Courses offered at the
Department of Mathematics, the University of
Bergen.
Please note that the
information on this page might not be completely updated.
For the updated
official information - please take a look at the following web-page: http://students.uib.no/
| MAT101 | Elementary calculus I |
| Content: | The course is an elementary introduction to functions of one variable, exponential and trigonometric functions, differentiation and integration, vectors, simple differential equations, extremal points for functions of two variables. |
| Objectives: | To provide knowledge and ability in mathematics and applications thereof for those students who will continue to study subjects which are less demanding with respect to mathematics. |
| Builds on: | 2MX (Intermediate level of mathematics from Norwegian high school) |
| Semester: | Autumn |
| Language: | Norwegian |
| Exam: | Written examination Offical link for MAT101 |
| MAT111 | Calculus I |
| Content: | Introduction to mathematical analysis with emphasis on differentiation and integration. The course includes the real and complex number systems, limits, continuity, logarithmic, exponential and trigonometric functions and their inverse functions, Taylor expansion with remainder, sequences, series and introductory differential equations. |
| Objectives: | To extend central areas of high school mathematics and give students an introduction to real analysis. |
| Builds on: | 3MX (Highest level of mathematics from Norwegian high school) |
| Semester: | Autumn |
| Language: | Norwegian |
| Exam: | Written examination Offical link for MAT111 |
| MAT112 | Calculus II |
| Content: | An introduction to real analysis with an emphasis on the Riemann integral, basic properties of curves and surfaces, convergence of sequences and series, and also vectors and functions of several variables. Complex numbers are also introduced. |
| Objectives: | To give the students insight in central and basic ideas and results in real analysis, and the properties of complex numbers. |
| Builds on: | MAT111 |
| Semester: | Spring |
| Language: | Norwegian |
| Exam: | Written examination Offical link for MAT112 |
| MAT121 | Linear algebra |
| Content: | The course contains linear systems of equations, determinants, matrix algebra, vector spaces, linear transformations, and diagonalization. It also applies this to the theory of conics. |
| Objectives: | The students get knowledge and skills of central techniques and ideas of linear algebra for use in other subjects and more advanced courses. |
| Builds on: | MAT111 or MAT101 |
| Semester: | Spring |
| Language: | Norwegian |
| Exam: | Written examination Offical link for MAT121 |
| MAT131 | Differential equations I |
| Content: | Linear ordinary differential equations of second and higher order, systems of first order equations, Fourier series, boundary and eigenvalue problems for partial differential equations. |
| Objectives: | To make students of applied mathematics, physics and geophysics etc., familiar with methods for solving differential equations. |
| Builds on: | MAT111, MAT112 and MAT121. (MAT112 and MAT121 can be taken together with MAT131.) |
| Semester: | Spring |
| Language: | Norwegian |
| Exam: | Written examination Offical link for MAT131 |
| MAT160 | Scientific computing 1 |
| Content: | The course gives an introduction to basic computational algorithms from these areas: Solving equations and systems of equations (only linear), interpolation and approximation methods including curve fitting, numerical derivations, integration and extrapolation. Implementation of algorithms will play a central role. A short introduction to Matlab is given to be used in exercises. |
| Objectives: | To provide knowledge, understanding and ability of computational technics that are presented |
| Builds on: | INF100, MAT111, MAT121 |
| Semester: | Autumn |
| Language: | Norwegian |
| Exam: | Written examination Offical link for MAT160 |
| MAT211 | Real analysis |
| Content: | The course includes axioms of real number systems, uniform convergence of sequences and series of functions, equicontinuity, compact and complete metric spaces, the inverse function theorem, the Stone-Weierstrass theorem and contraction maps. |
| Objectives: | The students will be able to demonstrate basic knowledge within the central parts of classical real analysis, and establish a platform for further studies within functional analysis, topology and function theory. |
| Builds on: | MAT112 |
| Semester: | Autumn |
| Language: | English if exchange students attend the seminars, otherwise Norwegian. |
| Exam: | Oral examination Offical link for MAT211 |
| MAT212 | Functions of several variables |
| Content: | Theory of curves and surfaces, vector analysis, integration in two and three dimensional space, theorems of Green, Stokes and Gauss. |
| Objectives: | To enable students to use basic tools of analysis related to functions of several variables. |
| Builds on: | Prerequisites: MAT112 , MAT121 |
| Semester: | Autumn |
| Language: | Norwegian |
| Exam: | Written examination Offical link for MAT212 |
| MAT213 | Functions of a complex variable |
| Content: | Some theory of analytic functions of one complex variable, complex integrals, series of Taylor and Laurent, many-valued functions, calculus of residues. |
| Objectives: | To enable students to use basic tools of complex methods. |
| Builds on: | MAT112 |
| Semester: | Spring |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Written examination Offical link for MAT213 |
| MAT214 | Theory of complex functions |
