If you find really nice links that I should know about please let me know what they are. A topological space is a universe in which you can make sense of continuity. Our second task will be to develop an abstract framework that encompasses all these spaces and produces useful theorems. Part of the beauty of the subject comes from the examples and part of the beauty comes from seeing how to lend rigour to intuitive ideas about spaces we can visualize and use the rigour to carefully extend the intuition to spaces that are very hard to visualize. If you take the course I will try to direct the topics so as to match your personal interests and so as to work with your particular mathematical background as much as possible.
Topology is at the foundation of almost all other mathematics in one way or another.
There's really no other course here at the undergraduate level that's anything like this, and this course hasn't actually run in the last few years because not enough people have enrolled. This year it will run, so it will be a really unique opportunity for you. If you are thinking about graduate school in math or science, a good background in topology will help you immensely. We will touch on examples from many different fields so it will be a good opportunity to taste many flavors of math under one roof. Topology is one of those rare mathematical fields where you can actually tell non-math people a little bit about what you are studying, so it makes for good conversation.