MATH 249 LEC A: INTRO LIE GROUPS (45094)

Math 249 Fall 2024

Instructor Contact Information:

Isaac Goldbring
Email: isaac@math.uci.edu
Homepage:  https://www.math.uci.edu/~isaac/

Office: RH 417
Office Hours:  Mondays at 9am by Zoom.  Here's the Zoom link Links to an external site..

Course Information:

  • Text:  "An elementary introduction to groups and representations" Links to an external site. by Brian Hall

  • Course Description: We will cover the basic facts about matrix Lie groups, their Lie algebras, and their representations.  The goal is to cover Chapters 2 through 5 from the notes.  We assume that the student is familiar with very basic group theory (as covered in Chapter 1 of the above notes) as well as some basic topology.

  • Alternate references:  The above notes were later greatly expanded and turned into a book "Lie groups, Lie algebras, and representations:  an elementary introduction." Links to an external site.  We might occasionally refer to that book for extra material.  Another great introduction to elementary Lie theory, again with a focus on matrix Lie groups, is "Naive Lie theory" Links to an external site. by John Stillwell; I recommend this book for additional examples and alternate explanations of important results.  We will use Stillwell's book when we cover the Baker-Campbell-Hausdorff theorem rather than Chapter 4 of the Hall notes.
  • Class Meetings: The class meets twice a week:  Tuesday and Thursday, 10-11:20am in RH 306.

  • Grading will be based solely on one problem set, to be turned in on Canvas by Friday, December 6, 11:59pm.  I will post a list of problems from the Hall notes and you are to choose and solve any 8 problems that you wish from this problem set.  You may work together on the problems, but please acknowledge who you worked with on each problem.  I highly encourage you to type up your solutions using LaTex.

Course Summary:

Date Details Due