| Content: | The course studies complex integration, conformal maps, harmonic and subharmonic functions, Dirichlets problem, series and product expansions, elliptic functions, and analytical continuation. |
| Objectives: | The students shall document insight in advanced complex analysis with an emphasis on applications to number theory, algebraic geometry and general analysis. |
| Builds on: | MAT213 |
| Semester: | Every second autumn - odd-numbered years |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for MAT214 |
| MAT215 | Theory of measure and integration |
| Content: | Contents are the Lebesgue integral, general theory of measure spaces and measurable functions, Lebesgue-Stieltjes measure on the real line, the Radon-Nikodym theorem, Fubinis theorem, Lp-spaces and related topics. |
| Objectives: | To document insight in modern theory of integration as a tool in advanced analysis and in statistics. |
| Builds on: | MAT211 |
| Semester: | Irregular - spring |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Written examination Offical link for MAT215 |
| MAT220 | Algebra |
| Content: | Basic theory for groups and permutations. Normal subgroups, group homeomorphisms and factor groups, group actions and Sylow Theory. In addition one studies basic theory of rings and fields, polynomial rings, ideals and factor rings. One also studies field extensions, finite fields and unique factorization domains. In the last part one focuses at groups of utomorphisms of fields, and treats the Galois Theory necessary to show the insolvability of the general quintic by radicals. |
| Objectives: | The students shall demonstrate knowledge of the basic theory of groups, rings, and some Galois Theory. They shall know how these concepts are used to prove classical results in mathematics, and obtain a basis of knowledge and insight which enables them to embark on further studies in algebra or related fields. |
| Builds on: | MAT121 |
| Semester: | Spring |
| Language: | English if exchange students attend the seminars, otherwise Norwegian. |
| Exam: | Written examination Offical link for MAT220 |
| MAT221 | Combinatorics I |
| Content: | The subject gives an introduction to combinatorial structures on finite sets. One part consists of counting theory, binomial coefficients, recursion formulas and generating functions. The other part consists of graph theory, paths and circuits, trees, planarity, and colouring. |
| Objectives: | To provide the students with basic knowledge of graph theory and counting theory. The subject is useful for further studies in mathematics and informatics. |
| Builds on: | MAT111 |
| Semester: | Autumn |
| Language: | Norwegian |
| Exam: | Written examination Offical link for MAT221 |
| MAT224 | Commutative algebra |
| Content: | Commutative algebra shows how geometric and number theoretical ideas can be interpreted by means of algebraic structures. One studies Noetherian and Aritinian rings and modules over such rings. Topics are dimensions of rings and modules, localization, tensor products, primary decomposition, and integral extensions. |
| Objectives: | The students shall document insight into central ideas and constructions in commutative algebra, which are essential in algebraic geometry, algebraic topology, parts of informatics, and algebraic number theory. |
| Builds on: | MAT220 |
| Semester: | Autumn |
| Language: | English if exchange students attend the seminars, otherwise Norwegian. |
| Exam: | Oral examination Offical link for MAT224 |
| MAT225 | Number theory |
| Content: | The course is an introduction to quadratic reciprocity, binary quadratic forms, continued fractions, the Pell equation, algebraic number fields, and rational points on curves. |
| Objectives: | The students shall document insight in important ideas and techniques in number theory. Their application in for instance cryptology is also stressed. |
| Builds on: | MAT220 |
| Semester: | Irregular |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for MAT225 |
| MAT227 | Combinatorics |
| Content: | One studies advanced graph theory and theory of counting. In addition one studies combinatorial designs, Ramsey theory, and theory of partially ordered sets, lattices, and matroids. |
| Objectives: | The students shall document insight in the most important parts of combinatorial theory and graph theory. |
| Builds on: | MAT221 , MAT220 |
| Semester: | Irregular |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for MAT227 |
| MAT230 | Differential equations II |
| Content: | 0 |
| Objectives: | 0 |
| Builds on: | MAT131 |
| Semester: | Autumn |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Written examination (80 %) and
exercises (20 %) Offical link for MAT230 |
| MAT232 | Functional analysis |
| Content: | The course includes convergence in normed spaces, the contraction-mapping theorem with applications to differential and integral equations, functionals on normed spaces and in Hilbert space, the spectral theorem for compact self-adjoint operators and an introduction to Sobolev space and the theory of distributions. |
| Objectives: | To make the student of applied mathematics or mathematical physics familiar with basic concepts and results about operators on Banach spaces and in Hilbert space. The course provides an important tool for analysing and solving integral-differential equations. |
| Builds on: | MAT131 , MAT212 |
| Semester: | Spring |
| Language: | English if exchange students attend the seminars, otherwise Norwegian. |
| Exam: | Oral examination Offical link for MAT232 |
| MAT233 | Stability and perturbation theory |
| Content: | Stability of the solution of linear and non-linear ordinary differential equations, asymptotic series, techniques for solving ordinary differential equations based on asymptotic series |
| Objectives: | To make the students of applied mathematics familiar with qualitative methods (stability theory) and enable them to solve differential equations by means of asymptotic series. |
| Builds on: | MAT131 , MAT213 |
| Semester: | Autumn |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for MAT233 |
| MAT234 | Partial differential equations |
| Content: | The course includes initial and boundary value problems for PDEs of first and second order, and to some extent systems of such equations. Emphasis is on qualitative behaviour of solutions. |
| Objectives: | The aim of the course is to give students a theoretical understanding of properties of partial differential equations that are central in applied mathematics, physics and in geophysics. |
| Builds on: | MAT131 , MAT212 , MAT230 |
| Semester: | Autumn |
| Language: | English if exchange students attend the seminars, otherwise Norwegian. |
| Exam: | Oral examination Offical link for MAT234 |
| MAT235 | Vector and tensor analysis |
| Content: | More on the theory of functions of several variables (MAT212): Integral theorems in several dimensions, coordinate transformations, vector functions, tensors. |
| Objectives: | To provide working tools for students in some branches of applied mathematics, physics and geophysics. |
| Builds on: | MAT212 |
| Semester: | Every second autumn - even-numbered years. |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for MAT235 |
| MAT236 | Fourier analysis |
| Content: | An introduction to continuous and discrete Fourier analysis and its applications on linear systems and filters. Sampling of continuous signals and discretization of continuous linear signals and a short discussion of the Z-transform |
| Objectives: | To provide working tools for graduate work within signal treatment in, among other subjects, physics and geophysics. |
| Builds on: | MAT131 |
| Semester: | Autumn |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Written examination Offical link for MAT236 |
| MAT242 | Topology |
| Content: | One studies topological spaces. An important part is to attach algebraic and combinatorial invariants to these spaces. |
| Objectives: | The students shall document insight in topics of topology which are central for most directions in pure mathematics. |
| Builds on: | MAT121 , MAT211 |
| Semester: | Autumn |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for MAT242 |
| MAT243 | Manifolds |
| Content: | Elementary points set topology. Manifolds, differentiable structures. Tangent bundles and vector bundles. Riemannian manifolds. Embeddings and immersions. Tranversality. Integrability. |
| Objectives: | The goal of the course is to give the students insight in basic geometric concepts and methods in differential topology, partly as a tool for solution of differential equations on manifolds. |
| Builds on: | MAT121, MAT212 |
| Semester: | Spring |
| Language: | English if exchange students attend the seminars, otherwise Norwegian. |
| Exam: | Portfolio assesment (20%) and
oral examination (80%) Offical link for MAT243 |
| MAT251 | Classical mechanics |
| Content: | Derivation of the fundamental equations in continuum mechanics with special emphasis on the equations of fluids and gases. |
| Objectives: | To provide the students of applied mathematics with an understanding of basic parts of continuum mechanics. |
| Builds on: | MAT131 , MAT212 , PHYS111 |
| Semester: | Spring |
| Language: | Norwegian |
| Exam: | Written examination Offical link for MAT251 |
| MAT252 | Continuum mechanics |
| Content: | Derivation of the fundamental equations in continuum mechanics with special emphasis on the equations of fluids and gases. |
| Objectives: | To provide the students of applied mathematics with an understanding of basic parts of continuum mechanics. |
| Builds on: | MAT251 |
| Semester: | Spring |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for MAT252 |
| MAT253 | Hydrodynamics |
| Content: | Flow of ideal and real fluids, boundary layers, stability and waves, effect of stratification, rotation and compressibility, and some topics of geophysical hydrodynamics. |
| Objectives: | To enable students to use the basic working tools in hydrodynamics. Primarily for students who intent to specialize in hydrodynamics, but is also useful for students of geophysics. |
| Builds on: | MAT252 |
| Semester: | Spring |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for MAT253 |
| MAT254 | Flow in porous media |
| Content: | The course includes equations for one- and multiphase flow in porous media with emphasis on qualitative and quantitative properties for models studied. |
| Objectives: | To make the students familiar with the basic concepts with regard to the flow of fluids, primarily water, oil and gas in a reservoir. |
| Builds on: | MAT252 |
| Semester: | Autumn |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for MAT254 |
| MAT255 | Reservoir simulation |
| Content: | An introduction to an industrial numerical code for flow of oil, gas and water in a reservoir. Special emphasis on geometry, fluid property, wells and oil production in a numerical model. |
| Objectives: | To enable students to carry out industrial reservoir simulation on a computer. |
| Builds on: | MAT254 , INF100 , PTEK212 |
| Semester: | Spring |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination and semester
