Institution body for approving the study programme:

Board for Internal Quality Verification at Pavol Jozef Šafárik University

Date of the latest change in the study programme description:

31.03.2022

1. - Basic information about the study programme

a) - Name of the study program and its number according to the register of study programmes.

12267 Discrete mathematics, DMd

b) - Degree of higher education and ISCED-F education degree code.

III. - doctoral degree, 864

c) - Place(s) of delivery of the study programme.

Košice

d) - Name and number of the field of study in which higher education is obtained by completing the study programme, or a combination of two fields of study in which higher education is obtained by completing the study programme, ISCED-F codes of the field/fields.

22 - Mathematics, 0541

e) - Type of the study programme: academically oriented, professionally oriented; translation, translation combination study programme (listing the specializations); teaching, teaching combination study programme (listing the specializations); artistic, engineering, doctoral, preparation for regulated profession, joint study programme, interdisciplinary studies.

academically oriented

f) - Awarded academic degree after the name

PhD.

g) - Form of study.

Full-Time

i) - Language or languages in which the study programme is delivered.

Slovak, English

j) - Standard length of the study expressed in academic years.

4

k) - Capacity of the study programme (planned number of students), the actual number of applicants and students.

planned number of students: 7, actual number of applicants: 1, actual number of all students: 4

2. - Graduate profile and learning objectives

a) - The institution defines the learning objectives of the study programme such as student's abilities at the time of completion of the programme and the main learning outcomes.

The profile of a graduate of the Discrete Mathematics study programme corresponds to level no. 8 of knowledge, skills and competences according to the National Qualification Framework of the Slovak Republic in the European area of higher education.

The graduate of this study programme has deep theoretical and methodological knowledge of discrete mathematics, masters the theoretical foundations and scientific methods of research in this area, is

As for the skills, during the studies, the graduate will learn methods of presenting the results of scientific research in various forms, including publication in scientific journals and appearances at scientific conferences, as ways of teamwork in research or principles of leading a research team.

Concerning the competences, the graduate is able to discover the deep laws of discrete structures and to design resp. to solve discrete mathematical models of problems from various scientific fields with the help of computer technology. The graduate is also able to maintain contacts with the latest developments in his discipline and continue his own professional progress.

b) - The institution indicates the professions for which the graduate is prepared at the time of completion and the potential of the study programme from the point of view of graduate's employability.

UPJŠ applies the statistical classification of occupations SK ISCO-08 to indicate occupations for which the student is prepared after completing the study programme, see https://www.kvalifikacie.sk/sites/nsk/files/employers/sk_isco-08_0.pdf.

The potential of the Discrete Mathematics doctoral study program lies in the comprehensive training of qualified employees for the following selected professions according to the ISCO-08 classification:

2120004 Mathematics specialist (except actuarial mathematics)

2120999 Specialist in mathematics, actuarial and statistics (not classified elsewhere))

2310001 Professor

2310002 Associate Professor

2310003 University assistant professor

2330003 High school teacher

2421003 Project Specialist (project manager)

2511003 Information and Communication Technology Analyst

2511999 Systems analyst (not classified elsewhere)

2512001 Software Developer

2512002 Software architect, designer

2519999 Other developer, software and application analyst (not classified elsewhere)

3314999 Statistician, mathematician and similar specialist (not classified elsewhere)

3. - Employability

a) - Evaluation of the study programme graduates employability.

The applicability of graduates of the Discrete Mathematics study programme covers the academic sphere resp. education in general (where they work as university and high school teachers or researchers in research-funded research projects), as well as the corporate sector (typically held positions include software developer, complex IT solutions architect, data analyst, information systems designer or project manager). The success of the employment of graduates in both mentioned branches can also be documented by the list of selected institutions in which the graduates of the study program Discrete Mathematics worked resp. operate (PF UPJŠ Košice, faculties FEI, EF, BERG and FME of TU Košice, PHF EU Bratislava with seat in Košice, IBM Košice, NESS, Google Zurich, Koger, VSL). The societal need of graduates of this program is also confirmed by professionally oriented job search engines when entering the search for the above-mentioned corporate positions (see, for example, http://profesia.sk, http://istp.sk).

b) - If applicable, indicate the successful graduates of the study programme.

The most successful graduates of the study program to date include:

Before 2013:

RNDr. Milan Tuhársky, PhD. (supervisor prof. Jendroľ), https://sk.linkedin.com/in/milan-tuharsky-8b3644a3

RNDr. Karla Čipková, PhD. (supervisor prof. Studenovská),https://uim.fei.stuba.sk/pracovnici/karla-cipkova/

RNDr. Július Czap, PhD. (supervisor prof. Jendroľ), https://www.portalvs.sk/regzam/detail/3005

RNDr. Jana Zlámalová, PhD. (supervisor prof. Horňák), www.linkedin.com/in/jana-zl%C3%A1malov%C3%A1-80b55071

RNDr. Kristína Budajová, PhD. (supervisor prof. Jendroľ),

RNDr. Erika Fecková-Škrabuľáková (supervisor prof. Jendroľ), https://www.portalvs.sk/regzam/detail/2978

After 2013:

RNDr. Dávid Hudák, PhD. (supervisor prof. Madaras), www.linkedin.com/in/david-hudak-885a3588

RNDr. Peter Šugerek, PhD. (supervisor prof. Jendroľ), https://www.portalvs.sk/regzam/detail/20599

RNDr. Ľudmila Šebestová, PhD. (supervisor doc. Ivančo),

RNDr. Gabriela Karafová, PhD. (supervisor doc. Soták), www.linkedin.com/in/jana-zl%C3%A1malov%C3%A1-80b55071

RNDr. Martina Mockovčiaková, PhD. (supervisor doc. Soták), https://www.portalvs.sk/regzam/detail/21081?mode=full

RNDr. Jana Coroničová Hurajová, PhD. (supervisor prof. Madaras), https://www.portalvs.sk/regzam/detail/22834

RNDr. Peter Hudák, PhD. (supervisor prof. Madaras),

RNDr. Mária Maceková, PhD. (supervisor prof. Jendroľ), https://www.portalvs.sk/regzam/detail/26409

RNDr. Michaela Tomková, PhD. (supervisor prof. Jendroľ),

RNDr. Pavol Široczki, PhD. (supervisor prof. Madaras),

RNDr. Mária Timková, PhD. (supervisor prof. Jendroľ, konzultant Dr. Fabrici), https://www.portalvs.sk/regzam/detail/25658

RNDr. Juraj Valiska, PhD. (supervisor prof. Jendroľ), https://www.portalvs.sk/regzam/detail/31351

RNDr. Lucia Janičková, PhD. (supervisor prof. Studenovská) https://www.upjs.sk/PF/zamestnanec/lucia.janickova/

c) - Evaluation of the study programme quality by employers (feedback).

