Course overview
The main aim of the course is to set the stage for and prove Stokes' theorem, a vast generalisation of the fundamental theorem of calculus. Stokes' theorem is an important tool for relating local and global properties of manifolds. This is a major theme in modern mathematics, known as cohomology. Basic ideas of algebraic topology will be developed from the differentiable viewpoint, using Stokes' theorem and homological algebra, and some important applications will be pursued.
Course learning outcomes
- Demonstrate an understanding of the basic theory of smooth manifolds
- Demonstrate advanced skills in constructing rigorous mathematical arguments
- Apply the theory in the course to solve a variety of problems at an appropriate level of difficulty
- Demonstrate advanced skills in communicating mathematics
- Complete a small research project as a member of a team