Differential Geometry

This course is an introduction to the basic concepts in differential geometry. The topics to be discussed are the local and the global geometric properties of curves and of surfaces in three-dimensional Euclidean space: parametric representation of curves and surfaces, curvature, the normal, the tangent, and the binomial vectors of a curve, orientation, Jacobian matrix, the four-vertex problem, the index number, Gaussian curvature of a surface, and the Gauss map.