The suitability and compliance of the doctoral study program Discrete Mathematics with the needs of practice was assessed and approved by several key representatives of employers in the region:

doc. RNDr. Jozef Bucko, PhD. (Faculty of Economics, Technical University of Košice, Head of the Department of Applied Mathematics and Business Informatics):

“Employees of the Department of Applied Mathematics and Business Informatics who have completed their studies in the doctoral study program Discrete Mathematics at PF UPJŠ (Dr. Czap, Dr. Šugerek) form an important part of the department's teaching in key subjects teaching (Mathematics I, Mathematics II, Informatics I and Informatics II) as well as in specialized subjects teaching (Applied Graph Theory in Economics) in the study programmes of Finance, Banking and Investment and Economics and Public Administration Management. Every year they conduct students' final theses at Faculty of Economics, which proves their ability to adapt to the needs and focus of the Faculty of Economics not only in the teaching process, but also in scientific research and project solutions (where they followed up on their own and related topics of their dissertations in business informatics and applied mathematics in economics). Based on previous experience and past results, we can truly assume that any additional graduates applying for employment at the Faculty of Economics TUKE will be a valuable contribution to the further development of the faculty and our workplace. ”

doc. RNDr. Marián Klešč, PhD. (Faculty of Electrical Engineering and Informatics, Technical University of Košice, Deputy Head of the Department of Mathematics and Theoretical Informatics):

"Due to the fact that a large part of computer science subjects taught for different fields of study and different degrees of their studies at the Faculty of Electrical Engineering and Informatics of the Technical University in Košice is based on knowledge and methods of discrete mathematics, from the point of view of our faculty it is desirable, for teachers of corresponding subjects, to have as good as possible knowledges, skills and competences in this are. In this direction, the Department of Mathematics and Theoretical Informatics of FEI TUKE can rely on the competent work of several quality graduates of the doctoral study program PF UPJŠ Discrete Mathematics, who currently work at our institution (Dr. Draženská, Timková , Valiska), and, it is in our interest that other graduates of this study programme also could work for us in the future. "

4. - Structure and content of the study programme

a) - The institution describes the rules for the design of study plans within the study programme.

The rules for creating study plans are governed by the Study Regulations of Doctoral Studies, https: //www.upjs.sk/prirodovedecka-fakulta/studium/d-studium/, which defines the student's workload, evaluation, control stages of studies, method of graduation and other requirements . Responsibility for the content of the study and for the correct evaluation of course quality is defined by:

· Rector's decision no. 7/2021: UPJŠ Accreditation Order, available at: https://intranet.upjs.sk/op/op.Public.php?documentid=4252

· Rector's decision no. 8/2021: Rules of the internal quality assurance system and verification of education, scientific, research, development, artistic or other creative and support activities at UPJŠ, available at: https://intranet.upjs.sk/op/op.Public.php?documents=4253.

b) - The institution compiles the recommended study plans for individual study paths.

An overview of study programs provided by UPJŠ with links to personal websites of teachers with contacts is available at: https://studijne-programy.upjs.sk/. The student compiles, together with his / her supervisor, a concretized study plan in accordance with the provisions of the UPJŠ Study Regulations for the 1st, 2nd and combined 1st and 2nd degree studies and with the requirements of the doctoral study programme Discrete Mathematics. Relevant information on the subjects is given in their information sheets, which are accessible online at https://studijne-programy.upjs.sk/program/DMd.

c) - The study plan generally states:

All data and information are listed in the study plan, which is generated from AIS2 and is also a part of the submitted documentation.

d) - The institution states the number of credits, the achievement of which is a condition for proper completion of studies and other requirements that the student must meet within the study programme and for its proper completion, including the requirements for state examinations, rules for re-study and rules for the extension, interruption of study.

The rules for proper completion of studies at UPJŠ, control stages of study and rules for repetition of studies, extension of studies or interruption of studies are specified in the UPJŠ Study Regulations for the 3rd level at UPJŠ (https://www.upjs.sk/public/media/15322 /studijny-poriadok-doktorand-upjs-maj-2019-dopl.pdf). The study regulations also regulate the organization of state exams. Specific conditions for passing the state exams for this SP are available in the study plan. The student duly completes the doctoral study by completing the study according to the relevant study program. The length of the study may not exceed the standard study period by more than two years. The condition for the proper completion of the study program is successful completion of the study in the composition prescribed in the study plan, successful completion of the dissertation examination and successful defense of the dissertation. For all activities (study, scientific work, dissertation examination, defense of dissertation and complementary activities) the student must achieve a minimum of 240 credits during the study. The student is obliged to pass the dissertation exam in full-time form no later than 24 months and in external form within 36 months from the beginning of the study. Only a student who has met the following conditions is admitted to the dissertation examination: 1. He / she has successfully completed all compulsory subjects, as well as other subjects and evaluated activities of the study program in the prescribed composition, and has achieved at least 90 credits. 2. Prepared and submitted the written work for the dissertation exam in time. A student who has received a positive recommendation from the supervisor and has achieved at least 210 credits, while must have at least 60 credits for the study part and 120 credits for the scientific part of the study program, is admitted to the defense of the dissertation. The student is obliged to obtain another at least 30 credits for complementary activities specified in detail in the study plan. Specific deadlines for fulfilling these obligations are updated centrally at the faculty level and published in the schedule of the current school year. Fulfillment of all conditions for the completion of the study is consistently registered in the electronic system AiS2 and checked by the relevant clerk of the Study Department of PF UPJŠ.

e) - For individual study plans, the institution states the requirements for completing the individual parts of the study programme and the student's progress within the study programme in the given structure:

The following requirements apply to the completion of the Discrete Mathematics study programme:

Minimum number of credits for the study part: 60, of which

· Number of credits for compulsory subjects: 41

· Minimum number of credits for compulsory elective courses: 19

Minimum number of credits per scientific part: 120, of which

at least 25 credits for publishing activity

at least 16 credits for active presentation of results

Minimum number of credits for other activities: 25

20 credits are awarded for successful completion of the dissertation examination and 30 credits for the defense of the dissertation.

