18.704

In 18.704, students take turns presenting the subject matter week by week. The Spring ’22 topic is harmonic analysis on finite groups and its applications. In the first half of the course, we introduce the discrete Fourier transform and apply it to graph theory, probability, coding theory, and physics. In the second half, we discuss its nonabelian generalization, focusing on matrix groups over finite fields.

pdf Syllabus

pdf Tentative schedule

Time & Place: MWF, 1–2 PM, Room 2-151

Textbook: Terras, Fourier Analysis on Finite Groups and Applications

Supplements:

Etingof et al., Introduction to Representation Theory
pdf Mackey, “Harmonic Analysis as the Exploitation of Symmetry”
Piatetski-Shapiro, Complex Representations of \(GL(2, K)\) for Finite Fields \(K\)
pdf Sloane, “An Introduction to Association Schemes and Coding Theory”

Notes

pdf My notes for the first week

pdf Susan Ruff’s slides about known vs. new information in scientific writing

pdf Xiangkai’s notes on Laplacians and their spectra

Final Papers

pdf tex \(\LaTeX\) template for the final paper

Note (5/28/24): The list of final papers has been temporarily removed.