Course content

Elementary general topologi. Inverse function theorem. Manifolds, differentiable structures. Regular/critical points, imbeddings, submersions and immersions. The rank theorem. Tangent bundles, flows, vector fields, and integrability. Projective spaces an matrix groups.

Learning outcome

The purpose of this course is to give the students insight into basic geometric concepts and methods in differential topology, for example, solving differential equations on manifolds. The course is intended for students of mathematics, theoretical physics and cybernetics.

Learning methods and activities

Lectures and exercises. The lectures will be given in English if they are attended by students from the Master's Programme in Mathematics for International students. Written examination. Retake of examination may be given as an oral examination.

Recommended previous knowledge

The course is based on TMA4100/05/15/ Calculus 1/2/3 or equivalent. For students who have their background from mathematical sciences: The course is based on MA1101 Basic Caluculus I, MA1102 Basic Calculus II, MA1103 Vector Calculus, MA1201 Linear Algebra and Geometry, MA1202 Linear Algebra with Applications, MA2105 Complex Function Theory with Differential Equations, or eqivalent.

Course materials

Will be announced at the start of the course.

Credit reductions