Erik Elfving

Erik Elfving, Ilkka Holopainen, and Pekka Pankka

MAST31003 Topology II (10cr)

**Specialization course,** at least 10 from this list

MAST31005 Algebra II (10 cr)

MAST31023 Introduction to algebraic topology (10 cr)

MAST31017 Introduction to differential geometry (10 cr)

MAST31026 Riemannian geometry (10 cr)

Other advanced courses from the list of core courses, mathematics, applied mathematics, statistics courses and/or courses from other programmes as approved in the personal study plan

MAST30001 **Master's thesis seminar **(5 cr)

MAST30000 **Master's thesis **(30cr) (the link includes grading scale and criteria)

Other requirements, such as possibly required bachelor's level mathematics courses (which can be included in the module 0-35cr of other studies).

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.

Personal study plan form (for Mathematics and Applied Mathematics):

Personal Study Plan

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 Introduction to real and Fourier analysis (previously Real analysis I) 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)

Introduction to real and Fourier analysis (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)

P.O. Box 4
(Yliopistonkatu 3)
00014 University of Helsinki
Switchboard:
+358 (0) 2941 911 (mobile call charge / local network charge)