VILNIUS UNIVERSITY

STUDY FIELD MATHEMATICS SECOND-CYCLE STUDY PROGRAMME

MATHEMATICSCODE: 621G10001

SELF-EVALUATION REPORT

Pro-rector of Vilnius University ……..............…………… Assoc. Prof. Dr Valdas Jaskūnas(signature)

Head of self-evaluation group .......…………………….. Prof. Dr Artūras Štikonas(signature)

Vilnius14 February 2017

Key data on the study programme

Title Mathematics

Code 621G10001

Study area Physical Sciences

Study field Mathematics

Kind of study University studies

Language of instruction Lithuanian, English

Study cycle Second-cycle

Mode of study and length in years Full-time (2 years)

Scope in credits 120

Qualification awarded Master of Mathematics

Date of registration and Order No 1997-05-19, No.565

Abbreviations used in the Self-Evaluation Report:

SER - Self-Evaluation ReportSP - Study Programme SEG - Self Evaluation Group

2

Composition of the self-evaluation group (SEG)* and their responsibilities

Name, surname, contact information

Position Area and scope of responsibility in SEG

Artūras Štikonas+370 6 188 6910arturas.stikonas@mif.vu.lt

Professor at department of Differential Equations and Numerical Mathematics

Head of the Study Programme Committee, Purpose and learning outcomes of the study programme

Artūras Dubickas+370 6 052 5317arturas.dubickas@mif.vu.lt

Professor,Head of departmentof Probability Theory and Number Theory

Academic staff

Paulius Drungilas+370 5 219 3080paulius.drungilas@mif.vu.lt

Vice-dean for science,Assoc. prof. departmentof Probability Theory and Number Theory

Study Programme management, Introduction

Mindaugas Skujus+370 5 219 3057mindaugas.skujus@mif.vu.lt

Vice-dean for international affairs and publicity of information,lecturer at at departmentof Differential Equations and Numerical Mathematics

Study process and assessment

Gailė Paukštaitė+370 6 830 6413gpaukstaite@gmail.com

3rd year doctoral student of Mathematics study programme

Curriculum design

Gediminas Ziezys+370 6 293 0658vilkabrolis@gmail.com

1st year master student of Mathematics study programme

Facilities and learning resources

Romualdas Zovėrzoves@gmail.com

Head of Asset Allocation Division in Investment management department, Banking Service, Bank of Lithuania

Self-evaluation summary review and advisory function to provide comments

*Approved by the Dean of the Faculty (Order No. D-43, 20 October 2016).

Schedule of task implementation

Task Date of implementation

Collecting all relevant information for the self-evaluation 2016-11-23

First draft of the text of SER 2016-11-26

Discussing the first draft of SER focusing on three areas of evaluation: purpose and learning outcomes, curriculum design and academic staff

2016-12-03

Discussing the first draft of SER focusing on three areas of evaluation: facilities and teaching/learning resources, study process and assessment of academic progress, SP management

2016-12-10

Presentation of the SER to the teaching staff, social partners of the SP, discussing their feedback 2016-12-17

Final draft of SER 2016-12-31

3

Table of Contents

INTRODUCTIONANALYSIS OF THE STUDY PROGRAMME

1. Purpose and learning outcomes of the study programme2. Curriculum design3. Academic staff4. Facilities and learning resources5. Study process and assessment6. Study Programme management

APPENDICES

4

INTRODUCTION

Vilnius University (hereinafter also University or VU), founded in 1579, is the oldest and largest institution of higher education in Lithuania. The University management structure is defined in the Statute of Vilnius University (approved 6 May 2014 by Law of the Republic of Lithuania No XII-862), which stipulates that the University community shall exercise its self-governance through the bodies of governance of the University: the Senate, the Council and the Rector. As of 1 October 2016, the University had 3662 employees (including 1370 teaching staff and 1164 research staff) and had 20864 students. The University comprises 23 core academic units: twelve faculties, seven institutes (with two of them of faculty status), four research and study centres and seven core non-academic units.

The University implements study programmes of three study cycles in the areas of the humanities, social, physical, biomedical and technological sciences; the total number of undergraduate (bachelor) study programmes is over 87, the number of (graduate) master and integrated study programmes exceeds 123. Doctoral students may enrol in almost 30 and residents in more than 50 study programmes.

The Faculty of Mathematics and Informatics (hereinafter also Faculty) was founded in 1965 as The Faculty of Mathematics and Mechanics. In 1971 at the Department of Applied Mathematics a new study program has been started - Informatics, although at that time it was called Science of Calculating Machines or Science of Computing. In 1998 the Faculty of Mathematics and Mechanics was renamed into the Faculty of Mathematics and Informatics. The Faculty operates in accordance with the Statute of Vilnius University. The Faculty is headed by the Faculty Council and the Dean. Presently, the Faculty comprises 10 departments (Computer Science I, Computer Science II, Didactics of Mathematics and Informatics, Differential Equations and Numerical Mathematics, Econometric Analysis, Mathematical Analysis, Mathematical Computer Science, Mathematical Statistics, Probability Theory and Number Theory, Software Engineering) and 3 centres (Digital Science and Computing Centre, Information Technology Research Centre, Mobile Application Laboratory). They are engaged in research and studies. The main research areas of the Faculty include Fundamental and Applied Mathematics, Informatics and Information Technologies. The journals published by the Faculty are as follows: Proceedings of the Lithuanian Mathematical Society, Ser. A; Nonlinear Analysis: Modelling and Control. The research results are disseminated in national and international conferences.

The Faculty implements 8 first cycle (Bioinformatics, Information Technologies, Informatics, Software Engineering, Mathematics and Applications of Mathematics, Econometrics, Financial and Actuarial Mathematics, Statistics) and 8 second cycle (Computer Modelling, Informatics, Software Engineering, Mathematics, Modern Didactics of Mathematics, Econometrics, Financial and Actuarial Mathematics, Statistics) study programmes. The Faculty also implements doctoral studies in the fields of Mathematics and Informatics.

Presently, the Faculty has 208 staff members (teaching, research and administrative), including 28 professors and chief research fellows, 38 associate professors and senior research fellows, 45 lecturers with a PhD, 56 lecturers, assistant lecturers and 2 junior research fellows, 39 administrative staff (more detailed: about 1820 Bachelor students, about 290 Master students and about 40 PhD students).

The study programme of Mathematics is implemented by the Department of Differential Equations and Numerical Mathematics and Department of Probability Theory and Number Theory. The programme has been implemented for 19 years. The Programme went through external assessment in 2011. The overall assessment of the programme was positive and it was accredited for 6 years. The Assessment Report Recommendations and Summary are included in Appendix No.5 and the changes induced thereof are discussed in below in appropriate sections.

5

ANALYSIS OF THE STUDY PROGRAMME

1. Purpose and learning outcomes of the study programme1.1. Purpose and learning outcomes of the study programme. Learning outcomes across the

course units (modules)The purpose of the study programme is to train qualified specialists who have advanced

knowledge in pure and applied mathematics as well as strong problem solving skills so that they can successfully tackle challenging scientific, industrial, economic problems. The competences and learning outcomes of the study programme (hereinafter also SP) are as follows:

Generic competences of the SP Learning outcomes of the SP

1.Abstract and critical thinking skills

1.1 Will be able to think abstractly for solving various problems and to decide whether existing methods are applicable.

1.2 Will be able to apply critical thinking skills to solve problems that can be modelled mathematically.

2. Life-long learning skills 2. Will be able to acquire new knowledge, to examine, understand and master the new non-standard methods.

3.Communication and collaboration skills

3.1 Will be able clearly communicate mathematical ideas, research ideas in appropriate contexts both orally and in writing to a range of audiences.

3.2 Will be able to work independently and in interdisciplinary team, generate ideas, integrate knowledge and skills.

Subject-specific competences of the SP

Learning outcomes of the SP

4.Advanced theoretical knowledge of mathematics (theory, methods)

4.1 The student has advanced and in-depth knowledge and understanding of complex theories, models, methods in areas of pure and/or applied mathematics.

4.2 Will be able to use modern mathematical methods for solving mathematical problems.

4.3 Will be able to understand latest results and trends of knowledge in selected branch of mathematics.

5.Ability to apply mathematical knowledge and skills

5.1 Will be able to create mathematical models of the analysis of real-world processes.

5.2 Will be able to analyze the simulation results of the search for optimal solutions, assessing the adequacy and accuracy of the model, if needed to improve models.

6.Ability to perform mathematical research

6.1 Will be able to conduct a primary research of scientific literature in their chosen field of investigation.

6.2 Will be able to use pure mathematical or applied methods to understand some aspects of the frontiers of mathematical knowledge.

6.3 Will be able to select and use specific software for research or practical activity data needed for the synthesis, processing and analysis.

6.4 Will be able to present mathematical results of the research and to describe it in the modern high-level mathematical language.

6

Learning outcomes of the SP Mathematics across course units (modules) are presented in Study Plan (see 2nd part of SER “Curriculum design”)

All learning outcomes were updated according to the Confirmation of the Description of Study Programme in Mathematics approved by Order No V-813 of the Minister of Education and Science, July 23, 2015 1.

Upon completion of the SP of Mathematics, a student may engage in further studies in doctoral (PhD) studies in mathematics, informatics and related areas of physical sciences.Students will be able to work in science and education institutions, high-technology industries, agencies of data analysis and social investigations, management institutions. Graduates will also be able to pursue a career in any other sphere, where their mathematical knowledge, analytical skills and ability to use specialized software are needed.

A qualification obtained upon the completion of the second-cycle SP Mathematics is in conformity with qualification VII as specified in the Qualifications Framework of the Republic of Lithuania.

1.2. Availability of information about the purpose and learning outcomes of the SP

Information on the purpose, learning outcomes, content of the SP and admission requirements is accessible on the internet to all prospective students, academic community and the society at large. The information is freely accessible at:

● In the catalogue of study programmes of Vilnius University on its official website2.● On the official website of the Faculty 3;● On the official website of the University intended to prospective students4.● On the official website of the Open System of Providing Information, Tutoring and

Vocational Orientation, or AIKOS (a Lithuanian acronym)5

Every year, the University issues a special publication intended for the dissemination of information about the second cycle study programmes Kviečia Vilniaus universitetas. Antroji pakopa. (Vilnius University is calling. Second cycle study)6

The promotion is realized during a variety of promotional events, including meetings in the Faculty of Mathematics and Informatics, where teachers offer advices on further studies, also in the internet, where all interested in studying in Vilnius University can easily access it, etc.

Every year the SP, its purpose/s and learning outcomes are introduced at the following promotional events:● Vilnius University Discovery Days, when the administration, the teaching staff and the students of

the Faculty of Mathematics and Informatics deal with study-related issues on the individual basis;● Study Fair Mokymasis, studijos, karjera (Learning, Studies and Career) held at LITEXPO, where

all information related to the studies in the SP is given by the administration, the teaching staff and the students of the Faculty of Mathematics and Informatics;

● During Vilnius University teachers’ visits to other higher schools, where SP Mathematics is introduced.In order to gain capable master students programme, executors popularize mathematics:

● by presenting the programme during the science and study days, and at the various student festivals;

● by actively cooperating with capable students; .

1 https://www.e-tar.lt/portal/lt/legalAct/96ceca70311f11e5b1be8e104a1454782 https://klevas.vu.lt/pls/pub/public_ni$www_progr_app.show3 http://mif.vu.lt/lt3/studijos/studiju-programos/ma-studiju-programos/matematika4 http://www.vu.lt/kviecia/5https://www.aikos.smm.lt/Registrai/Studiju-programos/_layouts/15/Asw.Aikos.RegisterSearch/ObjectFormResult.aspx? o=PROG&f=Prog&key=4378&pt=of&ctx_sr=NOAJZ8Kgp7rQy5e34aTmdDoVpQI%3d6 http://www.vu.lt/kviecia/rinkis-studijas/priemimas/2-pakopos-studijos

7

● by presenting department‘s scientific work and study perspectives in the science popularization releases.

1.3. Information about the revision of learning outcomes and participation of social partners in the SP implementation

Each semester the meetings (one or two) of the study programme committee (including one social partner) are organised. During such meetings we have discussions concerning the improvement of SP implementation, where recommendations from the students, social partners and the previous evaluation report are addressed. The last year common meetings were organised for the first (Mathematics and Applications of Mathematics) and the second (SP Mathematics) cycles study programme committees.

Last time learning outcomes were revised in 2016 during the self analysis in order to make the improvements considering the recommendations from students and social partner, as well as to match the requirements specified in “Mathematics study area description” (Approved by the Education Minister of Lithuania, order number V-813 8. The clear need of advanced communication abilities of the students was highlighted by social partners; therefore study programme committee (SPC) involved the training of communication abilities during several courses of the study program. Clear communication of mathematical ideas, research ideas in appropriate contexts both orally and in writing to a range of audiences was specified as one of the graduates’ learning outcome. All the improvements of the learning outcomes were adopted taking into account the description of Mathematics study field programs - “Mathematics study area description”, approved by the Ministry of Education and Science of the Republic of Lithuania7. This document lists the minimum set of skills and competences that each graduate with a Mathematics diploma must possess (more information in Section 1.4). Further improvements of the learning outcomes are planned as soon as additional feedback from the students, graduates and social partners is available.

1.4. Conformity of learning outcomes to the requirements specified in international and domestic documents focusing on academic and professional standards

Generic/Subject-specific competences and learning outcomes were formulated taking into account the concept of Mathematics and the description of knowledge and abilities necessary for Mathematics according to national and international documents focusinh on academic and professional standarts.

Firstly, the list of learning outcomes was designed with reference to the major descriptors defining levels in the European Qualification Framework8 and so-called “Dublin Descriptors”. Qualifications are based on second-cycle graduates’ advanced knowledge and understanding in the field of study, its application, making judgements, communication and lifelong learning skills. The learning outcomes of SP ensure the conformity with these international requirements.