The minimum number of credits required for proper completion of studies is 240.

f) - The institution describes the rules for verification of learning outcomes, students assessment and the possibilities of appealing against the assessment.

The verification of the methods and objectivity of grading the students is governed by the Principles for Verification of the Quality of Higher Education at UPJŠ (https://intranet.upjs.sk/op/op.Public.php?documentid=4253).

The examination of complaints by students is governed by the Act on Quality Assurance in Higher Education (https://www.slov-lex.sk/static/pdf/2018/269/ZZ_2018_269_20210101.pdf), the Act on Complaints (https: // www. slov-lex.sk/static/pdf/2010/9/ZZ_2010_9_20190201.pdf), the Rector's Decision on Handling Complaints and the Study Regulations for the 3rd level at UPJŠ (https://www.upjs.sk/public/media/15322/ studijny-poriadok-doktorand-upjs-maj-2019-dopl.pdf).

Further information is publicly available at: https://www.upjs.sk/univerzita/kvalita/programy/#4.

g) - Conditions for recognition of studies or a part of studies.

The rules for the recognition of studies or its parts are regulated by the Study Regulations for the 3rd level at UPJŠ (https://www.upjs.sk/public/media/15322/studijny-poriadok-doktorand-upjs-maj-2019-dopl.pdf). Further information is publicly available at: https://www.upjs.sk/univerzita/kvalita/programy/.

h) - The institution states the topics of final theses of the study programme (or a link to the list).

The topics of the final theses of the doctoral study program Discrete Mathematics are published annually on the faculty's website and registered centrally in the academic information system AiS2: https://ais2.upjs.sk/ais/portal/changeModul.do?modul=ES.

The following supervisors and topics are currently active within the study program:

(1) prof. RNDr. Tomáš Madaras, PhD. (tomas.madaras@upjs.sk):

Walks in planar and embedded graphs

Mgr. Daniela Matisová, beginning of doctoral studies: September 2021

Consultant: RNDr. Juraj Valiska, PhD. (Faculty of Electrical Engineering and Informatics, Technical University, Košice)

(2) prof. RNDr. Tomáš Madaras, PhD. (tomas.madaras@upjs.sk):

Edge coloring of graphs determined by chromatic properties of subgraphs

RNDr. Alfréd Onderko, beginning of doctoral studies: September 2019

(3) prof. RNDr. Tomáš Madaras, PhD. (tomas.madaras@upjs.sk):

Structure of sparse graphs

RNDr. Martina Tamášová, beginning of doctoral studies: September 2015

(4) prof. RNDr. Mirko Horňák, CSc. (mirko.hornak@upjs.sk):

Facially-proper colorings of plane graphs

RNDr. Simona Rindošová, beginning of doctoral studies: September 2017

Consultant: RNDr. Igor Fabrici, Dr. rer. nat.

(5) doc. RNDr. Roman Soták, PhD. (roman.sotak@upjs.sk):

Interval colorings of graphs

RNDr. Zuzana Šárošiová, beginning of doctoral studies: September 2019

Consultant: RNDr. Mária Maceková, PhD.

(6) doc. RNDr. Roman Soták, PhD. (roman.sotak@upjs.sk):

Structural properties of embedded graphs

RNDr. Katarína Čekanová, beginning of doctoral studies: September 2018

Consultant: RNDr. Mária Maceková, PhD.

(7) doc. RNDr. Miroslav Ploščica, CSc. (miroslav.ploscica@upjs.sk):

Clones of compatible operations

RNDr. Ivana Varga, beginning of doctoral studies: September 2018

i) - The institution describes or refers to:

The rules for defining, processing, opposing, defending and evaluating final theses in the study programme are set out in the Study Regulations for the 3rd level at UPJŠ (https://www.upjs.sk/public/media/15322/studijny-poriadok-doktorand- upjs-maj-2019-dopl.pdf) and the Principles for Verifying the Quality of Higher Education at UPJŠ (https://intranet.upjs.sk/op/op.Public.php?documentid=4253).

International mobility of students and employees is an essential area of the university's international activities. All information is available at: https://www.upjs.sk/univerzita/cinnost/medzinarodne-vztahy/, as well as at https://www.upjs.sk/univerzita/kvalita/programy/#3.

· The principles for verifying the quality of higher education at UPJŠ declare compliance with the general principles and rules of ethical behavior:

UPJŠ Code of Ethics
UPJŠ Student Code of Ethics,

to which there are closely linked

Principles of good scientific publishing practice,
Plagiarism assessment rules,
Principles of good research practice at UPJŠ, and
Principles for verifying the quality of higher education at UPJŠ.

(see https://www.upjs.sk/univerzita/kvalita/programy)

The following support services are available to students with special needs:

- Counseling: psychological, social, legal, career.

- Technical support (special devices and aids).

- IT consulting - assistance and support in the use of IT resources. Advice on setting up AiS2 for visually impaired students. PC settings for visually impaired students.

- Library and lending services tailored to the special needs of students.

- Erasmus +: UPJŠ students with special needs have the opportunity to apply for a grant, which is used to cover expenses related to special needs during the implementation of mobility abroad. More information at the Foreign Relations Department.

More information at: https://www.upjs.sk/univerzita/kvalita/programy/#7.

The examination of suggestions by UPJŠ students is governed by the Higher Education Quality Assurance Act (https://www.slov-lex.sk/static/pdf/2018/269/ZZ_2018_269_20210101.pdf), the Complaints Act (https://www. slov-lex.sk/static/pdf/2010/9/ZZ_2010_9_20190201.pdf), Rector's decision on complaints handling (https://intranet.upjs.sk/op/op.ViewOnline.php?documentid=1075&version=1) and the Study Regulations for the 3rd level at UPJŠ (https://www.upjs.sk/public/media/15322/studijny-poriadok-doktorand-upjs-maj-2019-dopl.pdf). The verification of the methods and objectivity of grading the students is governed by the Principles for Verifying the Quality of Higher Education at UPJŠ in Košice (https://intranet.upjs.sk/op/op.Public.php?documentid=4253).

