Graduates of Mathematical Analysis doctoral study programme are able to achieve previous scientific results. They have broad theoretical and general knowledge of selected uses with significant value. They are able to independently read demanding publications and grasp them theoretically and practically, and efficiently use their findings in solving theoretical and practical problems. They are able to present to the scientific community their own findings together with other research. They have pedagogical experience with teaching at university.

Graduates are able to perform their job as university teachers of mathematics, as well as scientific and research workers in mathematics. They track not only the current development in their field, but are able to adapt to other scientific disciplines in mathematics, as in other sciences using mathematical methods.

Knowledge:

· Students have broad general knowledge of mathematical disciplines in the field of mathematical analysis,

· They have deep theoretical knowledge in a more specific field of mathematical analysis according to the focus of their dissertation (dynamic systems, real analysis, differential equations, etc.),

· they know the methods of scientific work within their specialization and related fields.

Skills:

· efficiently use the latest existing scientific results when solving theoretical as well as practical problems,

· create mathematical models of natural phenomena and socio-economic processes using tools linked to the focus of their dissertation theses (dynamic systems, differential equations, etc),

· stay in contact with the scientific development in the narrow focus of their dissertations at minimum,

· ability to independently extend theoretical knowledge in a broader spectrum of mathematical disciplines,

· use book and magazine scientific literature as well as sources on the Internet for research purposes,

· ability of independent research in various fields of mathematical analysis,

· publish scientific work within the specialization,

· present research results in seminars and conferences at home and abroad,

· teach mathematical analysis and other mathematical disciplines at university.

Competences:

· the ability to communicate with professionals in mathematics and other practitioners within the field,

· the ability to use non-standard approaches in order to creatively address theoretical or practical problems,

· the ability to organise and plan work,

· adhering to the ethics of scientific work.

University teacher

Research worker in Mathematics field of study

212 Specialists in mathematics, insurance mathematics and statistics

Mathematical Institute of the Slovak Academy of Sciences (SAS)

Beset spol. s r.o., Jelenia 18, 811 05 Bratislava

Since 2000, there have been in total 26 students in Mathematical Analysis field of study, mainly on internal study. 7 out of them did not complete their studies (this was mostly true in the first years of the study programme; back then, mass character of doctoral studies was supported by the state authorities). So far 14 students have successfully completed their studies (5 more are still studying). All of them have found employment, some abroad. From all 14 graduates, 7 graduates currently teach at universities, 1 works for the SAS, the rest works in businesses inside and outside of the country.

Selected successful graduates who completed external form of study:

· Pavol Král (MBU Faculty of Economics),

· Vladimír Špitalský (associate professor on the Department of Mathematics at FNS MBU),

Selected successful graduates who completed internal form of study:

· Katarína Lendelová (MI SAS),

· Alžbeta Michalíková (Department of Computer Science at FNS MBU),

· Matúš Dirbák (Department of Mathematics at FNS MBU, undergoing habilitation procedure),

· Kan Hu (School of Mathematics, Zhejiang Ocean University, People’s Republic of China),

· Naer Wang (School of Mathematics, Zhejiang Ocean University, People’s Republic of China),

· Vladimír Kobza (Department of Mathematics at FNS MBU)

Quality assessment of the study programme has been performed by employers who created evaluation reports attached to the accreditation file.

The rules for the design of study plans within this field of study are specified in Directive No. 1/2021 Creation, modification and approval of study programmes and submission of applications to the Slovak Accreditation Agency for Higher Education,

The study plan for the study program is inserted in the system AIS.

The study plan for the study program together with the subjects' information sheets is inserted in the system AIS.

Number of credits for compulsory courses: 161 (from this number: 20 for doctoral examination and 40 for dissertation defence)

number of credits for professional practice:  -

Number of credits from elective courses: 79

Number of credits for optional courses:  any

Number of credits for the state examination: 60 (20 = doctoral examination; 40 = dissertation defence)

The requirements and rules for successful completion of the study and state examinations as well as other study-related rules are defined in the Faculty of Natural Sciences (FNS) MBU Study Regulations.

Link: https://www.fpv.umb.sk/studium/pre-studenta/studijny-poriadok-a-ine-dokumenty/studijny-poriadok.html

One of the important “courses” in the scientific part of study is a “publication registered in WoS or Scopus databases (at least in printing queue before the dissertation defence)”.

The requirements and rules for successful completion of the study and state examinations as well as other study-related rules are defined in the Faculty of Natural Sciences (FNS) MBU Study Regulations.

Link: https://www.fpv.umb.sk/studium/pre-studenta/studijny-poriadok-a-ine-dokumenty/studijny-poriadok.html

One of the important “courses” in the scientific part of study is a “publication registered in WoS or Scopus databases (at least in printing queue before the dissertation defence)”.

doc. RNDr. Vladimír Špitalský, PhD. / Topological Dynamics on One-dimensional Continua (Mgr. Michaela Mihoková); Recurrent Quantitative Analysis (Mgr. Miroslava Poláková)

doc. RNDr. Roman Hric, PhD. / Dense Orbits in Dynamic Systems (Mgr. Miroslav Výbošťok); Non-compact Dynamics

prof. RNDr. Vladimír Janiš, CSc. / Mappings on Bounded Lattices Applied in Multivalued Logics (Mgr. Michaela Bruteničová); Convexity in ordered structures (Pedro Huidobro)

doc. RNDr. Ľubica Holá, DrSc. / Generalised Compact-Open Topology on Partial Functions

doc. RNDr. Milan Matejdes, CSc. / Spojitostné vlastnosti multifunkcií; Fragmented Topological Spaces and Projections

prof. RNDr. Ľubomír Snoha, DSc., DrSc. / Stroboscopic and Collective Dynamics

Rules for the assignment, reviewing, defence a assessment of final theses are defined in the FNS MBU Study Regulations

link: https://www.fpv.umb.sk/studium/pre-studenta/studijny-poriadok-a-ine-dokumenty/studijny-poriadok.html

Detailed rules for the writing of final theses are specified in Directive No. 9/2021 on final, rigorous, and habilitation theses at MBU in Banská Bystrica

link: https://www.fpv.umb.sk/studium/pre-studenta/zaverecne-prace-a-statne-skusky.html

Student mobility opportunities and participation conditions are specified in Directive No. 2/2017 on mobilities abroad at MBU Faculty of Natural Sciences in Banská Bystrica. Other relevant information related to mobility opportunities is available at the faculty website.

link: https://www.fpv.umb.sk/medzinarodne-vztahy/mobility-erasmus/

At MBU, there is an Ethics Committee, which addresses the questions and issues related to adherence to academic ethics (employees and students). Relevant information related to Ethics committee and its activity can be found on the university website.

link: https://www.umb.sk/univerzita/univerzita/o-univerzite/akademicka-etika-umb/eticka-komisia/

Students with special needs follow the Study Guide for Students with Special Needs published at the university website.

link: https://www.umb.sk/studium/student/student-so-specifickymi-potrebami/informacie-pre-studentov-so-specifickymi-potrebami.html

FNS MBU has an SSN Coordinator who supports students with special needs and helps them adapt to the university environment, and resolve any study-related issues.

link:https://www.fpv.umb.sk/studium/pre-studenta/studijny-poriadok-a-ine-dokumenty/sprievodca-studiom-pre-studentov-so-specifickymi-potrebami.html

Complaints and appeals related to studies, results assessment may be addressed in written form/request filed to the Vice-Dean for Pedagogical Activities. Requests for a board examination, if any, are complied with according to academic regulations of FNS MBU.

link: https://www.fpv.umb.sk/studium/pre-studenta/studijny-poriadok-a-ine-dokumenty/studijny-poriadok.html

Complaints related to violation of the Code of Ethics can be submitted directly to the Ethics Committee in writing.

link: https://www.umb.sk/univerzita/univerzita/o-univerzite/akademicka-etika-umb/eticka-komisia/

Subjects' information sheets are available in the system AIS.