Secondly, study program and its learning outcomes comply also with the descriptions of Lithuanian Qualifications Framework,9 describing the 7th level (or second-cycle study programs) of qualifications, by putting emphasis on extensive theoretical knowledge that provides basis or opportunity for originality; creative thinking in application of research findings complex theoretical knowledge based on the results of new fundamental and applied research; making independent solutions focused on operational excellence and improvement in new or unfamiliar environment within broader (interdisciplinary) contexts related to the study field. Similar qualifications of second-cycle study programs are indicated in the Regulation of Study Programs of Vilnius University (2012)10. Finally, the important part of competences was based on the description of Mathematics study field programs (already mentioned in Section 1.3) where five major groups of competences are specified: theoretical knowledge in Mathematics, ability to conduct research, subject-specific skills, social and individual

7https://www.e-tar.lt/portal/lt/legalAct/96ceca70311f11e5b1be8e104a145478 (in Lithuanian)8 https://ec.europa.eu/ploteus/content/descriptors-page9http://www.kpmpc.lt/10 goo.gl/0drSBg

8

skills. Even if implementation and ahcievements of the new learning outcomes take time, all the above mentioned standarts were involved when creating a list of learning outcomes of SP of Mathematics. This helped to crarify the information of study programme for students and ensure consistency of delivery across study-units and programmes.

1.5. The SP in the context of other study programmes implemented by VU and other universities

The study programmes of the Mathematics field at master level are accomplished by the faculties of six Lithuanian universities: Vilnius University (VU) (Mathematics, Financial and Actuarial Mathematics, Vilnius Gediminas Technical University (VGTU) (Technomathematics), Kaunas University of Technology (KUT) (Applied Mathematics), Vytautas Magnum University (VMU) (Applied Mathematics), and Šiauliai University (ŠU) (Mathematics).

The programme Mathematics (ŠU) is proposed for preparation of high level teachers for secondary schools and colleges of corresponding districts, therefore, it includes education science subjects; thus the study of fundamental mathematics is not deep. The programmes Applied Mathematics (KUT and VMU) are entirely preparing masters of applied mathematics, all subjects of those programmes have various aspects of applications of mathematics. The programme Technomathematics (VGTU) joins the above programmes Applied Mathematics, the most of time is devoted to various mathematics models, differential equations and Numerical Mathematics. In the programme Financial and Actuarial Mathematics (VU) together with financial and insurance subjects some subjects of pure mathematics are also proposed.

VU master study programme Mathematics differs essentially from all other study programmes of the mathematics field at the master's level in Lithuania because it is directed to in-depth study of fundamental mathematical subjects with tendency to continue postgraduate studies.

The programme provides a solid background applicable branches of mathematics (differential equations, number theory, probability theory), develops necessary skills for research and applications.

Courses of Pure Mathematics in Study Programme make about two-thirds of the course. Much attention is paid to the theory of various equations (functional, differential, integral, stochastic) and various methods (numerical, variational, asymptotic) for solving such equations. More extensive studies are implemented in Number theory, Measure theory and Probabilistic models.

Scientific research in number theory, differential equations and numerical analysis is realized.

1.6. Strengths and weaknesses of the area under evaluation and improvement measures to be taken

Strengths:● The programme is the only one in Lithuania that provides Master studies in Pure

Mathematics. Students obtain the in-depth knowledge and understanding of complex theories, models, methods in the areas of pure and/or applied mathematics;

● Students can obtain modern scientific knowledge both in lectures and in scientific seminars; ● Employers often ask and appreciate specialist, who have advanced mathematical knowledge,

programming and mathematical skills;● Purpose and learning outcomes of the study programme are clearly stated and provide

students with clear information when choosing the SP;● Study program develops skills highly desirable in the current jobs market. According to

various sources (e.g., careercast.com, linkedin.com) the demand for math-skilled specialists is high and will increase in future.

Weaknesses:● It is well known that there are many areas in the science of Mathematics, therefore, it is

impossible to acquire an in-depth knowledge in all of them in only two years period;● Advertisement of study program of Mathematics is rather limited.

9

Improvement measures:● SP of Mathematics must be oriented to the several fields of mathematics (differential

equations, probability theory, number theory) that are successfully developed in Lithuania, having supervisors for further postgraduate studies.

● More strategic advertisement of the second-cycle SP of Mathematics in other Universities is being planned.

2. Curriculum design

2.1. Study plan, conformity of curriculum design with the provisions of legal acts

The curriculum design of the currently implemented study programme of Mathematics is in conformity with the General Requirements for Master Study Programmes approved by Order No V-826 of the Minister of Education and Science 3 June 2010, the Regulation of Study Programmes of Vilnius University approved by Decree No SK-2012-12-4 of Vilnius University Senate Commission 21 June 2012 and a description of the study field of Mathematics approved by Order No V-813 of the Minister of Education and Science of the Republic of Lithuania 23 July 2015.

Table 2.1. The conformity of the SP of Mathematics to the general requirements of the second cycle study programmesRequirements In the study programme

The scope of the second cycle study programme shall be between 90 and 120 credits.

120 credits

The total number of course units per semester shall be no more than 5. 5 units per semesterA student’s individual work shall make no less than 30% of each course unit. at least 43%Course units within the study field shall make at least 60 credits; their content shall be of higher quality level than corresponding first-cycle course units within the same study field.

Course units within the study field take 78 credits; their content is of a higher quality level than a corresponding first-cycle course units within the same study field. For example, Functional Analysis for the first-cycle studies analyzes function spaces but the Supplementary Chapters of Functional Analysis, the corresponding course of Functional analysis in the second-cycle studies, investigates in the operators, mapping one function space to another.

Optional course units offered by the university are intended for specialized studies and shall make no more than 30 credits.

30 credits

The scope of the graduation thesis shall be at least 30 credits. 30 credits

10

STUDY PLAN (full-time studies)(COMPETENCES AND LEARNING OUTCOMES ACROSS COURSE UNITS (MODULES))

Cod

e

Cou

rse

units

[link

to u

nit

desc

ript

ion]

Cre

dits

Stud

ent's

w

orkl

oad

Con

tact

hou

rs

Self-

stud

y ho

urs Competencies

General competencies Subject-specific competencies1. 2. 3. 4. 5. 6.

Learning outcomes

1.1 1.2 2 3.1 3.2 4.1 4.2 4.3 5.1 5.2 6.1 6.2 6.3 6.4

1st YEAR 60 1600 725 875

SEMESTER 1 30 800 363* 437*Compulsory course units

MM11FA Supplementary Chapters in Functional Analysis 6 170 102 68 X X X X X X X

MM11MW Mathematical Writing at Higher Level 6 160 72 88 X X X XMM11FS Function Spaces 6 150 56 94 X X X X X X

Optional course unitsMM11PC0 Probabilistic Combinatorics 6 160 72 88 X X X X X X

MM11ANT0 Analytic Number Theory 6 160 66 94 X X X X X X XMM11IE0 Integral Equations 6 160 72 88 X X X X X X X

MM11MMF0 Mathematics in Modern Finance 6 160 56 104 X X X X X XSEMESTER 2 30 800 362 438

Compulsory course unitsMM12PDE Partial Differential Equations 6 160 86 74 X X X X X X X

MM12PTMS Probability Theory and Mathematical Statistics 6 160 68 92 X X X X X X XMM12PC Parallel Computing 6 160 64 96 X X X X X X X

Optional course unitsMM12DS0 Dynamical Systems 6 160 72 88 X X X X X X

MM12SPT0 Stochastic Processes Theory 6 160 72 88 X X X X X XMM12SDE0 Stochastic Differential Equations 6 160 72 88 X X X X X X XMM12NM0 Numerical Methods for Differential Equations 6 160 72 88 X X X X X X X X X

2nd YEAR 60 1600 394 1206

SEMESTER 3 30 800 330* 470*Compulsory course units

MM23SP Packages of Statistics 6 160 72 88 X X X XMM23AA Abstract Algebra 6 160 72 88 X X X X X

Optional course units

11

MM23FSR1 Fundamentals of Scientific Research. Problems of Number Theory and Probability Theory 6 160 48 112 X X X X X

MM23FSR2 Fundamentals of Scientific Research. Models of Mathematical Physics 6 160 48 112 X X X X X X

MM23RM0 Insurance Probability Risk Models 6 160 64 96 X X X X X X XMM23WCM0 Weak Convergence of Measures 6 160 70 90 X X X X X X

MM23GT0 Graph Theory 6 160 72 88 X X X X X XMM23NSE0 Mathematical Theory of Navier-Stokes

Equations 6 160 68 92 X X X X XMM23VM0 Variational Methods for Nonlinear

Phenomenons 6 160 64 96 X X X X X X X XMM23AM0 Asymptotic Methods for Partial Differential

equations 6 160 70 90 X X X X X X

SEMESTER 4 30 800 64 736Compulsory course units

MM24MT Master’s Thesis 25 670 32 638 Х Х Х Х Х Х Х Х Х Х Х Х XOptional course units

MM24MTS1 Master’s Thesis Seminar in Probability Theory and Number Theory 5 130 32 98 X X X X X

MM24MTS2 Master’s Thesis Seminar in Differential Equations 5 130 32 98 X X X X X

* Calculation based on their optional subjects or optional studies by taking the average number of hours. Grey color marks units of study fields

Orange color marks master thesis: preparation and defense matters

12

2.2. Principles of curriculum design and rationale of the SPThe greater revision of the programme was in 2010. Possibilities to take optional courses were

added. Now up to 42 credits of courses can be chosen freely by student. Few courses were moved to bachelors SP Mathematics and Applications of Mathematics (for example, Measure and integral theory), some courses were removed (for example, Object oriented programming and data structures, Optimization methods in economics, Financial models with MS Excel), few new courses were added (for example, Function Spaces, Parallel Computing, Graph Theory, Integral Equations, Abstract Algebra). The changes were made according to the recommnedations of previous self-evaluation (2010) and common decisions of SPC of Mathematics and of SPC of Mathematics and Mathematics Applications.

The scope of the SP of Mathematics is 120 credits; the length of the SP is two years. The SP consists of the following blocks: compulsory course units developing the main subject-specific competences of the SP (78 credits) and optional course units (42 credits). 42 credits are allocated for higher specialization in the same study field (30 credits) and course units, those are not of high specialization (12 credits). Mentioned 30 credits are composed of optional course units of 6, 12,12 credits within the first, second and third semester, respectively. 12 credits for course units of not high specialization are obtained as follows. In the first semester, students choose two optional course units from Differential Equations (Integral Equations, Mathematics in Modern Finance) or two courses from Probability Theory and Number Theory (Probabilistic Combinatorics, Analytic Number Theory). Here Probabilistic Combinatorics and Mathematics in Modern Finance are not of high specialization. In the third semester, students choose one optional course of Fundamental Scientific Research, which is not of high specialization as well.

In the first semester, Supplementary Chapters in Functional Analysis, Mathematical Writing at Higher Level, Function Spaces and optional course units give advanced and in-depth knowledge of mathematics, develop critical and analytical thinking. In the second semester, Partial Differential Equations, Probability Theory and Mathematical Statistics, Parallel Computing and optional course units also develop mentioned abilities integrating mathematical models of real world processes and their analysis, selecting and using software for research or practical activity, analyzing models and modern mathematical methods, their applicability. In the third semester, course units develop other analytical and practical skills as well as abilities to clearly communicate mathematical ideas, integrate mathematical skills analyzing textbooks, doing laboratory works and presentations, select literature, understand and master mathematical models and modern mathematical methods. In the last semester, students prepare graduation theses and participate in seminars, where students demonstrate obtained advanced knowledge and mathematical skills using higher-level mathematical language, modern methods and selected software for solution to problems.

After previous self-evaluation two existing study plans (for two branches: Differential Equations and Numerical Mathematics and Probability Theory and Number Theory) were combined into one. More possibilities to take elective courses were added, compared with previous study programme plan of Mathematics. In the study programme we included the compulsory course Packages of Statistics on different data analysis tools (SAS, SPSS, etc.) that are often used in practice (for students without previous knowledge of such tools), and optional course Parallel Computing in order to match the need of labor market. Few courses were moved to bachelors SP Mathematics and Applications of Mathematics (for example, Measure and integral theory), some courses were exchanged with the more appropriate ones (for example, Object oriented programming and data structures, Optimization methods in economics, Financial models with MS Excel were removed and Function Spaces, Parallel Computing, Graph Theory, Integral Equations, Abstract Algebra were added).

13

2.3. Study methods, proportion between contact hours and students’ individual work

Study methods as lectures, seminars and presentations, tutorials and supervision, practical and laboratory work, individual reading, modelling, tests, examinations, graduation thesis are used for the study process.

● Lectures contribute advanced and in-depth knowledge and understanding of complex theories, models, methods in areas of pure and/or applied mathematics. They also develop abilities to think abstractly and critically for solution to various problems, to use modern mathematical models and decide whether existing models are applicable as well as to analyze and present mathematical results in the modern high-level mathematical language.

● Seminars and presentations teaches how clearly communicate mathematical ideas, research ideas in appropriate contexts both orally and in writing to a range of audiences as well as how present mathematical results of the research and described in the modern high-level mathematical language. Abilities to understand latest results and trends of knowledge in selected branch of mathematics are also developed.

● Tutorials and supervision training of abilities to use modern mathematical methods for solving mathematical problems are also involved. Training of abilities to understand and apply modern mathematical methods for solving mathematical problems. Abstract thinking skills required to find the best ideas and approaches for different classes of problems. Presenting solutions in a clear way understandable to other people.

● Practical and laboratory work assist in developing abilities to work independently and in interdisciplinary team, generate ideas, integrate knowledge and skills as well as to select and use specific software for research or practical activity data needed for the synthesis, processing and analysis. It also leads to an intercommunication among students, where they discuss, develop their abilities to present clearly their knowledge and ideas, formulate problems.

● Individual reading as well as lectures develop abilities to think abstractly for solving various problems and decide whether existing methods are applicable. It also evolve acquirement of new knowledge, trains to examine, understand, master the new mathematical methods and conduct primary research of scientific literature in their chosen field of investigation.

● Modelling trains abilities to use abstract and critical thinking for solving problems that can be modelled mathematically, also to examine, use modern mathematical methods, decide whether methods are applicable, understand latest results and trends of selected branch of mathematics. It teaches students how to create mathematical models of the analysis of real-world processes as well as to analyze the simulation results of the search for optimal solutions, assessing the adequacy and accuracy of the model, if needed to improve models. Skills to select and use specific software for research or practical activity data needed for the synthesis, processing and analysis are also developed.

● Tests and examinations grow acquirement of new knowledge, understanding and skills to master the new mathematical methods. They also trains abilities to clearly communicate mathematical ideas, research ideas in appropriate contexts, analyze simulation results, conduct primary literature searches, develop abstract and critical thinking.

● Preparation and presentation of graduation thesis require advanced and in-depth knowledge of understanding of complex mathematical theories. It also needs abilities to analyze the real-world processes and modelling skills. Usage of modern mathematical methods, abstract and critical thinking for solution to various problems are also necessary. Abilities to communicate research ideas and results clearly according to the audience, present results in modern high-level mathematical language, train qualified specialists who have advanced knowledge in pure and applied mathematics as well as strong problem solving skills developed according to challenging scientific, industrial, economic problems are required.

Proportion between contact hours and student’s individual work is presented in Table 2.2. The higher proportion of student’s individual work hours, firstly, creates environment, where students obtain advanced in-depth knowledge and understanding of pure and applied mathematics, develop their abilities

14

to use abstract and critical thinking for solution to various problems and decide whether existing methods are applicable. Individual work involve preparation for lectures, seminars, presentations for seminars, individual reading, homeworks, literature searches, analysis of various problems, tests, exams and preparing the graduation thesis. Working individually, student inevitably understands and experiences the need of acquirement of new knowledge, it leads to communicate with lecturers, other students, participation in seminars and literature searches, to present knowledge and formulate problems, ideas clearly for other students, supervisors and audience. During individual work hours students solve problems, formulated by lecturers or supervisors, conduct literature searches and apply modern methods, test, analyze results.

Table 2.2. Proportion between contact hours and students’ individual work Compulsory course units Optional course units

Semester Contact hours

Individual work, hrs

Total Contact hours

Individual work, hrs

Total

1 230 250 480 133 187 3202 218 262 480 144 176 3203 144 176 320 188 292 4804 32 638 670 32 98 130

Total 624 1326 1950 497 753 1250

2.4. Requirements for graduation theses

Graduation theses are prepared in accordance with the Procedure for the Preparation, Defence and Safekeeping of Graduation Theses approved by Decree No R-446 of Vilnius University Pro-Rector on 17th of November, 2015. Other information related to students’ graduation theses and other papers are accessible on the website of the Faculty of Mathematics and Informatics11. Here we give more regulations and recommendations for the graduation theses, i.e., the regulations for the title page, the bibliography, general format, and so on. The criteria for assessing the graduation theses are also given here. The student has 10 minutes for the presentation of his/her work and 5 minutes for questions from the defence comittee. Later he/she can be asked questions related to his/her work or to mathematics in general.

The aim of the master thesis is to present student’s ability to apply acquired knowledge and problem solving skills, select and use scientific literature (present, analyze and etc.), apply and/or modify mathematical methods, solve personally mathematical problems or real world problems that can be described mathematically, present conclusions or recommendations and graduation thesis in modern high-level mathematical language.

By working on their graduation theses, students develop independent research skills that are in detail explained in the description of the master‘s thesis unit. The recommended scope of the graduation thesis is not strictly determined, it depends on the theme of the graduation thesis and obtained results. For example, if results are short, original and important, the graduation thesis can be of several pages only.

The theses are supervised by the academic staff of the SP, sometimes consultants are invoked. The topics of the theses are generally provided by the academic staff of SP, however, students are welcome to offer their own subjects for the thesis. If there is a request from the labor market of mathematical research to be implemented, the topics are also presented for the students, giving the ability to make the reseach of the real-life problems. Topics for the theses are chosen by the students after having discussed them with potential supervisors and approved by the Department of Differential Equations and Numerical Mathematics and Department of Probability Theory and Number Theory.

Preparation of the graduation thesis consists of individual consultations lead by the supervisor, participation in seminars, participation and presentations in Master’s Thesis seminars and, finally, writing the graduation thesis. The defence of the graduation thesis takes about 15 minutes for a student. Each student presents Master’s thesis in the open defence meeting, where participants and commission of the defence can ask a student about the presentation, graduation thesis or other knowledge of

11 http://mif.vu.lt/lt3/struktura/katedros/ttsk#informacija-studentams15

mathematics. Finally, commission evaluates the presentation of Master’s Thesis considering the opinions of the supervisor and reviewer.

There were no changes in the order of the defence of graduation thesis during the analyzing period.

2.5. Strengths and weaknesses of the area under evaluation and improvement measures to be taken

Strengths:● Important changes of the curriculum were implemented according to the recommendations of

the students and social partners.● A large part of individual work encourages students for the self-research skills. ● The structure of the programme is consistent with a similar Bachelor programme of

Mathematics and Applications of Mathematics.

Weaknesses:● Optional courses are often chosen before deciding the topic of Master thesis and therefore in

some cases students choose the courses that are inconsistent with the topic chosen for Master thesis;

● The flexibility of SP of Mathematics is rather limited;● The majority subjects of the programme are fully theoretical. It would be good to include the

more labaratory work, where students could obtain more practise and experience examining models and methods.

Improvement measures:● Even though several courses (e.g. Packets of Statistics, Parallel Computing) already include

labaratory works, it is planned to increase the amount of labaratory works in other courses.● Steps will be taken to ensure that students have an opportunity to choose topic of Master

thesis earlier than the 3rd semester. ● There is a plan to provide students with a tutor that could help to choose the appropriate study

plan.● SPC will consider to create more various optional courses in order to increase flecxibility of

the study program.

3. Academic staff

3.1. Composition of academic staff and its conformity to requirements

Currently, the study programme of Mathematics is implemented by 13 academic staff members, including 6 full professors, 2 associate professors and 5 lecturers with a doctoral degree (see Table 3.1 below). The teaching experience of the above 13 academic staff, whose main employer is Vilnius University, is about 21 years on average; their work experience is about 23 years on average. The total number of the academic staff involved in the programme is 16, however, 2 courses (Stochastic Processes Theory and Stochastic Differential Equations) were not chosen by students as an optional courses, therefore, 2 professors of th SP weren‘t involved in the teaching in 2015-2016. Also, the course Packages of Statistics is taught by two lecturers depending on the year. Curicculum Vitae of all academic staff engaged in the SP can be found in the Appendixes 2 and 3. The majority of teachers are from the Faculty of Mathematics and Informatics, mainly from two departments (Differential Equations and Numerical Mathematics and Probability Theory and Number Theory). At the moment, there are no doctoral students engaged in the teaching of the SP, however, we expect their involvement in the future.

16

Table 3.1. Composition of academic staff according to academic titles and research degrees and scope of teaching in the SP of Mathematics (see study plan of the academic year 2015-2016)

Academic title, research degree No of people employed Scope of teaching in the SP*Credits Percentage

Professors (Dr Habil. or Prof. Dr) 6 86 65.6

Associate Professors (Dr) 2 12 9.2

Lecturers with a doctoral degree 5 33 25.2

Total 13 131 100

25 credits for master thesis are not taken into account, but the sum (131 credits) exceeds the required 120 credits for each student, since all optional course units are counted in Table 3.1 (although the students split among those courses).

The composition of the academic staff is in conformity to the requirements stipulated in legal acts of the Republic of Lithuania12, which is reflected in the following table:

Table 3.2. Conformity of the qualifications of academic and other staff in the second-cycle SP of Mathematics to the General Requirements and to the Regulation of Study Programmes of Vilnius University

Requirements In the study programmeNo less than 80% of the academic staff shall have a doctoral degree. 100% have a doctoral degreeAll staff involved in lecturing (reading theoretical courses) shall have a doctoral degree (Regulation of Study Programmes of Vilnius University).

100% have a doctoral degree

No less than 60% (or 40%, when a study programme focuses on developing practical skills) of academic staff teaching course units in the study field shall do research in the same field.

100% do research in mathematics

If a study programme focuses on developing practical skills, up to 40% of the academic staff involved in teaching course units (modules) in the study field may have practical work experience with no less than 3 years of professional experience during the last 7 years conforming to the content of their delivered course units (modules) of applied nature.

not applicable

No less than 20% of the course units in the study field shall be taught by Vilnius University professors (Regulation of Study Programmes of Vilnius University).

65% of course units is taught by professors

Graduation theses shall be defended in a meeting of a Viva Voce Defence Committee. The Chairperson of the Committee shall be from a Higher Education Institution other than the one where the second-cycle study programme has been implemented.

Master thesis is defended in a meeting of Defence Committee

Table 3.3. Composition of academic staff in the SP of Mathematics according to position, academic years 2012-2016Academic yearPosition

2012 2013 2014 2015 2016number % number % number % number % number %

Professors 8 50.0 7 46.7 9 60.0 8 53.3 6 46.2Associate professors 6 37.5 6 40.0 3 20.0 3 20.0 2 15.4Lecturers\doctors 2 12.5 2 13.3 3 20.0 4 26.7 5 38.4

Total 16 100 15 100 15 100 15 100 13 100

12General Requirements for Master Study Programmes approved by Order No V-826 of the Minister of Education and Science 3 June 2010.Regulation of Study Programmes of Vilnius University approved by Decree No SK-2012-12-4 of Vilnius University Senate Commission 21 June 2012. Available in Lithuanian at: http://www.vu.lt/lt/studijos/studiju-procesas/studijas-reglamentuojantys-dokumentai#vu_nutarimai

17

One can see from Table 3.3 that from 2012 all course units have been taught by professors, associate professors or lecturers with PhD degree. On average, about half of all units in SP Mathematics are taught by professors.

3.2. Recruitment of teaching staff, evaluation, turnover

On 17 December 2013 the Senate of Vilnius University (Decree No SK-2013-8-2) approved the Regulations for Organising Open Competition for Teaching and Research Staff of Vilnius University, which stipulate the procedure of evaluating the qualifications of the teaching and research staff of Vilnius University and the procedure of the competition as well as qualification requirements. At the University, teaching and research staff (except for invited professors and researchers) are recruited or promoted to higher positions on the basis of the results of open competition. The competition is started by the order of VU Rector. After the candidate wins the competition, he signs a contract for five years. If the person after five years of his/her work at the University, which is his/her main employer, wins the competition for the same position for the second time in succession, he/she signs a job contract for an unlimited period (although every five years some requirements concerning the number of published papers and teaching hours should be fulfilled).

To determine if the qualifications of the teaching and research staff members are adequate for the position taken, every five years they are evaluated. During the evaluation, the following aspects are taken into consideration: the number of research papers, participation in conferences, supervising research projects, lecturing, preparing teaching materials, participation in the third-cycle (doctoral) studies, supervising students’ papers, expert, managerial and other research-related activities. Moreover, the students’ feedback on the lecturer’s teaching is taken into account. During the last years, the system of students’ feedback has been expanded paying more attention to student satisfaction and thus contributing to a more objective representation of the student’s opinion.

During the period of self-evaluation, the turnover of the academic staff has been hardly noticeable. Most of the professors in 2016 are the same as those in 2012, although few new courses and seminars are given by recent PhD’s.

Table 3.4. Turnover of academic staff in the SP of Mathematics

Academic year

Full professors Associate professors Lecturers/doctors Lecturers Assistant lecturers

First-time agreement with VU

Left VU

First-time agreement with VU

Left VU

First-time agreement with VU

Left VU

First-time agreement with VU

Left VU

First-time agreement with VU

Left VU

20122013 12014 1 220152016 1 1

Total 1 2 2 1

Table 3.4 demonstrates the decreasing tendency of the number of teachers in the SP. The main reasons for termination were the retirement age, as well as not motivating current salary system and teaching load. The ones who left were changes by the existing teachers that engaged in other courses.

Almost all of admitted students are coming from our own bachelor program Mathematics and Applications of Mathematics. However, the graduates of the program are very important for our department. For instance, 4 out of 8 graduates of the year 2012 have started their PhD studies in the same year 2012. By now, 3 out those 4 have been finished their PhD’s and are working at the Department of Probability Theory and Number Theory as lecturers for other study programs. Therefore, the SPC is making efforts to strenthen the motivation of young researchers and doctorants of the Faculty to engage in the teachning activities. It is expected that the plan by Vilnius University to motivate young teachers

18

financially will be implemented in the near future so that they would stay or return to the department, or even attract students from other universities.

Table 3.5. Distribution of academic staff by age

PositionAge

25-34 35-44 45-54 55-64 65 and overProfessors - - 1 3 2Associate professors - 1 - 1 -Lecturers\doctors 4 1 - -Lecturers - - - - -Assistant lecturers - - - - -

Total 4 1 2 4 2

One can see from Table 3.5 that there are no huge disproportion in age distribution of the staff working in SP of Mathematics. The age of the academic staff implementing the SP of Mathematics is about 48 years on average and almost each age group is represented. 3.3. Teaching workload of academic staff

The annual teaching load of an academic working full-time is about 8-10 hours on average per week depending on a position. The table below shows the approximate distribution of work of an academic with a teaching position at our program.

Table 3.6. Full workload (per year) of an academic working full-time at the Faculty (on average)

PositionContact work with students

(in class)

Other work (out of class)

Research and experimental development

(RED)

Dissemination of information

about academic and RED activities

Improving qualifications,

managerial and organisational

activities

hours % hours % hours % hours % hours %

Professor 320 20.2 320 20.2 600 37.9 72 4.5 292 18.4

Associate professor

320 20.2 320 20.2 600 37.9 72 4.5 292 18.4

Lecturer \doctor

360 22.7 360 22.7 400 25.3 36 2.3 428 27

Lecturer 360 22.7 360 22.7 200 12.6 36 2.3 628 40

Assistant lecturer

420 26.5 420 26.5 0 0 0 0 744 47

The calculation is for 1584 hours (36 working hours a week during 44 weeks).

As it was mentioned in Section 3.2 the current salary system and teaching load are not encouraging the improvement of research output and teaching quality, however, the reorganization of salary system is foreseen by the University. Thus, it is expected that teaching load will be accounted and distributed in a more appropriate and motivating way.

The next table shows the contact and other work with students of 6 professors, 2 associate professors and 5 lecturers/doctors.

Table 3.7. Teaching workload in SP Mathematics

19

PositionContact work with students

(in class)

Other work (out of class)

hours % hours %Professors 1593 41.7 1221 57.9Associate professors

856 22.4 383 18.2

Lecturers\doctors

1370 35.9 503 23.9

Total 3819 100 2107 100

Here, the teaching hours only in this particular SP program are taken into account: an academic work is usually done not in one but in several programs of the department, and in some cases one has to teach general mathematics courses in other departments as well (Chemistry, Biology, Economics).

