Mentorship
Mentorship
The UCI Mathematics Directed Reading Program (DRP) pairs undergraduate students with graduate student mentors to participate in a reading course. Graduate student mentors choose a topic in math that is not typically covered in the undergraduate curriculum, and design a 10 week course on that topic for 1-3 undergraduate students. The goal of the program is to give undergraduate students the opportunity to learn interesting math and to build skills such as communication, reading math, and critical thinking. For more information, click here.
DRP Projects ran by me:
Introduction to Measure Theory - Winter 2025
Textbook: Measure, Integration & Real Analysis by Sheldon Axler
Description: Measure theory is an indispensable analytical tool and is crucial for probability theory, operator theory, spectral theory, and many other fields in modern mathematics. Despite its importance, measure theory is not usually covered in mathematics curriculum until the graduate level. This DRP will act as a jump-start for undergraduate students, giving them exposure and experience in this subject area. We will begin with Reimann integration and the limitations therein, followed by an introduction to sigma algebras, measures, Lebesgue integration, and classic limit theorems. Through this, we will gain a deeper understanding of modern analytical methods and possibly discuss applications in probability theory and ergodic theory.
Graph Theory - Fall 2024
Textbook: Combinatorics and Graph Theory by John M. Harris, Jeffry L. Hirst, and Michael J. Mossinghoff.
Description: Famously pioneered by Euler himself, graph theory is a crucial mathematical tool for the modern mathematician. Graphs have been used to tackle unsolved problems in statistical mechanics, generate entire subfields in dynamics and number theory, and understanding graphs has been key to building modern internet infrastructure. In this directed reading project, we will start from the beginning and establish the basics of graph theory. We will cover the classic ideas such as trees, paths, cycles, planarity, and colorings and we will see how, even with these relatively simple tools, rich theory and surprising applications arise.
Symbolic Dynamics and Information Theory - Winter 2024
Textbook: An Introduction To Symbolic Dynamics And Coding by Douglas Lind and Brian Marcus
Description: Originally developed as a way to approach otherwise intractable problems in dynamics, symbolic dynamics now has broad and sometimes surprising applications, particularly in probability theory and computer science. One famous branch that arose was information theory, which helped design some of the first compression and encryption algorithms and continues to be an important field of research. We will study symbolic dynamics by exploring the fundamentals of sequence space and its operators. We will also learn about shifts of finite type, where we will use the deep connections to infinite graphs.Â
Functional Analysis with the Volterra Operator - Fall 2023
Textbook: Volterra Adventures by Joel H. Shapiro
Description: This course introduces the basic concepts of functional analysis by exploring the Volterra integral operator. With ODE theory as a motivator, we establish the basics of Banach spaces including function spaces and operators. We apply this theory to the concrete case of the Volterra operator and uncover how operator theory has implications for the solutions to ODEs.