Differential Geometry is an important (and a fun) branch of mathematics in which one studies the shape of objects, such as curves, surfaces and their higher-dimensional analogs using tools from calculus, topology, algebra, etc. Besides of its own intrinsic interest and beauty, differential geometry plays a far-reaching role in a variety of fields such as mathematical physics, materials scieces, fluid mechanics, several complex variables, control theory, and econometrics.

This course, the first one in a sequence of three, serves as an introduction to the theory of curves and surfaces in Euclidean spaces. The topics will include space curves and their Frenet frames, calculus on surfaces, the Gauss map, curvature, and minimal surfaces.

Prerequisites: Working knowlegde of multivariable calculus (Mth 254, 255) and linear algebra (Mth 341, 342) will be assumed.

Text: M. do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall, 1976 (Corrigenda).

Grading: Your course grade will be based on two midterm exams and three homework assignments. The homework assignments count 40% towards the grade and the midterms 30% each.

The homework assignments will be due 1/27, 2/24, and 3/17. The midterms are scheduled for 2/10 and 3/17.

You can view a day-by-day course calendar by clicking here.