3.4. Competence and professional development of the academic staff

Academic staff of the Faculty of Mathematics and Informatics has the same opportunities as all other Vilnius University academia members to participate in various courses to increase pedagogical competence. Each year, for example, E-learning and Examination Centre at Vilnius University organises courses to help teachers grasp modern IT technologies useful in the learning process. Also the newly established Vilnius University Pedagogy Centre started organising qualification improvement courses with the aim to improve programmes throughout the university. We expect improvements in this direction, albeit information at the Faculty of Mathematics and Informatics about the teaching skills developing events is rather scarce. Unfortunately, one cannot say that it is in any way systematically encouraged. Raising pedagogical competence level, de facto, became the responsibility of each academic staff member individually. The study programme is involving only the teachers who are able to teach in English. This also encourages teachers to improve their language abilities.

The scope of research undertaken by the SP academic staff is shown in Table 3.8.

Table 3.8. Research output of the academic staff of the study programme in 2012-2016 01 02 03 04 05 06 07 08 09 Total

2012 3 1 52 10 4 11 812013 3 1 37 13 2 15 712014 3 1 30 14 1 16 652015 3 2 48 13 1 19 862016 2 2 39 13 2 9 67Total 14 7 206 0 63 10 70 0 0 370

01

BOOKS: (1) Monographs (monograph, study); (2) Literature intended for studies (textbook, teaching aid, other study-related literature); 3) reference publications (dictionary, guidebook, manual, encyclopaedia, atlases, maps, others); 4) other books (publications on the sources of research and scientific heritage, comments of legal acts, reports of projects, and other works, compiled and/or edited work, chapters in books)

02 SUMMARIES ((1) summary of a doctoral dissertation, (2) summary of a habilitation thesis, (3) an overview of research papers submitted for the habilitation procedure)

03

ARTICLES IN SERIAL PUBLICATIONS (JOURNALS) AND SINGLE VOLUMES ((1) article in DB Thomson Reuters Web of Science, (2) article in DB Thomson Reuters Web of Science, (3) article in the international DB and publishing houses, (4) article in other peer-reviewed publications, (5) popular science article, (6) article in a publication on research, arts or culture, (7) other articles (overviews, information, introductory)

04 PUBLICATIONS OF RESEARCH SOURCES AND PUBLICATION OF SCIENTIFIC HERITAGE

05

REVIEWS ((1) review in DB Thomson Reuters Web of Science, (2) review in DB Thomson Reuters Web of Science, (3) review refereed in the international databases and publishing houses, (4) review refereed in other databases, review in other peer-reviewed publications, (5) review in a science popular publication, (6) review in a publication on research, arts or culture)

20

06

ARTICLES IN CONFERENCE PROCEEDINGS: (1) Articles in peer-reviewed conference proceedings (article in DB Thomson Reuters Web of Science, article in conference proceedings in the international DB and (or) in the international publishing house, article in conference proceedings refereed in other databases, article in peer-reviewed international conference proceedings abroad, article in peer-reviewed international conference proceedings in Lithuania, article in peer-reviewed conference proceedings in Lithuania); (2) Articles in non-reviewed conference proceedings (article in non-reviewed international conference proceedings abroad, article in non-reviewed international conference

07CONFERENCE ABSTRACTS: (1) Conference abstracts in peer-reviewed publications (abstracts in DB Thomson Reuters Web of Science and abstracts in Thomson Reuters Master Journal List, abstracts in other databases, peer-reviewed extended abstracts, abstracts in other peer-reviewed publications); (2) Conference abstracts in non-reviewed publications

08PATENTS ((1) patents registered in the European Patent Office (EPO), (2) patents registered in the US Patent and Trademark Office (USPTO), (3) patents registered in the Japan Patent Office (JPO), (4) patents registered in other countries, (5) patents registered in Lithuania, (6) other patents)

09 TRANSLATION ((1) translated book, (2) chapter in a book, (3) article)

In Table 3.8 we summarized the research of about 15 professors/associate professors/lecturers (to be precise 16, 15, 15, 15, 13 in the years 2012-2016, respectively). On average they publish about 40 articles per year. More than half of those publications are papers published in the journals of ISI Master Journal List. The professors are editorial board members of international mathematical journals (e. g., “European Journal of Mathematics”, “Lithuanian Mathematical Journal”) and journals in their respective fields (mainly in number theory, differential equations and analysis, e.g., “International Journal of Number Theory”, “Uniform Distribution Theory”, “Moscow Journal of Combinatorics and Number Theory”, “Mathematical Fluid Mechanics”, “Journal of Elliptic and Parabolic Equations”, “Modern Stochastics: Theory and Applications”, “Mathematical Modelling and Analysis”, “Nonlinear Analysis: Modelling and Control”). Also, almost every year several professors and associate professors become members of the Program Committees of various international conferences held in Lithuania and abroad.

Table 3.9. Research projects implemented by the SP academic staff in 2012-2016Title of project Period Source of funding/Partner(s)

International projects

International research grant with University of Zurich “Asymptotic problems and applications”

2012–2016 Swiss-Lithuanian program “Research and Development”, Switzerland

Partner institution: University of Zurich

National projects

Research grant “Boundary value problems for Navier-Stokes system in unbounded domains”

2011–2012 Research Council of Lithuania

Research grant “Coupled systems of partial, ordinary, and integrodifferential equations”, MIP-12088

2012–2014 Research Council of Lithuania

Research grant “Sequences of algebraic numbers and their heights”

2013–2015 Research Council of Lithuania

Research grant “Nonlinear long memory, heavy tails and aggregation”

2013–2015 Research Council of Lithuania

Research grant “Investigation of stationary problems with nonlocal conditions, numerical analysis and applications”

2014–2016 Research Council of Lithuania

Research grant “Properties of zeta functions of order one and of order two”

2014–2016 Research Council of Lithuania

21

3.5. Exchange of academic staff

Even though Vilnius University has opportunities for academic staff to go for teaching visits abroad, e.g. under ERASMUS programme or taking advantage of bilateral agreements, teachers involved in the SP are often attending shorter conferences, workshops, and not going for teaching visits. Most of the exchange between our academic staff working in SP Mathematics and the colleagues from abroad is based on doing joint scientific research (and is not directly related to the particular study program). It seems that except for Dr. Mindaugas Skujus who had an internship at the Institute of Mathematics, University of Zurich (Switzerland), 2013 in July-December, our staff was not involved in teaching activities at the universities abroad. Also, we have few people from abroad who were coming on a research visits and gave some lectures to the students of SP Mathematics. The reasons for this scarce staff mobility vary depending on the teacher. The main cause perhaps would be a lack of academic staff that could teach instead of outgoing teachers. Incoming teachers are mostly coming for a short visit to present their scientific results at the seminars (Table 3.10).

Table 3.10. Invited academic staff from abroad in the study programme in 2012-2016Year Name of lecturer Institution (country)2014 Itzhak Fouxon Weizmann Institute of Science, Israel2016 Konstantin Nadolin, Alexey Karapetiants Rostov University, Russia

3.6. Proportion of academic staff to students in the study programme

From the table below one can see that the number of students starting their studies in SP Mathematics is low. In the years 2012-2015 we have had 8,12,7 and 6 graduates of the program, respectively.

Table 3.11. Proportion of academic staff to students admitted to the SP according to year of admission

Year of

admission

Number of academic staff

PlanProporti

onnumber

of academic staff /

plan

Number of candidates

Proportion

academic staff/

number of

candidates

Admitted students

Proportion

number of

academic staff/num

ber of admitted students

Students(sf and nsf)*

Students(sf and nsf)

Students(sf and nsf)

2012 16 15 1.07 25 0.64 12 1.332013 15 17 0.88 31 0.48 13 1.152014 15 16 0.94 16 0.94 6 2.52015 15 15 1 23 0.65 12 1.252016 13 16 0.81 16 0.81 5 2.6

Average: 0.94 Average: 0.70 Average: 1.77*sf—funded by the state; nsf—not funded by the state

The proportion of the number of staff to the number of admitted students varies from year to year, however, it is more than sufficient compared with other second-cycle study programs. It is imporntant to note that most of the staff is only giving one course to the students of this program (maximum two, a compulsory and an optional course): as it was said above, the staff is also teaching in other programs at the department (professors and associate professors) and also giving general courses at the university (some associate professors and some lecturers).

3.7. Strengths and weaknesses of the area under evaluation and improvement measures to be taken

22

Strengths:● The competence of academic staff is very high: in the past, three professors have won

Lithuanian national science awards; also several professors are editorial board members of international mathematical journals and journals in their respective fields (number theory, differential equations, etc.).

● Although the number of students in Mathematics program is small, the program produces majority of PhD students in mathematics. SP of Mathematics prepares students for study for third-cycle studies in Mathematics in the field Number Theory, Probability Theory, Differential Equations and Numerical Analysis. For example, in 2016 3 mathematicians, former students of our programme, were employed in the Faculty of Mathematics and Informatics.

Weaknesses:

● The possibilities of staff mobility are not sufficiently covered.● Part of young teachers leaves the Faculty due to financial, scientific, or other reasons.● The current salary system and teaching load are not encouraging the improvement of research

output and teaching quality.● There is a lack of young teachers who have graduated from the universities abroad.

Improvement measures:● Steps will be taken to more actively encourage teachers to participate in the international

academic exchange programmes.● It is expected to promote more active participation in international exchanges of teachers by

allocating more resources. ● There is a need of financial motivation for young researchers with PhD to stay at the

department (the corresponding decision of Vilnius University is needed).● Reorganization of salary system is foreseen by the University.● It is expected that Vilnius University will take measures to attract young academic staff from

universities abraod for the teaching positions.

4. Facilities and learning resources 4.1. Rooms available for studies and the number of workplaces

The Faculty of Mathematics and Informatics (FMI) is situated in two locations in Vilnius: two buildings are next to each other at Naugarduko st. 24 and Šaltinių st. 1A, and another building is located at Didlaukio st. 47. Both places of the Faculty are easy to reach by public transport. The lectures of Mathematics study programme take place mainly in two buildings: Naugarduko st. 24 and Šaltinių st. 1A. Besides that, students have optional courses at the Didlaukio st.building, and general university courses (GUS) at the other university facilities, depending on their choice. The most frequently used rooms and laboratories for the study programme are presented in Table 4.1. and 4.2.Table 4.1. Rooms most frequently employed for studies

Room No (or name) Address Area,

m2Number of workplaces Equipment available in the room

N101

Naugarduko st. 24

204,1 224 Projector, sound system, computer for presentations, blackboard

N102 135,1 140 Projector, sound system, computer for presentations, blackboard

N103 133,8 124 Projector, sound system, computer for presentations, blackboard

23

N105 32,4 25 Projector, computer for presentations, blackboard

N113 32,54 25 Projector, computer for presentations, blackboard

N203 53,36 40 BlackboardN300 48,87 45 Projector, blackboardN301 69,6 80 Projector, blackboardN303 67,07 80 Projector, blackboardN304 34,14 25 Projector, blackboardN306 32,9 25 BlackboardN309 32,9 25 BlackboardN311 34,8 25 BlackboardN312 34,8 25 Projector, blackboardN409 33,4 25 BlackboardN411 34,1 25 BlackboardN415 35,3 25 Blackboard

The average occupation of the class rooms in autumn semester is 76%, in spring - 51%. Table 4.2. Teaching and learning laboratories most frequently employed for studies

Room No (or name) Address Area,

m2

Number of workplace

sEquipment available in the room

S07

Saltiniu st. 1A

41,65 16 8 Windows computers, blackboardS10 30,9 16 8 Terminal computers, blackboardS11 35,4 16 8 Terminal computers, blackboardS12 35,4 16 8 Terminal computers, blackboard

S13 82,6 40 20 Terminal computers, projector, blackboard

S14 29,98 13 13 Terminal computers, projector, computer for presentations, blackboard

Video conference room

172,52 408 Terminal computers, projector, sound system, computer for presentations, blackboard

Students of SP Mathematics work about 62 of all contact hours in computer laboratories. This is

5,54% of all 1119 contact hours. Students have to use various software in the following subjects: Parallel Computing, Packages of Statistic.

The average occupation of laboratories in autumn semester is 37%, in spring - 30%. The number of rooms and computer laboratories are sufficient for successful study. Greater part of students is using available computers at the laboratories, others are using their own laptops. During the last 5 years, the building at Didlaukio st. was renovated and 8 new computer classes were installed. Therefore, computer laboratories at Šaltinių st. 1A became less crowded. This step gives the possibility to create more effective and convenient academic timetable for the students of Mathematics study programme.

There is a library reading room in Naugarduko st. with 90 seats (8 of them with computers). Opening hours of the library are 9:00-18:00. The occupation of the library varies during the study year: in July and August, it is approximately 5%, in September it reaches 70%, in December and May (before examination session) it rises up to 95%, and during the remaining time it ranges between 30-70%.

Students can also use the resources and self-study environment at the modern Vilnius University library (MKIC) located at Saulėtekio st. 5, which was opened in 2013. There are also several lounge rooms in Naugarduko st. and Didlaukio st. buildings, where students usually study, relax or use self-service cafeteria.

24

The ground floors of the Faculty buildings at Naugarduko st. and Šaltinių st. are accessible for disabled students. When planning the timetable, all lectures for study programmes with disabled students are being planned at the first floor so these students could have an easy access to the rooms. Three largest rooms in Didlaukio st. building are equipped with remote controlled cameras for online broadcasting of lectures for disabled students.

The following Table 4.3. represents the renovation of rooms at Naugarduko st. 24 facilities in 2015-2016.

Table 4.3. Renovation of rooms and laboratories for teaching and learning

No Room for teaching and learning The works completed and their cost during 2015-2016, EUR

1. N107 Renewal of the room, 1875 EUR

2. N113 Renewal of the room, 2120 EUR

In the earlier years this kind of renovation was also carried out, but no detailed records can be found. There are no major investments planned for renovation of Naugarduko st. 24 and Saltiniu st. 1A facilities, because a new building for the Faculty will be constructed in the near future at Visoriai, since there is already a funding of 32 millions Eur planned for this matter. 4.2. Equipment for studies

Usually rooms with blackboards and projectors are used for theory lectures. Some lecturers have their own laptops to connect to the projector, otherwise, they can use laptops kept at the security office. Lecturers use either rooms with blackboards and projectors at Naugarduko st. 24 or computer laboratories at Šaltiniu st. 1A during practice classes. There are 156 workplaces with computers in this building. When laboratories are not used for practice classes, students can use them for self-study. The larger rooms are also equipped with microphones.

The laboratories enable students to work on different operating systems (Linux, Windows, iOS). Students can use various software, statistical-econometric packages like SAS, Eviews, R, SPSS.

