Program Overview

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Program Overview

The University of Copenhagen offers a Master's program in Mathematics, with a course in Geometric Topology (GeomTop) denoted as NMAK21000U.

Course Description

Geometric topology is the study of geometric objects, most particularly manifolds, using tools from algebraic topology. The course covers a selection of the most important topics within this area, such as Poincaré duality, characteristic classes, Morse theory, and foundations of differential topology.

Learning Outcomes

• Knowledge: To display knowledge of the course topics and content, at the level of a beginning researcher.
• Skills: To be able to use the acquired knowledge to perform computations.
• Competencies: To be able to produce independent proofs in extension of the acquired knowledge.

Literature

Example of course literature:

• Introduction to Differential Topology by Bröcker and Jänich
• Characteristic Classes by Milnor and Stasheff
• Differential Forms in Algebraic Topology by Bott and Tu
• parts of the textbook Algebraic Topology by Hatcher
• Topology from the Differentiable Viewpoint by Milnor
• Morse Theory by Milnor

Recommended Academic Qualifications

Algebraic Topology (AlgTop) and Geometry 2 (Geom2) or equivalent is strongly recommended. Advanced Vector spaces (AdVec) and Homological Algebra (HomAlg) or equivalent are also recommended. Academic qualifications equivalent to a BSc degree are recommended.

Teaching and Learning Methods

4 hours lectures and 4 hours exercise session per week for 9 weeks.

Workload

• Category: Lectures
• Hours: 36
• Preparation: 134
• Theory exercises: 36
• Total: 206

Assessment

• Type of assessment: Continuous assessment
• Type of assessment details: Weekly homework counting 50% towards the grade and a 2 hours 'closed-book' final in-class problem set counting 50% of the grade.
• Aid: Only certain aids allowed for the final in-class test; personally created handwritten notes on paper are allowed.
• Marking scale: 7-point grading scale
• Censorship form: No external censorship; one internal examiner

Re-exam

30 minutes oral examination with no aids or preparation time. The oral examination will cover the entire material of the course, including the exercise sets.

Course Information

• Language: English
• Course code: NMAK21000U
• Credit: 7.5 ECTS
• Level: Full Degree Master
• Duration: 1 block
• Placement: Block 3
• Schedule: B
• Course capacity: No limitation – unless you register in the late-registration period (BSc and MSc) or as a credit or single subject student.

Study Board and Department

• Study Board of Mathematics and Computer Science
• Department of Mathematical Sciences
• Faculty of Science

Course Coordinators

• Nathalie Wahl
• Robert Wayne Burklund

Additional Information

The course is also available as continuing and professional education. The criteria for exam assessment require the student to convincingly and accurately demonstrate the knowledge, skills, and competences described under the intended learning outcome.