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Organization, Regulations, and Courses 2024-25


MATH 72.02 Lie Groups: An Introduction Via Matrix Groups

Created by Sophus Lie (1842-1899) with the intent of developing a “Galois theory” of differential equations, Lie groups are a mathematically rigorous realization of our intuitive notion of “continuous transformation groups” and play a fundamental role in the study of geometry and physics.

Formally, a Lie group is a group G equipped with the structure of a smooth manifold with respect to which the group operations (i.e., multiplication and inversion) are smooth. Our exploration of Lie groups will begin with the study of “matrix groups” (e.g., SO(n), SU(n), Sp(n) and SLn(R)). By focusing on this concrete class of examples, we will build our intuition and encounter many of the interesting themes that arise in the general theory of Lie groups.

Instructor

Sutton

Prerequisite

Math 13, and Math 22 or Math 24, or Permission of the Instructor

Degree Requirement Attributes

Dist:QDS

The Timetable of Class Meetings contains the most up-to-date information about a course. It includes not only the meeting time and instructor, but also its official distributive and/or world culture designation. This information supersedes any information you may see elsewhere, to include what may appear in this ORC/Catalog or on a department/program website. Note that course attributes may change term to term therefore those in effect are those (only) during the term in which you enroll in the course.

Offered

  • Spring