# Topics

The possible range of projects is completely open, and depends on the mutual interests and backgrounds of the mentor/mentee. The only prerequisites for undergraduates are completion of Math 19A/B and 20A/B. There is also the possibility of applied math/statistics or math education projects. Some suggestions from a subset of possible subject areas are:

**Algebra**

Modular Arithmetic/Fermat's Little Theorem

Braid Groups

Quadratic Reciprocity

**Analysis**

The Contraction Mapping Theorem

The Lorenz System and dynamics

Poincare-Bendixson Theorem, Recurrence

The Cantor set and Lebesgue measure

**Geometry/Topology**

Maxwell's Equations and Geometry

Matrix Groups/Lie groups and algebras

Projective Geometry

The Fundamental Group

Knot Polynomials

**Applied Math**

Persistent Homology

SIR Models in epidemiology

Signal Processing, Fourier Analysis

PageRank algorithm and Markov chains

The Capital Assets Pricing Model

Public-key cryptosystems

For more complete lists of past topics/projects visit the below links: