Faculty of Information Technology, BUT

Field of Study Details

Mathematical Methods in Information Technology

Abbreviation: MMM

Length of Study: 2 years

Min. Credits: 120

Degree Programme: Information Technology

Language of Instruction: Czech

Form of Study: full-time

Accredited from: 2008 Accredited till: 2024 Last admissions: 2019

Profile
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.
Key learning outcomes
Student of the branch acquire deeper theoretical knowledge in mathematics and informatics theory, which will be able to apply practically as well as to develop advanced technologies built on these roots. Study in this branch provide further extension of knowledge mainly in the area of compilers, methods of automated analysis, verification, and testing of correctness of computer-based systems, the area 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.
Guarantor
Occupational profiles of graduates with examples
  • A graduate has a deep knowledge of the mathematical roots of information technologies and their various advanced applications, in particular, compilers, automated methods of analysis, verification, and testing of correctness of computer-based systems, computer-aided modelling, simulation, and optimization, fault tolerance, game theory, high performance computing technologies, cryptography and codes, and/or unconventional and newly emerging computing platforms.
  • A graduate is qualified for research, development, and applications of various advanced technologies, including highly unconventional technologies, requiring a deeper understanding of the mathematical roots of computer science. The acquired knowledge of the theoretical basis of information technologies makes the graduate very flexible and able to easily get familiar with new discoveries and technologies.
  • Students graduating from the study branch can make their professional career especially in research and development divisions as well as production divisions of various companies and institutions interested in development and applications of advanced technologies from the areas of automated analysis, verification, and testing of computer-based systems; compilers; technologies for synthesis of hardware or software from high-level specifications; modelling, simulation, and optimization of systems (including companies and institutions interested in simulation, prediction, and optimization for the needs of energetics, economics, security, etc.); technologies for high performance computing in science and engineering; and/or technologies for development of critical systems with a special emphasis on reliability and security. Moreover, with respect to their deep knowledge of algorithmics, they can find positions also in other areas of the IT industry, focused on development and maintenance of complex, computationally demanding software products (e.g., within running and optimizing large databases, information systems, computer networks, etc.). An important possibility is also a career of the graduates in science and/or education.
Extent of the final state examinations
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.
Examples of theses
  • 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

Choose academic year and curriculum

1. year of study, winter semester

AbbrvTitleCredDutyCompl
MATMathematical Structures in Computer Science5CEx
TINTheoretical Computer Science7CCr+Ex
SMTSeminar of Mathematical Structures2ECr

1. year of study, summer semester

AbbrvTitleCredDutyCompl
PP1Project Practice 15ECr

2. year of study, winter semester

AbbrvTitleCredDutyCompl
SEPSemester Project5CClCr
PP2Project Practice 25EClCr

2. year of study, summer semester

AbbrvTitleCredDutyCompl
DIPMaster's Thesis13CCr

all years of study, winter semester

AbbrvTitleCredDutyCompl
SAVStatic Analysis and Verification5CCr+Ex
GALGraph Algorithms5CEx
THEGame Theory5CCr+Ex
VYPaCompiler Construction (in English)5CEx
BISInformation System Security5CEBCr+Ex
AEUEnglish for Europe3CEHCr+Ex
FCEEnglish: Practical Course of Business Conversation and Presentation3CEHCr
FIKPhilosophy and the Culture *)3CEHCr
FITHistory and Philosophy of Technology3CEHCr
HKOCommunication and Presentation Skills3CEHCr
HVRLeadership and Time Management3CEHCr
JA3Conversation through Hot Current Issues3CEHCr+Ex
PRMFundamentals of Law3CEHCr
RETRhetoric3CEHCr
AGSAgents and Multiagent Systems5CENEx
SFCSoft Computing5CENCr+Ex
AVSComputation Systems Architectures5ECr+Ex
AISInformation Systems Analysis and Design5ECr+Ex
BIOBiometric Systems5ECr+Ex
BMSWireless and Mobile Networks5ECr+Ex
C2PImplementing Cisco IP Switched Networks (SWITCH)5EClCr
EIPEconomics of Information Products5EEx
GJAGraphical User Interfaces in Java5ECr+Ex
GMUGraphic and Multimedia Processors5ECr+Ex
GUXGraphical User Interfaces in X Window System5EEx
GZNGraphical and Sound Interfaces and Standards5EEx
HSCHardware/Software Codesign5ECr+Ex
PCSAdvanced Digital Systems5EEx
PDBAdvanced Database Systems5ECr+Ex
PDIDistributed Application Environment5EEx
PGPaAdvanced Computer Graphics (in English)5EEx
PGRComputer Graphics5EEx
PKSAdvanced Communication Systems5ECr+Ex
POVaComputer Vision (in English)5EEx
ROBaRobotics (in English)5EEx
RTSaReal-Time Systems (in English)5EEx
SEMSensors and measurement5ECr+Ex
SINIntelligent Systems5EEx
SRIStrategic Management of Information Systems5EEx
TAMaApplication Development for Mobile Devices (in English)5EClCr
VINComputer Art5EClCr
ZPJaNatural Language Processing (in English)5EEx
ZPXProfessional Practice, Abroad5ECr
ZZNKnowledge Discovery in Databases5ECr+Ex

