Geometry, algebra and topology

Dir­ect­or of the spe­cial­iz­a­tion

Erik Elfving

Per­sons re­spons­ible for dis­cuss­ing the study plans

Erik Elfving, Ilkka Holopainen, Pekka Pankka and Johanna Rämö

Gen­eral in­struc­tions

The studies begin by contacting one of the persons responsible for the specialization in order to form a personal study plan. 

Apart from the required core and specialization courses, the student can choose any advanced courses from all other specializations in mathematics and statistics. It is possible to include courses from different master’s programs such as physics, machine learning or computer science if they have sufficient mathematical content.

Model study plans

Ex­ample 1

For a topologically or algebraically inclined student. The student will take Introduction to algebraic topology and a topics course in topology or algebra. The studies contain 20+20+10 cr math + 30 cr pro gradu + 5 cr seminar + 35 cr optional math or minor subject = 120 cr.

Year 1: Autumn
Introduction to algebraic topology (10cr)
Topology II (10cr)
Optional courses/Minor subject (10cr)

Year 1: Spring
Algebra II (10cr)
Complex analysis (10cr)
Optional courses/Minor subject (10cr)

Year 2: Autumn
Topics course in topology or algebra, e.g. Homotopy theory (10cr)
Optional courses/Minor subject (10cr)
Master´s thesis and Master´s thesis seminar start

Year 2: Spring
Master´s thesis (30 cr) and Master´s thesis seminar (5 cr) completed
Minor subject ( 5cr)           

Example 2

For a geometrically inclined student. The student will take Introduction to differential geometry and a topics course in geometry, e.g. Riemannian geometry. The course Real analysis is recommended. The student is also recommended to take the course Introduction to Algebraic topology to enhance the understanding in geometry. Studies contain 25+20+5 cr math + 30 cr Master´s thesis + 5 cr Master´s thesis seminar + 35 cr optional math or minor subject.

Year 1: Autumn
Introduction to algebraic topology (10cr)
Topology II (10cr)
Real analysis I (5cr)
Optional courses/Minor subject (5cr)

Year 1: Spring
Introduction to differential geometry (10cr)
Complex analysis (10cr)
Optional courses/Minor subject (10cr)

Year 2: Autumn
Topics course, e.g. Riemannian geometry (10cr)
Optional courses/Minor subject (10cr)
Master´s thesis and Master´s thesis seminar start

Year 2: Spring
Master´s thesis (30 cr) and Master´s thesis seminar (5 cr) completed
Minor subject (5 cr)