Category: Slides

In tomorrow’s lecture we will catch a first glimpse of the idea of manifolds, which are pretty central to differential geometry. Rather than giving a formal definition in the smooth case, we’ll introduce a notion of discrete manifolds that capture the most important ideas. These discrete manifolds build on the idea of a simplicial complex, introduced in the previous lecture.

• Video
• Slides

In this lecture we’ll really start from the beginning, and define some of the basic objects we’ll use throughout the class. In particular, we’ll look at the idea of a “mesh,” and study one very specific kind of mesh called an oriented simplicial complex.

• Video
• Slides

Our first lecture provides motivation for the topics we’ll cover in the course, and takes a deep dive into one specific example (curvature of curves in the plane) to highlight some of the basic principles of discrete differential geometry. This example moves pretty fast and uses some ideas that we’ll study at a slower, more careful pace later on. For now, don’t worry too much about the details—the goal here is to just get a sense of what the course is all about!

• Video
• Slides