Special Course Descriptions
Math
MAT 394 10 - Knots and Surfaces
TTH 10am - 11:15am
Prof. McLendon
See attached flyer
Course Description: In this course, you will explore the world of low-dimensional topology. Topology is the study of geometric objects as they are transformed by continuous functions. In your study of calculus, you have frequently encountered geometric concepts connected with continuous functions like the area under a curve, the volume of a solid of revolution, or the curvature of a parametric curve in 3-space.
In "Knots and Surfaces", you study similar geometric objects, but you will use fewer equations and more pictures!
Prerequisites: Topology merges the concepts from both geometry and algebra. Because visualization is important, MAT 203 is a prerequisite. It will also be useful for you to have some experience with proofs and abstract reasoning, so either MAT 240 or MAT 325 is suggested. I expect this course to be about the same level of difficulty as the other 300-level mathematics electives, like Foundations of Geometry or Number Theory, but not as challenging as "theory courses" like Abstract Algebra or Real Analysis. The most important traits you will need are a willingness to ask questions and the curiosity to explore these unusual topics.
Research Opportunities: Low-dimensional topology is the area of research that I specialize in. During this course, I hope to introduce you to various topics that you could continue studying after the course. The study of knots and surfaces would make for a nice summer research project and an excellent senior thesis.