Programme structure
This field of study is under revision and recommended topics and structure will change. Please see the Norwegian pages for updated programme structure. Please note that courses at bachelor level assumes that the student has been admitted to single course study directly or through a bachelor's program.
The duration of the Master’s programme is two years and consists of courses and thesis work. Should you choose a short thesis (30 ECTS credits), the first three semesters are assigned course work and the last semester is assigned thesis work.
Choosing a longer thesis (60 ECTS credits), is a more flexible solution to the execution of the programme. It is recommended that you take three courses during the first semester. In the second semester you can work on your Master’s thesis while taking one course consisting of 20 ECTS credits, and in the third semester you can take one course consisting of 10 ECTS credits while working on your thesis. The fourth semester is entirely assigned to thesis work.
| 4. semester | Master's thesis | |||||||||||||||||||||||||||||
| 3. semester | Master's thesis | Master's course | ||||||||||||||||||||||||||||
| 2. semester | Master's thesis | Master's course | Master's course | |||||||||||||||||||||||||||
| 1. semester | Master's course | Master's course | Master's course | |||||||||||||||||||||||||||
| 10 ECTS credits | 10 ECTS credits | 10 ECTS credits | ||||||||||||||||||||||||||||
Study plan suggestions for Computational Science are sorted according to the following research groups:
• Computational mathematics
• Simulation and visualisation
• Image processing
Computational mathematics
The Computational Mathematics group has its affiliation with two Centres of Excellence, one part is placed at the Centre of Mathematics for Applications (CMA) located in Nils Henrik Abels hus at Blindern, the other is placed at the Centre for Biomedical Computing (CBC) located in the Simula Centre at Fornebu.
Three main research activities are carried out by the Computational Mathematics group: geometrical modeling (at CMA), combinatorial optimization (at CMA) and partial differential equations (at CBC and CMA).
Please find a study plan suggestion for the Master’s study for each of the specialisations below. In general, a student at the Master’s programme in Computational Mathematics should have a good understanding of mathematics, numerical calculations and programming, preferably supplemented with a course or two from an applied field such as physics. A good point of departure is therefore a Bachelor’s degree in Mathematics, Informatics and Technology, specialised in Computational Science, Informatics or Mathematics. The other specialisations on the MIT-programme and other mathematics oriented Bachelor’s programmes at the MN Faculty may also be sufficient for the Master’s programme in CM, especially if you towards the end of the Bachelor’s programme include some courses which focus on numerical calculations. Bachelor’s programmes which may be relevant in this case are Physics, Astronomy and Meteorology; Mathematics, Economy and Informatics: Technical and Scientific Applications.
If you hold a Bachelor’s Degree from another institution than UiO with a similar academic profile as mentioned above, you are also welcome to apply for admission to the Master’s programme in Computational Science.
There are many courses to choose between (see relevant courses ), and the tables below are only suggestions. Based on what you are interested in, you can choose to focus the theory part of the programme in towards mathematics, informatics or computations by replacing courses. Even so it is recommended that everyone takes the course INF-MAT4350 – Numerical Linear Algebra . The tables below illustrate examples of a study plan based on a longer Master’s thesis. When it comes to oral curriculum, you may choose courses more freely. You should therefore discuss which courses to take with your supervisor, or study coordinator should you not have been provided with a supervisor yet.
The tables below give an illustration of a study plan for a longer thesis. It is also possible to write a shorter thesis. Should you be interested in this, please contact a supervisor to set up an appropriate study plan.
Geometric modelling, longer thesis
| 4. semester | Master's thesis | |||||||||||||||||||||||||||||
| 3. semester | Master's thesis | Master's course | ||||||||||||||||||||||||||||
| 2. semester | Master's thesis | INF-MAT5340 - Spline methods | INF5620 - Numerical methods for partial differential equations / INF-MAT5350 – Numerical analysis | |||||||||||||||||||||||||||
| 1. semester | INF4360 - Topics in Geometric modelling | INF-MAT5360 - Mathematical optimization | INF-MAT4350 - Numerical Linear Algebra | |||||||||||||||||||||||||||
| 10 ECTS credits | 10 ECTS credits | 10 ECTS credits | ||||||||||||||||||||||||||||
The central courses in this specialization are INF4360 - Topics in Geometric modelling and INF-MAT5340 - Spline methods . You should also take INF3320 – Computer graphics and geometric modelling on Bachelor’s level, or during the first semester on Master’s level. Please note that you are not permitted to take more than two courses with a 3000-code on Master’s level, and that these two must be applied for.
