(Fall, 2017) 화목 15:30-16:45 (24동 209호)
We will study and understand Gauss-Bonnet Theorem and Morse theory for surfaces.Week 1: What is a Euclidean space? What are the motions?
Week 2: What is a surface?
Week 3: What is a manifold? What is a Riemannian manifold?
Week 4: Euler characteristic and Classification of Surfaces
Week 5: First and Second Fundamental Forms
Week 6: Fundamental theorem for the theory of surfaces
Week 7 (Oct. 24, 화) : Midterm
Week 8: Principal Curvatures, Gauss Map, Gaussian Curvature, Theorema Egregium
Week 9: Geodesics
Week 10: Surfaces of Constant Curvature
Week 11: Trigonometry
Week 12: Vector fields and indices
Week 13: Gauss-Bonnet Theorem
Week 14: Morse Theory
Week 15 (Dec. 12, 화): Final Exam
Midterm 30%, Final 40%, Homeworks 20%, Etc. 10 %