Further information is publicly available at: https://www.upjs.sk/univerzita/kvalita/programy/#4.

5. - Course information sheets of the study programme

In the structure according to Decree no. 614/2002 Coll.

Information sheets are available in the monitoring panel of the study programme in the Academic Information System AiS2. They are available to the public in the Register of UPJŠ study programs https://studijne-programy.upjs.sk/study-program/DMd.

6. - Current academic year plan and current schedule

(or hyperlink).

The schedule of the academic year is publicly available at https://www.upjs.sk/studium/ resp. https://www.science.upjs.sk/prirodovedecka-fakulta/studium/harm/.

7. - Persons responsible for the study programme

a) - A person responsible for the delivery, development, and quality of the study programme (indicating the position and contact details).

prof. RNDr. Tomáš Madaras, PhD., full professor; tomas.madaras@upjs.sk, https://www.upjs.sk/PF/zamestnanec/tomas.madaras

b) - List of persons responsible for the profile courses of the study programme with the assignment to the course and provided with a link to the central Register of university staff and with contact details (they may also be listed in the study plan).

ÚMV/dTGF/10 Graph theory:

T. Madaras, /OZŠP/ https://www.portalvs.sk/regzam/detail/15368, tomas.madaras@upjs.sk

R. Soták, /OZPP/ https://www.portalvs.sk/regzam/detail/15290, roman.sotak@upjs.sk

I. Fabrici, /OZPP/ https://www.portalvs.sk/regzam/detail/14921, igor.fabrici@upjs.sk

ÚMV/dTGR/10 Group theory:

M. Ploščica, /OZPP/ https://www.portalvs.sk/regzam/detail/15289, miroslav.ploscica@upjs.sk

ÚMV/dTTG/10 Topological graph theory:

R. Soták, /OZPP/ https://www.portalvs.sk/regzam/detail/15290, roman.sotak@upjs.sk

ÚMV/dTPG/14 Theory of planar graphs:

T. Madaras, /OZŠP/ https://www.portalvs.sk/regzam/detail/15368, tomas.madaras@upjs.sk

ÚMV/dUAL/10 Universal algebra:

D. Studenovská, /OZPP/ https://www.portalvs.sk/regzam/detail/15277, danica.studenovska@upjs.sk

ÚMV/dPMK/10 Probabilistic method in combinatorics:

I. Fabrici, /OZPP/ https://www.portalvs.sk/regzam/detail/14921, igor.fabrici@upjs.sk

c) - Reference to the research/art/teacher profiles of persons responsible for the profile courses of the study programme.

VÚPCH of persons responsible for profile subjects are available in the monitoring panel of the study program in the Academic Information System AiS2.

Data from VÚPCH are also incorporated into the official personal pages of employees, which have a URL in the form: https://www.upjs.sk/PF/zamestnanec/name.surname/

prof. RNDr. Tomáš Madaras, PhD., https://www.upjs.sk/PF/zamestnanec/tomas.madaras

prof. RNDr. Danica Studenovská, CSc.., https://www.upjs.sk/PF/zamestnanec/danica.studenovska

doc. RNDr. Roman Soták, PhD., https://www.upjs.sk/PF/zamestnanec/roman.sotak

doc. RNDr. Miroslav Ploščica, CSc., https://www.upjs.sk/PF/zamestnanec/miroslav.ploscica

RNDr. Igor Fabrici, Dr. rer. nat., https://www.upjs.sk/PF/zamestnanec/igor.fabrici

d) - List of teachers of the study programme with the assignment to the course and provided with a link to the central Register of university staff and with contact details (may be a part of the study plan).

Teachers from PF UPJŠ:

prof. RNDr. Tomáš Madaras, PhD., https://www.portalvs.sk/regzam/detail/15368, tomas.madaras@upjs.sk

ÚMV/dTGF/10 Graph theory

ÚMV/dTPG/14 Theory of planar graphs

ÚMV/dVTGa/10 Selected topics in graph theory I

ÚMV/dVTGb/10 Selected topics in graph theory II

ÚMV/dPLT/10 Polyhedral theory

prof. RNDr. Danica Studenovská, CSc., https://www.portalvs.sk/regzam/detail/15277, danica.studenovska@upjs.sk

ÚMV/dUAL/10 Universal algebra

ÚMV/dUAS/10 Ordered algebraic structures

ÚMV/dVTGb/10 Selected topics in graph theory II

doc. RNDr. Roman Soták, PhD., https://www.portalvs.sk/regzam/detail/15290, roman.sotak@upjs.sk

ÚMV/dTGF/10 Graph Theory

ÚMV/dVTGa/10 Selected Chapters from Graph Theory I

ÚMV/dVTGb/10 Selected Chapters from Graph Theory II

ÚMV/dTTG/10 Topological graph theory

ÚMV/dCTG/21 Chromatic graph theory

ÚMV/dKOA/10 Combinatorial algorithms

doc. RNDr. Miroslav Ploščica, CSc., https://www.portalvs.sk/regzam/detail/15289, miroslav.ploscica@upjs.sk

ÚMV/dTGR/10 Group theory

ÚMV/dTZV/10 Lattice theory

RNDr. Igor Fabrici, Dr. rer. nat., https://www.portalvs.sk/regzam/detail/14921, igor.fabrici@upjs.sk

ÚMV/dVTGa/10 Selected topics in graph theory I

ÚMV/dVTGb/10 Selected topics in graph theory II

ÚMV/dPMK/10 Probabilistic method in combinatorics

prof. RNDr. Viliam Geffert, DrSc., https://www.portalvs.sk/regzam/detail/15260, viliam.geffert@upjs.sk

ÚINF/VYMD/15 Computational complexity and models

Teachers from FF UPJŠ:

PhDr. Helena Petruňová, CSc., https://www.portalvs.sk/regzam/detail/15418, helena.petrunova@upjs.sk

CJP/AJD1/07 English Language for PhD Students 1

CJP/AJD2/07 English Language for PhD Students 2

Mgr. Zuzana Kolaříková, PhD., https://www.portalvs.sk/regzam/detail/15420, zuzana.kolarikova@upjs.sk

CJP/AJD1/07 English Language for PhD Students 1

CJP/AJD2/07 English Language for PhD Students 2

PhDr. Anna Janovská, PhD., https://www.portalvs.sk/regzam/detail/6858, anna.janovska@upjs.sk

KPPaPZ/PsVU/17 Psychology for University Lecturers

prof. PhDr. Oľga Orosová, CSc., https://www.portalvs.sk/regzam/detail/15370, olga.orosova@upjs.sk

KPE/PgVU/17 Pedagogy for University Teachers

e) - List of the supervisors of final theses with the assignment to topics (indicating the contact details).

