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MATH 5345H Honors: Introduction to Topology (Fall 2017) |
Lecturer: Craig Westerland, 459 Vincent Hall, 612-625-0523, cwesterl@umn.edu.
Lecture: 11:15 -- 12:05 Monday, Wednesday, Friday, Vincent Hall 20.
Office Hours: 2:15-3:45 Monday, 9:30-11 Thursday.
We'll learn to work with abstract topological spaces, both the concrete and the very formal, the non-intuitive and the geometric. We will develop qualitative tools to characterize them (e.g., connectedness, compactness, second countable, Hausdorff...), and develop tools to identify when two are equivalent (homeomorphic). Several important results will be proved, notably the Tychonoff theorem on products, but an equal focus will be placed on understanding examples coming from geometry, algebra, and number theory. Towards the end of the class, we will study the fundamental group and if time permits, covering spaces.
Through this course, students will learn to develop formal proofs and careful mathematical arguments, and will be able to communicate them effectively in writing. They will have mastered the basics of point-set topology and have a good understanding of the examples and counterexamples that inform the development of the subject.
Homework assignments: