2023-2024 Academic Catalog

Dec 07, 2025

2023-2024 Academic Catalog [ARCHIVED CATALOG]

MATH 201 - Proseminar in Mathematics

Senior undergraduates study and speak on topics in mathematics to become acquainted with diverse subjects, learn to research known topics, practice presenting mathematics to peers, and present their research areas. Possible topics include: category theory, knot theory, automorphic forms, topos theory, low-dimensional topology, class field theory, group representation theory, and dynamical systems. This is a capstone course in mathematics.

Spring 2021
Geometric Analysis lies at the intersection of developments in differential geometry, partial differential equations, and modern physics. This advanced undergraduate course is an introduction to this field with applications to mathematical general relativity. The framework of this course is Riemannian geometry, Lorentzian geometry, and geometric differential equations, e.g., Einstein equations. We study special Lorentzian manifolds (i.e., spacetimes) that correspond to the cosmological universe and black holes in general relativity. Finally, we define geometric quantities related to energy in general relativity and review the proof of positive energy theorem for special spacetimes.

Prerequisites: 130 (Linear Algebra) and Math 131 (Multivariable Calculus) are formal prerequisites. Familiarity with Math 230 (Differential Geometry) is also recommended but not required.

Anticipated Terms Offered: Offered periodically