Differential Geometry (MA 313) uses calculus to study geometry. It is a subject with a number of really beautiful results and many applications to pure mathematics, applied mathematics, physics, and engineering. Our course will focus on the geometry of curves and surfaces in 3-dimensional euclidean space. We'll learn about such things how to find the shortest distance between two points, how to measure curvature, and how to find and use the shortest paths on a surface. We'll explore the relationship between the length of a curve and the area bounded by it (the isoperimetric inequality), applications to soap bubbles, and the relationship between the curvature and the topology of a surface (the Gauss-Bonnet theorem). Differential Geometry is a great place to see calculus in action - so be prepared for lots of derivatives and integrals.

Selected Course Notes and Study Guides:

  • Exam 1 Study Guide
  • Exam 2 Study Guide
  • Exam 3 Study Guide