High-speed and wireless internet connection is available in all Faculty buildings. Students and staff of the university can use Eduroam or MIF open wireless connection. All students of the Faculty of Mathematics and Informatics obtain additional electronic resources: each student receives 500 MB of space on servers for study purposes and can create, and set up his or her own websites. Students and academic staff can also use the supercomputer located at the Faculty of Mathematics and Informatics for scientific research purposes or educational activities free of charge. It is especially powerful computer designed to handle large amounts of information and to conduct scientific calculations more rapidly.

Vilnius University Centre of Information Technology Development provides various core IT services for staff and students (e-mail, e-mail conferences, web page hosting, etc.). Vilnius University E-learning and Examination Centre provides Virtual Learning Environment for lecturers and enables examination of large groups of students simultaneously in large computer classes in Saulėtekio st. buildings.

The available software and computer equipment meet teaching and learning needs. Each year the Faculty assigns budget for equipment renewal. Detailed information is provided in the following Table 4.4.

Table 4.4. Budget for equipment renewal

Year Hardware (Computers, multimedia, servers), Eur Software (servers and workplaces), Eur

2012 87975 87558

25

2013 255499 268573

2014 342547 48118

2015 51119 5311

2016 38261 3594

In 2013 there was an increase of budget for computer classes renovation in Didlaukio st. 47, most of the money for this renovation was gathered from the project EINFRA. In 2014 a new Apple computers class “Innovation Space” was established, which was financed by social partner - Barclays. Moreover, a new server equipment and software was purchased in 2014. Every year Faculty dedicates constant amount of money for hardware and software upgrading in classes and for supercomputer. 4.3. Teaching and learning resources

The Faculty library owns around 70 000 various resources and publications (books, journals, textbooks) on mathematics, statistics, probability theory, economics, informatics, information technologies, and other subjects in different languages (mostly in English and in Lithuanian).

The mathematical and statistical literature constitutes the majority of the library holdings. The Faculty library cooperates with the Central Vilnius University library and the Lithuanian library of the Science Academy. Funds are regularly renewed.

The resources of the Faculty library are constantly updated, according to the plan of the Central library of the University and teachers’ requests. Usually, teachers send their requests to the library staff. Books or journals are ordered after the list of requested resources is approved by the vice-dean for financial matters. Each year the amount spent on Faculty library resources renewal is about 14000 EUR. Detailed information about the budget for journals and books at the Faculty is provided in Table 4.5. Table 4.5. Budget for journals and books, EUR

2012 2013 2014 2015 2016

16398,20 15667,34 16726,31 11295,01 10007,49

The budget for purchasing books and journals has decreased in 2015, because students started

using electronic resources more often, for example, electronic books, publications in databases. Students can find relevant information in electronic databases (via Vilnius University library): Springer Link, Science Direct, JSTOR, Annual Reviews, etc. Vilnius university Library is subscribed to more than 60 databases. Students can also find lecture notes and study material of the subjects on lecturers’ webpages and in virtual learning environment.

4.4. Strengths and weaknesses of the area under evaluation and improvement measures to be taken

Strengths:● Material resources are sufficient for the successful implementation of the study programme.

Premises are sufficient, and their quality is appropriate.● Important measures were taken in order to adapt the Faculty for people with disabilities; their

needs are prioritized when conducting a timetable.● Learning resources (software, books in the library, etc.) are constantly updated according to the

needs of lecturers and students.

26

Weaknesses:● There is a lack of new versions of software, as well as some additional software is needed for

successful studies.● Capabilities of the Virtual Learning Environment are not fully appreciated and universally used.

Improvement measures:● The Faculty will continue consistently to invest in new books, better software and hardware.● Steps will be taken to encourage all teachers to employ the Virtual Learning Environment in their

courses.

5. Study process and assessment

5.1. Admission requirements, statistics and major tendencies

Candidates to the SP of Mathematics are admitted in accordance with the Rules of Admission to the Second-cycle Study Programmes of Vilnius University, approved by the VU Senate. The Rules are accessible on the VU website13. A prerequisite for admission is the completion of the first-cycle studies of every study program but completion of the first-cycle studies of Physical Sciences are recommended. The entrance score is calculated according to a formula, by adding up the mean value of the marks enumerated in the Diploma Supplement and a mark for the graduation thesis or marks for the final examinations. During the period of self-evaluation, the principles of calculating the entrance score have not been modified.

Table 5.1. Entrance scores of the candidates admitted to the SP of Mathematics during the period of self-evaluation

Year of admission

No of students funded by the state (sf) / not funded

by the state (nsf)

Entrance score of the students admitted to the study programme of Mathematics Mean value of the entrance

score of all Faculty programmes*Highest score Lowest score Mean value

2012sf 22,32 17,88 20,03 18,48nsf - - - -

2013sf 22,13 14,18 19,43 18,51nsf - - - 14,39

2014sf 22,57 14,64 19,52 18,41nsf - - - -

2015sf 21,25 12,78 18,66 18,78nsf - - - -

2016sf 18,35 11,83 14,91 18,32nsf - - - -

* - only Second-cycle study programmes included, because of different score calculation systems.

There were no students, who are not funded by the state, admitted to the study programme of Mathematics during the analyzed period. On the other hand, the entrance score of the funded by the state students admitted to the study programme of Mathematics was, in general, decreasing. The highest score, lowest score and mean value of the study program have the same tendency. The mean value of the entrance score of all Faculty programmes was decreasing as well but it remains quite stable around 18,5. However, the mean value of the entrance score of the study program of Mathematics was higher than the mean value of entrance score of the Faculty programmes during the analyzed period, except the last two years. In 2016, the mean value of entrance score of the study program was about 19% lower than the mean value of the entrance score of all Faculty programmes. It seems that there is the decreasing tendency of the entrance score of the students admitted to the study programme of Mathematics.

13 See http://www.vu.lt/kviecia/rinkis-studijas/kaip-istoti/2-pakopos-studijos 27

Table 5.2. Results of candidate admission to the SP of Mathematics during the period of self-evaluation

Year of admission

Number of students funded by the state (sf) / not funded by

the state (nsf)

Planned number of students

Number of applicationsRegular

competition*

Number of admitted students

Admitted students (% of

planned number)1st priority Total

2012

sf 12 17 24 2 12 100%

nsf 3 1 0,33

Total 15 17 25 1,67 12 80%

2013

sf 12 18 29 2,42 13 108%

nsf 5 3 0,6

Total 17 18 31 1,82 13 76%

2014

sf 13 7 14 1,08 6 46%

nsf 3 2 0,67

Total 16 7 16 1 6 38%

2015

sf 13 12 23 1,77 12 92%

nsf 2

Total 15 12 23 1,53 12 80%

2016

sf 14 6 15 1,07 5 36%

nsf 2 1 0,50

Total 16 6 16 1 5 31%

* Regular competition defines the competition to the study programme in terms of the total number of applications (candidates) per place

There were no students admitted whithout state funding during the analyzed period. The number of admitted students funded by the state seems to repeat periodically during the last four years. Precisely, on 2012, 2013 and 2015, planned numbers of students were basically fulfilled. However, on 2014 and 2016, number of admitted students decreased approximately twice. The number of admitted students is decreasing because the number of admitted students of the first-cycle students is decreasing.The SPC of Mathematics plan to advertise the SP of Mathematics in other Universities, since this SP of pure Mathematics is only in Vilnius University.

5.2. Changes in the number of students: dropout rate and its causes

Table 5.3. Dropout rate in the study programme of Mathematics

Year of admission

Number of admitted students

Number of dropouts Dropout rate, %

1st year of study

2nd

year of study

Year of graduation

Total during the SP

implementation period

Total during the SP implementation

period

2012sf 12 5 2

20147 58%

nsf 0 0 0 0 0Total sf + nsf 12 5 2 7 58%

2013sf 13 5 0

20155 38%

snf 0 0 0 0 0Total sf + nsf 13 5 0 5 38%2014 sf 6 1 0 2016 1 17%

28

nsn 0 0 0 0 0Total sf + nsf 6 1 0 1 17%

2015sf 12 0 0

20170 0

nsf 0 0 0 0 0Total sf + nsf 12 0 0 0 0

2016sf 5 1 0

20181 20%

snf 0 0 0 0 0Total sf + nsf 5 1 0 1 20%

Grand total during the

period

sf 48 12 2 14 29%nsf 0 0 0 0 0

sf + nsf 48 12 2 14 29%

The average dropout rate for admission years 2012–2018 is about 29%. This figure may be within acceptable limits keeping in mind quite difficult curriculum (based on pure mathematics). The analysis of reasons of all dropouts gives the clearer view of the situation (see Table 5.4).

Table 5.4. Causes of leaving the university in the period between 2012 and 2016 Year of study

Year of admission Total2012 2013 2014 2015 2016

Failure to meet financial obligations 1st

2nd

Unsatisfactory academic results 1st

2nd 2 2Academic dishonesty during the assessment of

academic progress1st

2nd

Family reasons 1st

2nd

Failure to renew studies after academic leave or suspension of studies

1st

2nd

Of the student’s own free will 1st 5 4 1 1 112nd

Transfer to another higher education institution 1st 12nd 1

No dropouts occurred due to financial burden, such a result may be expected since only a few students pay for their studies. We had no dropouts due to academic dishonesty, e.g. cheating during exams. The programme management and Student Council do not tolerate academic cheating, so various measures are taken to prevent this problem rather than punish students when cheating happens. Two students were unable to maintain adequate academic standards and decided to terminate the studies. The SPC thinks that it is possible to manage such cases and, at least partially, to keep this figure as low as possible. Since the programme attracts students with sufficiently high scores, adequate academic support to students may help minimize dropouts due to unsatisfactory academic results. A major part of dropouts is due to students own will and reasons for such a decision may be very different. Some students find studies quite difficult and / or claim that studies do not meet their initial expectations. Others decided to change their study programme, e.g. they also found that their initial expectations were not met. There were one students who transfered to another higher education institution during analyyzed period of time.

5.3. Organization of studies and academic support to the students

29

The aim of the study process is to ensure an effective implementation of the study programme so that the purpose is attained and learning outcomes of the SP are developed.

Information on the studies is provided by different institutions, from the Administration of Studies and the Dean’s Office of the Faculty of Mathematics and Informatics to the academic staff of the study programme of Mathematics. The website set up by the Administration of Studies (www.klausk.vu.lt - in Lithuanian) provides access to the ask-and-get-an-answer system, where answers to questions are provided by representatives of the Administration of Studies or the Faculties. This is a very fast and convenient system saving time and replacing more time-consuming face-to-face communication in the office.

All information about the study process (study calendar, timetables of lectures and examinations, optional course and modules, the procedure of assessment and retaking the examinations), about partial studies abroad, tuition fees, grants, funding of studies is provided by the Faculty administrative staff responsible for studies, Vice-dean for Studies and Chair of the Study Programme Committee. The information is available at http://www.vu.lt/en/studies and http://mif.vu.lt/lt3/en/studies. Another option would be the Vilnius University information system of studies, or VUSIS. There the students can access personal data, copies of relevant orders, study plan, examination timetable and results, etc. The students can also actively participate in the process of study by enrolling in optional courses and modules or courses of general university education, etc.

All timetables of the upcoming semester become available online one month before a beginning of a forthcoming semester. Upon the completion of the first semester, as provided by the Regulations for Studies of Vilnius University, all students have an opportunity to study according to their individual study plans. For that purpose, their applications, including sound motivation, shall be submitted to the Dean’s office and approved by the Dean.

Questions related to the learning outcomes, the content of a course unit or module, career opportunities are within the responsibility of the Chair of the Study Programme Committee and the academic staff of the programme. They are all available for consultation at the time specified in advance or between/after the classes, or can be reached by electronic mail. Career opportunities are discussed during the classes, at the meetings with the Faculty alumni and potential employers. Every year, during a spring semester, the Students’ Representation organizes a conference devoted to give better insights on future careers for students. During the event, representatives from various private enterprises, e.g., Affecto, Asseco, Barclays, Neurotechnology, Swedbank, Adform, Insoft, Euromonitor International, share their personal career paths, discuss the skills and attitudes necessary for successful enrolment and carrier in their companies. Similarly, smaller scale events are organized for the students of Mathematics. Master students are also invited to attend research seminars organized in the Faculty of Mathematics and Informatics.

As provided in the Regulations for Studies of Vilnius University, students facing problems ensuing from unsatisfactory academic results are eligible for a second attempt. If they fail an examination, they may retake it once. If they fail the second time, they may repeat the whole course (module) by attending it together with other students who take it for the first time and resit the examination one year later. Those who have accumulated 15 credits of failed courses (modules) shall be expelled from the University and may renew their studies after having passed all relevant examinations.

Those who disagree with the examination procedure or the results, may launch an appeal to the Appeal Commission of the Faculty no later than five days after the results become available. A decision reached by the Appeal Commission on the results shall be final and not subject to further appeal. However, the examination procedure may be subject to further appeal at the VU Dispute Tribunal.

Students having health problems may take academic leave upon submitting a medical certificate; the leave shall be no longer than two years. Academic maternity leave may also be granted; it shall be no longer than three years. Upon the Dean’s approval, the student, having a sound reason, may suspend his/her studies for one year.

The Students’ Representation of Vilnius University deals with various problems of the students, defends their interests, takes care of their academic and social welfare, organizes events of culture, fosters University traditions of student life, helps first-year students in their integration into the University

30

community. Usually the Student Representation appoints a tutor, a senior student, who is a contact person in matters of different nature for all first-year students.

5.4 Social support to the students: grants, loans, tuition fees, hostels

The main form of social support to the students is financial allocations. The students may be eligible for the following: special grants for academic excellence (in the year 2012-2016 the students of the study programme received 22 such grants), social grants (in the year 2012-2016 the students of the study programme received 8 such grants), single social allowances, single special social allowances.

