51ÖØ¿ÚÁÔÆæ

The course is divided into two halves, the first covers probability theory and the second covers statistics. The course covers: Sample space, Events, Basic set theory, Axioms of probability. Conditional probability, Independent events…

Basic probability theory, random variables in one and several dimensions, multivariate Gaussian distribution, convergence of random variables and distributions, conditional distributions. Moment generating functions and characteristic…

The course treats: Markov chains: model graphs, Markov property, transition probabilities, persistent and transient states, positive and null persistent states, communication, existence and uniqueness of stationary distribution, and…

The course treats stochastic processes in discrete and continuous time. The main elements are: Models for stochastic dependence.Concepts of description of stationary stochastic processes in the time domain: expectation, covariance, and…

The student chooses in consultation with supervisors and examiner an independent examination assignment comprising 15 credits. The assignment can either be linked to current scientific projects at the Division of Mathematical Statistics or…

The course treats: The real numbers: axioms, examples of proofs of basic arithmetical rules. The elementary functions, polynomials, rational functions, the exponential function and the natural logarithm, the trigonometric functions…

The course treats: Elementary logic and set theory Basic properties of the natural numbers and the integers: induction, divisibility, Euclid’s algorithm Basic properties of polynomials: divisibility, Euclid’s algorithm Complex…

The course treats: Functions of several variables, basic topology in R^n. Continuity, theorems about continuous functions. Differentiable functions, gradients and directional derivatives. Taylor's formula. Extreme values…

Variable substitution, inverse and implicit functions, curve and surface integrals, Green's formula, Gauss Divergence Theorem, Stokes Theorem are treated.

The course treats Matrices: matrix operations, matrix inverse, matrix rank Determinants: definition and properties Linear spaces: subspace, span, linear dependence/independence, basis, dimension Euclidean spaces: scalar product,…

The course treats: Properties of the real numbers R: completeness axiom, Cauchy sequences, cardinality of rational and irrational numbers. Topology in Rn: open and closed sets, p-norms, convergence, compactness and the Bolzano…

The course treats: Basic properties of Fourier series of functions in one variable. Exponential form and trigonometric form. Riemann-Lebesgue lemma. Elementary conditions for pointwise and uniform convergence. Gibbs phenomenon. Basic…

The course treats: Number theory: divisibility, prime numbers, the Euclidean algorithm, Chinese remainder theorem, modular arithmetic Sets, functions and relations, equivalence relations Combinatorics: the four cases of counting with…

The aim of the course is to give necessary knowledge of digital image analysis for further research within the area and to be able to use digital image analysis within other research areas such as computer graphics, image coding, video…

The course treats basic theory of analytic functions: Elementary properties of analytic functions in one variable. Complex differentiability and Cauchy-Riemann equations. Calculation rules. Elementary examples of analytic functions:…

The course treats: Existence and uniqueness of solutions to initial value problems for systems of ordinary differential equations. Approximation of solutions and continuous dependence on parameters. Linear systems with variable and…

The course treats variational problems with and without constraints, Euler equations with and without constraints, Legendre, Jacobi and Weierstrass necessary condition for local minimum, Hilbert invariant integral and Weierstrass…

The course treats: Number theory: the fundamental theorem of arithmetic, modular artithmetic. Groups: definition, basic examples of groups, subgroups, normal subgroups, factor groups, isomorphisms and homomorphisms, Lagrange's theorem,…

The course treats multiplicative number theoretic functions, Möbius inversion formula, properties of Euler's totient function, primitive roots and indices, quadratic residues, the Legendre symbol and its properties, the quadratic…