Year plan:

https://www.fpv.umb.sk/studium/pre-studenta/harmonogram-studia.html

prof. RNDr. Ľubomír Snoha, DSc., DrSc.

member of the Department of Mathematics

048/4467229

lubomir.snoha@umb.sk

prof. RNDr. Ľubomír Snoha, DSc., DrSc. / Dynamic Systems, Ergodic Theory, Functional Analysis / 048/4467229 / lubomir.snoha@umb.sk

prof. RNDr. Vladimír Janiš, CSc. / Fuzzy Mathematical Analysis, Functional Analysis / 048/4467228 / vladimir.janis@umb.sk

prof. RNDr. Miroslav Haviar, CSc. / Topology / 048/4467224 / miroslav.haviar@umb.sk

doc. RNDr. Roman Hric, PhD. / Differential Equations, Ergodic Theory, Complex Analysis, Measure and Integral / 048/4467230 / roman.hric@umb.sk

doc. RNDr. Matúš Dirbák, PhD. / Topology, Dynamic Systems, Real Analysis / 048/4467226 / matus.dirbak@umb.sk

Link to the staff register:

https://www.portalvs.sk/regzam/?do=filterForm-submit&university=714000000&faculty=714070000&sort=surname&employment_state=yes&filter=Vyh%C4%BEada%C5%A5

Research/art/teacher profiles of persons are available in the system AIS.

prof. RNDr. Ľubomír Snoha, DSc., DrSc. / Methodology and Ethics of Scientific Work / 048/4467229 / lubomir.snoha@umb.sk 

doc. RNDr. Roman Hric, PhD. / Methodology and Ethics of Scientific Work / 048/4467230 / roman.hric@umb.sk

Seminar Instructor / Scientific Seminar 1-8, another scientific seminar

principal investigator / Participation in a research grant project in the first/second/third year (researcher) 

supervisor / Scientific Seminar 1-8, publication registered in WoS or Scopus databases, State Examination, all elective courses of the scientific part

Link to the staff register:

https://www.portalvs.sk/regzam/?do=filterForm-submit&university=714000000&faculty=714070000&sort=surname&employment_state=yes&filter=Vyh%C4%BEada%C5%A5

doc. RNDr. Vladimír Špitalský, PhD. / Topological Dynamics on One-dimensional Continua ; Recurrent Quantitative Analysis / 048/4467227

vladimir.spitalsky@umb.sk

doc. RNDr. Roman Hric, PhD. / Dense Orbits in Dynamic Systems / 048/4467230 / roman.hric@umb.sk

prof. RNDr. Vladimír Janiš, CSc. / Mappings on Bounded Lattices Applied in Multivalued Logics; Convexity in Ordered Structures / 48/4467228

vladimir.janis@umb.sk

Research/art/teacher profiles of persons are available in the system AIS.

Mgr. Miroslava Poláková / miroslava.polakova@umb.sk

Mgr. Michaela Bruteničová / michaela.brutenicova@umb.sk

Graduates:

Mgr. Michal Takács, PhD. / miskota@gmail.com

RNDr. Pavol Kráľ, PhD. / pavol.kral@umb.sk

Doc. RNDr. Matúš Dirbák, PhD. / 048/4467226 / matus.dirbak@umb.sk / https://www.fpv.umb.sk/madirbak/

Study Officer

PaedDr. Beata Dobríková / 048/4467406 / beata.dobrikova@umb.sk

International Relations Officer (mobilities)

Mgr. Viera Pavlovičová / 048/4467439 / viera.pavlovicova@umb.sk

Department of Mathematics at FNS MBU has a total of 14 offices, a secretariate office and a common room featuring one part of the department’s library (newer books). The second and third sections of the library (older books) are located in the other two offices. The department offers for teaching purposes one computer-equipped laboratory, a seminar room, four classrooms with a high-quality ceramic pylon boards and one tiered multimedia lecture room with a capacity of approximately 90 people equipped with a board, an interactive board and other specialised equipment making organised videoconferences available.

