18.395 - Group Theory with Applications to Physics (Fall 2012)


Instructor: Prof. Dan Freedman

Office: 2-381

Email: dzf [at] math . mit .edu

Lectures: T R 11:00 - 12:30 pm in 2-131

Course Overview: Syllabus


Description: The aspects of group theory discussed in this course have been selected because of their usefulness in physics. However there will probably be limited time for discussion of physics motivations or applications. In the past most students in the course have been graduate students or advanced undergraduates in applied mathematics and physics. The general philosophy is to use nite groups to bring out some major ideas in a simple context, but to emphasize Lie groups, Lie algebras, and their representations. The outline below gives an "approximate" list of topics to be treated.

Prerequisites: Students should have a good knowledge of linear algebra, i.e., vector space theory and matrices. They should have completed a course in quantum mechanics in which the theory of angular momentum was discussed and which (hopefully but not essentially) included a discussion of representations of the angular momentum algebra.


Problem Sets

Problem Set 1 (Due Thursday, September 20)

Problem Set 2 (Due Thursday, October 4)

Problem Set 3 (Due Thursday, October 18)

Problem Set 4 (Due Thursday, November 1)

Problem Set 5 (Due Thursday, November 15)

Problem Set 6 (Due Thursday, December 6)


Supplementary Materials

Group Representations

Invariant 1-forms (Tung)