Course goals: We will begin by covering certain fundamental notions in point-set topology, including metric spaces, open and closed sets in general topological spaces, compactness and connectedness. We will go on to cover the beginnings of algebraic topology, including the Euler characteristic, the fundamental group, and covering spaces. Sprinkled throughout the course will be applications to such ideas as fractals, configurations of robot arms, the five-color theorem for planar maps, and the topology of the universe.

Textbook: Topology and its Applications, by William Basener. We will cover most of Chapters 1-5. In addition, I will likely supplement Basener's narrative with handouts from other books.

Prerequisites: Undergraduate algebra and analysis. From analysis, the concepts we will need include infima and suprema, as well as open, closed, and compact sets in the Real line. From algebra, we will need groups, homomorphisms, and normal subgroups.

Homework policy: Homework assignments will be posted on the course webpage, and will typically be due on Thursdays. No late homework will be accepted, but I will drop your lowest homework score. I encourage you to start early and to discuss the problems with other students. By all means come by my office hours if you have trouble with a problem. The only real caveat to group work is that you must write up your own solutions, in your own words.

Presentations: At some point during the semester, every student will need to give a 30-40 minute, oral in-class presentation on a topic peripherally related to our course. The purpose of this is two-fold. First of all, this field of math has many interesting examples and special topics that don't fit neatly into a linear exposition. Some of these topics are mentioned in the "Coarse goals" above, others appear in the "Application" sections of the book, and many more lurk just below the surface. These presentations are a way for all of us to be exposed to these ideas. Second of all, these presentations are intended to help you practice the art of explaining difficult concepts. In fact, I've found that having to explain something makes me understand it on a much deeper level.

Starting in early October, we will begin scheduling weekly in-class presentations. You should definitely discuss the topic with me before presenting it. I would also be more than happy to suggest topics for presentations.

Final Exam: The take-home final will be handed out during the last week of classes, and will be due on December 15.