Faculty of Mathematics and Natural Sciences(30!10!2011)Arme(4)

Committee members who have designed the draft for the study programme in Financial Mathematics in Banking and Insurance are:

1. Prof.dr.Minir Efendija, Dean of FMNS

2. Prof. dr. Muhib Lohaj , Chief of the Department of Mathematics

3. Prof. dr. Qamil Haxhibeqiri

4. Prof. dr. Rexhep Gjergji

5. Prof. dr. Faton Berisha

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UNIVERSITY OF PRISHTINAFACULTY OF MATHEMATICS AND NATURAL SCIENCES – FINANCIAL MATHEMATICS IN BANKING AND INSURANCE 2012

SELF-EVALUATION REPORT

(DRAFT)

6. Mr.sc. Ramadan Limani

7. Mas. Sc. Armend Shabani

8. Dr. sc. Mimoza Dushi, coordinator academic development in FMNS

9. Vlera Mehmeti, student

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Contents1. Introduction...........................................................................................................6

Self-evaluation....................................................................................................62. General notes about faculty.................................................................................6

History of faculty................................................................................................6 The organization of decision-making structures.................................................7 Mission..............................................................................................................10 Vision................................................................................................................10

3. Academic staff.....................................................................................................10

Permanent and external academic staff.............................................................104. Quality assurance................................................................................................11

4.1. Regulations for quality assurance procedures...................................................114.2. Submission of evaluation procedures................................................................114.3. Mechanisms for implementation of security measures.....................................114.4. The following procedure for improvement (follow up) and use of evaluation results.......................................................................................................................124.5. Procedures and rules for curriculum development............................................12

5. Total number of students...................................................................................12

Numbers of students (Bsc, MA, PhD) in existing programs.............................12 Number of graduates in last three years............................................................13 Scheme of career development of young researchers.......................................13 Employment of graduates from last three years................................................14 Legal report between institution and students...................................................14 Study taxes – 50 euro per semester...................................................................14

6. Research...............................................................................................................14

7. International cooperation...................................................................................14

8. Finance and Infrastructure................................................................................15

Budget spending for 2009, 2010 and planned budget for 2011, according to mains specifications in FMNS.................................................................................15 Facilities, equipment and apparatuses...............................................................15

9. Study program....................................................................................................17

Name of study program (exact name of the study program).............................18 Profile and aim of program (basic description based on aims of the study program)...................................................................................................................18 Results of learning (level of study program – list 5-10 RN).............................19 Admission requirements for students and selection procedures.......................19 The title of academic degree (exact name)........................................................19 Exam regulation................................................................................................19 Study form the structure and duration...............................................................20

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Short description of syllabuses ..........................................................................23

Presentation of actual implementation by external exsperts....................................41 CURRICULUM VITAE...................................................................................58 Questionnaire for subject evaluation.................................................................64 One Contract....................................................................................................68

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Financial Mathematics in Banking and Insurance

1. Data about applying institution

Description (Name) of Institution FMNS –Department of MathematicsAddress Street “Mother Theresa, nr.5, PrishtinaAccredited by 1 October 2010 Accredited until to 30 September 2013Contact (Tel.,mob.,e-mail)

Dean, Minir EfendijaO38 249 872, 044 350 553, [email protected]

Academic programmes Financial Mathematics in Banking and Insurance

Application date 30/10/2011

1. Introduction

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Self-evaluation

This report presents the result of self-evaluation of Financial Mathematics in Banking and Insurance branch in Department of Mathematics in Faculty of Mathematical and Natural Sciences in cooperation with Faculty of Economics conducted in academic year 2011. Aim of this research program in Financial Mathematics and Banking and Insurance is education of student to be capable of solving problems that arise in banking and insurance sector, trading activities and managing health and pension funds. Graduates from this research program have sufficient theoretical knowledge to follow the study program of the second cycle (master) –Financial Mathematics in Banking and Insurance.The report is structured in a form that contains information about the management structure of the Department of Mathematics: academic staff, administrative staff, teaching and learning process and students. It is based in previous report, accredited for one-year period (academic year 2011 – 2012), and all proposals, observations and very valuable suggestions given by the Accreditation Agency and OAD (Office of Academic Development) instruction of UP are fully incorporated in this report. Given recommendations have contributed greatly to the quality and content of the document. During the working process we tried to present a true picture of the department and faculty as an institution. For preparation of this report the group from Department of Mathematics was engaged renewed with some new members. The same has been discussed by department staff and students and their suggestions and reasonable proposals were taken in consider.

2. General notes about faculty

History of faculty

Faculty of Mathematics-Natural Sciences (FMNS) in Prishtina was founded in 1971, under the decision of the Assembly of Kosovo (Official Gazette of SAP Kosovo No. 37/71). Studies of Natural Science and Mathematics (Biology, Physics, Chemistry and Mathematics) have started eleven years ago within the Faculty of Philosophy, founded in 1960. In 1971, from this faculty, the section of natural science is disunited and Faculty of Mathematics, Natural Sciences, which have been established, which organize regular and correspondence studies in five departments: Biology, Physics, Geography, Chemistry and Mathematics. These departments are still operating.Due to political and social circumstances in which Kosovo has been into, particularly in the last decade of the XX century, FMNS activity, as well as UP, time after time have faced with major challenges and obstacles. These obstacles many times have been successfully managed to overcome thanks to work of the academic personnel,

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who not only justified the establishment of this faculty but managed to successfully fulfill its mission, as professors and scientists. With aim of general advancement of studies, increase of quality and their efficiency, FMNS academic personnel undertook an action to change the curriculum. Taking into account the objective to achieve European study standards and goals for genuine cooperation with European universities, a study model according to Bologna agreement (3 +2 +3) proposed and adopted at the University of Prishtina. In this way, since 1st of October of the academic year 2001/2002 the bachelor studies under the new curricula have started. After review and evaluation of these curricula, in academic year 2005/06 plans approved by the Senate of the University of Prishtina started to be implemented, where several departments have re-formulated the study system in 4 +1 +3, always in compliance with Bologna agreement.

