## Course Web Page

Course: MATH 3980T

Title: Introduction to Differentiable Manifolds and Lie Groups

Section: 103 (Class Number 14592) (Tutorial for students in the Honors Tutorial College, HTC)

Department: Mathematics

Term: Spring Semester

Instructor: Mark Barsamian

Contact Information: My contact information is posted on my web page.

Office Hours for 2018 - 2019 Spring Semester: 8:45am - 9:30am Mon - Fri in Morton 538

Course Description: A previous tutorial on Differential Geometry explored curves and surfaces embedded in $$\mathbb{R}^{3}$$. In this course, we study abstract differentiable manifolds. As with surfaces in the previous tutorial, the definition of a manifold is based on coordinate neighborhoods. But there is a fundamental difference between the courses in their approach to differentiation. In the previous course, differentiation on surfaces was always obtained by differentiating in the ambient space $$\mathbb{R}^{3}$$. This simplified the initial notation, but it actually both complicated and limited the study of the curves and surfaces. In this course, differentiation on manifolds is obtained from differentiation in the coordinate neighborhood. The initial notational structure is much more complicated than in the previous tutorial, but it ultimately leads to a much deeper, much richer understanding. Topics will include Manifolds, Lie Groups and Lie Algebras, Vector Fields and Tensor Fields on Manifolds, Integration and Differentiation on Manifolds, and Curvature