Independent Studies-Mathematics 199B-WINTER 2018  LIE GROUPS AND THEIR LIE ALGEBRAS  

Fridays 4-4:50 Rowland Hall 340P (syllabus)

Introduction to Differential Geometry, by Joel W. Robbin and Dietmar A. Salamon (here)

Analysis in Several Variables, Math 140C Fall 2006 (here)

First Meeting, January 12, 2018 Overview of sections 11,15,16,17 in Analysis in Several Variables, Math 140C Fall 2006 (here)

Second Meeting, January 19, 2018 Informal notes for 1.2 and 1.4 of Robbin-Salamon: Chart, atlas, smooth manifold (pp 4-7,10-12) (here)

Pages 4-7 of Robbin-Salamon (here)

Pages 10-12 of Robbin-Salamon (here)

Third Meeting, January 26, 2018 Informal notes for 2.1 and 2.2 of Robbin-Salamon: Submanifolds of Euclidean space, tangent space (copies of pp 16, 24-27 included) (here)

Fourth Meeting, February 2, 2018 Informal notes for 2.2 (continued) of Robbin-Salamon: Derivative (copies of pp 28-30 included) (here)

Assignments 1-26 Math 140C (here) Exercise pages Buck, Advanced Calculus (here)

Fifth Meeting, February 9, 2018 Informal notes for 2.3 of Robbin-Salamon: Submanifolds of submanifolds of Euclidean spaces (copies of pp 33-36 included) (here)

Sixth Meeting, February 16, 2018 Informal notes for 2.4 of Robbin-Salamon (part 1): Vector fields and integral curves (copies of pp 37-39 included) (here)

Pages from Buck for Assignments 2,9,16,17,22(here)

Existence and Uniqueness of Initial Value Problem---Notes by James Buchanan(here)

Seventh Meeting, February 23, 2018 Informal notes for 2.4 of Robbin-Salamon (part 2: The Lie algebra of vector fields (here)

Pages 40-50 of Robbin-Salamon (here)

Eighth Meeting, March 2, 2018 Informal notes for 2.5 of Robbin-Salamon (part 1): The Lie algebra of a Lie group (here)

Pages 51-56 of Robbin-Salamon (here)

Ninth Meeting, March 9, 2018 Informal notes for 2.5 of Robbin-Salamon (part 2): Lie group homomorphisms (here)

Pages 57-60 of Robbin-Salamon (here)

Tenth Meeting, March 16, 2018 Informal notes for 2.5 of Robbin-Salamon (part 3): Diffeomorphisms, Algebra homomorphisms, Vector fields, Derivations (here)

Pages 61-64 of Robbin-Salamon (here)

Review of terms and Exercise suggestions (here)