Combinatorial optimization, longer thesis
| 4. semester | Master's thesis | |||||||||||||||||||||||||||||
| 3. semester | Master's thesis | Master's course | ||||||||||||||||||||||||||||
| 2. semester | Master's thesis | Master's course | Master's course | |||||||||||||||||||||||||||
| 1. semester | INF-MAT5360 - Mathematical optimization | INF-MAT4350 - Numerical Linear Algebra | Master's course | |||||||||||||||||||||||||||
| 10 ECTS credits | 10 ECTS credits | 10 ECTS credits | ||||||||||||||||||||||||||||
Obligatory courses for this specialisation are:
• INF-MAT4350 – Numerical Linear Algebra
• INF-MAT5360 - Mathematical optimization
We also recommend that you take INF-MAT3370 – Linear optimization on Bachelor’s level, or take this course in your second semester of the Master’s study.
Please find more information here .
The remaining courses can be chosen from courses available in mathematics, statistics, informatics and certain courses in economy.
Depending on subject for the thesis, some of the following courses may be relevant:
•INF-MAT3370 - Linear Optimization
• Special curriculum: within e.g. convexity, graph theory, nonlinear optimization, combinatorial matrix theory.
• INF-MAT5340 - Spline methods
• INF-MAT5370 - Trianguleringer og anvendelser
• MAT4000 - Numbers, Spaces and Linearity
• MAT4340 - Elementary Functional Analysis
• STK4030 - Modern Data Analysis
• ECON4240 - Game theory and economics of information
Partial differential equations
At CMA
As mentioned above, the activity within partial differential equations is split between CMA and CBC, and the focus differs slightly at the two places. Master’s theses at CMA will usually go in the direction towards theory for, and the development and analysis of numerical methods. It is therefore important with a solid mathematical foundation, especially in analysis, but preferably in differential geometry as well. You should also have a good background in general numeric calculations and be well-acquainted with programming.
| 4. semester | Master's thesis | |||||||||||||||||||||||||||||
| 3. semester | Master's thesis | MAT4350 - Functional Analysis / INF5670 - Numeriske metoder for Navier-Stokes likninger (Norwegian) | ||||||||||||||||||||||||||||
| 2. semester | Master's thesis | MAT-INF4310 - Partial differential equations and Sobolev spaces II | INF5620 - Numerical methods for partial differential equations | |||||||||||||||||||||||||||
| 1. semester | MAT-INF4300 - Partial differential equations and Sobolev spaces I | INF-MAT4350 - Numerical Linear Algebra | MAT4500 - Topology | |||||||||||||||||||||||||||
| 10 ECTS credits | 10 ECTS credits | 10 ECTS credits | ||||||||||||||||||||||||||||
The central courses here are MAT-INF4300 - Partial differential equations and Sobolev spaces I and MAT-INF4310 - Partial differential equations and Sobolev spaces II and INF5620 - Numerical methods for partial differential equations . For some students it may also be useful to take INF5631 - Numerical methods for partial differential equations; project assignment , perhaps as an introduction to the thesis work.
Partial differential equations, with focus on software and applications
At CBC
CBC’s main focus is on developing generic software for solving partial differential equations, simulation of the electromechanical activity in the heart, calculations linked to oil industry and simulating fluid flow (with a particular focus on blood flow).
CBC’s main focus is on developing generic software for solving partial differential equations, simulation of the electromechanical activity in the heart, calculations linked to oil industry and simulating fluid flow (with a particular focus on blood flow).
The Master’s theses at CBC can roughly be divided into four categories:
• Programming (C++, Python, Java) of simulators
• A more theoretical study of mathematical models
• Developing instruments for visualization
• Overview (comparison of various techniques and codes)
The student decides to a large extent which of these categories their work should enter into, however everyone is obliged to programme and codes will in many cases enter into the Master’s thesis as a central part.
Example of study plan, longer thesis
| 4. semester | Master's thesis | |||||||||||||||||||||||||||||
| 3. semester | Master's thesis | INF5691 - Advanced Finite Element Methods / INF5610 - Mathematical Modelling in Medicine / INF5670 - Numerical Methods for Navier-Stokes equations (Norwegian) | ||||||||||||||||||||||||||||
| 2. semester | Master's thesis | INF5681 - Introduction to Finite Element Methods | INF5620 - Numerical methods for partial differential equations | |||||||||||||||||||||||||||
| 1. semester | INF5661 | INF-MAT4350 - Numerical Linear Algebra | Master's course | |||||||||||||||||||||||||||
| 10 ECTS credits | 10 ECTS credits | 10 ECTS credits | ||||||||||||||||||||||||||||
The courses INF5661 (before INF3331), INF-MAT4350 - Numerical Linear Algebra and INF5620 - Numerical methods for partial differential equations are central courses and should be included as part of the Master's programme.
Recognition of Master courses from former education
If you are admitted to the Masters Programme and you have completed Master courses outside the University of Oslo, you may apply to have these courses recognised as part of your degree. Please contact the Department of Mathematics for more information.