Within the SIVVP (see http://www.hpcc.umb.sk/), Department of Mathematics at FPV UMB has (see http://www.hpcc.umb.sk/) access to the cluster for high-performance computers with the total number of 288 counting cores, performing at around 3 TFLOPS and storing capacity of approximately 100 TB. Cluster is connected to various other computing systems (grids). Multiple high performance computing systems are currently installed on the cluster, along with a set of program compilers. All MBU employees and students alike may, after registering, use the computing capacity of the cluster and the installed software for research and study purposes.

All rooms on the Department of Mathematics are equipped with computers with internet access. All academic staff members are given their own PC with unlimited access to the internet, and through the university library, they have the access to mathematics and statistics journal literature from publishers such as Elsevier, Springer and others, along with the databases (e.g. ISI Web of Knowledge, Scopus). The Department of Mathematics at FNS MBU features a computer laboratory for the needs of performing research grant tasks; this laboratory is used for teaching purposes as well. Technical parameters of the computer laboratory of the Department of Mathematics (room No. 237) Devices: 12 stations with the following configuration: HP Touchsmart 600-1030cs T6400 (2.0GHz), 23" NV9400 chipset, 4GB, 500GB, DVDRW, WireLess, BlueTooth, Windows 7 Premium, wired keyboard, wired mouse.

Library and information services are also provided by the University Library of Matej Bel University at the central workplaces at Tajovského 40 and 51 and at dislocated workplaces on each faculty, also in a form of partial libraries in the departments. The university library provides absence and presence book loans, consulting, research, reference service, copying, and Internet access 54 hours/week plus online services and access to electronic information sources 24/7.

The library collection contains over 277,000 scholarly and specialized monographs, textbooks, edited volumes, encyclopaedias, dictionaries and other types of documents. Acquisition is managed in cooperation with teachers according to the current academic and scholarly duties of the university. The collection also includes 251 periodicals, 120 of which are from abroad. Final theses and other qualification theses defended at the university have been available online since 2009. Over 700 textbooks and study materials published by the university press are available via the MBU Virtual Reading Room.

The University Library manages access do databases courtesy of national grants – Web of Science and Scopus scientometric databases, and full-text scholarly publication databases e.g. ACM, ProQuest Central, ProQuest Ebook Central, ScienceDirect, SpringerLink, Springer Nature, Wiley Online Library. Using its own funds, the library also offers access to the Cambridge Journals and Emerald full-text databases, and educational videos on the HSTalks platform.

The General Reading Room at Tajovského 51 features a reference collection of over 16,500 printed documents and 134 periodicals. All fields of study are covered. Office hours: Monday – Wednesday (8.30 am – 9.00 pm), Thursday – Friday (8:30 am – 4:00 pm). European Documentation Centre is a part of the reading room. The study room also manages the deposit of printed final and qualification theses.

The Circulation Branch at Tajovského 40 St is the library’s central branch for circulation services, allowing users to borrow from a collection of over 87,000 library documents. Office hours: Monday to Friday, 9:00 am to 4:00 pm. Interlibrary loan services are also offered.

Department of Mathematics also offers a partial library with over 6000 books and multiple periodicals on long-term subscription agreements. From the perspective of mathematical literature coverage, this library is one of the best in the country. The library is continually extended with important titles from mathematical disciplines linked to teaching as well as activities of its members. Students have free access to the library upon agreement at the department’s secretariate.

Since the number of students in each year is low (0-2), forced transitioning to distance learning can be done rather smoothly. During the COVID-19 pandemic, MS Teams was used along email for communication purposes.

