# Study plan for MAMN-MAT Mathematics, Master's, 2 years, fall 2023

## Name of qualification

The master¿s programme leads to the degree Master of Science in Mathematics.

## ECTS Credits

Two years of full-time study, where the normal workload for a full-time student is 60 credits for one academic year.

## Full-time/Part-time

Full-time

## Language of Instruction

English

## Semester

Autumn.

## Objectives and content

The programme is aimed at students with an interest in mathematics who intend to qualify for research, development or teaching and seek employment where education in mathematics is required or considered an advantage.

Within the Master's Programme in Mathematics, you can choose among the following specialisations, mirroring the four main research groups within pure Mathematics:

**Algebra**: The Master's programme in Algebra gives a general background in mathematics, with special focus on algebra and algebraic geometry. Algebra is a classical field that is associated with the study of polynomials in several variables.**Algebraic Geometry**: The Master's programme in Algebraic geometry gives a general background in mathematics, with special focus on algebraic geometry. This is an area where one uses techniques from algebra and topology, and often also complex analysis or number theory, to study geometric objects as curves, surfaces and higher dimensional manifolds that can be defined through polynomial equations.**Mathematical Analysis**: 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.**Topology**: The Master's 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.

## Required 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. The candidate can relate general and abstract concepts and methods to calculations and applications.
- has extensive experience in problem solving and a knowledge of strategies for combining different methods.
- The candidate can explain and discuss the basic theory of the structures of his/her specialization.

**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 perform 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.
- demonstrates understanding and respect for scientific values such as openness, precision and reliability

## Admission Requirements

A first degree (bachelor´s degree) in Mathematics of three or four years´ duration from an approved institution of higher education, as well as proficiency in the English language.

As a minimum, previous knowledge in Mathematics must include courses in: Calculus, Real Analysis, Linear Algebra, Algebra, Functions of several variables, Commutative algebra, Complex functions, Topology and Manifolds. 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.

Specializations: Mathematical Analysis, Topology, Algebra, and Algebraic Geometry.

**For international self-financing applicants**

The programme is not open for applicants outside EU/EEA/EFTA in 2020-2021.

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.

In your letter of motivation, please indicate which specialization (or specializations in prioritized order) you are mostly interested in.

**How many places?**

Up to 5 places in total, combined for all specializations, are reserved for qualified international applicants in the Master's Programme in Mathematics.

## Recommended previous knowledge

Specialization 1) Mathematical analysis: MAT215, MAT243 or MAT234.

Specialization 2) Topologiy MAT213, INF223.

Specialization 3) Algebra: MAT221.

Specialization 4) Algebraic geometry: MAT213

## Recommended electives

Elective course credits have to be chosen in agreement with the supervisor

## Master thesis credits

In agreement with your academic supervisor, you will choose a master¿s thesis (60 ECTS credits) and make a progression plan containing important milestones for your project. At this programme it is possible to have a 30 study point thesis, extending the course part of the programme to 90 study points.

## Study period abroad

You can plan study periods abroad in consultation with the supervisor as part of the master agreement

## Teaching and learning methods

In the work with your master¿s thesis you will, in an independent way, make use of methods and scientific working techniques from the subject field in the research of a relevant material. The subject of the research of a relevant material. The subject of the thesis decides which methods you will use.

You will find more information in the course descriptions.

## Assessment methods

The final step in the programme is an oral examination. The examination is held when the master¿s thesis is submitted, evaluated and approved. The assessment methods for each course are described

in the course description.

## Diploma and Diploma supplement

The Diploma, in Norwegian, and the Diploma Supplement, in English, will be issued when the

degree is complete.

## Administrative responsibility

The Faculty of Mathematics and Natural Sciences by the Department of Informatics, holds the administrative responsibility for the programme.

## Contact information

Study section: advice@math.uib.no

Department of Mathematics: http://www.uib.no/en/math