assignment Offical link for MAT255 |
| MAT256 | Plasma dynamics |
| Content: | Theory of ionized gases (plasmas) in electric and magnetic fields, including particle trajectories, statistical mechanics, kinetic theory, continuum theory and wave propagation. Some applications to space plasmas. |
| Objectives: | To prepare students in applied mathematics (and physics) for graduate work where knowledge of plasma dynamics is essential. |
| Builds on: | MAT252 (or PHYS205), PHYS111, PHYS112 |
| Semester: | Irregular |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for MAT256 |
| MAT257 | Reservoir simulations in practice |
| Content: | An introduction to an industrial numerical code for flow of oil, gas and water in a reservoir. |
| Objectives: | To enable students to carry out industrial reservoir simulation on a computer. |
| Builds on: | MAT254, INF100, PTEK212 |
| Semester: | Spring |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination and semester
assingment. Offical link for MAT257 |
| MAT258 | Numerical ocean modelling |
| Content: | An introduction to the use of and properties of numerical ocean models will be given. Numerical methods for studies of circulation and processes in the ocean will be described and analysed. Important topics include stratification, effects of the earth's rotation, turbulence, operator splitting, validation and coupling of physical and biological variables. |
| Objectives: | To give the students a platform for setting up and using numerical models for studies of physical and biological processes in the ocean in a critical way. |
| Builds on: | MAT131. It is an advantage to have some knowledge of continuum mechanics, hydrodynamics, geophysics, numerical analysis and use of computers. |
| Semester: | Every second autumn - odd-numbered years. |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination (50 %) and
semester assignment (50 %) Offical link for MAT258 |
| MAT260 | Scientific computing 2 |
| Content: | The course gives an introduction to algorithms and theory for numerical solution of systems of ordinary differential equations, iterative solution of systems of non-linear equations and basic methods for calculating eigenvalues. Computation of the best approximation in the least square theory with focus on orthogonal polynomials and trigonometric approximation including the fast Fourier transform (FFT) are also treated. In addition one looks at special problems in numerical integration and Gauss quadrature. |
| Objectives: | To provide substantial understanding for techniques and algorithms and the mathematical theory behind. Convergence and numerical stability is a central part. The course is very useful for a master thesis in computational science. |
| Builds on: | MAT160 |
| Semester: | Spring |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Written exam. It is
opportunity for grades on exercises, which can be included in the final
grade. If less than 20 students are taking the course, it can be oral
exam. Offical link for MAT260 |
| MAT261 | Numerical linear algebra |
| Content: | This course deals with algorithms to solve: The eigenvalue problem superdeterminant equation systems and linear equation systems (onlyKrylov subspace iteration). Algorithms for matrix decomposition as QR-factorisation and Singular-value decomposition will be discussed and analysed with respect to stability and complexity. |
| Objectives: | To provide substantial understanding of the most important algorithms, the mathematical theory behind them, their numerical stability and efficiency. The course is very useful for a master thesis in computational science. |
| Builds on: | MAT160 |
| Semester: | Autumn |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Written exam. It is
opportunity for grades on exercises, which can be included in the final
grade. If less than 20 students are taking the course, it can be oral
exam. Offical link for MAT261 |
| MAT262 | Image processing |
| Content: | The course deals with basic algorithms and mathematical theory that constitute foundation for modern digital image and sound processing. Fourier analysis, Fast Fourier Transformations, Gabor and wavelet analysis and also digital filter theory will be considered. During practical use of for instance noise filtering and data compression of image and sound will this theory become object of further examination. |
| Objectives: | To provide a solid knowledge and understanding of the most important algorithms: the mathematical theory behind them, their numerical stability and efficiency. The course is very useful for master students in computational mathematics. |
| Builds on: | MAT160 |
| Semester: | Spring |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Written exam. It is
opportunity for grades on exercises, which can be included in the final
grade. If less than 20 students are taking the course, it can be oral
exam. Offical link for MAT262 |
| MAT263 | Fluite difference methods for initial value problems |
| Content: | This course gives an introduction to finite difference methods for time dependent partial differential equations and stiff ordinary differential equations. The stability of such methods, when doing time integrating, is discussed. |
| Objectives: | To provide good understanding of the different techniques for time integration of partial differential equations. The course is useful both for students in numerical analysis and for students working with modelling of time dependent phenomenon. |
| Builds on: | MAT260 (INF260) |
