Welcome to the Math 460 (Topology) course website!
Topology is the study of "continuous deformations" of objects. What is a continuous deformation? For now, imagine an object as being made of a very stretchy rubber (or Play-Doh). A continuous deformation of the object is some warping (stretching, shrinking) of the object where one doesn't tear or glue the object. We will start by developing a sufficiently general notion of a continuous function using set theory. We will then consider the problem of identifying when two spaces are equivalent (i.e., when they can be continuously deformed into each other) using notions of compactness and connectedness. As time permits we will explore additional concepts that can distinguish spaces such as orientation (or lack thereof) and the fundamental group.
In Math 460, students will:
- Understand the topological concepts of continuity, connectedness, and convergence.
- Connect geometric intuition (e.g. from calculus) about these concepts to their abstract definitions.
- Further develop logic and proof-writing skills.
- Hone mathematical communication skills (both spoken and written).
- Have fun!
See the course syllabus for further details. Please note that Math 222 (Foundations) is a prerequisite for this course.