The organization of decision-making structures

The Faculty is managed by Dean and Vice Deans. Vice Dean for lecturing process supervises the progress of learning within Departments, examines the work of clerks in the students service and consults with the Coordinator for ECTS. Meanwhile, Vice Dean for financial matters deals with budget management of faculty and is closely related to Cashier, lecturing and finances.

Organization of decision-making structures related to academic affairs

Each department has its Professional Science Lecturing Council (SLC), where lecturing and scientific issues pertaining to that certain department are raised and discussed. Department’s Proposals are submitted to the Science Lecturing Council of FMNS.

The Science Lecturing Council of FMNS is constituted out of 37 members; all of them have the right to vote. These SLC members are elected under a secret vote of all members of academic and administrative personnel. Three members of this council are from the Dean’s Office, one from the Administration, two from students Union and others are academic personnel. The SLC working method is defined under Regulation on the work of SLC. The work of the council is administrated by the Dean of the Faculty.

As any academic unit, the FMNS as well, in order to evaluate and control the work, has a large number of Committee. Some of Committees are established directly by the Dean of FMNS and some by the SLC of FMNS. Amongst them:- Established by Dean

o Committee for Equivalency of Diploma

o Disciplinary committee

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o Committee for drafting the self-evaluation report

o Committee for students questions as per complaints

o Committee for the receiving the assets – equipment

o Committee for registration of equipment and inventory

o Committee for recruitment of new workers

o Committee for enrolment of new students

o Committee for complaints

- Established by SLC of FMNS o Committee for review

o Committee for PhD, and

o Master Committee for lecturing

Organization of decision-making structures within administration

The Administration is a body which assists the work of academic personnel. It is managed by several structures, depending on the sector and nature of work. These sectors are: Student service, which is divided for Bachelor, Masters and PhD students.

Persons in this sector are responsible for submitting exams submitting diplomas from students and preparation of examination reports for academic personnel. As a sector is managed by Vice Dean for lecturing matters.

Finances have the responsibility to manage the budget within the university and handover the budget requests in the supreme bodies, Rector’s Office. This sector is managed by Vice Dean for financial matters.

Rest of the administration, including computer network administrators, librarians and laboratory technicians are managed by the Secretary of the Faculty.

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Vice-Dean for financesVice-Dean for teaching

STC

Secretariat Other administrative staff

Financial services

Dep. of CHEMISTRY

Dep. of MATHEMATICS

Dep. of PHYSICS

Dep. of BIOLOGY

Dep. of GEOGRAPHY

Technicians – student’s service

Coordinator for ECTS – quality assurance

DEAN

Organizational scheme of FMNS (organogram)

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Mission

The mission of the Faculty of Mathematical and Natural Sciences is to provide education for students in three levels: bachelor, master and doctorate. To lead the scientific research work and to contribute in society, including the contribution in economy and culture. It is the responsibility of all professors to teach, to be active in their professional and scientific research and provide services to their university and society. Moreover, to prepare new cadres with high qualification who will be willing to face the demands of Kosovo society. Their common aim (teacher-student) is to provide high quality of research through various disciplines.

Vision

Trainig of teaching staff for more successful implementation of modern teaching methods

Continuous improvement of study programs, always conform Bologna declaration.

Providing laboratory and technical infrastructure to meet the requirements for advancement in teaching and scientific work.

To ensure the public funds and other funds that will affect the implementation of teaching and scientific research and increase their quality.

Finding the opportunity to use the results of scientific research in learning process so that students become familiar with methods, methodologies and present them to the key processes that will contribute to solve different problems.

3. Academic staff

Program of Financial Mathematics and Banking Insurance will be carried out from teachers from Department of Mathematics in FMNS and teachers from Faculty of Economics.

Permanent and external academic staff

Total number of academic staff (permanent and external)Full Prof. Associated Prof. Assitant Prof. Asistant New Asistant

Permanent 7 2 6External 7 4 24

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4. Quality assurance

4.1. Regulations for quality assurance procedures

Faculty of Mathematical and Natural Sciences implements the directives and instructions from respective structures of Rectorate. Directives published in 2008 as “Directives for quality assurance in University of Prishtina”.

4.2. Submission of evaluation procedures

To be more objective in evaluating the teaching process the Faculty of Mathematical and Natural Sciences uses questionnaires formulated within the University of Prishtina for academic staff, administration and students. All of these separately questionnaires containing questions relevant to each category.

Questionnaire for academic staff includes three categories of questions: for faculty, teaching and learning and for scientific research activity. Its purpose is to draw the sufficient data that will influence the continuous improvement of these three categories.

Questionnaire for administrative staff and support staff of university contains questions that correspond to their nature of duties and responsibilities in the workplace. Mainly, the aim is to draw information on professional training of administrative staff, their working conditions and the relationship with academic staff.

Questionnaire for students has to do more with bachelor level students through which the data will be provided for teaching and learning, practical/laboratory work for infrastructure services.In addition to these three questionnaires is the student evaluation questionnaire for subjects and teaching, which is organized within the academic year by the mechanisms responsible in Rectorate. Through this survey the student has the opportunity to give his estimates for each subject including the teacher so that based on their responses to take steps for further improvements.

4.3. Mechanisms for implementation of security measures

Unit of quality assurance at the University in cooperation with units at the faculty achieve survey with academic staff, administrative and students. While at UP, the quality assurance unit continuously organizes data analysis each semester through evaluation questionnaires for subjects and teaching (see attached appendix). It is organized with two classes for each school year.