| Semester: | Every second spring, odd-numbered years |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Written exam. It is
opportunity for grades on exercises, which can be included in the final
grade. If less than 20 students are taking the course, it can be oral
exam. Offical link for MAT263 |
| MAT264 | Computational Science II |
| Content: | The course looks at the whole process within computational science from the formulation of a physical model, to estimation of mathematical properties of the model and to the choice of numerical methods to be used and finally to simulation of the model in a numerical experiment. The course gives insight into programming, graphical plotting of results and experience with advanced computers. The course includes compulsary exercises with emphasis on practical aspects of the methods. |
| Objectives: | To exercise students in ways of working in computational science, and provide them with practical knowledge of working tools in the field. |
| Builds on: | MAT230, MAT160 |
| Semester: | Spring |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Exercises + oral
presentation Offical link for MAT264 |
| MAT265 | Parameter estimation and inverse problems |
| Content: | 0 |
| Objectives: | 0 |
| Builds on: | MAT121, MAT160, MAT212, STAT110/101 |
| Semester: | Spring |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for MAT265 |
| MAT291 | History of mathmatics |
| Content: | The course surveys important developments in mathematics from antiquity till the end of the nineteenth century. Topics are Greek mathematics, development of the theory of equations and analytical geometry. Further topics are the development of differential and integral calculus, of rigor in analysis, and of modern algebra and the modern axiomatic approach. An essential part of the course is to get to know some of the foremost mathematicians, like Newton, Euler, and Abel and how they have shaped the development of mathematics. |
| Objectives: | The students shall document insight in how mathematical ideas naturally have arisen and developed, partly due to the development of society and science, and partly due to the dynamics in mathematics itself. |
| Builds on: | It is recommended to have taken 30 ECTS in mathematics before attending this course. |
| Semester: | Every second spring - odd-numbered years. |
| Language: | Norwegian |
| Exam: | Written examination Offical link for MAT291 |
| MAT311 | General functional analysis |
| Content: | Topics are general topology, Bancah spaces, Hahn Banach theorem, Baire categories with applications, weak convergence, Krein Milman theorem. Also applications of this to Lp spaces. |
| Objectives: | The students shall document insight in basic methods and ideas of functional analysis. |
| Builds on: | MAT211, MAT215 |
| Semester: | Irregular |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for MAT311 |
| MAT321 | Algebraic geometry I |
| Content: | The course is a first introduction to algebraic geometry, algebraic curves and algebraic varieties. |
| Objectives: | The students shall document insight in important ideas and techniques in algebraic geometry. |
| Builds on: | MAT224 |
| Semester: | Irregular |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for MAT321 |
| MAT322 | Algebraic geometry II |
| Content: | The course is a continuation of MAT321. The content may vary. |
| Objectives: | The students shall document deep insight of modern concepts and techniques of algebraic geometry. |
| Builds on: | MAT224 , MAT321 |
| Semester: | Irregular |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for MAT322 |
| MAT323 | Representation theory |
| Content: | One studies how groups can be realized as symmetry groups of a finite dimensional space. The space is then called a representation of the group. Representations of finite groups and their character tables are studied. In particular representations of the symmetric group Sn. Further topics are representation of the matrix group GL(n) and the close connection to representations of Sn, and the corresponding combinatorics for the associated Young diagrams. |
| Objectives: | To give the students insight in basic representation theory which is useful for most directions in pure mathematics and also theoretical physics. |
| Builds on: | MAT220 |
| Semester: | Irregular |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for MAT323 |
| MAT331 | Topics in analysis |
| Content: | The content of the course may vary from semester to semester. Subjects can be mathematical analysis/numerical methods for the laws of conservation and non-linear partial differential equations, selected topics from the functional analysis and non-linear ordinar differential equations. |
| Objectives: | To extend theoretic background for students doing graduate work in this area. |
| Builds on: | MAT211 , MAT232 |
| Semester: | Irregular |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for MAT331 |
| MAT333 | Topics in stability and perturbation theory |
| Content: | The lectures may focus on specialized topics related to stability and perturbation of ordinary and partial differential equations |
| Objectives: | To extend theoretic background for students doing graduate work in this area. |
| Builds on: | MAT233 |
| Semester: | Irregular |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for MAT333 |
| MAT341 | Algebraic topology |
| Content: | The course is an introduction to algebraic topology, including homotopy and homology. |
| Objectives: | The goal of the course is to give the students insight into basic ideas and methods of algebraic topology. |
| Builds on: | MAT220, MAT242 |
