 Specialization

# Topology

• Years2 years
• ECTS credits120

## Introduction

### Objectives and content

The Master programme in Topology provides a general background in mathematics, with a special focus on topology and geometry. Topology is a branch of mathematics where geometrical shapes, such as curves, surfaces and higher dimensional spaces, are studied. These objects occur naturally in related disciplines, such as physics. Thus, a topological analysis can provide information about the evolution, for example, of a physical system. One of the key topological problems is to classify geometrical shapes. This is commonly done by introducing so-called algebraic invariants, which measure the qualitative geometric phenomena. Hence, there is a close relationship between the fields of topology and algebra

The programme provides training in abstract thinking and in analyzing mathematical problems in which the method of solution is not known. During the programme, the students will develop skills needed for independent study of new fields and for communicating mathematics.

Learning outcomes:

A candidate who has completed his or her qualifications should have the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

The candidate

• has a thorough knowledge of mathematics, especially the study of geometrical and topological objects, and is able to relate this to other branches of mathematics.
• has extensive experience with problem solving and a knowledge of strategies combining different methods.
• can explain and discuss the fundamental questions and theories in key parts of the field, such as manifolds, homotopy, homology and K-theory.

Skills

The candidate

• can assess and explain his/her choice of methods for solving mathematical problems and can analyze complex mathematical structures.
• can conduct a research project in an independent and systematic way, including the development of mathematical proofs and performing independent mathematical reasoning and calculations.
• can write and produce mathematics at professional standards and in an understandable and readable manner.

General competence

The candidate

• can analyze mathematical texts and simplify mathematical reasoning by outlining the structure and the most important elements.
• can use the knowledge mentioned above as a basis for a critical approach to the application of the discipline.

can solve complex problems, even in cases where the choice of method is not obvious or where several different methods must be combined.

## How to Apply

This programme is avalible for citizens from within the European Union/EEA/EFTA.

Follow these links to find the general entry requirements and guidelines on how to apply:

A bachelor degree with the following minimum of mathematical prerequisite knowledge: MAT111 - Calculus I, MAT112 - Calculus II, MAT121 - Linear Algebra, MAT211 - Real Analysis, MAT212 - Functions of Several Variables, MAT220 - Algebra , MAT242 - Topology and MAT243 - Manifolds.

Recommended prerequisite knowledge is MAT213 - Functions of a Complex Variable and INF223 Category Theory.

The minimum requirement is grade C or better (in the Norwegian grading system) in the courses that are required. If there are more applicants to a program than there are vacant places, applicants will be ranked according to grades in their application for admission. For international students residing abroad, the admission is extremely competitive.

It is important to document the content and learning outcomes of the central mathematics subjects, either with attached course descriptions or with links to web pages where course descriptions can be found.