The following supervisors and topics are currently active within the study program:

(i) prof. RNDr. Tomáš Madaras, PhD. (tomas.madaras@upjs.sk):

Walks in planar and embedded graphs

Mgr. Daniela Matisová, beginning of doctoral studies: September 2021

Consultant: RNDr. Juraj Valiska, PhD. (Faculty of Electrical Engineering and Informatics, Technical University, Košice)

(ii) prof. RNDr. Tomáš Madaras, PhD. (tomas.madaras@upjs.sk):

Edge coloring of graphs determined by chromatic properties of subgraphs

RNDr. Alfréd Onderko, beginning of doctoral studies: September 2019

(iii) prof. RNDr. Tomáš Madaras, PhD. (tomas.madaras@upjs.sk):

Structure of sparse graphs

RNDr. Martina Tamášová, beginning of doctoral studies: September 2015

(iv) prof. RNDr. Mirko Horňák, CSc. (mirko.hornak@upjs.sk):

Facially-proper colorings of plane graphs

RNDr. Simona Rindošová, beginning of doctoral studies: September 2017

Consultant: RNDr. Igor Fabrici, Dr. rer. nat.

(v) doc. RNDr. Roman Soták, PhD. (roman.sotak@upjs.sk):

Interval colorings of graphs

RNDr. Zuzana Šárošiová, beginning of doctoral studies: September 2019

Consultant: RNDr. Mária Maceková, PhD.

(vi) doc. RNDr. Roman Soták, PhD. (roman.sotak@upjs.sk):

Structural properties of embedded graphs

RNDr. Katarína Čekanová, beginning of doctoral studies: September 2018

Consultant: RNDr. Mária Maceková, PhD.

(vii) doc. RNDr. Miroslav Ploščica, CSc. (miroslav.ploscica@upjs.sk):

Clones of compatible operations

RNDr. Ivana Varga, beginning of doctoral studies: September 2018

f) - Reference to the research/art/teacher profiles of the supervisors of final theses.

The list of current supervisors and their research/art teacher profiles are also available from the public register of study programs https://studijne-programy.upjs.sk/study-program/DMd. The research/art teacher profiles of persons responsible for profile subjects are available in the monitoring panel of the study programme in the Academic Information System AiS2. Data from these profiles are also incorporated into the official personal pages of employees:

prof. RNDr. Tomáš Madaras, PhD., https://www.upjs.sk/PF/zamestnanec/tomas.madaras

prof. RNDr. Mirko Horňák, CSc., https://www.upjs.sk/PF/zamestnanec/mirko.hornak

doc. RNDr. Roman Soták, PhD., https://www.upjs.sk/PF/zamestnanec/roman.sotak

doc. RNDr. Miroslav Ploščica, CSc., https://www.upjs.sk/PF/zamestnanec/miroslav.ploscica

g) - Student representatives representing the interests of students of the study programme (name and contact details).

Students are represented in the Study Programme Board by RNDr. Alfréd Onderko, alfred.onderko@student.upjs.sk. The current and previous members of the Study Programme Board are available in the monitoring panel of the study program in AiS2, and in the public register of study programmes of UPJŠ (http://studijne-programy.upjs.sk/study-program/DMd). Students are also represented in the Board for Internal Quality Verification at UPJŠ in Košice (https://www.upjs.sk/univerzita/kvalita/rada/).

h) - Study advisor of the study programme (indicating contact details and information on the access to counseling and on the schedule of consultations).

RNDr. Igor Fabrici, Dr. rer. nat., igor.fabrici@upjs.sk; consultation and advice by prior agreement by e-mail. https://www.upjs.sk/PF/zamestnanec/igor.fabrici/

i) - Other supporting staff of the study programme – assigned study officer, career counselor, administration, accommodation department, etc. (with contact details).

The study programme is standardly supported through the study department of the Faculty of Science UPJŠ in Košice (https://www.upjs.sk/prirodovedecka-fakulta/studium/so/) using the Academic Information System AiS2. The student is able to efficiently handle most of the agenda through the information system, without direct personal interaction with the study department.

Students can also use the services of the University Counseling Center of UPJŠ in Košice (UNIPOC), which is a specialized workplace of UPJŠ established by the Rector of UPJŠ with university-wide competence. UNIPOC's mission is to provide all UPJŠ students with free counseling, specifically psychological, career, legal and social counseling and counseling in effective learning. UNIPOC is also in charge of support

and caring for students with special needs. Students can use counseling services in personal and online form, in Slovak and English. The purpose of the services provided is to improve the employability of students and graduates in the labor market, to act preventively and to help with problems that could jeopardize the successful completion of our students' studies. More information can be found on the UNIPOC website: https://www.upjs.sk/pracoviska/unipoc/.

Students can learn more about the possibilities of employability on the labor market during UPJŠ Career Day (https://www.upjs.sk/pracoviska/unipoc/den-kariery/) or on the UPJŠ My Career website: https://www.upjs.sk/workplaces/unipoc/aktuality/e-learning-moja-kariera/.

UPJŠ University Counseling Center in Košice also provides support for students with special needs: https://www.upjs.sk/pracoviska/unipoc/specialne-edukacne-potreby/.

UPJŠ in Košice also offers students accommodation (https://www.upjs.sk/pracoviska/studentske-domovy-jedalne/studentske-domovy/) and catering services (https://www.upjs.sk/pracoviska/studentske-domovy-jedalne/studentske-jedalne/) through UPJŠ Student Dormitories and Canteens or at contractual partners. The accommodation subsystem is part of AiS2, catering in ŠDaJ is administered by a separate information system, which is integrated within UIS UPJŠ.

8. - Spatial, material, and technical provision of the study programme and support

a) - List and characteristics of the study programme classrooms and their technical equipment with the assignment to learning outcomes and courses (laboratories, design and art studios, studios, workshops, interpreting booths, clinics, priest seminaries, science and technology parks, technology incubators, school enterprises, practice centers, training schools, classroom-training facilities, sports halls, swimming pools, sports grounds).