all years of study, summer semester

AbbrvTitleCredDutyCompl
FLPFunctional and Logic Programming5CCr+Ex
LOGLogic5CCr+Ex
MBAModel-Based Analysis5CEx
PRLParallel and Distributed Algorithms5CCr+Ex
VNVHigh Performance Computations5CEx
KKOData Coding and Compression5CEBCr+Ex
KRYCryptography5CEBCr+Ex
AEUEnglish for Europe3CEHCr+Ex
FIKPhilosophy and the Culture3CEHCr
FITHistory and Philosophy of Technology *)3CEHCr
HKOCommunication and Presentation Skills3CEHCr
HVRLeadership and Time Management3CEHCr
JA3Conversation through Hot Current Issues3CEHCr+Ex
PRMFundamentals of Law3CEHCr
RETRhetoric3CEHCr
DJADynamic Languages5CELEx
SLOaComplexity (in English)5CELEx
OPMOptimization4CEMCr+Ex
SNTSimulation Tools and Techniques5CEMCr+Ex
SSPStochastic Processes4CEMCr+Ex
BINBio-Inspired Computers5CENEx
PPPPractical Parallel Programming5ECr+Ex
BIFBioinformatics5EEx
BZASecure Hardware Devices5EEx
CSOaCCNA Cybersecurity Operations (in English)5EClCr
C1PImplementing Cisco IP Routing (ROUTE) *)5EClCr
C3PTroubleshooting and Maintaining Cisco IP Networks (TSHOOT)5EClCr
DFAaDigital Forensics (in English)5EEx
EVOApplied Evolutionary Algorithms5EEx
FVSFunctional Verification of Digital Systems5EEx
FYOPhysical Optics5EEx
GISGeographical Information Systems *)5ECr+Ex
MARMarketing *)5ECr+Ex
MEKEconomics for Managers *)5ECr+Ex
MMATMatrices and Tensors Calculus5ECr+Ex
MPRProject Management5ECr+Ex
MULMultimedia5EEx
NAVDesign of Embedded Systems5EEx
NSBProjecting, Administration and Security5ECr+Ex
PDSData Communications, Computer Networks and Protocols5EEx
PISAdvanced Information Systems5ECr+Ex
PMAProject Manager5EClCr
POSAdvanced Operating Systems5EEx
SPPFault Tolerant Systems5ECr+Ex
STMStrategic Management *)5ECr+Ex
UXIaUser Experience and Design of User Interfaces and Services (in English)5EClCr
VGEComputational Geometry5EEx
VIZaVisualization and CAD (in English)5EClCr
VYFComputational Photography5EClCr
WAPInternet Applications5ECr+Ex
ZPOImage Processing5EEx
ZPXProfessional Practice, Abroad5ECr
ZRESpeech Signal Processing5EEx
Course is not open in this academic year
Compl: Course completion: Ex - examination, Cr - credit, ClCr - classified credit, Co - colloquium
Duty: C - compulsory, CEx - compulsory-elective group x, R - recommended, E - elective

Compulsory-elective groups

AbbrvMin. coursesMax. coursesMin.credOver asCoursesTitle
B190EBIS, KKO, KRYCryptography, Coding and Security
H113EAEU, FCE, FIK, FIT, HKO, HVR, JA3, PRM, RETSocial Course
L190EDJA, SLOaProgramming Languages, Computability and Complexity
M190EOPM, SNT, SSPModelling, Simulation and Optimalization
N190EAGS, BIN, SFCUnconventional Computing Methods
If you are allowed to enroll more CE courses than the required minimum, then successfully completed courses that exceed Min. courses (or Min.kred, if not 0) of the CE group, will be assigned as courses of duty Over as.
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