study programme

Applied Mathematics

Original title in Czech: Aplikovaná matematikaFaculty: FMEAbbreviation: D-APM-KAcad. year: 2023/2024

Type of study programme: Doctoral

Study programme code: P0541D170030

Degree awarded: Ph.D.

Language of instruction: Czech

Accreditation: 25.6.2020 - 25.6.2030

Mode of study

Combined study

Standard study length

4 years

Programme supervisor

Doctoral Board

Chairman :
prof. RNDr. Jan Čermák, CSc.
Councillor internal :
prof. RNDr. Josef Šlapal, CSc.
prof. Ing. Ivan Křupka, Ph.D.
prof. RNDr. Miloslav Druckmüller, CSc.
prof. RNDr. Miroslav Doupovec, CSc., dr. h. c.
Councillor external :
doc. RNDr. Ing. Miloš Kopa, Ph.D.
prof. RNDr. Jan Paseka, CSc.
prof. RNDr. Roman Šimon Hilscher, DSc.
doc. RNDr. Tomáš Dvořák, CSc.

Fields of education

Area Topic Share [%]
Mathematics Without thematic area 100

Study aims

The doctoral study programme in Applied Mathematics will significantly deepen students' knowledge acquired during the study of the follow-up master's study programme in Mathematical Engineering at FME BUT in Brno and other master's programmes focused on mathematics and its applications. Students of this doctoral programme can gain in-depth knowledge of the relevant mathematical apparatus in all areas of applied mathematics, in connection with the solution of demanding practical tasks (especially technical). The offer of professional subjects of the doctoral study programme in Applied Mathematics is also adapted to this, including subjects with a deeper theoretical basis, subjects related to the applications of mathematics, and finally also subjects with a special engineering focus.
The topics of doctoral theses are listed mainly by the staff of the Department of Mathematics, and depending on the nature of the topic, experts from other FME institutes or other scientific institutions may also be involved, as specialist trainers. During their doctoral studies, students become members of scientific teams led (or in which they work) by their supervisors. The assigned topic of the doctoral thesis is usually part of a more complex problem that this team solves in various professional projects. Students will gradually learn all the basic principles of scientific work, especially the creation of professional texts and their publication in scientific journals, and the presentation of the results of their scientific work at seminars or conferences. Cooperation with foreign workplaces is a matter of course, where students can gain other useful experiences. After successfully passing the prescribed state doctoral exam, which examines both the knowledge of the theoretical foundations needed to master the topic, but also the state of development of the dissertation and the direction of research conducted within it, students focus primarily on completing their work. In order to submit it for defence, they must meet the requirements related primarily to publishing activities, the purpose of which is to ensure that dissertations submitted for defence in this study programme are at a comparable level to defended works at other mathematical institutions in the Czech Republic and abroad. After defending the doctoral thesis, students obtain a Ph.D degree.
The main goal of this doctoral study programme is to educate experts in the field of applied mathematics who will be able to continue in the scientific career begun within their doctoral studies. The means to fulfil this goal is to expand students' knowledge of non-trivial mathematical tools needed for modelling and solving practice problems, as well as to deepen the principles of their mathematical, logical and critical thinking.

Graduate profile

The graduate will gain deep expertise in a number of special areas of modern applied mathematics, focusing on selected parts of image analysis, computer graphics, applied topology, 3D image reconstruction and visualization, continuous and discrete dynamical systems, and advanced statistical methods. They will also have a high degree of geometric perception of problems related to engineering applications. They will also gain quality knowledge of engineering disciplines related to the topic of work, and will be able to work with modern programming tools (Python, C ++, ...). The language equipment enabling professional cooperation with foreign workplaces and the presentation of the obtained results at an international forum is a matter of course.

Within the scope of his/her professional competence, the graduate is able to create mathematical models of engineering problems and, according to their nature, to search for and develop suitable mathematical tools and procedures for their solution. They are able to use mathematical software at a high level and has acquired programming skills. In a broader sense, the graduate is able to participate in solving challenging tasks in the field of technical practice.

In terms of more general skills, the graduate is capable of independent creative scientific work. They will learn the principles of teamwork at a high professional level. The team will learn to manage in terms of professional and administrative, it will also be familiar with project issues. He can also work as a mathematician in multidisciplinary teams. He is able not only to participate in solving research problems, but he can find and formulate current scientific problems. He is able to present the results of his work, both in the form of scientific publications and in the form of professional lectures.

The graduate will have a developed ability of analytical thinking, which in combination with knowledge of advanced methods of applied mathematics and computer technology will allow him to seamlessly participate in scientific teams in various types of academic institutions or in the field of applications.

Profession characteristics

Graduates find a wide job in the labour market for their adaptability, which is made possible by extensive knowledge of applied mathematics. These graduates are interested in companies engaged in development in the field of autonomous systems, robotics, automation and image analysis, as well as institutions engaged in science, research and innovation in the fields of informatics, technology, quality management, finance and data processing. Graduates of this doctoral study programme also find significant employment in the academic sphere. In addition to the Institute of Mathematics, FME (among whose employees the share of graduates of the doctoral study program Applied Mathematics reaches almost a quarter), these graduates currently work as academic staff at other FME institutes, other BUT faculties and other universities. In addition to adaptability in various areas of applied mathematics, the continuing interest in these graduates is mainly due to their scientific erudition (in many cases these graduates are already habilitated, and in increasingly monitored indicators publishing activities are often at the top of relevant educational institutions).

