MATH 739 - Lie Groups

(3 units)

A rigorous introduction to the theory of Lie groups with an emphasis on their structure, geometry, and representations. Students will explore Lie groups as smooth manifolds with group structures, the associated Lie algebras, exponential maps, matrix groups, and their actions. The course will provide the foundations needed to understand the role of symmetry in modern mathematics and theoretical physics. Applications to geometry, differential equations, and representation theory will be given.

Maximum units a student may earn: 3

Recommended Preparation: A solid foundation in advance calculus, linear algebra, and topology, e.g., MATH 283, MATH 330, MATH 440.

Grading Basis: Graded
Units of Lecture: 3
Offered: Every Fall - Odd Years

Student Learning Outcomes
Upon completion of this course, students will be able to:
1. articulate the definitions and basic properties of Lie groups and their tangent spaces.
2. compute examples of Lie groups and their tangent spaces.
3. apply the theory of Lie groups to problems in geometry and mathematical physics.

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