幾何學(一)

The goal of this course is to give an introduction to the basics of differential geometry. We will at least cover the following topics in this course . Curvature of plane curves. Curvature of curves in the 3-dim. Euclidean space. The Serret-Frenet formulas. Euler theorem for surface in 3-dim. Euclidean space. The Gauss map for surface in 3-dim Euclidean space The Gauss curvature for surface in 3-dim Euclidean space. The First and the Second Fundamental forms. Introduction to the theory of differentiable manifolds. The basics of tensor analysis and the use of differential forms. The basics of Riemannian manifolds The covariant derivatives, and the Levi-Civita connections. The curvature tensor.

Calculus I, II, Linear Algebra

Attendance 20% Notes taking 20% Quiz 10% Mid-Term 15% Final Exam 15% Final Project 20%

There is no required textbook for this course. However, the following reference could be helpful: M. Spivak. "A Comprehensive Introduction to Differential Geometry, Volume II". Publisher: Publish or Perish.