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 State Final 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

1st year of study, winter semester

AbbrvTitleCredDutyComplFa
MATMathematical Structures in Computer Science *)5CExFME
TINTheoretical Computer Science7CCr+ExFIT

1st year of study, summer semester

AbbrvTitleCredDutyComplFa
PP1Project Practice 15ECrFIT

2nd year of study, winter semester

AbbrvTitleCredDutyComplFa
SEPSemester Project5CClCrFIT
PP2Project Practice 25EClCrFIT

2nd year of study, summer semester

AbbrvTitleCredDutyComplFa
DIPMaster's Thesis13CCrFIT

all years of study, winter semester

AbbrvTitleCredDutyComplFa
SAVStatic Analysis and Verification5CCr+ExFIT
GALGraph Algorithms5CExFIT
THEGame Theory5CCr+ExFIT
VYPaCompiler Construction (in English)5CExFIT
BISInformation System Security5CEBCr+ExFIT
AEUEnglish for Europe3CEHCr+ExFEEC
FCEEnglish: Practical Course of Business Conversation and Presentation3CEHCrFIT
FIKPhilosophy and the Culture *)3CEHCrILL
FITHistory and Philosophy of Technology3CEHCrILL
HKOCommunication and Presentation Skills3CEHCrFIT
HVRLeadership and Time Management3CEHCrFIT
JA3Conversation through Hot Current Issues3CEHCr+ExFEEC
PRMFundamentals of Law3CEHCrILL
RETRhetoric3CEHCrILL
AGSAgents and Multiagent Systems5CENExFIT
SFCSoft Computing5CENCr+ExFIT
AVSComputation Systems Architectures5ECr+ExFIT
AISInformation Systems Analysis and Design5ECr+ExFIT
BIOBiometric Systems5ECr+ExFIT
BMSWireless and Mobile Networks5ECr+ExFIT
C1PImplementing Cisco IP Routing (ROUTE)5EClCrFIT
C2PImplementing Cisco IP Switched Networks (SWITCH) *)5EClCrFIT
EIPEconomics of Information Products *)5EExFIT
GJAGraphical User Interfaces in Java5ECr+ExFIT
GMUGraphic and Multimedia Processors5ECr+ExFIT
GUXGraphical User Interfaces in X Window System5EExFIT
GZNGraphical and Sound Interfaces and Standards5EExFIT
HSCHardware/Software Codesign5ECr+ExFIT
PCSAdvanced Digital Systems5EExFIT
PDBAdvanced Database Systems5ECr+ExFIT
PDIDistributed Application Environment5EExFIT
PGPaAdvanced Computer Graphics (in English)5EExFIT
PGRComputer Graphics5EExFIT
PKSAdvanced Communication Systems5ECr+ExFIT
POVaComputer Vision (in English)5EExFIT
ROBaRobotics (in English)5EExFIT
RTSaReal-Time Systems (in English)5EExFIT
SEMSensors and Measurement5ECr+ExFIT
SINIntelligent Systems5EExFIT
SRIStrategic Management of Information Systems5EExFIT
TAMaApplication Development for Mobile Devices (in English)5EClCrFIT
VINComputer Art5EClCrFIT
ZPJaNatural Language Processing (in English) *)5EExFIT
ZPXProfessional Practice, Abroad5ECrFIT
ZZNKnowledge Discovery in Databases5ECr+ExFIT

all years of study, summer semester

AbbrvTitleCredDutyComplFa
FLPFunctional and Logic Programming5CCr+ExFIT
LOGLogic5CCr+ExFME
MBAModel-Based Analysis5CExFIT
PRLParallel and Distributed Algorithms5CCr+ExFIT
VNVHigh Performance Computations5CExFIT
KKOData Coding and Compression5CEBCr+ExFIT
KRYCryptography5CEBCr+ExFIT
AEUEnglish for Europe3CEHCr+ExFEEC
FIKPhilosophy and the Culture3CEHCrILL
FITHistory and Philosophy of Technology *)3CEHCrILL
HKOCommunication and Presentation Skills3CEHCrFIT
HVRLeadership and Time Management3CEHCrFIT
JA3Conversation through Hot Current Issues3CEHCr+ExFEEC
PRMFundamentals of Law3CEHCrILL
RETRhetoric3CEHCrILL
DJADynamic Languages5CELExFIT
SLOaComplexity (in English)5CELExFIT
OPMOptimization4CEMCr+ExFME
SNTSimulation Tools and Techniques5CEMCr+ExFIT
SSPStochastic Processes *)4CEMCr+ExFME
BINBio-Inspired Computers5CENExFIT
PPPPractical Parallel Programming5ECr+ExFIT
BIFBioinformatics5EExFIT
BZASecure Hardware Devices5EExFIT
CSOaCCNA Cybersecurity Operations (in English)5EClCrFIT
C1PImplementing Cisco IP Routing (ROUTE) *)5EClCrFIT
C3PTroubleshooting and Maintaining Cisco IP Networks (TSHOOT) *)5EClCrFIT
DFAaDigital Forensics (in English)5EExFIT
EVOApplied Evolutionary Algorithms5EExFIT
FVSFunctional Verification of Digital Systems5EExFIT
FYOPhysical Optics5EExFEEC
GISGeographical Information Systems *)5ECr+ExFIT
MMATMatrices and Tensors Calculus5ECr+ExFEEC
MPRProject Management5ECr+ExFIT
MULMultimedia5EExFIT
NAVDesign of Embedded Systems5EExFIT
NSBProjecting, Administration and Security5ECr+ExFIT
PDSData Communications, Computer Networks and Protocols5EExFIT
PISAdvanced Information Systems5ECr+ExFIT
PMAProject Manager5EClCrFIT
POSAdvanced Operating Systems5EExFIT
SPPFault Tolerant Systems5ECr+ExFIT
UXIaUser Experience and Design of User Interfaces and Services (in English)5EClCrFIT
VGEComputational Geometry5EExFIT
VIZaVisualization and CAD (in English)5EClCrFIT
VYFComputational Photography5EClCrFIT
WAPInternet Applications5ECr+ExFIT
ZPOImage Processing5EExFIT
ZPXProfessional Practice, Abroad5ECrFIT
ZRESpeech Signal Processing5EExFIT
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
H110EAEU, 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.cred, if not 0) of the CE group, will be assigned as courses of duty Over as.
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