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Also within FMNS in each end semester in permanent way the evaluation of courses is done by teachers. They also assess the achievements on the field which in order to make improvements in the next semester, as working conditions permit.

4.4. The following procedure for improvement (follow up) and use of evaluation results

System of quality assurance has no tradition at the University of Prishtina, therefore is required to undertake some basic measures so that gradually in coordination with relevant units at the University this could be expanded. Within this the students are provided with information about studies according to Bologna system and information with results from questionnaires.

4.5. Procedures and rules for curriculum development

Continuous improvement of the curriculum is the responsibility of teachers. Based on the results that is obtained from the student evaluation questionnaire for subject and teaching, teacher has an obligation to investigate possible criticism and improve curriculum. This is one of evaluation mechanisms and the other depends on literature and newness that meets the specified area so the teacher continually updates subjects that is teaching.

5. Total number of students

Numbers of students (Bsc, MA, PhD) in existing programs

The current program of this study provides only bachelors level of studies. Later it is planned to provide studies in master level.

Bachelor Master PhDM F M F M F39 41 - - - -Total: 80 total total

Department of MathematicsFinancial Mathematics in

80 39 41

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Banking and InsuranceTotal 80 39 41

Number of graduates in last three years

Bachelor MasterAcademic year 2008/2009 Academic year 2008/2009Number of students Number of

graduatesNumber of students Number of students

195 4 8 1Academic year 2009/2010 Academic year 2009/2010Number of students Number of


200 74 7 2Academic year 2010/2011 Academic year 2010/2011Number of students Number of


200 71 21 3Computer Science 358 196 162Totali 595 329 266

Scheme of career development of young researchers

After successful completion of bachelor studies in this direction the young researchers will be able to develop their career in three choices: educational, banking system and scientific.Graduates can decide for their professional career development to continue in banking system by involving in various banks, insurance companies and other microfinance and macro finance institutions. Also future graduates will be able to engage in teaching in professional secondary schools.Also another opportunity for them is continuing their careers in further studies at master level (which are planned to be organized after first generation graduates).

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Employment of graduates from last three years

As it is first year of studies, we can not talk about employment.

Legal report between institution and students

Legal report between FMNS and students is regulated by the statute of UP.

Study taxes – 50 euro per semester.

6. Research

For this refer to form in Annex “Work and scientific projects”

7. International cooperation

In international cooperation, Department of Mathematics has done these activities (visits): (three last years)

1) Dr.sc. Qëndrim Gashi, Institut des Hautes Études Scientifiques (IHES)http://www.ihes.fr/jsp/site/Portal.jsp (january 2010 ‐ avgust 2010)

2) Dr.sc. Qëndrim Gashi, The Hausdorff Research Institute for Mathematics (HIM)http://www.hausdorff‐research‐institute.uni‐bonn.de/ (april 2010)

3) Mr.sc. Bujar Fejzullahu, Universidad Carlos III de Madrid, December 2010 ‐ March 2011

4) Mr.sc. Elver Bajrami, Mr.sc. Kajtaz Bllaca, University of Sarajeva, Hyperbolic geometry and arithmetic, 03.10.2010‐10.10.2010

5) Mr.sc. Kajtaz Bllaca, Mr.sc. Elver Bajrami, University of Sarajeva, Number Theory ‐ Sarajevo, January 31 ‐ February 25, 2011

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8. Finance and Infrastructure

Budget spending for 2009, 2010 and planned budget for 2011, according to mains specifications in FMNS

Year WageGoods and services

Utilityexpenses Total

2009 924 394 217 983 81 829 1 224 206

2010 805 897 228 924 94 375 1 129 196

2011 920883 169316 94375 1 129196Total 2651174 616223 270579 3482598

Facilities, equipment and apparatuses

Department of Mathematics has in use the surface of 1388 m2. Offices are available to permanently employed academic staff and retired teachers. Offices are equipped with computers, printers and Internet connection tools needed for working process. Large number of offices is used by one teacher (mainly full professors) and in some offices are two or more teachers (assistants).By reforming the study system the space required for lectures and exercise (teaching rooms and laboratories) it is desirable to be greater. The large number of directions in Department of Mathematics and large group number of students, causes problems in teaching schedule during working days. Also it is necessary to posses another computer lab for which we have promises from Rectorate. Work equipment is divided in two parts: first part deals with the administration and faculty including Dean and the second part with equipment in offices and tools necessary for progress of learning in Department of Mathematics.

Working equipment in administration

The faculty administration is divided into several sectors: Dean office and other administrative services. Necessary working equipment are:

Working equipment in Dean office

Computer 5Printer 5Photocopy apparatus 1

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Working equipment in administration

Computer 6Printer 6

Working equipment in Department of Mathematics

All working equipment that are in use for preparation, learning process and scientific research in Department of Mathematics are:

Teaching equipment Computer 81Screen projector 3

Equipment (classrooms, teacher offices, laboratories, libraries, IT infrastructure, etc)

EquipmentClassrooms 4 (390 m2)Teacher offices 11 (200 m2)Computer labs 3 (150 m2)Library 1 (60 m2)

Information technologyComputers, Laptops, Projectors, wireless etc.

