Familiarity with linear algebra, including matrix mutiplication, change of basis, determinant, trace, eigenvalues and eigenvectors;
Some exposure to abstract algebra, including vector spaces and groups;
Comfort with elementary differential calculus;
Some acquaintance with complex numbers.
Course description
Lie groups are groups of continuous symmetries, generalizing the familiar notion of rotation groups; Lie algebras are their infinitesimal versions. Lie groups describe the symmetries of many physical henomena, combining algebra and geometry in beautiful ways. This course provides an introduction to the rich theory of Lie groups and Lie algebras, using explicit matrix groups to demonstrate concepts from differential geometry and abstract algebra. In particular, the properties of the orthogonal and unitary groups will be studied, along with several applications.