External supervisors (Mgr. Juraj Holos a successful graduate led by doc. Ján Borsík from IM SAS Košice). Scientific seminar (a new course, 8 semesters), or another scientific seminar may be completed by doctoral candidates elsewhere, based on the offer of seminars and the students’ interest (e.g. as Mgr. Michaela Bruteničová completed a seminar in fuzzy mathematical analysis, while on her stay in Universidad de Oviedo).

The university offers other opportunities besides education in various study programmes. Students may participate in various cultural, sport, spiritual activities. At the university there are several sports clubs, art ensembles, students may even use university sports grounds. There is also the University Pastoral Centre. All information related to the mentioned opportunities can be found at the university website.

link: https://www.umb.sk/studium/student/volny-cas/

link: http://upcbb.sk/o-upc/kto-sme/

Other relevant information related to mobility opportunities is available at the faculty website.

link: https://www.fpv.umb.sk/medzinarodne-vztahy/mobility-erasmus/

Each department has its own mobility coordinator for students, who offers the students introductory information about mobility opportunities for them and directs them during other related activities and formal processing.

link: https://www.fpv.umb.sk/medzinarodne-vztahy/mobility-erasmus/koordinatori-programu-erasmus.html

Opportunities and admission requirements for study, as well as syllabuses of admission proceedings for individual study programmes for the following academic year are described in Opportunities and requirements of admission to study for the year xx/xx.

link: https://www.fpv.umb.sk/studium/pre-uchadzaca/podmienky-prijatia-na-studia-v-roku-2022-2023/

The primary requirement for applicants is a Master's degree study completed in the Mathematics field of study, or a related field (e.g. Teaching of Mathematics). Students are also required to have creative problem-solving skills when approaching mathematical problems, thorough knowledge of university-level mathematics – predominantly mathematical analysis – in the extent of bachelor’s and master’s study programmes. They are expected to have high working pace and efficient work distribution skills. Another requirement is a good command of the English language which will allow students to study mathematics literature in English. Applicants are expected to be also highly motivated.

Procedures and requirements of admission proceedings are specified in the FNS MBU Study Regulations.

link: https://www.fpv.umb.sk/studium/pre-studenta/studijny-poriadok-a-ine-dokumenty/studijny-poriadok.html

Before admission proceedings to doctoral studies begin, the faculty announces dissertation topics, which applicants may apply for during the admission proceedings. Each of the listed topics has a supervisor assigned (dissertation theses topics may be further specified in the preparatory phase). Doctoral studies applicants must enrol on one of the listed topics. Successful admission examination is required for a student to be admitted. Admission board consists of a chairman with another two members, appointed by dean, based on the chairman’s recommendation. Supervisor of the announced topic for which at least one student enrolled, is also a member of the Admission board.

Applicants’ suitability for doctoral studies is verified based on their results in their previous studies, their previous creative and publication activity, but mostly on their admission examination.  

Admission examination has two parts:

·        Written part (75% importance value), where applicants must solve the given mathematical tasks equivalent to university-level mathematics. The biggest emphasis is on mathematical analysis (differentials and integrals, metric space), not excluding tasks in algebra, geometry, measure theory, and probability theory. Tasks are chosen in such a way so as to prove the applicants’ creative ability when solving the tasks. Routine tasks, often found in mathematical exercises at the university level, are avoided.

·        Oral part (25% importance value). Oral part requires knowledge equivalent to a final state examination at master’s level in mathematics study programme.

Admission (rejection) is determined by the order in which applicants rank according to the achieved number of points received from the admission examination. Every applicant must reach at least 65% success rate in the admission examination. In justified causes, mainly in case of applicants with excellent study results during their studies and in case of applicants with relevant publication activity or multiple achievements in Student Scientific Activities (ŠVOČ), applicants may be admitted by the Dean without undergoing the admission examination, based on the recommendation of the admission board chairman.

Essential requirement of admission to study is command of the English language on a level which will allow students to study mathematics literature in English. This is determined in two ways. Firstly, the assignments in the written part of the examination are in English (applicants may request for translation to Slovak. This, however, is later taken into account when verifying the students’ command of English). Secondly, applicants’ command of English is verified orally, which is in form of a conversation in English, and in written form by asking applicants to translate a portion of text from a university textbook of mathematical analysis. 