Another form of social support is loans provided to the students by the state (administered by the State Studies Foundation) and allowances for students with disabilities (This is administered by the Department for the Affairs of the Disabled under the Ministry of Social Security and Labour of the Republic of Lithuania). Information on the procedure of allocating and disbursing the above allowances is accessible on the VU website14. All the above forms of social support are introduced to the students admitted to the study programme of Mathematics during the introductory lectures of the first semester All information concerning financial support is available also at:

- http://www.vu.lt/studijos/studentams/finansine-parama (in Lithuanian),- http://www.vu.lt/en/studies/financial-support-for-international-students (for international

students).Especially talented students manifesting academic excellence and taking part in research may be

eligible for special VU grants according to study and research fields. More information is available on the VU website15. A number of such scholarships has been awarded to the students of the program Mathematics:

● Vytautas Statulevičius’ scholarship: Raivydas Šimėnas (2012), Gražvydas Šemetulskis (2012, 2013).Accommodating students, residents of towns and villages outside Vilnius, in the hostels of Vilnius

University might also be treated as social support. The demand for hostels is fully satisfied (95 % of all applications). Students in need of social support or with disabilities are eligible for a reduction when paying for the hostel.

Moreover, Vilnius University offers professional psychological assistance to students and staff through the Psychological Training and Research Centre. Single consultations or cycles of consultations might be helpful to those facing problems of private or family life, social integration or studies.

5.5. Students’ participation in research, sports and arts

A number of students of Mathematics takes part in research actively. Some of their results are published as research papers. For example, G. Paukštaitė (studied in 2012-2014), L. Kaziulytė (2014-2016) and V. Šumskas (2015-2017) has the following publications:

1. G. Paukštaitė, A. Štikonas, Generalized Green’s functions for second-order discrete boundary-value problems with nonlocal boundary conditions, Liet. matem. rink. Proc. LMS, Ser. A, 53: 96-101, 2012.

2. G. Paukštaitė, A. Štikonas, Investigation of matrix nullity for the second order discrete nonlocal boundary value problem, Liet. matem. rink. Proc. LMS, Ser. A, 54: 49-54, 2013.

3. A. Ambrazevičius, A. Eismontaitė. Solvability of a mathematical model of dissociative adsorption and associative desorption typer, Central European Journal of Mathematics, 11(6),p. 1129–1139.

4. G. Paukštaitė, A. Štikonas, Generalized Green’s functions for the second-order discrete problems with nonlocal conditions, Lith. Math. J., 54 (2): 203-219, 2014. doi: 10.1007/s10986-014-9238-8G.

5. G. Paukštaitė, A. Štikonas, Classification of the nullity for the second order discrete nonlocal problems, Liet. matem. rink. Proc. LMS, Ser. A, 55: 40-45, 2014.

14 See http://www.vu.lt/lt/studijos/studiju-procesas/finansine-parama.15 See http://www.vu.lt/lt/studijos/studiju-procesas/finansine-parama#vardines_stipendijos.

31

6. Skujus, M., Šumskas, V., Asymptotics of a solution to the time-periodic heat equation set in domains with corner points, Lith. Math. J., 56(4), pp 552–571, (2016)

7. L. Kaziulytė “On the mean value of the reciprocal of the divisor function in arithmetic progressions”, accepted to Šiauliai Mathematical Seminar.

The research results are also presented in the following conferences:1. J. Novickij, F. Ivanauskas, M. Sapagovas. On the stability of an explicit difference scheme for

hyperbolic equation with integral conditions. 17th International Conference on Mathematical modelling and analysis, June 6-9, 2012, Tallinn, Estonia.

2. G. Paukštaitė, A. Štikonas. Generalized Green’s functions for discrete boundary value problems. 18th International Conference on Mathematical Modelling and Analysis and 4th International Conference on Approximation Methods and Orthogonal Expansions, May 27–30, 2013, Tartu, Estonia.

3. G. Paukštaitė, A. Štikonas. Investigation of matrix nullity for the second order discrete problem with nonlocal conditions. 54th Conference of Lithuanian Mathematical Society, Vilnius, LEU, June 19–20 d., 2013.

4. G. Paukštaitė, A. Štikonas. Ordinary and generalized Green’s functions for discrete nonlocal problems. 19th International Conference on Mathematical Modelling and Analysis, May 26–29, 2014, Druskininkai, Lithuania.

5. G. Paukštaitė, A. Štikonas. General classification of the nullity for the second order discrete problems with nonlocal conditions. 55th Conference of Lithuanian Mathematical Society, Vilnius, MRU, June 26–27 d., 2014.Students also have an opportunity to take part in research on the international level. For example,

a student Moisej Braver investigates, jointly with his supervisor M. Skujus (VU) and H.J. Choe (Yonsei University, Seoul), mathematical models of electric potential distribution in composite materials.

The students enrolled in the study programme of Mathematics, like any other VU students or staff, have multiple opportunities of self-expression outside their classes, usually in sports, arts and music16.

The Health and Sport Centre of Vilnius University offers the programme of healthy lifestyle intended for the students and academic staff. The Centre has three gyms and/or stadiums in Vilnius (Saulėtekio al. 2, Saulėtekio al. 26, M. K. Čiurlionio g. 21/27). The students may make use of the facilities and equipment of the Centre, join general training classes or enrol in individual training programmes, choose a particular sport. In the Centre, people may, individually or in groups, engage in a number of sporting activities such as jogging, fitness, basketball, football, table tennis, volleyball, etc.

A number of choirs, drama troupes, orchestras and ensembles are available at the VU Centre of Culture. They can be frequently seen performing in many national and international festivals in Lithuania and abroad.

The students are offered multiple opportunities of participation in the activities of the Students’ Representation of the Faculty of Mathematics and Informatics and of Vilnius University (the latter is referred to as VUSA). The bodies representing the students aim at ensuring that such representation at all levels in VU is based on the students’ needs and is high-quality, also at strengthening the self-governance of the students, etc. VUSA issues student-oriented newspaper Studentų era, which is the largest publication of its type in Lithuania.

5.6. Student exchange programmes

Studies abroad and processes of international cooperation in Vilnius University are administered by the International Programmes and Relations Office. At the Faculty of Mathematics and Informatics, such responsibility is assigned to Dr. Mindaugas Skujus (until the year 2016 international cooperation was coordinated by Dr. Paulius Drungilas). One coordinates the process of exchange studies (both leaving and incoming students) and professors visiting the Faculty in the frame of exchange programmes,

16 http://www.ssc.vu.lt/cms/ and http://www.kultura.vu.lt/32

e.g., Erasmus+, etc. The coordinator is responsible also for extending the network of academic exchange partners.

The students of the Faculty have multiple opportunities to enrol in partial studies of one semester or one academic year study within the exchange programmes Erasmus+ and bilateral agreements. The Faculty of Mathematics and Informatics has Erasmus+ agreements with more than 100 academic institutions across Europe. Erasmus+ agreements conducted by the Institute of Mathematics and Informatics are also available for our students.

The complete list of Erasmus+ partners is available at http://www.erasmus.tprs.vu.lt/partneriai/# (please use the filters “Matematikos ir informatikos fakultetas” and “Matematikos ir informatikos institutas”) while the most popular institutions among the students of Faculty of Mathematics and Informatics are

● Universiteit Utrecht, Vrije Universiteit Amsterdam, Tilburg University, Rijksuniversiteit Groningen (the Netherlands).

● Universität Basel, Universität Zürich, ETH Zürich (Switzerland).● Libera Università di Bolzano, Università degli Studi di Ferrara (Italy).● Universidade Nova De Lisboa, Universidade do Porto, Universidade Técnica de Lisboa

(Portugal).● Athens University of Economics & Business (Greece).

Even though Vilnius University provides wide enough opportunities to study abroad, participation in exchange programmes of students of Mathematics is low (see the table below). The reason for this may be mainly due to the fact that majority of the students already have jobs.

Table 5.5. Student mobility in the SPYear of study Number of outgoing students Institution (country)

2012 NA NA2013 02014 02015 1 Universite de Savoie (France)2016 2 Universität Zürich (Switzerland), Universita degli Studi di Ferrara (Italy)

Faculty of Mathematic and Informatics extended a list of courses for exchange students in 2016. Two courses from study programme Mathematics, namely, Integral Equations and Function Spaces, have been included in this list. As a result, four exchange students from abroad selected these courses as a part of their curriculum at Vilnius University. The accurate statistics of incoming ERASMUS + students of exceptionally for SP of Mathematics is unavavailable due to the fact that students coming from abroad chose courses from different study programmes in the Faculty.

5.7. Assessment of academic progress

The procedure of assessing academic progress, retaking the examinations and of appeals of students dissatisfied with their assessment results is stipulated in Vilnius University by the Regulations for Studies, the Procedure of Assessing Academic Progress and the Regulations of the Appeal Commission for Assessing Academic Progress in a Core Academic Unit of Vilnius University17.

17 Regulations for Studies approved by Decree No SK-2012-12-8 of Vilnius University Senate Commission 21 June 2012; available in Lithuanian at http://www.vu.lt/site_files/SD/Studentams/SP/SRD/VU_studiju_nuostatai_naujoji_redakcija.pdf; Procedure of Assessing Academic Progress approved by Decree No SK-2012-20-6 of Vilnius University Senate 13 December 2012, available in Lithuanian at http://www.vu.lt/site_files/SD/Studentams/Studiju_pasiekimu_vertinimo_Tvarka_12.21.pdf; Regulations of the Appeal Commission for Assessing Academic Progress in a Core Academic Unit of Vilnius University approved by Decree No SK-2012-20-3 of Vilnius University Senate Commission, available in Lithuanian at http://www.vu.lt/site_files/SD/Studentams/Padalinio_akademines_etikos_komisijos_nuostatai.pdf ).

33

All information on the assessment of academic progress, schedule of examinations, failed examinations and retaking them is available on the VU website18.

During the first class, each teacher shall introduce the syllabus of the course (module) by focusing on its aim, learning outcomes, content, study and assessment methods as well as assessment strategy. The assessment criteria and the importance of meeting the deadlines are also discussed. The system of assessment is specified in the course unit (module) description.

Academic progress may be assessed in different ways; several methods may be combined, such as continuous, mid-term and final assessment. The final assessment is mandatory19. The final mark for the course unit may be cumulative, calculated on the basis of the proportions specified in the course unit description. The form of the final assessment in Vilnius University is an examination. If the course unit extends over several semesters, all but final semester of the course unit end in a pass/fail assessment.

The examinations may be oral and/or written. Currently, Vilnius University employs a 10-point assessment scale20. The points on the scale are defined as “excellent, exceptional knowledge and skills”, average knowledge and skills, some inessential mistakes”, etc.

Table 5.6. Vilnius University scale of assessment and marks Pass, fail System of assessment Description

PASS

10 (excellent) Excellent, exceptional knowledge and skills

9 (very good) Very good knowledge and skills

8 (good) Knowledge and skills are above average

7(average) Average knowledge and skills, some inessential mistakes

6 (satisfactory) Knowledge and skills are below average, there are errors

5 (weak) Knowledge and skills meet the minimum requirements

FAIL 4, 3, 2, 1 (unsatisfactory) Below minimum requirements

The final mark is usually calculated on the basis of the marks for the examination paper, participation in seminars, individual or group project, final (oral and/or written) examination. All general principles of the assessment and of ensuring feedback are specified in the documents of Vilnius University: the Procedure of Assessing Academic Progress and the Procedure of Ensuring Feedback to all Involved in the Study Process21.

The master graduation thesis is assessed by the Viva Voce Defence Committee of Graduation Theses. is assessed by the Viva Voce Defence Committee of Graduation Theses. The members of the Committee take into consideration the graduation thesis, its presentation during the defence, the responses of the author of the thesis to the questions of the reviewer and the members of the Committee, and the reviews and opinions of the reviewer and the supervisor of the thesis. If there is no unanimous agreement about the final grade, the final decision is taken by the chairperson of the Committee.

18 See http://www.vu.lt/lt/studijos/studiju-procesas/egzaminu-sesija.19 In the modular system, mid-term assessment is also mandatory.20 http://www.vu.lt/lt/studijos/studiju-procesas/egzaminu-sesija/45-studijos/studijos/2591-vertinimo-sistema. Also see the Procedure of Assessing Academic Progress: http://www.vu.lt/lt/studijos/studiju-procesas/studijas-reglamentuojantys-dokumentai#vu_nutarimai [1 June 2012]21 See http://www.vu.lt/site_files/SD/SK/SP_dalyviu_GR_tvarka.pdf. Approved by VU Rector’s Order No 115 2009 05 29.

34

To ensure academic honesty during the studies, Vilnius University has taken various measures. The academic staff and the students shall adhere to the principles of ethics laid down in the Code of Academic Ethics of Vilnius University22, which defines general norms of academic, teaching, studies and research ethics. The Code also defines the notion of violation involving cheating, plagiarism, bribery, unsolicited dishonest assistance to the peers, etc. Students’ organisation also provide help for the teaching staff by delegating, under teacher’s request, 1-2 students for additional supervision of exams.

5.8. Professional activities of SP graduates

The employment rates of graduates of study programme Mathematics are high. According to students career monitoring system www.karjera.lt (in Lithuanian) aproximately 85% of graduates has work contracts 6 months after their graduation. In fact, the majority of students combine their Master studies with part-time or full-time work activities. They are usually employed by IT, telecommunication companies, various financial institutions. Every year several graduates of Mathematics starts PhD studies at Vilnius University or other research institutions.

0,5 year 1 year 3 years0

20

40

60

80

100

120

Employment rate of the graduates in 0,5, 1 and 3 years after graduation (2012)

Employment rate Employment rate of womenEmployment rate of men

Figure1. Employment rate of the graduates in 0,5, 1,3 years after graduation (2012)

The tendencies of employment are presented in the Figure 1 that illustrates the employment rate of graduates of 2012 in 0,5, 1 and 3 years period. The graph shows rather high employment rate of the graduates. It can be noticed that men employment rate throughout the year is 100%, thereas women graduates were less successful. However, male students represents significantly greater part of all students in the SP.

22 Code of Academic Ethics of Vilnius University approved by the Senate Commission of Vilnius University 13 June 2006, Minutes No S-2006-05, available in Lithuanian at http://www.vu.lt/lt/studijos/studiju-procesas/studijas-reglamentuojantys-dokumentai/45-studijos/studijos/2564-akademines-etikos-kodeksas.

35

20%

40%

20%

20%

Employment type of the graduates after 1 year of the graduation (2012)

Teachers in the higher ed-ucation institutionsNo informationManagers of the IT and connection servicesAnalytics of the man-agement and organiza-tion

Figure 2. Employment type of the graduates in 1 year after graduation (2012)

The Figures 2 and 3 specifies the type of employment of gradutes of 2012. Positions of the graduates varies, but remains in the field of Mathematics and Informatics (the teachers at the higher education institutions, managers of IT and connection services, Analytics of management and organization, Consultantas of finance and investments.

