Differential Geometry MAS 520

MWF 13:00-13:50

Room: E6-1 2412

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



This course is designed for the first year graduate students to give 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 to deal with the concept of manifold. The course covers the concepts
of a differential manifold, submanifolds,  Lie groups, vector fields and more generally tensor fields on manifold, integration on manifold 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:
       William M. Boothby, "An Introduction to Differentiable Manifolds and Riemannian Geometry", Academic   
Press

Supplementary textbooks (use the latest versions):
       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
       미분다양체론 입문, 윤옥경, 김홍종, 서울대학교 대역해석학연구센터 1993


Grading Policy:
     Midterm : 30 % (Chapters 1--4.8)
     Final: 35 % (Chapters 4.9, 5, 6)
     Homework: 25 % (2 or 3 problems almost every week)
     Attendance, Reading Assignments, and Class contribution etc.: 10 %


Course Schedule and Reading Assignments (tentative):

Week 1: Chapters 1, 2 (reviews)
Week 2. 3.1, 3.2, 3.3
Week 3: 3.4, 3.5, Holidays
Week 4: 3.6, 3.7, 3.8
Week 5. 4.1, 4.2, 4.3
Week 6: 4.4, 4.5, 4.6
Week 7: 4.7, 4.8, 4.9
Week 8: Midterm
Week 9:  5.1,5.2, 5.3
Week 10:  5.4, 5.5      
Week 11:  5.6, 5.7
Week 12:  5.8, 6.1, 6.2
Week 13: 6.3, 6.4
Week 14:  6.5, 6.6
Week 15 : 6.7, 6.8
Week 16: Final Exam


HW will be announced here.