Master University of Ljubljana FACULTY OF MATHEMATICS AND PHYSICS
Email: Phone: +386 1 4766 517
No.
Subjects in English 2023/2024 (Master)
Number of ECTS credit points
First semester (Winter / Autumn)
1
Complex analysis (mathematics)
Complex analysis (mathematics)
Cauchy integral formula for holomophic and non holomorphic functions. Solution to the non homogeneous debar equation on planar domains using Cauchy integral. Schwarz lemma. Automorphisms of the unit disc. Convex functions. Hadamard three-circle theorem.Phragmen-Lindelöf theorem. Compatness and convergence in the space of holomorphic functions. Normal families. Montel's theorem. Hurwitz's theorem. Riemann mapping theorem. Koebe's theorem. Bloch's theorem. Landau's theorem, Picards' theorem. Schottky's theorem. Product convergence. Weierstrass factorization theorem. Runge's theorem on approximation by rational functions. Mittag-Leffler's theorem on existence of holomorphic functions with prescribed principal parts. Interpolation by holomorphic functions on discrete sets. Schwarz reflection principle. Analytic continuation along path. Monodromy theorem.Complete analytic function. Sheaf of germs of analytic functions. Riemann surface. Other possible topics: Harmonic and subharmonic functions. Poisson kernel and the solution of the Dirichlet problem on zhe disc. Properties of Poisson integraland connection to the Cauchy integral. Mergelyan theorem. Entire functions. The genus and the order of entire function. Hadamard factorization theorem.
6
2
Computational complexity (mathematics)
Computational complexity (mathematics)
Models of computation. Time and space complexity. Determinism and nondeterminism. Reductions and completeness. NP-completeness. Some selected NP-complete problems. Techniques to prove NP-completeness. Structure of the class NP. Probabilistic algorithms. Types of probabilistic algorithms. Related computational classes. Pseudorandom generators. Approximation algorithms. Quality of approximation. Hardness of approximation. Approximation schemes. Selected approximation algorithms. Additional content may be selected among the following topics: Boolean circuits, interactive proofs, quantum computing, PCP theorems, communication complexity, parameterized complexity.
6
3
Experimental reactor physiscs (physics)
Experimental reactor physiscs (physics)
Exercises are provided at the training reactor. Each exercise consists of practical (individual) experimental work and theoretical introduction. Reactor instrumentation with reactivity meter is used to perform all the measurements and exercises. Basic knowledge of reactor physics, kinetics and radiation detection is required to perform all the exercises. A set of exercises is chosen to match the measurements that are necessary for the operation of a nuclear reactor (including nuclear power plant).
6
4
Materials in Nuclear Engineering (physics)
Materials in Nuclear Engineering (physics)
To acquire basic knowledge about properties and the behaviour of materials and the effects of irradiation on material properties. Application of thermodynamics, properties of solid materials combined with irradiation effects to understand the properties of materials. Ability to solve problems of materials in nuclear engineering.
6
5
Nuclear safety (physics)
Nuclear safety (physics)
Nuclear safety principles: -Levels (measures) of nuclear safety, defence-in-depth. -Definitions and principles of safety, risk, reliability and availability of systems, structures and devices. - Safety systems and their characteristics: redundancy, independence, separation, variety, fail-safe principle and single failure - Safety analyses. Analyses of transients and accidents. - Basic probability theory and Boolean algebra. -Databases and probabilistic models. Methods for evaluation of safety and reliability - Theory and Practice: fault tree, event tree, analysis of failure modes and effects. - Common cause failure - methods and examples. - Safety culture - the organization and management. - Measures of reliability and safety of systems and facilities. Risk criteria. - Risk based decision making. - Periodic safety review. - Quality assurance: program, procedures, implementation.
6
6
Physics of fission reactors (physics)
Physics of fission reactors (physics)
Nuclear reactions with neutrons and fission, characteristics of the cross-sections for the most important nuclides. Prompt and delayed neutrons, fission products. Chain reaction and multiplication factor. Boltzmann equation for neutron transport in a matter. Diffusion approximation and its validity. Time-independent cases, non-fissile and fissile agent. Slowing down the neutrons in the moderator, resonant absorption, thermalisation. Solving the time-dependent transport and diffusion equations, the derivation of point kinetics equations. Linear kinetics of the reactor and control over the chain reaction. Feedback effects on the reactivity and non-linear kinetics.