43%

14%

29%

14%

Employment type of the graduates after 3 years of the graduation (2012)

Teachers in the higher ed-ucation institutionsConsultants of finance and investmentsMathematicians, Actuaries and StatisticiansAnalytics of the man-agement and organiza-tion

Figure 3. Employment type of the graduates in 3 years after graduation (2012)

Comparing the employment in 1 year and in 3 years after graduation, it can be noticed that there is an increase of graduates involved in the teaching activities in post-secondary education institutions, which is a promising tendency in order to increase the number of young teachers and quality of higher education in Lithuania. Obviously, the data analysed is only of the cohort graduated in 2012, therefore, it is expected to obtain more data about graduates for broader analysis in order to grasp the more significant trends of employment rates of the graduates.

5.9. Strengths and weaknesses of the area under evaluation and improvement measures to be taken

Strengths:● A number of students are involved into research activities every year. Talented ones are

supported financially via special scholarships or using external funds.

36

● The programme is valued by the labor market. According to 2012 statistics, 87.5 % of our graduates are employed within three years of graduation.

Weaknesses:● Relatively few students are taking part in exchange programmes. ● As the level of knowledge of enrolled students in the program is not uniform, the organized

adaptation process for the first year students is needed.● Motivation of those students which do not plan to continue with subsequent PhD studies in

mathematics seems to be quite low; also, most of the students are working (full time) for different companies and have not enough time to study.

● The number of students is quite low (and decreasing), so some optional course units become impossible due to the restrictions of our department (at least 5 students per course), since too few students are choosing a particular subject.

Improvement measures:● In order to increase the student international mobility, we are planning to promote Erasmus+

and other programs more extensively.● Steps will be taken in order to organize the adaptation process for the students of the first

year.● It is important to improve the encouragement of students to undertake scientific research so

that they could develop their abilities in PhD studies.● Perhaps, on behalf of the Faculty, the restrictions on the number of students registering for a

course to take place should be removed (or at least the minimal numbers of students decreased). This would allow a better preparation at least for those who are aiming to continue with PhD studies.

6. Study Programme management

6.1. Regulation of study quality assurance

Fostering quality culture is a strategic aim of Vilnius University. It is made feasible by adhering to the values specified in the VU mission and in the Standards and Guidelines for Quality Assurance in the European Higher Education Area23. In Vilnius University, all study programmes and their implementation are administered by the Administration of Studies, which is also responsible for ensuring the quality of functioning of the units of different levels in VU24.

The main document concerned with the internal quality assurance of studies is: Vilnius University. Quality Manual25.

When implementing and improving the processes and procedures of internal quality assurance, Vilnius University takes the responsibility for approving, monitoring and evaluating its study programmes and qualifications awarded, the evaluation criteria applicable to the new study programmes, the programme intended for newly recruited academic staff (see the publication Manual of Vilnius University Lecturer26). The University also organises courses intended for the professional development of the academic staff, etc.27.

As stipulated by the Regulation of Study Programmes of Vilnius University28, a study programme shall be updated and its quality monitored on a regular basis. The quality is assured and improved through 23 Standards and Guidelines for Quality Assurance in the European Higher Education Area . See http://www.enqa.eu/index.php/home/esg/24 See http://www.kvc.cr.vu.lt/site.25 Vilnius University. Quality Manual. Vilnius, 2013. available in Lithuanian at http://skvis.vu.lt/pub/book/qm/topic/10298430.26 Manual of Vilnius University Lecturer. Vilnius, 2013. available in Lithuanian at http://www.kvc.cr.vu.lt/site/sites/default/files/VU_destytojo_vadovas_4_16.pdf.27 See http://www.kvc.cr.vu.lt/site/?q=node/90.

37

its internal evaluation and external assessment, by making the results of such evaluation and assessment accessible to the community, by accumulating and analysing the data about the programme and the process of study, by monitoring the feedback, ensuring the availability of facilities and learning resources, improving the qualifications of the academic staff, promoting the application of innovative methods of teaching, learning and assessment, improving the management of the programme and disseminating good practice29.

All modifications of the study programme shall be subject to discussion and approval by the Study Programme Committee and the Faculty Council. When modifications involve changes in the title, field (branch) of studies of the SP, qualification degree, awarded as a result of its completion, professional qualification or scope of the SP, they shall be approved by the SP Committee, the Faculty Council and finally, by the Senate. The process of SP updating is supervised by the Administration of Studies of Vilnius University.

In accordance with the Regulation of Study Programmes of Vilnius University, assuring and improving the SP quality is the responsibility of the SP Committee, which operates in accordance with the Regulations of the Study Programme Committee30. The Committee is in charge of the SP and the assurance of the quality of its implementation. It is accountable to the Faculty Council for the SP implementation and shall report to it at least once a year. The Committee is composed of academic staff, student and employer representatives; the composition is approved by the Senate upon the recommendation of the Faculty Council. The aims of the Committee are also enumerated in the Regulations for Studies of Vilnius University, the Procedure of Approving Academic Results and other documents.

6.2. Aims and responsibilities of the Study Programme Committee

The composition of the Study Programme Committee (hereinafter also SPC) is as follows: Paulius Drungilas, Artūras Dubickas, Kristina Kaulakytė, Konstantinas Pileckas, Mindaugas Skujus, Artūras Štikonas (chairman of SPC), Gediminas Ziezys (student), Romualdas Zovė (social partner). The SPC was approved in 15 December 2015 upon the Decision of the Senate No. S-2015-10-5. One of the key goals of the SPC is to seek the high quality of the programme so that its purpose is attained, its learning competences are developed, its content is compatible with the teaching, learning and assessment methods and the programme is competitive and relevant to the society. The SPC analyses feedback about the programme and its implementation received from different units of the Faculty, students, academic staff. In addition to standardised questionnaires launched by the Administration of Studies, the SPC may, on its own initiative, launch its own questionnaire focusing on the improvement measures to be taken as well as any other issue relevant to the students. In search of viable solutions, the problems are usually discussed by the SPC members with the Faculty administration and the academic staff of the SP. The SPC shall ensure the update of the SP purpose and content; moreover, it shall participate in preparing and approving all documents related thereof (e.g. new course units descriptions prepared by the academic staff). All decisions of the SPC are taken by the simple majority of votes of its members. Another function of the SPC, usually performed by the chair, is concerned with evaluating the competences acquired by the students in other SPs and deciding about the approval or disapproval of the academic results attained by those students in those SPs.

6.3. SP management database: Vilnius University information system of studies

The Faculty administration and the academic staff make use of the Vilnius University information system of studies (VUSIS), which consists of several sub-systems. One of them is meant for managing

28 Approved 21 June 2012. See http://www.vu.lt/site_files/SD/Studiju_programu_reglamentas_2014_01_27.pdf. The document also specifies requirements for new study programmes (their preparation and registration) and the accreditation, evaluation and improvement of the existing study programmes. 29 For more information about the processes of study quality improvement see http://www.kvc.cr.vu.lt/site/ 30 Approved 6 March 2014. http://www.vu.lt/site_files/SD/Studentams/SP/SRD/SPK_nuostatai_03.06.pdf

38

study programmes, offering access to people responsible for studies (Vice-dean for Studies, administrative staff, etc.). The administrative sub-system is an instrument for making, reviewing and editing study plans. Another subsystem is meant for managing the students and thus helps deal with the students’ personal data, their marks for course units (modules), registration for optional course units (modules), titles of graduation theses; it helps issue certificates, approve the course units (modules) attended and assessed in another higher education institution. The sub-system also gives access to the results of considering the students’ applications, marks for the course units (modules), etc. All orders related to the student affairs issued by the Dean or Rector (e.g. on the titles of annual papers or graduation theses, on business trips when going for partial studies in foreign universities, etc.) are prepared by VUSIS. The system also assists in issuing diploma supplements. VUSIS also stores admission data (competition, the number of admitted candidates by priority), various statistics related to students and studies. The academic staff members have online workplaces, where they can enter examination results, descriptions of course units (modules); they have access to the list of students enrolled in their course. VUSIS makes information management and the implementation of studies much easier.

6.4. Students’ and graduates’ feedback about the programme and its implementation

Ways of getting feedback and handling it in Vilnius University are defined in the Procedure of Ensuring Feedback to all Involved in the Study Process31. Twice a year, at the end of each semester, the University launches questionnaires to be filled in by first and second cycle students through an electronic database. The questionnaires focus on the following:

1) On specific course units (modules) attended during the semester. For that purpose, the same standardised course questionnaire is used in all the faculties of the University. Upon registration in the VU information system, a special slot on questionnaires opens up. There

● the students may anonymously evaluate their studies, including specific course units (modules);● the academic staff members have direct access to the students’ evaluation and feedback about

their course units (modules);● chair of the SPC has direct access to the students’ evaluation and feedback on all course units

(modules) of the SP;● The Faculty administration has direct access to the students’ evaluation and feedback on all

course units (modules) of the study programmes implemented by the Faculty.2) On general satisfaction with the studies during the last semester.

Detailed results of the questionnaires according to units and study programmes are available in the slot “Feedback” of the section of the Administration of Studies on the VU intranet. Vilnius University makes use of the results of the standardised questionnaires for the following:

● to improve the SP and a particular course unit (module);● to ensure the quality assurance and improvement by the SPC and the Faculty administration;● to prepare for external assessment when drafting the self-evaluation report;● to analyse new study programmes;● to evaluate the qualifications of the academic staff;● to improve other activities of the Faculty and the University.

At least once a year SPC discusses the results of the abovementioned questionnaires and makes decisions regarding the improvement of the SP. Then the Faculty administration and teachers of related courses are informed about the decisions taken by the SPC.

6.5. Cooperation with social partners

Social partners are always invited to participate in the regular meetings (1 or 2 in a semester) of SPC and encouraged to propose ideas for the improvement of the SP. Currently, there is one social

31 Approved 29 May 2009. See http://www.vu.lt/site_files/SD/SK/SP_dalyviu_GR_tvarka.pdf 39

partnee – Romualdas Zovė- who is invited to be a member of the Master thesis defence committee. The clear need of advanced communication abilities of the students was highlighted by social partner; therefore study programme committee (SPC) involved the training of communication abilities during several courses of the study program. Clear communication of mathematical ideas, research ideas in appropriate contexts both orally and in writing to a range of audiences was specified as one of the graduates’ learning outcome. SPC appreciate the cooperation with social partner because of his innovative ideas for improvement of SP and expect to strengthen and broaden cooperation in the near future. The direct contact is maintained between social partners, teachers and the representatives of students of the SP.

6.6. Strengths and weaknesses of the area under evaluation and improvement measures to be take

Strengths:● SPC maintains close relationship with the departments responsible for the implementation of

the SP as well as the representatives of social partners and employers.

Weaknesses:

● There is a lack of approriate system to collect feedback from graduates of the SP.● The implementation of SP is not fully controlled by the SPC.● Students are facing difficulties to evaluate the program due to the deficiencies of the students’

survey system.

Improvement measures:● The necessary steps will be taken in order to create a system and encourage the feedback of

the graduates.● SPC should be fully responsible for the implementation of the SP (the decision of University

is needed).● Discussions in the Council of the Faculty have been initiated concerning the simplification of

the student survey system.

40

APPENDICES

41

Appendix No 1

COURSE UNIT DESCRIPTIONS

COURSE UNITS CREDITS STUDENT'S

WORKLOADCONTACT

HOURSSELF-STUDY HOURS

1ST YEAR 60 1600 725 875

SEMESTER 1 30 800 363* 437

SUPPLEMENTARY CHAPTERS IN FUNCTIONAL ANALYSIS

6 170 102 68

MATHEMATICAL WRITING AT HIGHER LEVEL 6 160 72 88

FUNCTION SPACES 6 150 56 94

PROBABILISTIC COMBINATORICS 6 160 72 88

ANALYTIC NUMBER THEORY 6 160 66 94

INTEGRAL EQUATIONS 6 160 72 88

MATHEMATICS IN MODERN FINANCE 6 160 56 104

SEMESTER 2 30 800 362 438

PARTIAL DIFFERENTIAL EQUATIONS 6 160 86 74

PROBABILITY THEORY AND MATHEMATICAL STATISTICS

6 160 68 92

PARALLEL COMPUTING 6 160 64 76

DYNAMICAL SYSTEMS 6 160 72 88

STOCHASTIC PROCESSES THEORY 6 160 72 88

STOCHASTIC DIFFERENTIAL EQUATIONS 6 160 72 88

NUMERICAL METHODS FOR DIFFERENTIAL EQUATIONS

6 160 72 88

2ND YEAR 60 1600 394 1206

SEMESTER 3 30 800 330* 470

PACKAGES OF STATISTICS 6 160 72 88

ABSTRACT ALGEBRA 6 160 72 88

FUNDAMENTALS OF SCIENTIFIC RESEARCH. PROBLEMS OF NUMBER THEORY AND

6 160 48 112

42

PROBABILITY THEORY

FUNDAMENTALS OF SCIENTIFIC RESEARCH. MODELS OF MATHEMATICAL PHYSICS

6 160 48 112

INSURANCE PROBABILITY RISK MODELS 6 160 64 96

WEAK CONVERGENCE OF MEASURES 6 160 70 90

GRAPH THEORY 6 160 72 88

MATHEMATICAL THEORY OF NAVIER-STOKES EQUATIONS

6 160 68 92

VARIATIONAL METHODS FOR NONLINEAR PHENOMENONS

6 160 56 74

ASYMPTOTIC METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

6 160 70 90

SEMESTER 4 30 800 64 736

MASTER’S THESIS 25 670 32 638

MASTER’S THESIS SEMINAR IN PROBABILITY THEORY AND NUMBER THEORY

5 130 32 98

MASTER’S THESIS SEMINAR IN DIFFERENTIAL EQUATIONS

5 130 32 98

43

APPENDIX No 2List of Academic Staff

List of academic staff engaged in SP Mathematics

No Name, surname[link to CV]

Research degree, academic title

Year of

birth

Teaching load in the SP Research field

Exp

erie

nce

in r

esea

rch

(yea

rs)

Exp

erie

nce

in r

esea

rch

(yea

rs)

Aff

iliat

ion

Course unit title[link to course unit description]

Credits

1. Paulius Drungilas

Ass. Prof. 1980 Abstract Algebra 6 Algebraic numbers, polynomials

12 11

2. Artūras Dubickas

Prof. 1964 Mathematical Writing at Higher Level

6 Algebraic numbers, distribution modulo 1.

29 19

3. Dainius Dzindzalieta

Lecturer 1985 Packages of Statistics 6 Probability theory 7 6

4. Audrius Kačėnas

Lecturer 1969 Dynamical Systems 6 Value distribution of the Riemann zeta-function

20 15

5. Kristina Kaulakytė

Lecturer 1983 Integral Equations 6 Mathematical models of viscous fluids.

