M,W 13:00-14:45

Room: E2 1225

Lecturer: Suhyoung Choi schoi at math.kaist.ac.kr



This course is designed for the first year graduate students to provide them with basic concepts of differential geometry and help them to prepare for the more advanced topics:
Riemannian geometry, symplectic geometry, complex geometry, and any other topics that need the concept of manifolds. The course covers the concepts
of smooth manifolds, submanifolds, Lie groups, vector fields, differential forms, tensor fields on manifolds, integration on manifolds and Stokes's theorem.
Some theorems and their proofs will be only sketched in this course, and so it will be important to read the course material before the class.


Main textbook:
John M. Lee, Introduction to Smooth Manifold, Springer Verlag 2012 (downloadable from the main library)

Supplementary textbooks (use the latest versions)
William M. Boothby, "An Introduction to Differentiable Manifolds and Riemannian Geometry", Academic Press

Related books: S. S. Chern et al. "Lectures on differential geometry", World Scientific Kobayashi and Nomizu, Foundations of Differential Geometry, Vol 1. John Wiley 1996 M. Spivak, "A comprehensive introduction to differential geometry", Vol I, Publish or Perish, Inc. F. Warner, "Foundations of differentiable manifolds and Lie groups", Springer

Grading Policy:
Midterm : 35 %
Final: 35 %
Homework: 0 %
Attendance 5%,
Class contribution 5%
Assignment 20 %

This is an EDU4.0 course. Each week, you will study the material and watch the videos for that week before the classes. We will meet in class for discussions on the problems assigned for each week. This will begin from the second week. Lecture videos will be on KLMS. We will divide the class intro groups of three to four students. Groups will be assigned discussion problems on Monday, and groups will give presentations on Wednesday.

The exams will be offline open book exams. Grades will be in A, B, C, D, F, I, P, NP. (Notice P/NP policies are not completely determined by KAIST yet.) Also, A+ will be given for only the work surpassing the expectations. A0 is the normal highest grade for any work in this course. These are all graded by the subjective judgement of the instructor which follows the long traditions in the universities in the world. (We will experiment with "peer grading". This is strictly experimental. We will tell you precise policies later. The points will go into the class contribution points. Of course, we will only consider these and not be bound by what you assign.)