Undergraduate Special Topics

Department: 
MATH
Course Number: 
4803
Hours - Lecture: 
3
Hours - Total Credit: 
3
Typical Scheduling: 
Most Fall and Spring Semesters

The following table contains a list of all undergraduate special topics courses offered by the School of Math within the last 5 years. More information on courses offered in the current/upcoming semester follows below. 

Semester Instructor          Title                                                                               
Spring 2026 Jennifer Hom Knot Theory
Fall 2025 Hannah Choi Introduction to Computational Neuroscience
  Cheng Mao Advanced Statistical Theory for Machine Learning
Fall 2024 Hannah Choi Introduction to Computational Neuroscience
  Anton Leykin Nonlinear Algebra
  John McCuan Mathematical Capillarity
Spring 2024 Austin Christian Low-Dimensional Geometry
Fall 2023 Anton Leykin Bridge to Mathematics
Spring 2023 Martin Short Science Based Data Science
  Hannah Turner Introduction to Knot Theory
Spring 2022 Marissa Loving Introduction to Combinatorial Topology
  Martin Short Science Based Data Science
Fall 2021 Zhiyu Wang Spectral Graph Theory
Spring 2021 Dan Margalit Geometric Group Theory
  John McCuan Mathematical Capillarity

 

In the lists below, Math 4803-XXX refers to the special topics course taught by the instructor whose last name begins with XXX. 

Prerequisites: 

Spring 2026:

4803-HOM: Math 4107 (Abstract Algebra)

Course Text: 

Spring 2026:

4803-HOM: See syllabus

Topic Outline: 

Spring 2026:

4803-HOM: This course is an introduction to knot theory. A (mathematical) knot can be thought of as a piece of string which has been knotted (in the traditional sense) with its ends glued. Two knots are the "same" if one can be moved through space to look exactly like the other (without breaking the gluing). A fundamental question in knot theory is: when are two knots the same? To distinguish knots, mathematicians use tools called invariants. We will discuss various ways to present a knot, invariants which can be used to distinguish them, and applications of knot theory to low-dimensional topology more broadly.