| Semester: | Irregular |
| Language: | English if exchange students attend the seminars, otherwise Norwegian. |
| Exam: | Oral examination Offical link for MAT341 |
| MAT342 | Differential geometry |
| Content: | The course gives an introduction to the techniques of differential geometry. In particular we will study connections and curvature of smooth manifolds. Further topics may wary, for example the coruse can cover homogeneous spaces, Lie groups, semi-Riemannian geometry and general relativity theory. |
| Objectives: | The students shall gain insight in important differential geometric methods and learn about applications of differential geometry. |
| Builds on: | MAT121, MAT212, MAT243 |
| Semester: | Irregular |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for MAT342 |
| MAT353 | Special topics in hydrodynamics |
| Content: | The lectures may discuss specialized topics from hydrodynamics that may be related to theoretical oceanography and meteorology. |
| Objectives: | The course is meant for dr. students and staff within fluid dynamics from applied mathematics and geophysics. |
| Builds on: | MAT253 |
| Semester: | Irregular |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for MAT353 |
| MAT360 | Finite element methods and domain decomposition |
| Content: | The course considers the theory for finite element method to discrete partial differential equations, especially elliptical, and also solution techniques for the discrete equation system that become result. Domain decomposition as solving technique will become subject to special attention. |
| Objectives: | The course will provide a good basis for work with element method and domain decomposition in Master- and doctoral thesis. |
| Builds on: | MAT260 (INF260), MAT261 (INF261) |
| Semester: | Irregular - autumn |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Written exam. If less than 20
students are taking the course, it can be oral exam. Offical link for MAT360 |
| MAT361 | Conservation methods for hyperbolic differential equations |
| Content: | The course gives and introduction to hyperbolic conservation laws and to numerical methods for solving the equations. In the analytic part of the course one considers both for scalar equations and for a system of equations, topics as waves, entropy conditions and the solution of the Riemann problem. In the numerical part of the course one discusses topics as conservation, monotony, stability and accuracy of methods used. |
| Objectives: | The course is meant special for students on Master- and Phd. levels |
| Builds on: | MAT234, MAT263 (INF263) |
| Semester: | Every second autumn - odd-numbered years. |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for MAT361 |
| MAT362 | Conservation methods for elliptical differential equations |
| Content: | The course gives three equivalent formulations of elliptical equations: the integral formulation, the variational formulation and the saddle point formulation. From each of these formulations one derives different numerical methods and properties of these methods are discussed. |
| Objectives: | The lectures will be on special topics on Master- and Phd. levels |
| Builds on: | MAT234, MAT263 (INF263) |
| Semester: | Every second spring - even-numbered years. |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for MAT362 |
| MAT369 | Selected topics in scientific computing |
| Content: | The course deals with current topics in Scientific computing, which is not covered by the permanent courses, and its content will vary from time to time. |
| Objectives: | Teaching in special topics at Master- and PhD-level. |
| Builds on: | 0 |
| Semester: | Irregular |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Written exam. If less than 20
students are taking the course, it can be oral exam. Offical link for MAT369 |
| STAT101 | Elementary statistics |
| Content: | This course gives an introduction to statistics using the program package S-plus as an important tool. It contains descriptive statistics, discrete probability models, distributions of one and two variables and a little about covariance and correlation. In the statistics part the basic theory of hypothesis testing and p-values is explained. Moreover, one looks at categorical data for one and two samples, linear and multiple regression and introductory one way analysis of variance. The students also have to go through a number of computer exercises interpreting output from S-plus. |
| Objectives: | The course should make the students able to use common statistical methods. Moreover, the students should be able to use the MINITAB package and interpret its output. Another important point is that they students should be capable of distinguishing between theoretical and empirical quantities. The course makes it possible to continue with further studies in statistics in Stat200. |
| Builds on: | 2MX (Intermediate level of mathematics from Norwegian high school) |
| Semester: | Autumn |
| Language: | Norwegian |
| Exam: | Written midterm examination
(20 %) and final examination (80 %). The result from the midterm
examination is valid for one semester only. In spring semesters there is
only the final examination (100 %). Examination support: Calculator and
approved list of formulaes. Offical link for STAT101 |
| STAT110 | Basic course in statistics |
| Content: | The main emphasis in this course is on probability models. Discrete and continuous distributions, among others the binomial, the hypergeometric, the exponential, the Poisson and the normal distributions are treated. Examples are given from many areas. The last part of the course deals with principles for estimating unknown quantities using least squares, method of moments, maximum likelihood, and with the construction of confidence intervals. |
