# Study plan for MAMN-MAB Applied and Computational Mathematics, Master's, 2 years, spring 2023

## Name of qualification

The master¿s programme leads to the degree Master of Science in Mathematics. It is a two year programme (120 ECTS credits).

## Semester

Autumn and spring. This program is only open for applicants residing in Norway and for Nordic and EU citizens.

## Objectives and content

Applied and Computational Mathematics (ACM) is a field in which mathematics is used to solve practical and theoretical problems for different applied areas. Applied problem areas are often found within the natural sciences, in industry, resource management, medical image processing and other areas. The relevant problems are described mathematically in one or more equations through a modelling process. These equations are solved by using numerical tools, and the results are used to improve the understanding of the original problems. Another essential part of the field includes basic method development within applied mathematics, where one examines how different classes of mathematical problems can be represented and solved efficiently by using computers.

An education in Applied and Computational Mathematics enables the student to solve practical problems within different applied areas by using mathematical modelling, analysis and numerical calculation. Moreover, the student is taught a theoretical fundament which contributes to the understanding of relevant academic literature and how to make use of new methods and results in applied work.

The Master programme in ACM has two mandatory courses, both offered in the spring semester: MAT252 Continuum Mechanics and MAT260 Scientific Computing 2. For course recommendations, see specializations below and course lists at the bottom of the page. The Master programme usually consists of 60 ECTS courses and a 60 ECTS Master's thesis, alternative 90 ECTS courses and a 30 ECTS thesis.

The master thesis in ACM can be written within one of the following specializations: applied analysis, image processing, fluid mecanics and ocean modelling, inverse problems, mechanics and dynamical systems, environmental mathematics, numerical mathematics, computational science, or reservoir mathematics:

- Applied Analysis: involves developing of analytical and constructive methods for solving differential- and integral equations from several areas of application. Recommended previous knowledge: MAT211, MAT213, MAT230. Central courses: MAT211, MAT234.
- Image Processing: involves development and analysis of numerical methods for processing images from medical research, data technology and similar large simulation tasks. Recommended previous knowledge: STAT110, MAT213, MAT261. Central courses: MAT234, MAT262, INF270.
- Fluid mechanics and ocean modelling: involves analytical and numerical studies of waves and flow on an industrial and geophysical scale. A backgound in physical oceanography is useful for studying ocean currents. Recommended previous knowledge: MAT213, MAT230, MAT252. Central courses: MAT234, MAT253.
- Inverse problems: involves estimations of magnitudes based on indirect measures, for instance dynamical reservoir characterization and monitoring. Recommended previous knowledge: STAT110, MAT230. Central courses: MAT234, MAT254, MAT265.
- Mechanics and Dynamical systems: involves modelling of physical and biological systems emphasizing correlations between processes on the microscopic and macroscopic level. Recommended previous knowledge: MAT213, MAT230. Central course: MAT251.
- Environmental Mathematics: involves problems associated with intervention and management of the environment. Modelling and differential equations are central subjects. Recommended previous knowledge: MAT213, MAT230, MAT260. Central courses: MAT234, MAT254.
- Numerical Mathematics: involves development and discussion of numerical methods used in computational tasks. Recommended previous knowledge: MAT213, MAT230, MAT260. Central courses: MAT236, MAT261, MAT360.
- Computational Science: uses calculations/computations to seek insight in complex phenomenon not easily found by theoretical vurderinger and laboratory experiments alone. Modelling, simulation and visualization are used. Recommended previous knowledge: MAT230, MAT260. Central courses: MAT261, MAT360.
- Reservoir Mathematics: involves analytical and numerical studies of flow in oil reservoirs. These are problems encountered when extracting oil and gas. Recommended previous knowledge: MAT213, MAT230, MAT260. Central courses: MAT234, MAT254.

Course list: http://www.uib.no/en/math/courses

and: http://www.uib.no/en/matnat/courses

## 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 deep knowledge of basic mathematical theory, such as calculus, linear algebra and differential equations.

¿ has insight into mathematical models in physics and the natural sciences.

¿ has a comprehensive understanding of how computers work.

Skills

The candidate

¿ has extensive experience with practical problems, can recognize mathematical structures and formulate problems mathematically.

¿ can use a wide range of methods and techniques to analyze and solve problems in mathematics and modelling.

¿ can program, interpret data and present results in a scientifically appropriate manner.

¿ Can use statistical and numerical methods, and interpret the results.

General competence

The candidate

¿ can collaborate, even across disciplines, with other specialists.

¿ can write scientific texts and present mathematics in an understandable manner.

¿ can solve complex problems, also in cases where the choice of method is initially uncertain or where several methods must be combined.

## Admission Requirements

In order to apply for the Master Programme in Applied and Computational Mathematics you need a bachelor degree in Applied Mathematics, Mathematics or the like. You must hold a minimum of 70 ECTS in relevant courses such as Calculus, Linear Algebra, Differential Equations, Functions of several Variables, Programming and at least one of Numerics/Analysis/Mechanics/Advanced Differential Equations/Statistics.

Your last Mathematics course should not be older than 10 years.

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.

**Bachelor degrees that qualify **

- Usually, a Bachelor degree in Applied Mathematics/Mathematics is required for admission.
- Other bachelor degrees can qualify if you can document at least 70 ECTS relevant courses.

** Bachelor degrees that do not qualify **

- Bachelor in Economics/administration/similar: the degree does not contain relevant courses. Courses named «Matematics for economy» etc do not correspond to Calculus courses.
- Engineering degrees will seldom qualify without additional courses from a Mathematics department.

**You also need to document**

- Average grade of minimum C (equivalent to Norwegian grade C)
- Proficiency in English

## Compulsory units

The master¿s programme consists of an individual research project (master¿s thesis) of 60 ECTS credits, and courses or special topics of 60 ECTS credits. Some of the courses are compulsory within the specialisations. You will choose the other courses in agreement with your academic supervisor.

## Teaching methods

In the work with the 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 master¿s programme in applied and computational mathematics aims to give knowledge and understanding of mathematical methodics and mathematical methods. The subject of the thesis decides which methods you will use.

## Administrative responsibility

Department of Mathematics, E-mail: advice@math.uib.no