Curved manifolds: from soap bubbles to crumpled paper
June 29 - July 8
TIME: 10:00 am - 12:20 pm
INSTRUCTOR: Andrew Belmonte
COURSE DESCRIPTION: The concept of a manifold will be introduced for the specific case of curves and surfaces embedded in Euclidean 3D space. We will start with the parameterization and geometry of a curve, and eventually surfaces. There will be some focus on curves and surfaces that satisfy variational equations, as these often correspond to things in the physical world.
From linear algebra to functional analysis: an introduction
July 25 - August 5
TIME: MTWR 10:00 am - 12:15 pm
INSTRUCTOR: Nate Brown
COURSE DESCRIPTION: I will spend the first couple days on basic linear algebra (vector spaces, linear operators, etc.), but this is only to motivate and illustrate the functional analysis that will follow. We will travel as far into functional analysis as the students' background and interest allow, hopefully covering some fundamental results such as the Hahn-Banach theorem.