Program Overview

Program Overview

The University of Copenhagen offers a Master's program in Mathematics with a minor subject, which includes a course on Geometry 2 (Geom2).

Course Description

The course covers differentiable manifolds in Euclidean spaces, abstract differentiable manifolds, tangent spaces, differentiable maps, and differentials. It also includes submanifolds, immersions, and imbeddings, as well as vector fields, Lie groups, and Lie Algebras. Additionally, the course covers differential forms, integration, and Stokes' Theorem.

Learning Outcomes

Upon completing the course, students will have acquired knowledge of central definitions and theorems from the theory. They will be able to decide whether a given subset of R^n is a manifold, determine the differential of a smooth map, and work with tangent vectors, including the Lie algebra of a Lie group. Students will also be able to utilize topological concepts in relation to manifolds, find the Lie bracket of given vector fields, and work with exterior differentiation and pull-back of differential forms.

Recommended Academic Qualifications

The course requires prior knowledge of Analyse 1 (An1), Geometri 1 (Geom1), Topologi (Top), and Advanced Vector Spaces (AdVec) or similar. Academic qualifications equivalent to a BSc degree are recommended.

Teaching and Learning Methods

The course consists of 35 hours of lectures and 28 hours of exercises during 7 weeks.

Workload

The total workload for the course is 206 hours, broken down into:

• Lectures: 35 hours
• Preparation: 142 hours
• Theory exercises: 28 hours
• Exam: 1 hour

Assessment

The course is assessed through an oral examination, which includes a 30-minute preparation time. A mandatory assignment must be approved before the exam, and all aids are allowed during preparation, but not during the examination.

Course Information

The course is taught in English and is worth 7.5 ECTS credits. It is a full-degree Master's course, and there is no limitation on course capacity unless students register in the late-registration period.

Study Board and Department

The course is offered by the Study Board of Mathematics and Computer Science, and the contracting department is the Department of Mathematical Sciences. The contracting faculty is the Faculty of Science.

Course Coordinators

The course coordinators are Damian Longin Osajda.