- Unit Coordinator: Josef Bednář
- ECTS Credits: 4
- Semester: 1
- Year: 2
- Campus: Brno University of Technology
- Language: English
- Aims:
The course objective is to make students majoring in Mathematical Engineering acquainted with methods of the reliability theory for modelling and assessing technical systems reliability, with methods of mathematical statistics used for quality control of processing, and with a personal project solution using statistical software.
- Content:
Basic notions of objects reliability. Functional characteristics of reliability. Numerical characteristics of reliability. Probability distributions of time to failure. Truncated probability distributions of time to failure, mixtures of distributions. Calculating methods for system reliability. Introduce to renewal theory, availability. Estimation for censored and non-censored samples. Stability and capability of process. Process control by variables and attributes (characteristics, charts). Statistical acceptance inspections by variables and attributes (inspection kinds). Special statistical methods (Pareto analysis, tolerance limits). Fuzzy reliability.
- Pre-requisites:
Mastering basic and advanced methods of probability theory and mathematical statistics is assumed.
- Reading list:
- Montgomery, Douglas C.:Introduction to Statistical Quality Control /New York :John Wiley & Sons,2001. 4 ed. 796 s. ISBN 0-471-31648-2
- Ireson, Grant W. Handbook of Reliability Engineering and Management.Hong Kong :McGraw- Hill,1996. 1st Ed. nestr. ISBN 0070127506
- Additional info:
The course is concerned with the reliability theory and quality control methods: functional and numerical characteristics of lifetime, selected probability distributions, calculation of system reliability, statistical methods for measure lifetime date, process capability analysis, control charts, principles of statistical acceptance procedure. Elaboration of project of reliability and quality control out using the software Statistica and Minitab.
- ECTS Credits: 12
- Semester: 2
- Year: 2
- Campus: Ivan Franko National University of Lviv
- Aims:
The aim of Industrial Internship is to engage the student in commertial projects, usually connected with mathematical modelling or software development.
- Additional info:
Depending on student's interests he/she can be temporarily enrolled at IT company, scientific institute, university or other organization which deals with mathematical, computer modelling, simulation or similar problems. Lviv has a wide range of possibilities, hosting over 200 IT companies with nearly 15000 of employees, a dozen of universities and over 30 scientific institutes.
- Code: DT0652
- Unit Coordinator: Sabine Le Borne, Daniel Ruprecht
- ECTS Credits: 9
- Semester: 2
- Year: 1
- Campus: Hamburg University of Technology
- Language: English
- Aims:
Students can list classical and modern iteration methods and their interrelationships, repeat convergence statements for iterative methods and explain aspects regarding the efficient implementation of iteration methods.
They will learn the fundamental concepts of parallel programming and how to translate them into efficient, parallel code.
They will learn how to compile parallel code and how to model and measure performance of parallelized software.
- Content:
- Sparse systems: orderings and storage formats, direct solvers;
- Classical methods: basic notions, convergence;
- Projection methods;
- Rylov space methods;
- Preconditioning (e.g. ILU);
- Multigrid methods;
- Domain decomposition methods, shared versus distributed memory parallelization;
- Message Passing Interface;
- OpenMP;
- Threads;
- Processes;
- HPC architecture;
- Performance models;
- Speedup and parallel efficiency
- Pre-requisites:
- Analysis,
- Linear Algebra,
- Programming experience in C and C++, FORTRAN, Python or a similar programming language.
- Reading list:
- Y. Saad. Iterative methods for sparse linear systems
- M. Olshanskii, E. Tyrtyshnikov. Iterative methods for linear systems: theory and applications
- Thomas Rauber, Parallel Programming : for Multicore and Cluster Systems, Berlin [u.a.] Springer 2010
- Bertil Schmidt, Parallel programming : concepts and practice, Amsterdam Morgan Kaufmann 201
- Additional info:
Parallel programming for interdisciplinary mathematics (DT0857)
Scientific programming for interdisciplinary mathematics (DT0858)
- ECTS Credits: 3
- Semester: 1
- Year: 2
- Campus: Ivan Franko National University of Lviv
- Language: English
