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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.