Mathematical Methods in Information Technology

The goal of the study branch of Mathematical Methods in Information Technologies is to acquaint students with deeper mathematical roots of information technologies and teach them how to understand, practically apply as well as further develop advanced technologies built on these roots. Within the compulsory courses of the study branch, the students will mainly improve their knowledge of mathematics and of the theoretical basis of computer science and will get familiar with their advanced applications in selected areas of information technologies. In particular, this concerns the areas of compilers, methods of automated analysis, verification, and testing of correctness of computer-based systems, the areas of high performance computing, modelling, simulation and optimization, and/or applications of the game theory as a support of rational strategic decision-making in conflict situations (e.g., in economics, security, etc.). The choice of optional courses together with the diploma thesis will then allow the students to individually narrow down their focus on various theoretical or application areas. The obtained deeper theoretical knowledge and acquaintance with their various applications will allow the graduates to practically apply various highly advanced modern technologies, including non-standard technologies as well as technologies currently under development, will allow them to find positions in companies (or divisions of companies) focused on research and development of new information technologies with a mathematical basis, and/or will give them a solid training for subsequent PhD studies.

Student of the Follow-Up Master Degree Programme acquire deeper knowledge in a chosen branch of study and will give him knowledge and skills base to analyse, design and verification of problems solved in research and scientific as well as in the practice This guarantee that the alumni will be successful creative worker in the appropriate information technology branch.

An alumnus of the master degree programme is ready to solve problems of information technology in praxis with utilization of contemporary scientific knowledge independently. The alumnus is able to act as an independent creative worker in the appropriate information technology branch, namely information systems and their security and safety, intelligent systems, computer systems, networks and communications, computer graphics and multimedia or a leader of a team composed of workers of various branches of IT.

The final state examination has two parts: A defense of the master thesis and a discussion about selected topics from predefined areas of the study branch. These areas cover the compulsory courses of the study branch, in particular: Mathematical Structures in Computer Science, Theoretical Computer Science, Logic, Graph Algorithms, Parallel and Distributed Algorithms, Functional and Logic Programming, Formal Analysis and Verification, Petri Nets, High Performance Computations, Compiler Construction, and Game Theory. The concrete areas of possible questions must be approved by the Study Branch Council, and students will be informed about the selected topics at least 2 months before the state final examination is held in the particular academic year.

• Formal verification of correctness of drivers in operating systems
• Automated methods for finding bugs in compilers
• Automated support for programming application-specific processors
• Grammatical systems with scattered context and natural language processing
• Simulation of  selected phenomena from the Linux kernel influencing its performance
• Applications of the mathematical game theory in simulation and analysis of the market with electricity
• Model-driven design of critical applications based on the systems theory
• Highly precise computations in real time
• Concurrent solution of simple differential equations of higher orders
• Isomorphism in general as well as special graphs

Master's theses are stored at the FIT library, Božetěchova 2, Brno. The list of the master's theses, including the details is available at:
https://www-dev.fit.vutbr.cz/study/theses/