Fulfilment criteria

See applicable regulations, DEAN’S GUIDELINE Rules for the organization of studies at FME (supplement to BUT Study and Examination Rules)

Study plan creation

The rules and conditions of study programmes are determined by:
STUDY AND EXAMINATION RULES of Brno University of Technology (USING "ECTS"),
DEAN’S GUIDELINE Rules for the organization of studies at FME (supplement to BUT Study and Examination Rules)
DEAN´S GUIDELINE Rules of Procedure of Doctoral Board of FME Study Programmes
Students in doctoral programmes do not follow the credit system. The grades “Passed” and “Failed” are used to grade examinations, doctoral state examination is graded “Passed” or “Failed”.

Availability for the disabled

Brno University of Technology acknowledges the need for equal access to higher education. There is no direct or indirect discrimination during the admission procedure or the study period. Students with specific educational needs (learning disabilities, physical and sensory handicap, chronic somatic diseases, autism spectrum disorders, impaired communication abilities, mental illness) can find help and counselling at Lifelong Learning Institute of Brno University of Technology. This issue is dealt with in detail in Rector's Guideline No. 11/2017 "Applicants and Students with Specific Needs at BUT". Furthermore, in Rector's Guideline No 71/2017 "Accommodation and Social Scholarship“ students can find information on a system of social scholarships.

What degree programme types may have preceded

The doctoral study programme in Applied Mathematics follows on from the follow-up master's study programme in Mathematical Engineering, which is accredited (and taught) at FME BUT in Brno.

Issued topics of Doctoral Study Program

  1. Differential equations in control theory

    Control thory provides a significant application area of differential equations. Standard as well as novel types of differential equations are studied in the frame of this theory. Reaction time delay of a controlled system, as well as an order of this system, provide important tools in the control process. Stabilization, destabilization, synchronization, optimization a chaotification of studied system belong among basic issues. The topic of this doctoral study will be focused on analysis of these properties for corresponding types of differential equations, and on related numerical and graphical simulations.

    Tutor: Čermák Jan, prof. RNDr., CSc.

  2. Dual numbers, Weil algebras and applications

    The topic of the doctoral study is focused on research in the field of applications of quotient algebras of multivariable polynomials, where the prototypical case is the algebra of dual numbers widely used in kinematics. Weil algebras represent a more general model, which play an important role in differential geometry. Here, in particular, the case of non-homogeneous ideals has not yet been systematically investigated, and research in this area thus represents a new and demanding scientific research. Last but not least, one can focus on special subrings of the mentioned algebras, which can be suitable, for example, in a use in lattice cryptosystems.

    Tutor: Kureš Miroslav, doc. RNDr., Ph.D.

Course structure diagram with ECTS credits

1. year of study, winter semester
AbbreviationTitleL.Cr.Com.Compl.Hr. rangeGr.Op.
9EMMEmpiric Modelscs, en0RecommendedDrExP - 20yes
9FMSFuzzy Models of Technical Processes and Systemscs, en0RecommendedDrExP - 20yes
9GTRGeometric Control Theorycs, en0RecommendedDrExP - 20yes
9MKPFEM in Engineering Computationscs0RecommendedDrExP - 20yes
9STHStructure of Mattercs, en0RecommendedDrExP - 20yes
9SLTSturm-Lieouville Theorycs, en0RecommendedDrExP - 20yes
9TTDTheory of Measurements, Measurement Techniques and Technical Diagnosticscs, en0RecommendedDrExP - 20yes
9TKDBasics of Category Theorycs, en0RecommendedDrExP - 20yes
1. year of study, summer semester
AbbreviationTitleL.Cr.Com.Compl.Hr. rangeGr.Op.
9ARAAlgebras of rotations and their applicationscs, en0RecommendedDrExP - 20yes
9AMKAnalytical Mechanics and Mechanics of Continuumcs, en0RecommendedDrExP - 20yes
9AHAApplied Harmonic Analysiscs, en0RecommendedDrExP - 20yes
9APTApplied Topologycs, en0RecommendedDrExP - 20yes
9DVMDynamic and Multivariate Stochastic Modelscs, en0RecommendedDrExP - 20yes
9FKPFunctions of a Complex Variablecs, en0RecommendedDrExP - 20yes
9FAPFunctional Analysis and Function Spacescs, en0RecommendedDrExP - 20yes
9FZMPhysical Base of Materials Fracturecs0RecommendedDrExP - 20yes
9ISYInvariants and Symmetrycs, en0RecommendedDrExP - 20yes
9MORMathematical Methods Of Optimal Controlcs, en0RecommendedDrExP - 20yes
9MPKMathematical Principles of Cryptographic Algorithmscs, en0RecommendedDrExP - 20yes
9NMTNonlinear Mechanics and FEMcs, en0RecommendedDrExP - 20yes
9PVPProgramming in Pythoncs, en0RecommendedDrExP - 20yes
9UMSOrdered Sets and Latticescs, en0RecommendedDrExP - 20yes
1. year of study, both semester
AbbreviationTitleL.Cr.Com.Compl.Hr. rangeGr.Op.
9AJEnglish for Doctoral Degree Studyen0CompulsoryDrExCj - 60yes
9APHApplied Hydrodynamicscs, en0RecommendedDrExP - 20yes
9ARVAutomation and Control of Manufacturing Systemscs, en0RecommendedDrExP - 20yes
9FLIFluid Engineeringcs, en0RecommendedDrExP - 20yes
9GRAGraph Algorithmscs, en0RecommendedDrExP - 20yes
9MBOMathematical Modeling of Machine Mechanisms cs, en0RecommendedDrExP - 20yes
9IDSModelling and Control of Dynamic Systemscs, en0RecommendedDrExP - 20yes
9PARControl Equipmentscs, en0RecommendedDrExP - 20yes
9VINComputational Intelligencecs, en0RecommendedDrExP - 20yes
9VMTComputational Modeling of the Turbulent Flowcs, en0RecommendedDrExP - 20yes