| Objectives: | Students will get a basis for further studies in statistics, both for those who wish to specialize in statistics, and for those who need statistics in other disciplines. |
| Builds on: | MAT101 or MAT111 (can be taken together with STAT110) |
| Semester: | Autumn |
| Language: | Norwegian |
| Exam: | Written midterm examination
(20 %) and final examination (80 %). The result from the midterm
examination is valid for one semester only. In spring semesters there is
only the final examination (100 %). Examination support: Calculator Offical link for STAT110 |
| STAT111 | Statistical methods |
| Content: | The course contains methods for testing of hypotheses and construction of confidence intervals based on data. Moreover, an elementary introduction to regression and analysis of variance with multiple comparisons and experimental design is given. Finally, nonparametric methods including the Wilcoxon test is treated. Examples are given from several areas of application. |
| Objectives: | This course gives an introduction to statistical methods and will be well suited to students of science. Together with STAT110 it is a natural unit in statistics. |
| Builds on: | STAT110 |
| Semester: | Spring |
| Language: | Norwegian |
| Exam: | Written midterm examination
(20 %) and final examination (80 %). The result from the midterm
examination is valid for one semester only. In spring semesters there is
only the final examination (100 %). Examination support: Calculator and
approved list of formulaes. Offical link for STAT111 |
| STAT200 | Applied statistics |
| Content: | This course deals with statistical methods that are commonly used in software packages. In the exercises one uses a large statistical software package. Among other things one looks at various types of analysis of variance, simple and multiple regression, Chi-square tests and nonparametric statistics. |
| Objectives: | The course gives an overview over statistical methods that are much used in various disciplines. At the same time it gives the students a basis for understanding the ideas behind the methods and for using the methods in a rational way by means of statistical software. |
| Builds on: | STAT110 or STAT101 |
| Semester: | Spring |
| Language: | Norwegian |
| Exam: | Written examination.
Examination only once a year: Spring. Examination support: All printed and
written aids, calculator. Offical link for STAT200 |
| STAT201 | Generalised linear models |
| Content: | The theory for linear normal models is looked at and applied to regression and analysis of variance. Furthermore the topics of binary variables logistic regression, log-linear models, contingency tables and life time analysis are treated. |
| Objectives: | This course is a continuation of regression and analysis of variance from STAT111 or STAT200. It gives an introduction to modern and useful methods that are being used in computer-intensive generalized linear models. |
| Builds on: | MAT121, STAT210, STAT200 or STAT111 |
| Semester: | Every second autumn - odd-numbered years. |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for STAT201 |
| STAT210 | Theory of statistical inference |
| Content: | The course will consider transformations of random variables and the principles of estimation and hypothesis testing. In this relation one will consider sufficiency, the exponential family and maximum likelihood estimation. |
| Objectives: | The course will give the conceptional and mathematical basis for a further study of statistical methods at a theoretic level. |
| Builds on: | MAT112 , MAT121 , STAT111 |
| Semester: | Spring |
| Language: | English if exchange students attend the seminars, otherwise Norwegian. |
| Exam: | Written midterm examination
(20 %) and final examination (80 %). The result from the midterm
examination is valid for one semester only. Examination only once a year
(spring). Offical link for STAT210 |
| STAT211 | Time series and econometrics |
| Content: | This course gives an introduction to linear time series models, such as autoregressive, moving average and ARMA models. Moreover, it is shown how the empirical autocorrelation and partial correlation can be used to identify the model. The Durbin- Levinson, the innovation algorithm and the theory for optimal forecasts are explained. The last part of the course gives an introduction to methods of estimation. Empirical modelling using the AIC and FPE criteria is mentioned as is ARCH and GARCH models. |
| Objectives: | The purpose of the course is to give an introduction to the analysis and use of time series models. |
| Builds on: | MAT121, STAT210, STAT111 or STAT200 (or something equivalent). |
| Semester: | Every second spring - odd-numbered years. |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for STAT211 |
| STAT220 | Stochastic prosesses |
| Content: | The course will consider Markov processes in discrete and continuous time. The theory is illustrated with examples from operation research, biology and economy. |
| Objectives: | The course will give an introduction to the formulation and analysis of models for phenomena where the future has an element of uncertainty. |
| Builds on: | MAT112, MAT121 (can be taken together with STAT220), STAT110 |
| Semester: | Autumn |
| Language: | English if exchange students attend the seminars, otherwise Norwegian. |
| Exam: | Written examination.
