Master of Science in Mathematics for international students

Degree Program

The degree program for the Master of Science in Mathematics for international students at NTNU is stipulated to take two years. One year of full studies corresponds to 60 credit points, i.e. in total 120 credit points are needed. The degree consists of two parts. The program starts with course work corresponding to 82.5 credit points and concludes with writing a thesis corresponding to 37.5 credit points.

Admission requirements

To be accepted as a student to this program one has to have:

• Bachelor's degree consisting of at least three years of university studies.
• Studied mathematics at a university for at least 1½ years.
• For the study directions in algebra, analysis and topology: Reached the level and covered material equivalent to
  • MA1101 Basis calculus I,
  • MA1102 Basis calculus II,
  • MA1201 Linear algebra and geometry,
  • MA1202 Linear algebra with applications,
  • MA1103 Vector calculus,
  • MA1301 Number theory,
  • MA2201 Algebra,
  • MA2104 Differential equations and complex function theory.
• For the study direction in numerical analysis: Reached the level and covered material equivalent to
  • MA1101 Basic calculus,
  • MA1102 Basic calculus II,
  • MA1201 Linear algebra and geometry,
  • MA1202 Linear algebra with applications,
  • MA1103 Vector calculus,
  • ST1101 Probability,
  • ST1201 Statistical methods.
• For the study direction in statistics: Reached the level and covered material equivalent to
  • MA1101 Basic calculus,
  • MA1102 Basic calculus II,
  • MA1201 Linear algebra and geometry,
  • MA1202 Linear algebra with applications,
  • MA1103 Vector calculus,
  • ST1101 Probability,
  • ST1201 Statistical methods,
  • and at least one of TMA4265 Stochastic processes and TMA4267 Linear statistical models.

Applications for this program is filed through the Office of International Relations. Application forms are available electronically. For further information and requirements see the homepage of the Office of International Relations.

Description of the degree

The Department of Mathematical Sciences offers various courses at graduate level in addition to more specialized graduate seminars. Currently we offer five directions of study, algebra, analysis (functional analysis and complex and harmonic analysis, differential equations), numerical analysis, statistics and topology.

Algebra, analysis and topology: All students in must take at least 30 credit points amongst the courses

• MA3201 Rings and modules,
• MA3202 Galois theory,
• TMA4145 Linear methods,
• TMA4225 Foundations of analysis,
• TMA4190 Manifolds,
• MA3402 Analysis on manifolds

For the algebra direction, which builds upon MA3201 Rings and modules, MA3202 Galois theory, the courses MA3203 Ring theory and MA3204 Homological algebra should be taken. Some possible areas for topics for the thesis in algebra are presently representation theory of finite dimensional algebras, homological algebra and higher dimensional rings and orders.

For the analysis direction, which builds upon TMA4145 Linear methods, TMA4225 Foundations of analysis, the courses TMA4230 Functional analysis and TMA4175 Complex analysis should be taken. Some possible areas for topics for the thesis in analysis are presently geometric function theory, function spaces, harmonic analysis, continued fractions, dynamical systems, operator theory, topological measure theory and partial differential equations.

For the topology direction, which builds upon TMA4190 Manifolds, MA3402 Analysis on manifolds, the course MA3403 Algebraic topology should be taken, and at least one more topology course. Some possible areas for the thesis in topology are homotopy theory, K-theory, generalized cohomology theories, category theory, non-linear dynamics, Lie-groups and differential geometry.

Numerical analysis: If the admission bacground does not cover TMA4215 Numerical Mathematics and TMA4212 Numerical Solution of Differential Equations these should be taken. In addition TMA4220 Numerical Solution of Partial Differential Equations Using Element Methods and TMA4205 Numerical Linear Algebra should be taken. Some possible areas for the thesis in numerical analysis is numerical solution of ordinary and partial differential equations, numerical linear algebra and topics within computational sciences.

Statistics: For the statistics direction the courses TMA4295 Statistical inference and TMA4300 Modern statistical methods should be taken. If the admission background does not cover both of TMA4265 Stochastic processes and TMA4267 Linear statistical models, the missing one must be taken as part of the master program. Some possible areas for the thesis in statistics are biomodelling, computational statistics, design of experiments, functional genomics, life time analysis and spatial statistics.

As mentioned above, the coursework will take almost 1½ year (87.5/60 year). All the courses in the degree must be approved by the Department of Mathematical Sciences, NTNU.

The Thesis

The thesis could contain some independent research, but could also be of purely expository nature. The student may be required to follow seminars on the topic of the thesis. These seminars will in addition to the courses help the student to obtain the necessary background needed for writing the thesis. The work with the thesis should correspond to a workload of 37.5 credit points.

Exams

The exam in each of the courses is either a written exam or an oral exam normally at the end of the semester when the course is taught.

Grades

For all exams and also for the thesis the scale of grading is from A (highest) to F (lowest) or Fail.