Program Overview

Program Overview

The University of Copenhagen offers a Master's program in Mathematics with a specialization in Algebraic Topology. This program is designed to provide students with a comprehensive understanding of algebraic topology, including its fundamental concepts, techniques, and applications.

Program Description

The program introduces students to the area of mathematics where algebra is used to study topological spaces. It covers topics such as homotopy, homotopy equivalence, fundamental group, covering space, chain complex, and homology. The program aims to equip students with the knowledge, skills, and competencies necessary to pursue a career in mathematics or related fields.

Learning Outcomes

The program is designed to achieve the following learning outcomes:

• Knowledge: Students will gain a deep understanding of the fundamental concepts and techniques in algebraic topology.
• Skills: Students will be able to:
  • Define and apply the concepts introduced in the program.
  • Understand the main results, their proofs, and their significance.
  • Compute the fundamental group and singular homology of simple topological spaces.
• Competencies: The program will strengthen students' competencies in:
  • Abstract and precise thinking.
  • Elegance of exposition.

Program Structure

The program consists of 4 hours of lectures and 4 hours of exercises each week for 7 weeks. The workload is distributed as follows:

• Lectures: 28 hours
• Preparation: 149 hours
• Theory exercises: 28 hours
• Exam: 1 hour
• Total: 206 hours

Assessment

The program uses a 7-point grading scale, and the assessment is based on an oral examination with a 20-minute preparation time. All aids are allowed, and the examination is conducted with external censorship.

Program Details

• Language: English
• Course code: NMAA05038U
• Credit: 7.5 ECTS
• Level: Full Degree Master
• Duration: 1 block
• Placement: Block 1
• Schedule: C

Study Board and Department

The program 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 Nathalie Wahl and Robert Wayne Burklund.

Additional Information

The program is also available as continuing and professional education, and there is no limitation on course capacity unless students register in the late-registration period or as credit or single subject students.