Mathematical models are essential tools in modern science. In this course, we use tools from analysis, linear algebra, and topology to introduce a model that has not only been used in mathematics but also classically is used in physics such as e.g. in Hamiltonian mechanics and Einstein's theory of relativity. Other applications are found in chemistry, economics, engineering, computer graphics and computer vision, as well as recently in statistical learning and machine learning. Some of the key concepts covered in the course are manifolds, tangent spaces, vector fields, tensors, and differential forms. The course concludes with Stokes' theorem on manifolds.
