Dear all,
next semester I will be teaching Math 462 (Differential Geometry)
The main focus of the course will be curves and surfaces, which are fundamental objects in the field of differential geometry. We will study basic local concepts, such as length, area and curvature, as well as global properties such as the rotation index of a closed curve, which is a number that measures the net number of counterclockwise loops that a unit-speed curve performs. We will also go over some really interesting theorems, such as the Jordan curve theorem (a simple closed curve in the plane separates it into two components) and the Gauss-Bonnet theorem (the total curvature of a closed surface depends only on how many “holes” it has).
The prerequisites for this class are the basic calculus and linear algebra classes.
The book we will follow is “Differential Geometry of Curves and Surfaces” by Kristopher Tapp. This book has many examples and pictures which provide a great geometric intuition, which is something that we will try to develop in this class.
Best, Theodora
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