Hall of academic staff 1 (30 m2)

Administration and common space 1 (528 m2)

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9. Study program

Page #2 of the request for re-accreditation of the study program – launched from AAK

Description (name) of institutionUniversity of PrishtinaFaculty of Mathematical and Natural Sciences

Description of the study programFinancial Mathematics in Banking and Insurance

Level (abbreviations: Bsc, MA, PhD doctorate program, university course,

certificate or professional program

Bsc in Financial Mathematics in Banking and Insurance

Academic grade and title of diploma in complete and abbreviated form

Bachelor in Financial Mathematics in Banking and Insurance

Profile of academic program Professional

Groups of interestAll candidates who have completed secondary education with mature diploma

Minimal duration of study 3 yearForm of study (regular, without, severance, distance learning, etc)

regular

ECTS credit points (total per year) Total 180 ECTS, 60 ECTS per yearModules /Courses Obligatory courses

Analysis I, Analysis II, Algebra I,II, Discrete Mathematics I, Microeconomics, Optimization methods, Computer Lab, Introduction to programming, Stochastic processes I, Elective course, Analysis III, Theory of probability I, Financial mathematics, Macroeconomics, Banking management, Programming I, Numerical Methods I, Financial accounting, Elective course, Marketing, Statistics, Statistics applied in business, Theory of probability II, Stochastic processes II, Financial practicum, Risk and Insurance management, Game theory, Elective course, Albanian language, Academic writing

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Elective course at Department of Mathematics:Mathematical Modeling .Discrete mathematics II, Coding theory and cryptography, Applied mathematics in business and economy, Data structure and algorithms II, Database, Algorithm analysis, Numerical methods II, Nonlinear programming.

Elective course at Faculty of EconomicsFinancial management, Finance of corporate, Fundamentals of management, Public finances, Econometry, E-business, Financial management, Management of small and middle businesses.

Number of students enrolled for study 80 Head of study program Dr. sc. Muhib Lohaj, full professorPermanent academic staff, scientific/artistic)(categorized)

4 professors, 3 associate professors,3 lecturers, 7 assistante, 7 outer fellow collaborators

Study fee 50 euro per semester

Name of study program (exact name of the study program)

Financial Mathematics in Banking and Insurance

Profile and aim of program (basic description based on aims of the study program)

The main aim of the research program in Financial Mathematics in Banking and Insurance is creating experts capable to solve problems that arise in banking and insurance sector, in trade activity of exchanging goods and in managing health and pension funds. Graduates from this research program will have sufficient theoretical knowledge to follow the study program of the second cycle (master) – Financial Mathematics in Banking and Insurance.

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Results of learning (level of study program – list 5-10 RN)

1) basic knowledge of Mathematics2) basic knowledge of Economics and Finance3) basic knowledge of Informatics4) ability to solve non determinate problems through probability theory and

statistics5) ability to solve deterministic problems through optimization and operational

research6) ability to find approximate result for problems with numerical methods7) ability to use computer for problem solving and presentation of results

Level of studies: Bachelor

Admission requirements for students and selection procedures

If the program passes all foreseen stages the Department of Mathematics in FMNS plans to register 80 students every academic year. Based on opinions available, the interest of candidates is quite large which further increases the need for this program. Who can register in this program:

a) Everyone who possesses a graduation certificate (diploma)b) Everyone who possesses a graduation certificate (diploma) from professional

school with four year program. In this case there should be a mature examination which is not in professional mature examination (mathematics), if the Senate of UP decides otherwise.

For other conditions decides the Senate of UP.

The title of academic degree (exact name)

Bachelor of Mathematics – Program of Financial Mathematics in Banking and Insurance

Exam regulation

The procedure of examinations, methods of student evaluation will be conform Statute of UP.

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Study form the structure and duration

Regular studies will be organized with special courses. Financial Mathematics study program consists of:

1. Obligatory modules from Mathematics and Economics, and2. Elective modules

This shows the direct connection with the nation economy. Number of ECTS credits foreseen is 180 for a period of three years. Distribution of credits is 30 ECTS credits for each semester or 60 ECTS credits per year.The program takes place through lectures, exercises and laboratory exercises. Studies are regular. The program relies on those universities that have a long tradition in this program, which are accredited and are in Bologna system. Our program is based on program of Faculty of Mathematics and Physics in University of Ljubljana and DCU (Dublin City University).

Study plan

First year – First semester

Nr. SubjectHour

(L+U+L)ECTS Obligatory Teacher

1. Analysis I 3+3 6 Oblig.. Dr. sc. Naim Braha2. Algebra I 3+3 6 Oblig.. Dr. sc. Rexhep Gjergji3. Discrete Mathematics I 2+2 5 Oblig. Dr. sc. Qamil Haxhibeqiri4. Stochastic processes I 3+3 7 Oblig. Mr. sc. Ramadan Limani5. Computer Lab 1+0+3 6 Oblig.

Total 12+11+3 30

First year – Second semester Nr. Subject Hour ECTS Obligatory Teacher1. Analysis II 2+2 5 Oblig.. Dr. sc. Muhib Lohaj2. Algebra II 2+2 5 Oblig.. Dr. sc. Rexhep Gjergji3. Microeconomics 3+3 5 Oblig.. Dr. sc. Ramiz

Livoreka4. Optimization

methods3+3 5 Oblig.. Mr. sc. Ramadan

Limani5. Introduction to

programming2+1+2 5 Oblig.

Dr. sc. Faton Berisha.

Subject Hour ECTS Elective Teacher1. Applied

mathematics in 2+2 5 Z Dr.sc. Minir Efendija

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business and economy

2. Management of small and middle businesses

2+2 5 Z Dr.sc. Justina Pula

Total 14+13+2 30

It is compulsory to select one elective subject

Second year – First semesterNr. Subject Hour ECTS Obligatory Teacher1. Analysis III

2+2 5 ODr.sc. Minir Efendija

2. Theory of probability I

2+2 5 ODr.sc. Naim Braha

3. Programming I2+1+2 5 O

Dr.sc. Faton Berisha

4. Numerical methods I2+1+1 5 O

Dr.sc. Bujar Fejzullahu

5. Macroeconomy4+2 5 O

Dr.sc. Sinan Ademaj

Subject Hour ECTS Elective Teacher1. Mathematical

modeling2+2 5 Z

Dr.sc. Abdullah Zejnullahu

2. Databases2+0+2 5 Z

Dr.sc. Naim Braha

3. Fundamentals of management

2+2 5 ZDr.sc. Berim Ramosaj

Total 14+10(8)+3(5) 30


Second year – Second semesterNr. Subject Hour ECTS Obligatory Teacher1. Analysis IV

