## PhD studies in mathematics

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**General eligibility**

A general eligibility of 240 credits is required, corresponding to 4 years full time university studies, or a university degree at an advanced (master) level or the equivalent competence.

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**Special eligibility**

To be qualified you must have a university degree containing at least the following courses in mathematics:

- Algebra: groups, rings, euclidean and principal ideal rings, fields, extension fields.
- Foundation of analysis: real numbers, Bolzano-Weierstrass, derivation and integration in Rn, series of functions, implicit functions.
- Analytic functions: integral and series expansion, residue calculus, conformal mappings, harmonic functions.

The textbooks we use are

Rudin: Principles of mathematical analysis,

Beachy and Blair: Abstract algebra, and

Saff and Snider: Fundamentals of complex analysis.

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**Selection and admission**

The selection of candidates is made from certificate of courses, quality of thesis, references, and interviews. Information about admission will be given latest in June.

Those who are accepted are normally financed with study grants. If you intend to finance your education in some other way, you must inform us about that.

## PhD studies in mathematical statistics

###
**General eligibility**

A general eligibility of 240 credits is required, corresponding to 4 years full time university studies, or a university degree at an advanced (master) level or the equivalent competence.

###
**Special eligibility**

To be qualified you should have taken courses including most of the

following material:

- Probability Theory: Simultaneous and conditional distributions; conditional expectation and variance, multidimensional normal distribution, limit/convergence theorems (Law of Large Numbers; Central Limit Theorem), convergence of random variables (in distribution, probability, mean or almost surely); transforms (probability generating, moment generating, characteristic); martingales.
- Stochastic Processes: Finite state Markov processes in discrete and continuous time, in particular Poisson and birth-death processes; queueing theory; renewal processes; Brownian motion; stationary stochastic processes; methods of stochastic simulation.
- Statistical inference: Exponential families; likelihood; sufficiency; information bounds; consistency; efficiency; maximum likelihood theory; likelihood ratio tests; uniformly most powerful tests.

The books we use in courses that are prerequisists are:

Gut: An intermediate course in probability,

Ross: Introduction to probability models, and

Lindgren, B. W.: Statistical Theory.

###
**Selection and admission**

The selection of candidates is made from certificate of courses, quality of thesis, references, and interviews. Information about admission will be given latest in June.

Those who are accepted are normally financed with study grants. If you intend to finance your education in some other way, you must inform us about that.

## Further information

If you want further information or have any query, please contact our directors of PhD studies (see contact information in the right hand column).