Course overview
The course is an introduction to topology and develops the basic theory and applications of metric spaces and topological spaces. Such spaces occur throughout mathematics; important examples will be studied throughout the course.
- Metric spaces
- Contractions and Compactness
- Topological spaces
Course learning outcomes
- Demonstrate an understanding of the concepts of metric spaces and topological spaces and familiarity with a range of examples of these structures.
- Prove basic results about completeness, compactness, connectedness, and convergence within these structures.
- Demonstrate skills in constructing rigorous mathematical arguments.
- Apply the theory in the course to solve a variety of problems at an appropriate level of difficulty.
- Demonstrate skills in communicating mathematics.
- Complete a small research project as a member of a team.