8 8

Function Spaces 6

6. Arvydas Kregždė

Ass. Prof. 1956 Mathematics in Modern Finance

6 Mathematical modelling of sovereign risk

34 34

7. Antanas Laurinčikas

Prof. 1948 Analytic Number Theory 6 Analytic and probabilistic number theory, value distribution of zeta-functions

45 42

Weak Convergence of Measures

6

Supplementary Chapters in Functional Analysis

6(L)

Fundamentals of Scientific Research. Problems of Number Theory and Probability Theory

6

8. Eugenijus Manstavičius

Prof. 1947 Probabilistic Combinatorics 6 Analytic and probabilistic combinatorics,

47 44

44

probabilistic number theory

Probability Theory and Mathematical Statistics

6

Stochastic Processes Theory 6

Graph Theory 6

Master’s Thesis Seminar in Probability Theory and Number Theory

6

9. Konstantinas Pileckas

Prof. 1954 Partial Differential Equations 6 Elliptic differential equations, Navier–Stokes equations, asymptotical methods

37 32

Mathematical Theory of Navier-Stokes Equations

6

Fundamentals of Scientific Research. Models of Mathematical Physics

6

Master’s Thesis Seminar in Differential Equations

6

10. Mindaugas Skujus

Lecturer 1984 Asymptotic Methods for Partial Differential equations

6 Asymptotic conditions at infinity for non-stationary Stokes and Navier–Stokes problems

7 7

11. Artūras Štikonas

Prof. 1962 Numerical Methods for Differential Equations

6 Numerical Methods for Non-Linear Problems, Mathematical Modelling, Problems with nonlocal Boundary Conditions

27 23

Function Spaces 6

12. Rimantas Vaicekauskas

Prof. 1964 Parallel Computing 6 Modelling of lighting systems with advanced colour rendering properties. Parallel computing.

25 21

13. Algirdas Javtokas

Lecturer 1979 Packages of Statistics 6 Non-classical zeta-functions

10 7

14. Kęstutis Kubilius

Prof. 1953 Stochastic Differential Equations

6 Stochastic differential equations

33 21

15. Stasys Rutkauskas

Ass. Prof. 1951 Variational Methods for Nonlinear Phenomenons

6 Partial differential equations

40 26

16. Jonas Šiaulys

Prof. 1960 Insurance Probability Risk Models

6 Risk theory, actuarial mathematics, Probability theory

29 25

45

APPENDIX No 3Curricula Vitae of Academic Staff

For Curriculum Vitae use link at Name Surname at Appendix No 2 or use link All CV

APPENDIX No 4List of Students’ Graduation Theses (2012–2016)

No Student(surname,

name)

Title of graduation thesis Supervisor’s name, surname, position,

research degree

Mark

Graduation theses of 2012

1. Alicija Eismontaitė

Solvability of a Mathematical Model of Dissociative Adsorption and Associative Desorption Type

Doc. Dr.Algirdas Ambrazevičius

10

2. Rūta Jegnoraitė-Juškienė

Asymptotic Analysis of Poiseuille Type Flow in a Thin Pipe

Prof. Habil. Dr.Konstantinas Pileckas

10

3. Jelena Lukina On two Species Interaction Model Prof. Dr. (HP)Vladas Skakauskas

10

4. Aušra Mikalajūnaitė

The Joint Universality of Dirichlet L-functions

Prof. Habil. Dr.Antanas Laurinčikas

9

5. Jurij Novickij On the Stability of an Explicit Difference Scheme for Hyperbolic Equation with Integral Conditions

Prof. Habil. Dr.Feliksas. Ivanauskas

10

6. Robertas Petuchovas

Distribution of combinatorial Multisets Component Vectors

Prof. Habil. Dr.Eugenijus Manstavičius

10

7. Vytautas Stepanauskas

Lithuania’s inhabitants Mortality Prognosis

Prof. Dr. (HP)Jonas Šiaulys

9

8. Raivydas Šimėnas

On the Speiser Equivalent for the Riemann Hypothesis

Prof. Dr. (HP)Ramūnas Garunkštis

10

Graduation theses of 2013

1. Evelina Balčiūnaitė

Ruin Probability of the Rationally Distributed Claims

Prof.(HP), dr.Jonas Šiaulys

9

46

2. Audrius Buivydis

Approximation of analytic functions by shifts of Hurwitz zeta-functions

Prof. Habil. Dr.Antanas Laurinčikas

9

3. Darius Eimontas

Modelling of Cell Microparticles Transport

Prof.(HP), dr.Vladas Skakauskas

10

4. Marius Domarkas

Frequency of Decomposable Combinatorial Structures with Restrictions

Prof. Habil. Dr.Eugenijus Manstavičius

9

5. Šarūnas Germanas

Power Approximation of Transmission Disequilibrium Test Using Poisson Distribution

Doc. Dr.Audronė Jakaitienė

10

6. Laura Gineitytė Universality of Periodic Hurwitz zeta-Functions

Prof. Habil. Dr.Antanas Laurinčikas

10

7. Dmitrij Mochov

Extension of the universality theorem for the periodic Hurwitz zeta-function

Prof. Habil. Dr.Antanas Laurinčikas

10

8. Rasa Nauckūnaitė

One universality theorem for Dirichlet L-functions

Prof. Habil. Dr.Antanas Laurinčikas

6

9. Mazgelis Rimgaudas

Sustainability of Government Debt in the Baltic States and Poland

Doc. Dr.Arvydas Kregždė

8

10. Daiva Suchockaitė

A Generalization of the Universality Theorem for Drichlet L-functions

Prof. Habil. Dr.Antanas Laurinčikas

7

11. Aurelija Šadreikaitė

The Mellin transform of the Riemann zeta-function in the critical strip

Prof. Habil. Dr.Antanas Laurinčikas

9

12. Gražvydas Šemetulskis

On Polynomials with Flat Squares Prof. Habil. Dr.Artūras Dubickas

10

Graduation theses of 2014

1. Rokas Astrauskas

Numerical Qualitative Analysis of the Solutions Cancer Therapy Applicable Reaction-diffusion Equations

Prof. Habil. Dr.Feliksas Ivanauskas

10

2. Jaunius Eitmantis

Height reducing of cubic algebraic integers

Doc. Dr.Paulius Drungilas

10

3. Sigitas Laukevičius

Mathematical Modelling of the Half of Biosensors Current

Prof. Habil. Dr.Feliksas Ivanauskas

8

47

4. Gailė Paukštaitė

Generalized Green’s Functions for Discrete Boundary Value Problems with Nonlocal Multipoint Conditions

Prof. Dr. (HP)Artūras Štikonas

10

5. Viktorija Suško A Limit Theorem for one Class of Hurwitz zeta-functions

Prof. Habil. Dr.Antanas Laurinčikas

9

6. Piotr Tarasov Cycle Lengths in Cubic Graphs Prof. Habil. DrMindaugas. Bloznelis

10

7. Gediminas Viliūnas

The Number of Zeros of a Linear Combination of Dirichlet L-functions

Prof. Habil. Dr.Antanas Laurinčikas

9

Graduation theses of 2015

1. Mantas Borodičas

On a Prime Generating Function Prof. Habil. Dr.Artūras Dubickas

10

2. Martynas Burbulevičius

Characteristic Curves for Problems with Nonlocal Boundary Conditions

Prof. Dr. (HP)Artūras Štikonas

8

3. Gediminas Drazdauskas

A Corollary of the Mishou Theorem for a Composite Function

Prof. Habil. Dr.Antanas Laurinčikas

9

4. Aurimas Makauskas

A Joint Discrete Universality Theorem for the Riemann and Hurvitc zeta-Function

Prof. Habil. Dr.Antanas Laurinčikas

9

5. Asta Mincevič A Discrete limit Theorem for the Hurwitz zeta-function

Prof. Habil. Dr.Antanas Laurinčikas

10

6. Eglė Šūmakarytė

About one Elliptic System Having an Anisotropic with Respect to the Small Parameter Epsilon Matrix

Prof. Habil. Dr.Konstantinas Pileckas

10

Graduation theses of 2016

1. Justas Jankūnas

Non-Steady Fluid Flow Modelling in Thin Tube Structure

Doc. Dr. Olga Štikonienė

10

2. Laima Kaziulytė

Asymptotic Distribution of Beurling Integers

Prof. Dr. (HP)Ramūnas Garunkštis

10

3. Martynas Kupšys

The Second Order Differencial Equations on Simple Graphs

Prof. Dr. (HP)Artūras Štikonas

8

4. Vaida Rokaitė Asymptotic Formulas for a Number of 2-regular Graphs

Prof. Habil. Dr.Eugenijus

8

48

Without Long Cycles Manstavičius

5. Adelė Vaiginytė Discrete Universality of Composite Functions

Prof. Habil. Dr.Antanas Laurinčikas

10

6. Mindaugas Venckevičius

Reccurent Formula of Finite Time ruin Probability in three Claims Risk Model

Dr. Andrius Grigutis 9

7. Paulina Žvirblytė

The Topological Proof of Abel-Ruffini Theorem. II

Prof. Dr. (HP)Ramūnas Garunkštis

9

APPENDIX No 5

Summary of Previous Assessment Report

The Lithuanian Centre for Quality Assessment in Higher Education has invited four university experts (hereinafter called Expert Team) from Estonia, Latvia, Lithuania and Norway to review and assess the Master level study programme “Mathematics” 62401P103 (621G10001) at the Vilnius University (VU). The Expert Team visited the Faculty on November 23-24, 2010.

The Expert Team met the administrative staff of the Faculty, the staff members responsible for preparation of the Self-assessment report, and teaching staff. The Expert Team also conducted interviews with some students, met graduates and employers. The Expert Team had possibility to observe various study support services (classrooms, computer services, library), as well as to familiarize with students' final works.

PROGRAMME ANALYSIS

Programme aims and learning outcomes. Study programmes in Mathematics at Master level are accomplished by the faculties of six Lithuanian universities, it seems that this programme is the most attractive one. The purpose of the study programme Mathematics is compatible with the mission VU. The aims of the programme are strongly correlated with its purpose. Learning outcomes are realistic. Graduates of this study programme get a good insight into mathematical statements, their proofs and interrelations. The intended learning outcomes of the study programme have a tendency to more practical objectives: to applications of mathematics and informatics. Development and implementation of the study programme is based on the requirements of VU and Ministry of Science and Education of Lithuania. Transformation of the learning outcomes is considered to take place when necessary.

Curriculum design. Study programme is adapted to meet the requirements of the consecutive study programmes regulation documents. Relations between study subjects, as well as their consequences, are preserved. The study programme content conforms to the requirements of legal acts and, undoubtedly, enables students to achieve nearly all learning outcomes. Topics delivered in the subjects are up-to-date and more or less sufficient to achieve respective learning outcomes. Forms and methods used in classes are satisfactory.

Staff. The competence of the teaching staff is sufficient to reach aims and learning outcomes of the programme. They have high qualification. The staff is stable and its changes are minimal. The study programme corresponds to the research interests of the teaching staff. During the assessment period, the

49

majority of teaching staff members participated in various international projects. On the other hand the scope of regulation and promotion of teachers' professional development is comparatively low.

Facilities and learning resources. There are sufficient number of lecture rooms and computer classes for both implementing the study programme and performing individual assignments. Working places and working conditions in libraries for maintaining high-level studies are quite good. The computer hardware and software are up-to-date and legal. According to the Self-assessment report, the number of the main textbooks is sufficient for students, and conditions to get necessary literature can be estimated as good. Access to electronic databases through personal Internet connection is available. The books (at least one copy) from the main reference list of each subject are available in the MIF library. Students have a possibility to borrow some books from funds of the responsible for the study programme departments.

Study process and student assessment. The established minimal requirements for admission are sufficient in order to have students who are prepared enough for studies. Increasing students' motivation for successful study is based on presentations of the speciality and achievements of graduates. All types of lectures and practical works are uniformly distributed over semesters, except possibly those which are given as intensive courses by invited lecturers. The outgoing mobility of teachers is not sufficient. The incoming mobility of students is sufficient. Informing students about the study programme is on good level. Student's knowledge assessment criteria are based on the learning outcomes of a particular study subject. The composition of final examination grades follows accumulative principle. The detailed guidelines and requirements of final Master theses are approved by the department of Differential Equations and Numerical Mathematics and the Department of Probability Theory and Number Theory using procedural instructions confirmed by the Senate Commission of VU. Neither non-formal non self-education studies are recognized. One of the greatest advantages gained in the programme of graduate studies is fairly well-developed abstract thinking that makes it easy to adapt to the ever-changing environment.

Programme management. Students' representative participates in the study programme committee as an observer. All the data on the programme implementation are collected accurately and sufficiently. The internal study programme quality evaluation process is more or less continuous. Following the Self-assessment report, urgent programme management questions are discussed during the meetings. The application of assessment results is observable - they are used efficiently to improve quality of the study programme. There is no data (in the Self-assessment report) on the participation of graduates in the study programme management process.

RECOMMENDATIONS

l. Either two existing study plans (for two branches) should be combined into one study plan or they should be registered as two separate study programmes.

2. A system for feedback from students during an academic year should be established at the department/faculty level, and visibility of taken actions should be made available to students.

3. Possibilities to take elective courses are limited; more flexibility via individual study plans should be implemented.

4. It is recommended to include into the study programme possibility to take brief elective courses on different data analysis tools (SAS, SPSS, etc.), which are often used in practice (for students without previous knowledge of such tools).

5. A system for staff professional development and promotion should be formalized (e. g . possibilities for sabbatical leave, etc.).

6. The outgoing mobility of students should be increased (more bilateral agreements with universities giving courses in English are needed).

50

7. Description of subjects should be revised (in many learning outcome is not described correctly or missing, detailed description of contents of credits is unclear, students' individual work is not specified, etc.).

8. Some business-oriented subjects should be added to the curriculum (possibly as electives).

GENERAL ASSESSMENT

The study programme Mathematics (state code -62401P103) is given positive evaluation.

51