9
7
Seminar 1 (physics)
Seminar 1 (physics)
The program is determined each year, and typically covers topics in physics and related fields research. Students can choose the seminar topic among the available topics or through the choice of the supervisor - teacher at the faculty. Students will perform literature search in various databases and on internet. Lecture can be up to 40 minutes long, allowing 5 minutes for discussion. Lecture is based on computer slides. After the lecture, final written version of the seminar must be submitted in two weeks. Text should not exceed 12 pages. Final form of the text must suitable for publication at the conference or in a journal. During the 1st semester students also attend some of the presentations at Seminar II in order to identify research areas rthey are interested in and conact potential supervisors.
4
8
Seminar 2 (physics)
Seminar 2 (physics)
The program is determined each year, and typically covers topics in physics research which are pursued at the faculty as well as in the related institutions. Supervisors of students are lecturers at UL as well as researchers at related institutions.
4
Second semester (Summer / Spring)
9
Cardinal arithmetic (mathematics)
Cardinal arithmetic (mathematics)
Sets and classes. Axioms of set theory. Axiom of choice, Zorn lemma and its applications, well ordering, transfinite induction, ordinal numbers and their arithmetic, Schröder-Bernstein theorem, cardinal numbers and their arithmetic. If time permits: filters and ultrafilters, large cardinal numbers.
6
10
Numerical methods for financial mathematics (mathematics)
Numerical methods for financial mathematics (mathematics)
Algorithms for option pricing in discrete models. Monte Carlo Methods for European options. Simulation methods of classical law. Inverse transform method. Computation of expectation. Variance reduction techniques. Tree methods for European and American options. Convergence orders of binomial methods. Estimating sensitivities. Numerical algorithms for portfolio insurance. Tree methods and Monte Carlo methods for Exotic options (barrier options, asian options, lookback options, rainbow options). American Monte Carlo methods. Finite difference methods for the Black-Scholes partial differential equation.
6
11
Time series (mathematics)
Time series (mathematics)
Introduction: Examples of time series. Trend and seasonality. Autocorrelation function. Multivariate normal distribution. Strong and week stationarity. Hilbert spaces and prediction. Introduction to R. Stationary sequences: Linear processes. ARMA models. Causality and invertibility of ARMA processes. Infinite order MA processes. Partial autocorrelation function. Estimation of autocorrelation function and other parameters. Forecasting stationary time series. Modeling and forecasting for ARMA processes. Asymptotic behavior of the sample mean and the autocorrelation function. Parameter estimation for ARMA processes. Spectral analysis: Spectral density. Spectral density of ARMA processes. Herglotz theorem. Periodogram. Nonlinear and nonstationary time series models: ARCH and GARCH models. Moments and stationary distrbutiopn of GARCH process. Exponential GARCH. ARIMA models. SARIMA models. Orecasting nonstationary time series. Statistics for stationary process: Asymptotic results for stationary time series. Estimating trend and seasonality. Nonparametric methods. Multidimensional time series: stacionarity, multidimensional ARMA and ARIMA models, parameter estimation, forecasting, variance decomposition.
6
12
Topics in analysis (mathematics)
Topics in analysis (mathematics)
The lecturer selects some important topics in analysis, such as: several complex variables, minimal surface theory, spectral theory and other topics chosen by the lecturer.
6
13
Topics in computer mathematics: Logic in computer science (mathematics)
Topics in computer mathematics: Logic in computer science (mathematics)
The course is divided into core and optional parts. Core part: syntax, formal system, bound variables, substitution. Lambda-calculus and simple types. Natural deduction, propostional and predicate calculus. Proof terms. Optional parts: Curry-Howard correspondence Constructive interpretation of logic, and its significance for computer science. Temporal logic and its use in computer science. Modal logic and its use in knowledge modeling. Other calcululi: pi-calculus, event calculus, etc. Automated theorem proving.
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