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                                                                               
Fall 2026 Hannah Choi (NSC) Introduction to Computational Neuroscience
  Anton Leykin Bridge to Mathematics
  Cheng Mao  Advanced Statistical Theory for Machine Learning
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. Fall 2026 courses will be updated soon. 

Prerequisites: 

Spring 2026:

  • 4803-HOM: Math 4107 (Abstract Algebra)

 

Fall 2026:

  • 4803- HP/LEY: There are no specific mathematical prerequisites, though maturity is expected and a willingness to work in groups is essential. 
  • 4803-NSC: Math 2552 (concurrent enrollment is satisfactory). Students with a strong background who have not completed this course may reach out to the instructor to inquire about the possibility of an override. 
  • 4803- MAO: A first course in probability/statistics: Math 3215, 3670, 3235, or 3740, or ISYE 3770 or 3030, or CEE 3770, or ECE 3077. 
Course Text: 

Spring 2026:

  • 4803-HOM: See syllabus

 

Fall 2026:

  • 4803- HP/LEY: See syllabus
  • 4803-NSC: See syllabus
  • MAO: 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.

Fall 2026:

  • 4803- HP/LEY: No, this is not a pre-math remedial course: "bridge" is a popular card game. We will learn how to play and then play. Studying parts of combinatorics and probability theory relevant to the game should help us play bridge better. We will split time between theory (both bridge and math) and practice (play and discussion). Bridge puzzles, math puzzles, mini-tournaments, post-game analysis -- all will be components of this course.
  • 4803-NSC: This course provides an introduction to computational neuroscience, focusing on mathematical model-based approaches used to understand neural dynamics and computations across single cells and networks of neurons. The course is designed for both students with mathematical and computational backgrounds interested in neuroscience, as well as for students with neuroscience backgrounds interested in mathematical models. Some basic knowledge and familiarity with Python, MATLAB, or other programming languages will be useful. The following topics will be covered in the course: single neuron spiking models,  networks of neurons and rate-based models, learning and memory in neural networks, and encoding/decoding in neural populations.
  • MAO: The course focuses on the theory of statistical inference and statistical learning, providing a rigorous treatment of a range of estimation and prediction problems. These include, for example, linear regression, classification, matrix estimation, nonparametric statistics, and neural networks. The course is theoretical and is intended for students who are interested in mathematical and statistical foundation of machine learning.