In the case of written admission examination, results are announced to the applicants at the faculty website on the day of the examination.

Applicants who meet the set requirements for admission to study receive a decision of admission to study with other relevant documents. The results of admission proceedings are recorded in the academic information system.

2017/18 – admission of Mgr. Miroslava Sartorisová (studies interrupted for 2 years due to maternity leave)

2018/19 – admission of Mgr. Michaela Mihoková and Mgr. Miroslav Výbošťok

2019/20 – no admissions. Based on the agreement on joint leadership of a doctoral candidate between MBU and the Universidad de Oviedo

 a Spanish doctoral candidate Pedro Huidobro has been studying at the MBU since autumn 2019.

2020/21 – admission of Mgr. Michaela Bruteničová

2021/22 – no applicants

1. University faculties annually conduct sociological surveys focusing on study programme assessment, asking graduates of the 1st and 2nd degree of studies after state examinations. The questionnaire focuses on the summary of their studies, contents of their study programme and conditions created for the purposes of their completion. The questionnaire is anonymous; students fill in the questionnaire form after they successfully complete their state examination. Questionnaire sheets are later processed in TAP software.

The questionnaire is evaluated at the university level and the results are included in the MBU Report on Pedagogical Activity. At the faculty level, the questionnaire is analysed in detail, focusing on evaluation of answer trends in survey questions in several years for every study programme delivered. At the faculty and department levels, measures after the evaluation improving on the specific aspects in question, are applied. The results of the questionnaire are presented at the Dean’s College and are a part of the Reports on Pedagogical Activity.

2. Another questionnaire conducted at the university is focusing on assessment of teachers. The aim of this questionnaire is to receive feedback from students on the quality of classes with a given teacher, their class delivery, their approach to teaching and student assessment. The questionnaire also includes an open-ended question, offering students an opportunity to give their personal opinions on teachers, their work, or articulate their dissatisfaction with them. The questionnaire is anonymous and takes place in AIS. Every teacher has access to results of the questionnaire regarding themselves, Chair of the Department has access to results of all teaching staff in the department. Any potential deficiencies and objections are resolved in cooperation with the Vice-Dean for Pedagogical Activities at the department level.

Results of the questionnaire focusing on the students’ opinions on their teachers’ performance are stored in the academic information system.

Results of the questionnaire on the study programme quality assessment filled in by graduates are included in the Reports on Pedagogical Activity at the university and the faculty levels.

FNS MBU Study Regulations

https://www.fpv.umb.sk/studium/pre-studenta/studijny-poriadok-a-ine-dokumenty/studijny-poriadok.html

Study Guide

https://www.fpv.umb.sk/studium/pre-studenta/studijny-poriadok-a-ine-dokumenty/sprievodca-studiom.html

Study Guide for Students with Special Needs

https://www.fpv.umb.sk/studium/pre-studenta/studijny-poriadok-a-ine-dokumenty/sprievodca-studiom-pre-studentov-so-specifickymi-potrebami.html

Directive No. 9/2021 on final, rigorous, and habilitation theses at MBU in Banská Bystrica

https://www.fpv.umb.sk/studium/pre-studenta/zaverecne-prace-a-statne-skusky.html

Disciplinary Code for students of Matej Bel University in Banská Bystrica

https://www.fpv.umb.sk/studium/pre-studenta/studijny-poriadok-a-ine-dokumenty/disciplinarny-poriadok.html

Directive on tuition and fees related to studies and awarding of scholarly-pedagogical titles at Matej Bel University in Banská Bystrica for the current academic year

https://www.fpv.umb.sk/studium/skolne-a-poplatky-spojene-so-studiom/

FNS MBU Scholarship Regulations

https://www.fpv.umb.sk/studium/stipendia/stipendijny-poriadok.html