 Specialization

# Mathematical Analysis

• Years2 years
• ECTS credits120

## Introduction

### Objectives and content

The Master's programme in Mathematical Analysis provides a general background in mathematics, with a special focus on mathematical analysis. The original meaning of the word "mathematical analysis" is closely associated with functions of one or more real variables, but modern analysis involves several other topics, some of a more abstract nature, such as general topology, measure theory and functional analysis. Instead of studying individual functions, functional spaces are an important topic. The vectors in the space are functions defined in a given domain. Key ideas from finite dimensional linear algebra play an important role. It is also of interest studying spaces of a more complex nature, where a straight line is not necessarily the shortest path between two points, and where not all movements are allowed. Such spaces occur in modern physics, and the study of these spaces, called geometric analysis, combines mathematical analysis, differential geometry and differential equations. Questions related to convergence, integration, derivation, approximation and the solution of partial differential equations are studied both in function spaces and in various geometric structures.

The study 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 areas 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 in the study of smooth geometric and analytical topics and is able to relate these to other branches of mathematics.
• has extensive experience with problem solving and a knowledge of strategies for combining different methods.
• can explain and discuss the fundamental questions and theories in key parts of the discipline, such as the theory of functions of real and complex variables, differential equations, approximations, functional rooms, analysis of smooth and analytic manifolds.

Skills

The candidate

• can assess and explain the choice of methods for solving mathematical problems and 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's degree with the following mathematical knowledge or equivalent prerequisite knowledge: MAT111 - Calculus I, MAT112 - Calculus II, MAT121 - Linear Algebra, MAT211 - Real Analysis, MAT212 - Functions of Several Variables, MAT213 - Functions of a Complex Variable, MAT220 - Algebra.

Recommended prerequisite knowledge is MAT215 - Theory of Measure and Integration and MAT243 - Manifolds.

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.