This course covers basic point set topology, in particular, connectedness, compactness, and metric spaces. We aim to cover a bit of algebraic topology, e.g., fundamental groups, as time permits. We will also apply these concepts to surfaces such as the torus, the Klein bottle, and the Moebius band.
Our primary goal this semester will be to get through the first four chapters of Munkres' book. We will cover other topics as time permits.
Students may work together on homework but must write up their work individually. The homework will be graded and it is the student's responsibility to make sure that his or her work is written clearly (this refers both to handwriting and style of prose).
The homework is the most important part of the course. No matter how well you think you understand the material presented in class, you won't really learn it until you do the problems. You are free to devise whatever strategy for learning the material suits you best. This may involve collaboration with other students. We believe, however, that most people will get the maximum benefit from the homework if they try hard to do all the problems themselves before consulting others. In any case, whatever you turn in should represent your own solution, expressed in your own words, even if this solution was arrived at with help from someone else. Remember, you are doing the homework in order to learn the material; don't try to defeat the purpose of it.
Make-up quizzes will NOT be given.
Prelim Dates: The take-home prelim will be handed out in class on Monday, October 18, and will be collected in class on Monday, October 25. No late exams will be accepted. The exam is open-text and open-notes, but students are not permitted to work together or to discuss any aspect of the exam with any other person. "Open-text and open-notes" means students should feel free to use Munkres' "Topology" but should not use any other reference material, including the internet, other than their class lecture notes.
(NOTE: While the material for the final exam will cover the entire course, there will be somewhat of an emphasis on the material covered after the prelim.)
Solutions to the final may be found HERE .
Last modified: 25 August 04