weeks, of which the best 5 will count toward your final grade. Each homework will be due at the beginning of class on a Thursday (mostly). LATE HOMEWORK WILL NOT BE ACCEPTED. Also, while you are encouraged to work together, your assignments are expected to be in your own words. Copying of any kind, including from the internet, is considered an academic offence and will be dealt with accordingly. Finally, if your final exam average is better than your homework average (after dropping the lowest three), then your grade will be reweighted: the final will be worth 40% and the homeworks 60%.