Examination only once a year: Autumn Offical link for STAT220 |
| STAT221 | Limit theorems in probability theory |
| Content: | This course gives an introduction to asymptotic methods in statistics. Types of convergence such as convergence in probability, convergence with probability one and convergence in distribution are discussed. A version of the law of large numbers and the Lindeberg central limit theorem are proved. The theory applied to maximum likelihood. |
| Objectives: | The purpose of the course is to give the basics of asymptotic analysis in statistics and probability. |
| Builds on: | MAT112 , STAT110, STAT210 |
| Semester: | Irregular |
| Language: | Norwegian |
| Exam: | Oral examination Offical link for STAT221 |
| STAT230 | Life insurance mathematics |
| Content: | The course gives an introduction in classical interest rate theory and basic mortality statistics. Calculation of net premiums and premium reserves are treated for various insurance covers for one or several lives. The problem of adding expenses and returning bonus is also covered. |
| Objectives: | The course is meant to give a broad introduction to the theory and the techniques of life insurance. It gives a good fundament for working in the life insurance business, both private and public. |
| Builds on: | STAT220 |
| Semester: | Every second spring - even-numbered years. |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Written examination.
Examination support: Calculator. Examination only once a year. Offical link for STAT230 |
| STAT231 | Non-life insurance mathematics |
| Content: | Topics covered are premium calculations, bonus systems and credibility theory. A further topic is the analysis of the risk process, including ruin theory. The calculations of total loss distributions is covered and also loss reserving methods. |
| Objectives: | The course is meant to give a broad introduction to central issues in non life insurance such as premium estimation, loss reserving, reinsurance methods and general risk theory. |
| Builds on: | STAT210 , STAT220 |
| Semester: | Every second autumn - even-numbered years. |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Written examination.
Examination support: Calculator. Examination only once a year. Offical link for STAT231 |
| STAT240 | Theory of finance |
| Content: | The theory of pricing financial derivatives, both in discrete and in continuous time is covered, including the Black-Scholes formula. Some theory of interest rate models is also included. The necessary theory of stochastic calculus and stochastic differential equations will be covered. |
| Objectives: | The course aims to give an introduction to the modern theory of mathematical finance. |
| Builds on: | STAT220, ECON361 is an advantage |
| Semester: | Irregular |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Written examination Offical link for STAT240 |
| STAT250 | Monte Carlo methods in statistics |
| Content: | Topics that are discussed are: Random number generation for various distributions. Monte Carlo estimation of higher dimensional integrals including variance reduction techniques such as importance sampling, antithetic sampling and Raolackwellization. Methods for finding maximum likelihood estimators such as Quasi-Newton methods, simulated annealing and the EM algorithm. Elements of Bayesian theory and Markov Chain theory on a general state space.The Metropolis-Hastings as well as the Gibbs sampling algorithm to calculate Bayesian estimators. The material covered is mainly from the book: Monte Carlo Statistical Methods by Christian P. Robert og George Casella. 2.ed. Springer-Verlag, 2004. |
| Objectives: | The objective of the course is to enable students to solve non-trivial problems in computational statistics. |
| Builds on: | The course is rather advanced, and the prerequisites should be at least corresponding to Stat 110, Stat 111 and one of the statistics courses at the 200 level. Stat 220 would be an advantage. Less background will make the course very demanding. |
| Semester: | Irregular |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for STAT250 |
| STAT310 | Multivariate analysis |
| Content: | The course contains descriptive multivariate statistics, multivariate distribution theory such as the multinormal and the Wishart distribution. Furthermore, it contains multivariate t-tests, simultaneous confidence intervals, multivariate regression, principal components and factor analysis. In addition discriminant analysis, cluster analysis and correspondence analysis are mentioned. Finally, the spectral and singular value decomposition is discussed. |
| Objectives: | The course gives an introduction to multivariate statistics with the emphasis on practical applications. The students get experience in using important methods through exercises with the software package S-plus. |
| Builds on: | MAT121, STAT101 or STAT110, STAT210 |
| Semester: | Irregular |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for STAT310 |
| STAT311 | Selected topics in statistics |
| Content: | Special topics are treated. The contents may vary. |
| Objectives: | The purpose is to give increased insight into one particular area of statistics. |
| Builds on: | STAT210 |
| Semester: | Irregular |
| Language: | Norwegian (English might be used if the lecturer decides so.) |
| Exam: | Oral examination Offical link for STAT311 |