**Taught at the University of Dar Es Salaam, Fall 2016**

Supported by the IMU’s Commission For Developing Countries: Volunteer Lecturer Programme.

**Instructor: **David Li-Bland

** Email:**

**Office:** 312

**Course Description:** This course is designed to be a rigorous introduction to the theory of smooth manifolds. Manifolds can be thought of a spaces which look *locally* like euclidean space,
, in a* smooth* way: one dimensional manifolds include the line and the circle; two dimensional manifolds include surfaces such as the plane, sphere, torus, cylinder, mobius strip, real projective space, the klein bottle, etc.

In addition to developing a general geometric intuition, we will explore the following main topics: Partitions of unity (which allow you to patch things together locally on a manifold), the inverse function theorem and it’s cousins (such as the regular value theorem), the Frobenius theorem, and Stoke’s theorem.

Time permitting, we may also touch on Lie groups and Riemannian geometry.

**Useful Resources **(Recommended Texts, and examples and videos).

**Grading Policy: **

%20 Homework, %20 Midterm Exam, %20 Presentation, %40 Final Exam

**Exams:**

**Midterm Exam:**Monday Oct. 31st.**Presentations:**To be scheduled from Oct. 31 - Nov 4.**Final Exam:**TBA