BUT was founded in 1899 as the first Czech higher education institution in Moravia. In the course of more than 110 years it has matured into an internationally recognized institution offering a cutting-edge education based on the latest scientific and professional knowledge. At the present time, more than 24,000 students are enrolled at BUT at 8 faculties and 2 university institutes. For the period 2009–2013, BUT has been awarded the European Commission’s prestigious ECTS and DS Label certificates, issued in recognition of quality higher education. According to the Quacquarelli Symonds Limited (QS) prestigious world university rankings, BUT has been among the best universities of the world for several years in succession. The Institute of Mathematics consists of four departments: Algebra and Discrete Mathematics, Mathematical Analysis, Statistics and Optimization, Computer Graphics and Geometry. The Institute offers BSc. and MSc. study programs Mathematical Engineering. An international MSc. study program of the same name is organized in collaboration with the University of L’Aquilla. A PhD. study program is offered in Applied Mathematics. The Institute participates in a number of research projects and develops international collaboration with several foreign universities.

InterMathsBUT Coordinator

Josef Slapal
Faculty of Mechanical Engineering, Brno University of Technology
Josef SlapalProfessor, Director of Departmentslapal@fme.vutbr.cz

InterMaths Double Degree Track :: Year 2 in Brno

Campus

Brno University of Technlogy

Year

2

ECTS Credits

60

Language

English

Degrees conferred

MSc Mathematical Engineering (UAQ)
MSc Mathematical Engineering (BUT)

Semester 1

Multi-valued logic applications

ECTS Credits: 4    |    Semester: 1    |    Year: 2    |    Programme: Double Degrees    |    Campus: Brno University of Technology    |    Language: English

Unit Coordinator: Miloslav Druckmüller

Aims:

The aim of the course is to provide students with information about the use of Multi-valued logic in technical applications.

Content:

1. Multi-valued logic, formulae.

2. T-norms, T-conorms, generalized implications.

3. Linguistic variables and linguistic models.

4. Knowledge bases of expert systems.

5-6. Semantic interpretations of knowledge bases

7. Inference techniques and its implementation

8. Redundance a contradictions in knowledge bases

9. LMPS system

10. Fuzzification and defuzziScation problem

11. Technical applications of multi-valued logic and fuzzy sets theory

12. Expert systems

13. Overview of AI methods

Pre-requisites:

Mathematical logic, fuzzy set theory.

Reading list:

Jackson P.: Introduction to Expert Systems, Addison-Wesley 1999

Additional info:

The course is intended especially for students of mathematical engineering. It includes the theory of multi-valued logic, theory of linguistic variable and linguistic models and theory of expert systems based on these topics. Particular technical applications of these mathematical teories are included as a practice.

Semester 2

Modern methods of solving differential equations

ECTS Credits: 5    |    Semester: 2    |    Year: 2    |    Programme: Double Degrees    |    Campus: Brno University of Technology    |    Language: English

Unit Coordinator: Jan Franců

Aims:

The aim of the course is to provide students an overview of modern methods applied for solving boundary value problems for differential equations based on function spaces and functional analysis including construction of the approximate

Content:

1. Motivation. Overview of selected means of functional analysis.

2. Lebesgue spaces, generalized functions, description of the boundary.

3. Sobolev spaces, different approaches, properties. Imbedding and trace theorems, dual spaces.

4. Weak formulation of the linear elliptic equations.

5. Lax-Mildgam lemma, existence and uniqueness of the solutions.

6. Variational formulation, construction of approximate solutions.

7. Linear and nonlinear problems, various nonlinearities. Nemytskiy operators.

8. Weak and variational formulations of the nonlinear equations.

9. Monotonne operator theory and its applications.

10. Application of the methods to the selected equations of mathematical physics.

11. Introduction to Stochastic Differential Equations. Brown motion.

12. Ito integral and Ito formula. Solution of the Stochastic differential equations.

13. Reserve.

Pre-requisites:

Differential and integral calculus of one and more real variables, ordinary and partial differential equations, functional analysis, function spaces, probability theory.

Reading list:

  • S. Fučík, A. Kufner: Nonlinear Differential Equations, Nort Holland, 1980.
  • K. Rektorys: Variational Methods in Mathematics, Science and Engineering, Dordrecht, D. Reidel Publ. Comp., 1980.
  • J. Nečas: Direct Methods in the Theory of Elliptic Equations, Springer, Heidelberg 2012. B. Oksendal: Stochastic Differential Equations, Springer, Berlin 2000.

Additional info:

The course yields overview of modern methods for solving differential equations based on functional analysis. It deals with the following topics: Survey of spaces of functions with integrable derivatives. Linear elliptic equations: the weak and variational formulation of boundary value problems, existence and uniqueness of the solution, approximate solutions and their convergence. Characteristics of the nonlinear problems. Weak and variational formulation of the nonlinear coercive problems, existence of the solution. Application to the selected nonlinear equations of mathematical physics. Introduction to stochastic differential equations.

About Brno

The city of Brno is lying in the centre of Europe at the crossroads of ancient trade routes joining the North and South European civilizations for centuries. Brno is second largest city in the Czech Republic with a population of over 370,000 inhabitants with a great number of university students, the metropolis of the Moravian region situated by the Prague–Bratislava highway and within easy reach to Vienna. In centre you may find cultural life in the region – 10 theatres, Brno Philharmonic Orchestra, the Brno Museum, Moravian Museum, Moravian Gallery in Brno, 2 cinema multiplexes, Moravian Library, many historical monuments (the Spilberk Castle, St.Peter's Cathedral, Tugendhat Villa, Old Town Hall, Brno underground, etc.) and great number of nearby places of interest – Austerlitz, Veverí Castle, Pernštejn Castle, Lednice Chateau, Moravian Karst with caves, Pálava natural landmarks,...

How to get to Brno

The Faculty of Mechanical Engineering is one of the faculties of the Brno University of Technology located in the campus Pod Palackého vrchem. In the same area there are dormitories, refectories, sports facilities and the Czech Technology Park. The campus is easily reached by the public transport from train station, bus stations and Brno – Tuřany airport.

Accommodation in Brno

Detailed information about the halls of residence and the dining services available at Brno University of Technology can be found here: www.kam.vutbr.cz/english