T,Th 14:00-15:45

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 : 30 %
Final: 35 %
Homework: 25 %
Attendance 5%,
Class contribution etc.: 5%

How the course will run in Zoom: 

Each week we will meet in Zoom (usually Tuesday 2:30-3:45) for which we will send Zoom links. Some of the homework problems will be assigned to the students and two or three will present their solutions. This will begin from the 5th or 6th week. The grades here will go to the class contribution points.    Also, we will use OneNote (downloadable from kftp.kaist.ac.kr) for lectures and your presentations. We will make a notebook in OneNote which you can share and send the links to you.    

The exams will be take-home exams. Grades will be in A, B, C, D, F, I, S, U. You can choose S/U as your grades. 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. For reports, you have to work within the relevant content of this course. There will be only 4-5 reports announced at the KLMS later. The attendances will be checked by attending the Zoom meetings. (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.)

For reports and homework, you are allowed to use internet searches and other books. However, you need to quote the sources. If you don't supply the sources, you will be considered to be cheating.         

This is the take-home exam policy: You are allowed to use textbooks and your note only. Internet searches and consulting other books will be considered cheating. By taking these courses, you are subject to these ethical rules which are very many and are in the university ethics. Note that you will need to agree to a contract with me about all these ethical issues. If you don't agree to these policies, I advise you to drop the course.


Course Schedule and Reading Assignments (tentative):

Week 1: Chapter 1
Week 2. Chapter 2
Week 3: Chapter 3
Week 4: Chapter 4
Week 5. Chapter 5 (one class)
Week 6: Chapters 5, 6
Week 7: Chapter 7
Week 8: Midterm Exam
Week 9: Chapter 8
Week 10: Chapter  9  
Week 11: Chapters  10, 11 
Week 12: Chapters  12, 13
Week 13: Chapters 14, 15
Week 14: Chapter 16
Week 15 : no class (KAIST entrance exams Dec. 7-10)
Week 16: Final Exam