UPJŠ in Košice provides spatial, material, technical and information resources of the study programme appropriate to the goals and outcomes of education. Ensuring a full-fledged infrastructure supporting higher education, creative scientific research and research activities is one of the university's priorities. The constant progress of the university is also reflected in the continuous expansion of the existing infrastructure, the reconstruction of buildings and the introduction of modern information and communication technologies.

The existence of university workplaces is essential to ensure the required quality of selected services, which are characteristic for a respected and materially well-equipped university. All current information on the security of study programs at the university is listed on the website: https://www.upjs.sk/univerzita/kvalita/programy/#7. Details on the technical and spatial support for all study programs can be found on the following websites:

- internet connection of the university with the Sanet 10Gbps network, throughput of the SANET network backbone-2 times 100GE channels, can be extended up to 500Gbps (https://www.upjs.sk/pracoviska/ciakt/saunet/)

- WIFI connection, covered all university buildings, part of the eduroam.org network

- AiS2 - comprehensive academic information system for managing the study (https://ais2.upjs.sk/ais/start.do)

- email for employees and students operating on the Office 365 platform (https://outlook.office.com/), own mail domain @upjs.sk

- support for distance education via MS Teams (https://www.upjs.sk/navody/teams/) and BigBlueButton (https://bbb.science.upjs.sk/b)

- cyber security - own CSIRT team (https://csirt.upjs.sk/#/)

- raising the security awareness: support for students in case of data leakage, compromise of email addresses, compromise of equipment by malware, Helpdesk IT support (https://www.upjs.sk/pracoviska/ciakt/, https://www.upjs.sk/helpdesk/kontakty/)

- the university is also involved in the CVTI National Telepresentation Infrastructure with the possibility of 10 connections (https://www.tp.cvtisr.sk/telekonferencne-miestnosti/)

- e-learning - portal for e-learning education (https://www.upjs.sk/elearning/)

- UPJŠ Technology and Innovation Park (https://www.upjs.sk/pracoviska/tip/), which includes an incubator and technology transfer support

- Education and Training Facility in Danišovce (https://www.upjs.sk/pracoviska/uvz-danisovce/).

Although the demands of mathematics on material and technical support are lower compared to experimental sciences, teaching and research in mathematics is currently increasingly based on appropriate computer software support and infrastructure based on modern audiovisual and presentation technologies. The lecture halls where the lectures, exercises and seminars take place are fully covered by the WiFi-faculty network (which is part of the Eduroam network) and are equipped with presentation PCs and data video projectors as standard; in some lecture halls, there is also the most modern didactic equipment represented by electronic boards, voting devices and visualizers, resp. touchpads with SmartPen pens. Part of the teaching covers also mastering the programming and working with mathematical software. An important software support tool (both for teaching and research in the field of discrete mathematics) is the Maple computer algebra system (currently in version 2020), which is installed on the desktop computers of each auditorium within the Institute of Mathematical Sciences, as well as in computer classrooms of Department of Informatics, which students have the opportunity to access. The Institute of Mathematical Sciences also has a sufficiently large number of floating Maple licenses, which are provided to students during their studies. In addition to the Maple computer algebra system, students have the opportunity to work with the dynamic geometric systems Cabri II Plus, Cabri 3D and Geogebra; there is also a multilicense for the authoring system ToolBook Instructor 8.6, an academic version of the Imagine programming environment, the LMS system Moodle and a light version of the Hot Potatoes system for creating tests. The Wolfram Mathematica environment can also be used at the Institute of Mathematics as a robust alternative to the Maple system; the freely available Wolfram Alpha platform (eventually, in pro version) is used for less demanding calculations and visualizations. In addition to these commercial programs, non-commercial programs TeX, Beamer, Asymptote are also installed in computer classrooms. The support of distance education at PF UPJŠ is implemented through the Microsoft Teams platform resp. BigBlueButton (available at https://bbb.science.upjs.sk/b).

b) - Characteristics of the study programme information management (access to study literature according to Course information sheets, access to information databases and other information sources, information technologies, etc.).

The primary source of information provision for the doctoral study program Discrete Mathematics is the UPJŠ University Library (in the next UK UPJŠ), which - as a university-wide workplace - participates in the information provision of teaching and research activities of university employees and students, creates conditions to support the educational process and stimulating user environment. Currently, the UK strives to combine traditional library and information services with digital services. The library provides its services to almost 7,400 users (of which 5,000 are students) at 6 workplaces. As part of providing the educational process, the library builds, at its workplaces at individual UPJŠ faculties, a quality collection of study literature, professional literature, including journals - 233,000 library units, 88 titles of periodicals. Comfort in searching for literature is offered to students by the library and information system, which is constantly supplemented with new functionalities (possibility of reservation, access to the full texts of electronic books, etc.). A comprehensive overview of library and information services provided by UK UPJŠ can be found at https://www.upjs.sk/pracoviska/univerzitna-kniznica/sluzby/.

The Science Library is one of the oldest workplaces of the university library. At present, it provides its services in two separate places: as a study room, it serves users of the UPJŠ Faculty of Science at the premises of the chapel of St. Angela Merici (Angelinum Park No. 9); lending services together with the possibility of individual study are provided by the library opened in 2007 in the renovated premises of the student dormitory on Medická ul. no. 6. In the study of St. A. Merici has 46 study places available, in the library on Medická ul. no. 6 there are 17 study places. The library fund of the Natural Science Library consists of more than 58,000 library units. This fund serves about 1,400 registered users, of which about 200 are teachers and other faculty staff. The sale of the PF UPJŠ publishing production is carried out through a script shop and study literature located on Tr. SNP 1, Košice. The Natural History Library is constantly expanding the offer of electronic books. Prestigio and Amazon Kindle e-book readers are available in the Park Angelinum 9 study room and the library at Medická 6. The library stock is constantly supplemented and its average annual growth in recent years is more than 1000 library units. An important activity of the library is also the provision of access to professional databases (electronic information sources, see https://www.upjs.sk/pracoviska/univerzitna-kniznica/e-kniznica/). Study literature is available to students in electronic or printed form. Every year, the university prepares an editorial plan, within which scripts and other study materials are published. Teaching texts and study materials in electronic form can be provided by teachers to students through the Moodle environment.