2+2 5 ODrs.sc. Minir Efendija

2. Financial mathematics

2+2 5 OMr.sc. Elver Bajrami

3. Theory of probability II

2+2 5 ODr.sc. Naim Braha

4. Banking management

4+2 6 ODr.sc. Gazmend Luboteni

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5. Financial accounting

3+3 5 ODr.sc. Skender Ahmetaj

Subject Hour ECTS Elective Teacher1. Data structure

and algorithms I2+1+1 4 Z

Dr.sc. Faton Berisha

2. Finance of corporate

2+2 4 ZDr.sc. Arben Dermaku

3. Numerical methods II

2+1+1 4 ZDr.sc. Bujar Fejzullahu

Total 15+11(12)+1(0) 30


Third year – First semesterNr. Subject Hour ECTS Obligatory Teacher1. Statistics 2+2 6 O Dr.sc. Muhib Lohaj2. Game theory 3+3 6 O Dr.sc. Qëndrim

Gashi3. Financial Practice 1+3 6 O4. Albanian

language2+1 4 O

Subject Hour ECTS Elective Teacher1. Web

programming2+0+2 4 Z Dr.sc. Faton

Berisha2. Coding theory and

cryptography2+0+2 4 Z Mr.sc. Kajtaz

Bllaca3. Analysis of

algorithms2+0+2 4 Z Mr.sc. Ramadan

Limani4. E – business 2+0+2 4 Z Dr.sc. Blerim

Dragusha5. Financial

management2+2 4 Z Dr.sc. Muhamet

AliuTotal 12+11(9)+2(4) 30

It is compulsory to select to elective subjects (one subject from rmathematics and one subject from economy).

Third year – Second semesterNr. Subject Hour ECTS Obligatory Teacher1. Statistics applied in

business2+2 5 O Dr.sc. Ajet Ahmeti

2. Risk and insurance 3+3 5 O Dr.sc. Fatos Ukaj

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management3. Stochastic processes

II2+2 5 O Dr.sc Naim Braha

4. Marketing 1+3 4 O Dr.sc. Nail Reshiti5 Academic writing 2+1 3 O

Subject Hour ECTS Elective Teacher1. Financial

management2+2 4 Z

2. Nonlinear programming

2+2 4 Z Dr.sc. Faton Berisha

3. Public finances 2+2 4 Z Dr.sc. Driton Balaj4. Econometrics 2+2 4 Z Dr.sc. Valentin Toçi

Total 14+15 30

It is compulsory to select one elective subject.

Remarks. Courses of third year: Albanian language and Academic Writing have been proposed based on the decision of the Senate of Prishtina University, of date 11/10/2011.

Short description of courses

Analysis I

Course Objective

Students will be introduced with basic concepts and techniques of mathematical analysis, such as, function, limit, continuity, derivative, and integral of a function with one variable. Analysis I is the foundation for other disciplines of mathematics through studying at the Departments of Mathematics, in technology and other sciences, as well as for differential geometry and its application in mathematics, science, technology and other fields.

Brief Content

Introduction: Numbers, series, limit. Functions with one variable: basic concepts, graph of a function, elementary functions, continuity, limit of a function, properties of continuous functions. Derivative: definition and the mechanical and geometric interpretation, rules of derivation, derivation of elementary functions, using the derivative for sketching the graph of a curve (monotony, extreme values, etc.).

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Integrals: indefinite integral, elementary table of integrals, methods of integration, definite integral and application.

Learning outcomes

After completing this course students will be able to: Recognize and understand the function with one variable, and its derivation

and integration.

Formulate correctly mathematical problems, select the method for their solving, and analyze the obtained results.

Literature

1. Brian S. Thomson, Judith B. Bruckner, Andrew M. Bruckner: Elementary real analysis, thomson・bruckner, 2001. (e preferuare)

2. Walter Rudin, Principles of mathematical analysis, McGraw-Hill, 1976.3. N. Braha dhe I. Shehu, Analiza matematike I, Prishtine, 2006(e preferuare)

Analysis II

Course Objective

Student will be introduced with basic concepts and techniques of mathematical analysis and differential geometry, and their application in mathematics, science, technology and other fields.

Brief Content

Different methods of representing a curve in a plane, the arc length, the area of a surface. Complex plane, elementary functions with complex variables. Series and power series; series given in the recurrent form; numerical series, functional series; Taylor series, Fourier series. Functions with two or more variables: notion of the function with two variables, graph, level lines, leves surfaces, functions with three variables, partial derivatives, gradient and directional derivative, Taylor’s formula, extremums and connected extremums. Theorem of implicit functions. Basic differential equations: basic concepts, equations with separable variables, homogeneous equation, first order linear equation .Second order ordinary differential equations, second order linear equation, set of linear equations.

Course aims

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Recognize basic concepts and techniques of mathematical analysis and differential geometry and their application in mathematics, technical science and other disciplines.

Learning outcomes

After completing this course student will be able to: Recognize and understand further notions of differentiation and integration;

Recognize and understand functions with several variables;

Recognize and understand basic concepts of differential equations.

Literature

1. M. Efendija, Analiza Matematike II, në botim të UP.2. M. Efendija, Analiza Matematike III & IV, Prishtinë, 2005.3. E. Kreyszig: Advanced Engineering Mathematics, Huboken, J. Wiley, 2006.

Discrete Mathematics I

Course Objective

Student will be introduced with some of the most important notions, methods and techniques of combinatory and discrete mathematics and their application in concrete situations.

