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.

In this course, the second one in a sequence of three, we focus on the theory of minimal surfaces (that is, soap bubbles), and on the Gauss-Bonnet theorem as covered in chapters 4, 5, 6 in Oprea.

Prerequisites: MTH 434 or 534, and working knowlegde of multivariable calculus (Mth 254, 255) and linear algebra (Mth 341, 342) will be assumed.

Text: John Oprea, Differential Geometry and its Applications, MAA, 2007 .

Grading: Your course grade will be based on two midterm exams and three homework assignments. The homework assignments count 30% towards the course grade and the midterm exams 35% each.

The homework assignments will be due 4/18, 5/16, and 6/6. The midterm exams are scheduled for 4/2 and 5/30.

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