The students of Discrete Mathematics programme can also use the services of a professional mathematics library located at the Institute of Mathematics, which falls under the administration of the Library of Faculty of Science. The study literature for this study programme was significantly enriched by the additions obtained through the ESF program DOKTORAND. During their studies, the students of mathematics also have at their disposal a partial library of the Institute of Mathematics with resources covering a wide range of mathematical disciplines; access to electronic information sources is provided within the intranet computer network of the faculty.

c) - Characteristics and extent of distance education applied in the study programme with the assignment to courses. Access, manuals of e-learning portals. Procedures for the transition from contact teaching to distance learning.

The standard form of education for the doctoral study program Discrete Mathematics is the full-time form. The distance form of education is used mainly in situations in which it is not possible to provide a full-time form (e.g. in case of pandemic restrictions imposed by the state or the UPJŠ management). In such exceptional cases, all teachers transfer to distance learning and proceed in accordance with the decision of the Rector of UPJŠ in Košice for the implementation of teleconferencing lectures (see Rector's Decision 22/2020). The transition from full-time to distance education as part of measures against the spread of COVID-19 virus infection is carried out according to current guidelines issued by the university (see also https://intranet.upjs.sk/op/op.Public.php?documentid=4067). An overview of available solutions at PF UPJŠ (of which MS Teams and BigBlueButton are currently the most frequently used) can be found at https://www.upjs.sk/elearning/distancne-vzdelavanie/nastroje/.

d) - Institution partners in providing educational activities for the study programme and the characteristics of their participation.

The university takes care to link knowledge with practice, which is supported by strong ties with important partners and organisations. The partners are officially associatied in the Career Club UPJŠ (https://www.upjs.sk/pracoviska/unipoc /career-club-upjs/). UPJŠ is a founding member of Košice IT Valley. The university also cooperates with other partners https://www.upjs.sk/univerzita/cinnost/medzinarodne-vztahy/clenstva/.

Partnerships of the Faculty of Science UPJŠ in Košice enabling the provision of educational activities of the study program:

- centers of excellence (https://www.upjs.sk/prirodovedecka-fakulta/centra-exc/),

- start-up projects (https://www.upjs.sk/prirodovedecka-fakulta/start-up/),

- Technicom University Science Park (https://www.upjs.sk/prirodovedecka-fakulta/technicom/),

- shared laboratories (https://www.upjs.sk/prirodovedecka-fakulta/spolocne-laboratoria/),

- Promatech Research Center (https://www.upjs.sk/prirodovedecka-fakulta/promatech/).

Providing the work of commissions of various types (joint study branch committees or the ones for the defense of dissertations), management of final theses and projects, long-term support for guarantors and teachers of the doctoral study program Discrete Mathematics is provided by partner workplaces of Košice universities creating the current basis of so-called Košice School of Graph Theory (Department of Applied Mathematics and Informatics, Faculty of Mechanical Engineering, TU, Department of Mathematics and Theoretical Informatics, Faculty of Electrical Engineering and Informatics, TU, Department of Applied Mathematics and Economic Informatics, Faculty of Economics, Faculty of Mining, Ecology, Management and Geotechnology).

e) - Characteristics of the possibilities for social, sports, cultural, spiritual and social activities.

The development of UPJŠ students is ensured not only by quality education, but also by social, sports, cultural, spiritual and social activities during their studies. An overview of what the university, its workplaces and also the city of Košice offer students can be found at https://www.upjs.sk/univerzita/kvalita/programy/#7. Sports activities for UPJŠ students are provided by the Institute of Physical Education and Sport (ÚTVŠ), which through the course Sports Activities offers a choice of 21 sports (https://www.upjs.sk/pracoviska/ustav-telesnej-vychovy/studenti-fakult-upjs/). Students can do sport activities not only within the compulsory or optional subject, but also beyond the credit form. In addition to the offered physical activities, students can participate in the university league in 4 sports (futsal, flotball, basketball, volleyball). The traditional addition to the ÚTVŠ offer are winter and summer courses (ski course, survival, cycling course, rafting on the river Tisza and exercise at sea coast). Another, much wider range of sports is offered by the TJ Slávia UPJŠ sports club. (http://www.upjs.sk/pracoviska/ustav-telesnej-vychovy/o-nas-utvs/tj-slavia-upjs-kosice/. There are 5 gyms available for students' sports, most of which have underwent substantial reconstruction in recent years. The gym is equipped for the needs of various levels - from beginners to advanced ones, and is regularly supplemented and innovated. In addition, the ÚTVŠ building has 4 tennis courts and 3 multifunctional concrete playgrounds, which students use mainly for sports games (for more details see https://www.upjs.sk/pracoviska/ustav-telesnej-vychovy/sluzby/telovychovne-objekty/) ÚTVŠ also regularly organizes university-wide sports events, such as University Sports Days (see https://www.upjs.sk/pracoviska/ustav-telesnej-vychovy/aktuality/uds-2019-sprava/) or sports competitions within Juniáles (see also https://www.upjs.sk/pracoviska/ustav-telesnej-vychovy/sportove-akcie-utvs/).

Social and social activities at UPJŠ and at the Faculty of Science include a number of events: annually organized Science Days (with a traditional trip to the Alpinka recreational area, https://www.upjs.sk/prirodovedecka-fakulta/sr/podujatia/alpinka/) and ScienceFest (https://www.upjs.sk/prirodovedecka-fakulta/sr/sciencefest/), matriculation ball (https://www.upjs.sk/prirodovedecka-fakulta/sr/podujatia/imatrikulacnyples/) or Juniales (organized by in the outdoor area of the UPJŠ Botanical Garden).

Spiritual care within UPJŠ is covered (within the complex operation in the environment of Košice universities) by the University Pastoral Center (http://upcke.sk).

f) - Possibilities and conditions for participation of the study programme students in mobilities and internships (indicating contact details), application instructions, rules for recognition of this education.