Learning outcomes:

After completing this course student will be able to: Carry out various calculations applying Venn’s diagrams for operations with

sets and computational representation of sets and operations with them; Use the method of mathematical induction for proving various facts; Apply various rules of computing (the rule of product, inclusive-exclusive

principle, the principle of ‘pigeon’s cage) in solving the respective problems; Make difference between various combinatory situations in which

permutations are used for solving and those in which combinations are used for solving different problems.

Literature

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1. Keneth Rosen: Discrete Mathematics and Its Applications, McGraw Hill, 2003. 2. D. Veljan, Kombinatorika i diskretna matematika, Algoritam Zagreb, 2001. 3. Peter Grossman, Discrete Mathematics for computing, Monach University, 1995.

Stochastic Processes I

Course Objective

The student will be introduced with elementary mathematics as a necessary tool to understand basic concepts of stochastic processes, such as free motion, discrete and continuous processes, Markov’s processes, Poisson’s processes, stationary processes.

Learning outcomes

After completing this course the student will be able to:

handle with basic concepts of elemantary mathematics,

undersatnd the stochastic processes,

describe basic concepts about the discrete processes,

describe continuous processes,

apply Markov’s adn Poisson’s processes.

Literature

1. Intermediate Algebra with applications, Terry H. Wesner, Harry L. Nustad,WCB Group 1991.

2. A First Course in Stochastic Models Henk C. Tijms, Wiley , 2003.

3. The elements of stochastic processes, Norma Bailey, John Wiley and Sons, 1964.

4. Stochastic processes, J. L. Doob, Wiley , 1990.

Optimization methods

Course Objective

The main objective of the course is to prepare students that from practical problem that may occur in production, transport, finance to be able to build a mathematical

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model so that mathematical solutions obtained thereby to be interpreted in the field of production, transport and finace.

Learning outcomes

After completing this course the student will be able to:

formulate a linar programming problem,

use graphical method for solving a linear programming problem,

formulate and solve the dual problem of a linear programming problem,

use the algorithm of the simplex method for solving different problems related to productivity, transport etc.

apply graphs in solving different problems in finace and economy.

Brief Content

This course will prepare students to use different methods to find optimal solutions to a problem that may occur in real life (economy, business, finance, production, transport etc). For this purpose in context of this course will be explained most popular methods for optimal solution: Linear programming (graphic method and simplex), Dynamic programming, Quadratic programming and some algorithms from Graph theory as Dijkistra-s.

Literature :

1. Edward T. Dowling, PhD: Mathematical methods for busines and economics, Schaum’s outline, Mc-Graw Hill.

2. Thomas H. Cormen; Charles E. Leiserson; Ronald L. Rivest: Introduction to Algorithms MIT Press, McGraw-Hill Book Company, 1999

Analysis III

Course Objective

Broadening of basic knowledge in analysis and its application in mathematics, science and technology and other fields.

Brief Content

27

http://www.amazon.com/Games-Strategy-Third-Avinash-Dixit/dp/0393931129/ref=dp_ob_title_bk

http://www.amazon.com/Games-Strategy-Third-Avinash-Dixit/dp/0393931129/ref=dp_ob_title_bk

Parametric integrals, beta and gamma functions. Double and triple integrals and their most important application. Curves and surfaces in space, tangent on a curve, normal on a surface. Line integral, surface integral, arc length, area of a surface and other applications. Vector calculus basics, Gauss’ and Stokes’ theorems. Partial differential equations. Basic concepts of metric spaces, theorem of the fixed point.

Learning outcomes

After completing this course student will be able to: Recognize and understand notions of differentiating and integrating functions

with several variables and of partial differential equations.

Formulate problems in mathematical language and select the method for their solving

Develop skills for use of relevant literature on the subject.

Literature

1. M. Efendija, Analiza Matematike III & IV, Prishtinë, 2005.2. E. Hamiti, Matematika III, Prishtinë,...3. P.DuChateau, D.W. Zachman, Schaum’s outline of Theory and Problems of

Partial Differential Equations, McGraw-Hill, New york, 1076

Financial Mathematics I

Course Objective

Student will be introduced with some of the mathematical concepts applied widely in economy and finance and the methods and techniques of their application in concrete situations.

Learning outcomes

After completing this course student will: Know how to use adequate mathematical formulas in solving various

problems in finance; Prove that he has knowledge about proportional calculation; Apply different rules of calaculation (in linear algebra, (differential) calculus,

etc.) in solving respective problems;

28

Apply calculation of simple and compound interest for solving various problem situations;

Literature

1. S. T. Karris, Mathematics for business, science, and technology, Orchard Publications, Premont 2003.

2. J. Slater, R. Ponticelli, Business mathematics for college, Irwin, 1997. 3. F. Rizvanolli, M. Dema, Matematika për ekonomistët, Prishtinë, 1995.

Numerical Methods I

Course Objective Student will be introduced with basic methods and techniques of numerical analysis for solving various problems. Student will gain skills for implementation of computer programmes of algorithms of numerical methods.

Learning outcomes:

After completing this course student will be able to: Apply different methods for estimation of errors in numerical calculation. Use different methods (method of segment line bisector, method of

iteration of the fixed point, Newton’s method) for solving non-linear equations.

Use different methods (direct method, Jacobi’s method, Gauss-Seidel method) for solving sets of linear equations.

Apply computer programmes of algorithms of numerical methods.

Literature

1. R. L. Burden, J. D. Faires, Numerical analysis, Brooks/Cole, 2001. 2. L. N. Trefethen, D. Bau, Numerical Linear Algebra, SIAM, Philadelphia, 1997. 3. C. F. Gerald, P. O. Wheatley, Applied numerical analysis, Addison-Wesley, 1994.

Algebra 1

Course Objective

Students learn basic concepts of linear algebra needed for study of mathematics. They learn about mathematical thinking and how to use the rigorous mathematical

29

language. They will be able to apply the knowledge earned during the study in practical work.

