(微分多樣體論, Differentiable Manifolds)
교과목 번호: 3341.505 (3-3-0)
- Linear Algebra
- Basic ODE
- Advanced Calculus (Inverse Function Theorem, Implicit Function Theorem)
- General Topology
Week 1: Topological Manifolds
Week 2: Smooth Structures and Smooth Manifolds
Week 3: Smooth Maps and Submanifolds
Week 4: Lie Groups
Week 5: Tangent Vectors and Cotangent Vectors
Week 6: Riemannian Manifolds
Week 7: Midterm
Week 8: Vector Fields and Flows
Week 9: Vector Bundles
Week 10: Tensors
Week 11: Differential Forms
Week 12: Cohomology
Week 13: Integration
Week 14: Classification
Week 15: Final Exam
John M. Lee, Introduction to Smooth Manifolds, 2nd ed., Springer-Verlag, 2013.
M. Spivak, A Comprehensive Introduction to DIFFERENTIAL GEOMETRY, Vol.
I, 3rd ed., Publish or Perish, 1999.
M. Spivak, Calculus on Manifolds, 1965.
L. W. Tu, An Introduction to Manifolds, 2nd ed., Springer, 2011.
Jeffrey M. Lee, Manifolds and Differential Geometry, Amer. Math. Soc., 2009.
C. H. Taubes, Differential Geometry, Oxford Univ. Press, 2011.
R. W. Sharpe, Differential Geometry, Springer, 1996.