Comprehensive information on the offer of mobilities and internships and on the process of selecting candidates can be found at https://www.upjs.sk/univerzita/cinnost/medzinarodne-vztahy/, https://www.upjs.sk/prirodovedecka-fakulta/vonkajsie-vztahy/erasmusplus/. Mobility administration within the university takes place using the academic information system AIS2 (https://ais2.upjs.sk/). Within the scientific work on own projects resp. supervisors projects, students can be sent to partner universities and research institutions in Europe. Students can also use bilateral international mobility projects (eg. through the Slovak Academic Information Agency and the National Scholarship Fund). The conditions for the recognition of completed studies are regulated by the UPJŠ Study Regulations.

Contact person for mobility related to mathematics at PF UPJŠ:

prof. RNDr. Katarína Cechlárová, DrSc., katarina.cechlarova@upjs.sk

9. - Required abilities and admission requirements for the study programme applicants

a) - Required abilities and necessary admission requirements.

Graduates of master studies in Mathematics, Applied Mathematics or in a related field of study, as well as graduates of teacher training in combination with mathematics, may be admitted to the Discrete Mathematics study program.

The applicant is required to have knowledge of the following subjects in the scope of the first two degrees of university study:

Combinatorics and Graph Theory: Classical Combinatorics. Basic combinatorial principles. Recursive methods. Enumeration of combinatorial objects. Classical graph theory - coloring, independence, Hamiltonian graphs. Turán's theorem, Ramsey theorem. Graph algorithms. Directed graphs. Introduction to topological graph theory.

Discrete optimization and algebraic structures: Linear and integer programming. Theory of edge-labelled graphs and networks. Game theory. Systems theory. Operational analysis. Linear algebra. Ordered algebraic structures. Finite group theory. Finite fields. Boolean algebras.

Emphasis is placed on subjects close to the topic in which the candidate is interested. The range of questions is determined by the members of the commission based on the requirements of the trainer. A necessary condition for admission is the ability to work with professional mathematical text in English.

Summary information for applicants for the doctoral study program Discrete Mathematics can be found at https://www.upjs.sk/prirodovedecka-fakulta/studium/d-studium/ and relevant subpages.

b) - Admission procedures.

Admission for doctoral studies is regulated by the documents "Principles of Admission Procedure for Studies at Pavol Jozef Šafárik University in Košice" and "Study Regulations for Doctoral Studies at Pavel Jozef Šafárik University in Košice" (https://intranet.upjs.sk/op/op.Public.php? documentid = 4414 or https://www.upjs.sk/public/media/15322/studijny-poriadok-doktorand-upjs-maj-2019-dopl.pdf).

The entrance examination takes place in front of an admissions committee appointed by the dean. The chairman of the at least four-member committee is the guarantor of the study program and the chairman of the commission for the corresponding branch of study. Other members of the admissions committee are supervisors nominated by the guarantor which have assigned topics for the admission procedure for doctoral studies. In the case of an applicant's admission procedure on a topic announced by an external educational institution, a representative of the external educational institution is also a member of the admission committee.

During the admission procedure, the commission will set time for the candidates for written preparation, followed by an oral interview on defined topics and verification of knowledge of a foreign language.

Based on the outcome of the interview, the committee will prepare the final ordering of candidates who have met the conditions for admission and, where appropriate, will explicitly appoint candidates who have not met the conditions. The reports of the entrance examination are sent by the chairman of the committee to the dean of the faculty, who, based on the results of the entrance examination, decides on the admission of the candidate within 30 days from the date of the entrance examination.

c) - Results of the admission process over the last period.

2021/22 Plan

Applicants 1

Accepted 1

Enrolled 1

2020/21 Plan

Applicants

Accepted

Enrolled

2019/20 Plan

Applicants 2

Accepted 2

Enrolled 2

2018/19 Plan

Applicants 2

Accepted 2

Enrolled 2

2017/18 Plan

Applicants 1

Accepted 1

Enrolled 1

10. - Feedback on the quality of provided education

a) - Procedures for monitoring and evaluating students' opinions on the study programme quality.

The general framework for monitoring and evaluating students' opinions on the quality of the doctoral study program Discrete Mathematics is determined by the internal quality evaluation system at UPJŠ (https://www.upjs.sk/prirodovedecka-fakulta/vnutorne-hodnotenie/); monitoring and evaluation of students' opinions on the quality of the study program is carried out through a questionnaire survey (https://www.upjs.sk/prirodovedecka-fakulta/studium/anketa/studentska-anketa/, https://www.upjs.sk/univerzita/kvalita/overovanie/prieskumy/). Quality indicators and results of quality monitoring at UPJŠ in Košice and its components are publicly available at https://www.upjs.sk/univerzita/kvalita/indikatory/.

b) - Results of student feedback and related measures to improve the study programme quality.

The university informs about the results of the evaluation of the quality of educational activities on its website https://www.upjs.sk/univerzita/kvalita/overovanie/prieskumy/. The procedure ensuring the projection of the results of the feedback evaluation from the interested parties into the adoption of measures to increase the quality of the study program will be part of the process of harmonizing the UPJŠ internal system with SAAVŠ accreditation standards within the statutory transitional period. Student feedback and the related adoption of regulations to improve the quality of the study program will also be the subject of regular meetings of the Discrete Mathematics Study Programme Board.

c) - Results of graduate feedback and related measures to improve the study programme quality.

UPJŠ and its faculties regularly conduct their own questionnaire surveys on the employment of university graduates in order to improve the profile of graduates, closer connection of studies with practice and improve the position of graduates in the labor market. UPJŠ Faculty of Science maintains contacts with its graduates through the Alumni Club - Alumni Space (implemented as part of the AIS2 information system, see https://ais2.upjs.sk/ais/absolvent.html; registered graduates can fill in a short employment feedback questionnaire after logging in their application) resp. through the cooperating association OZ Prírodovedec (https://www.upjs.sk/prirodovedecka-fakulta/informacie-pre-ostatnych-zaujemcov/verejnost-a-media/prirodovedec/).

11. - References to other relevant internal regulations and information concerning the study or the study programme student

(e.g study guide, accommodation regulations, fee directive, guidelines for student loans, etc.).

All information on study programs, which provide an overview of relevant internal regulations, fees or student loans, are available to the public and regularly updated on the website https://www.upjs.sk/univerzita/kvalita/programy/#7 and also in information for UPJŠ students, which can be found at: https://www.upjs.sk/studium/. Specific information for studies at the UPJŠ Faculty of Science in Košice is published by the faculty at https://www.upjs.sk/prirodovedecka-fakulta/studium/.