Brief content

Real three-dimensional space. Geometric and algebraic structures of three-dimensional space. Vectors: dot product, vector product and mixed product. Analytical geometry: plane and straight line in space. Elementary algebraic structures. Relations. Binary operations and homomorphism’s. Groups. Permutation group. Rings and bodies. Vector spaces of linear operators. Algebras.Spaces with finite dimension. Basis and dimension. Factor-space and direct sum of subspaces. Dual space and dual transforms. Linear operators. Space of linear operators and matrices. Change of bases, equivalence and rank. Sets of linear equations.

Literature

1. F. Križanič: Linearna algebra in linearna analiza, DZS, Ljubljana, 1993.2. J. Grasselli: Linearna algebra, 1. pogl. v I. Vidav: Višja matematika II, DZS,

Ljubljana, 1981.3. I. Vidav: Algebra, DMFA-založništvo, Ljubljana, 2003.

Algebra II

Course Objective

Students learn basic concepts of linear algebra needed for study of mathematics. They learn about mathematical thinking and how to use the rigorous mathematical language. They will be able to apply the knowledge earned during the study in practical work.

Brief content

Endomorphisms. Algebra of endomorphisms and square matrices. Congruence. Determinants. Characteristic polynomial and minimal polynomial of the operator. Eigenvalues. Jordan’s matrix of endomorphisms. Spectral expansion and matrix functions. Spaces with dot product Dot product and norm. Orthogonalization according to Gram-Schmidt. Riesz theorem for representation of linear functions. Hermitian operators.Normal endomorphisms. Diagonalization. Self-adjoint endomorphisms. Unitary endomorphisms. Unitary similarity of endomorphisms and matrices. Positive determined endomorphism and matrices. Quadratic forms. Bilinear forms.

30

Congruences and Sylvester’s theorem in relation to the Law of Inertia. Second order curves in a plane.

Literature

1. F. Križanič: Linearna algebra in linearna analiza, DZS, Ljubljana, 1993.2. J. Grasselli: Linearna algebra, 1. pogl. v I. Vidav: Višja matematika II, DZS,

Ljubljana, 1981.3. I. Vidav: Algebra, DMFA-založništvo, Ljubljana, 2003.

Theory of Probability I

Course objective

Student will be introduced with basic concepts of theory of probability and will gain skills to apply successfully earned knowledge in this course in other related coureses, such as Statistics and Risk and Insurance Management, as well as in his perspective professional work.

Brief Content of the Course

Algebra of events (elementary and complex) and elements of combinatorics. Basic concepts of the theory of probability (conditional probability, independent events, Bayes’ formula, total probability). Random variables (discrete and continuous type, distribution of probabilities and the distribution function, mathematical expectation, variance and the standard deviation). Some characteristic distributions (uniform, binomial, geometric, Poisson’s distribution, Student’s distribution and normal (Gauss’) distribution). Application of characteristic distributions in economy, business, health, etc.

Learning outcomes

After completing this course students will be able to: Define the space of all elementary events during an experiment.

Calculate the probability of a given event.

Use the random variables, mathematical expectation, variance, and standard deviation to draw relevant conclusions about an observed phenomenon (in society, economy, business, medicine, etc.).

Use the characteristic distributions to study various phenomena in nature and society, emphasizing the normal distribution.

Literature

31

1. Laurence D. Hoffman; Gerald L. Bradly: Finte Mathematics with Calculus, McGraw-Hill, INC.

2. Shpëtim Leka: Teoria e probabiliteteve dhe statistika matematike, Tiranë, 2004.

3. M. Efendija, Q. Haxhibeqiri, R. Limani: Matemtika 12-Analiza me teori të gjasës, gjimnazi Matematikë-Informatikë, 2008.

Microeconomics

Course objective

Student will be introduced with basic concepts of microeconomics and gain skills in order to apply successfully his knowledge in perspective practical work.

Brief contentBasic concepts of economics (economic thinking, positive and normative economics, insufficiency, opportune costs, limits of production capacity). Definition of the offer and demand, market equilibrium, elasticity of offer and demand, consumer behavior. Enterprise and its objectives, theory of production and marginal production, production cost, determination of price in total competitiveness. Monopoly and its characteristics, monopolistic competition, distribution of incomes and the market of factors of production. Public sector.

Learning outcomes

After completing this course student will be able to: Define basic concepts of microeconomics.

Define the offer and demand for a certain merchandise.

Apply the offer and demand to find the equilibrium price.

Define the cost of production.

Recognize monopoly and its characteristics.

Literature

1. Ahmet Mançellari, Sulo Hadëri, Dhori Kule, Stafan Qirici: Hyrje në Ekonomi, Pegi, Tiranë, 2000.

2. John Sloman: Ecomics, fifth edition 2003.3. Paul A. Samuelson, William D. Nordhaus: Economics

Macroeconomics

32

Course objective

Student will be introduced with basic concepts of microeconomics and gain skills in order to apply successfully his knowledge in perspective practical work.

Brief content

Basic concepts of microeconomics (notion, mission and the role of economic analysis). Analysis of technical progress and analysis of production development. Analysis of expenses and the offer. Analytic determination of the demand. Analytic determination of economic equilibrium. Analytic determination of incomes (economic growth policy). Economic models in economic theory and practice. Analysis of optimization.

Learning outcomes

After completing this course student will be able to: Define the basic concepts of microeconomics.

Describe analytically the offer, demand and economic equilibrium.

Analize general expenses (total cost) for an economic-financial subject.

Calculate the general incomes and the profit.

Apply optimization in order to minimize or maximize the profit.

Literature

1. Grup autorësh: Hyrje në Ekonom.2. Terli Mings: Studimi i ekonomisë.3. Paul A. Samuelson: Econimcs

Banking Management

Course objective

Student will be introduced with basic concepts in the field of banking and will gain skills in order to apply successfully his knowledge in their perspective practical work.

Brief content

33

Basic concepts of the operation of a bank (in the past and nowadays). Contemporary banking management. Bank capital and its management. Management of solvency. Management of incomes. Govern of credit policy. Management of bank’s active and passive (ALM). Electronic banking affairs and automatization of financial transactions.

Learning outcomes

After completing this course student will be able to: Define basic concepts of banking management.

Define the capital and the capacity of a bank.

Understand the conditions under which a bank can operate in our country.

Analyze the results of a good (bad) government of a bank and to built a strategy for further development.

Have a good knowledge about the electronic banking (advantages and deficiencies)

Literature

1. Eugene F. Brighman, Joel F. Huston: Fundamentals of Finacial Managment, ninth edition 2001.

2. James C. Van Horne: Finacial Managment and Policy, 1998.

Mathematical modeling

Course objectiveStudent wil be introduced with basic concepts of mathematical modeling and description of a system using mathematical concepts and language. Mathematical models are used not only in the natural sciences but also in the social sciences such economics.

Brief content

34

http://en.wikipedia.org/wiki/Social_sciences

http://en.wikipedia.org/wiki/Natural_science

http://en.wikipedia.org/wiki/Mathematics

http://en.wikipedia.org/wiki/System

Mathematical modeling is the process of creating a mathematical representation of some phenomenon in order to gain a better understanding of that phenomenon. The main goal of this course is to learn how to make a creative use of some mathematical tools such ordinary and partial diferential equations and numerical analysis, to build a mathematical description of some problems in economy.

Learning outcomesAfter completing this course student will learn:

Basic concepts concerning matrices, eigenvalues and eigenvectors

Fixed points, stability and iterative processes

Modeling with Ordinary Diferential Equations

Picard iterations, numerical metods

Empirical data fitting- least square method, fitting data with polynomials

Modeling with Partial Diferential Equations

Literature

1. Notes from the instructor

2. A First Course in Mathematical Modeling , by F. R. Giordano, M.D. Weir and W.P. Fox

Marketing

Course objective

Student will be introduced with basic concepts in the field of banking and will gain skills in order to apply successfully his knowledge in their perspective practical work, after graduation.

Brief content

Basic concepts of marketing. Marketing science (basic principles of marketing, marketing in normal and abnormal operating conditions, implementation of marketing, marketing policies). Organization and control of marketing (institutional marketing, marketing plan, marketing in profitable and nonprofit able organizations, research of trade and marketing, consumer behavior, practical examples).

35

Learning outcomes

After completing this course student will be able to: Define basic concepts of marketing.

Define basic principle of marketing.

Define the policies of marketing for profitable and nonprofitable organizations.

Study and analyze the demands in the trade and marketing.

Literature

1. Ali Jakupi: Bazat e marketingut, Prishtinë, 2000.2. Nexhmi Rexha, Nail Reshidi: Bazat e marketingut, Prishtinë, 2000.3. Phili Kotler: Marketing Managment, 2004

Statistics

Course objective

Nowadays the statistical methods have an extraordinary influence in many fields, such as, economy, business, education, agriculture, electronics, medicine, biology, physics, political sciences, psychology, sociology and in a number of other fields of science and technology.The objective of this course is that students gain skills in order to use statistical data, their interpretation, and to explore social, economic, natural, etc, phenomena through them. They will be able to collect, organize, classify, analyze, draw conclusions and present data or their conclusions. For this purpose, they use various scientific methods, such as mathematics in general and theory of probability in particular.

Brief content

Notion, importance, methods and the subject of statistics. Definition of the elements of statistical analysis. Stages of statistical study. Linear and quadratic function. Graphical representation of statistical data. Straight line graph. Bar graph. Graph of components in percentage. Surface diagrams of squares and surface diagrams of circles. Mean arithmetic values (arithmetic mean, mode, median, geometric mean and harmonic mean). Quartiles, deciles and percentiles. Standard deviation and other measures of distribution. Elements of combinatory (permutations, variations and combinations). Elements of probability (random experiments, events, axiomatic definition of probability, conditional probability, Bayes’ formula, independent

36

events). Random variables. Mathematical expectation. Dispersion and standard deviation. Binomial distribution. Normal distribution and Gauss’ distribution. Poisson’s distribution. Linear regression.

Learning outcomes

After completing this course student will be able to: Use the statistical data, carry out their interpretation and use them for

exploring social, economic, natural phenomena, etc. Find the ponderized means for statistical data; Apply quartiles, deciles, percentiles in different practical situations; Apply the binomial distribution, normal distribution and Gauss’ distribution in

solving practical problems; Solve concrete problems related to the linear regression.

Literature

1. Murray R. Spiegel: Theory and problems of statistiks, 2/ed., McGraw-Hill Company, New York, 1992.

2. Demodar Gujarati: Esentials of econometrics, McGraw-Hill Company, New York, 1999.

3. Rahmil Nuhiu, Ahmet Shala: Bazat e statistikës, Prishtinë, 2001.

Basics of Accounting

Course objective

Student will be introduced with basic concepts in the field of banking and will gain skills in order to apply successfully his knowledge in their perspective practical work.

Brief content

Basic concepts in the field of accounting and business.

Analysis of transactions in accounting (completion of the cycle of accounting, accounting of production enterprises, systems of accounting, accounting of acceptable accounts, accounting of inventory of merchandise, assets and investments on assets).

37

Obligations and long-term financing obligations, equity and financing equity, financial surveys of incomes and of the balance of state.

Learning outcomes

After completion of this course student will be able to: Define the basic concepts of accounting.

Make an analysis of various financial transactions.

Define equity and financing equity.

Carry out the economic-financial balance of an enterrprise for certain time period,

Literature

1. Robert Ingram: Kontabilitetit financiar.2. Thomas Albright, Bruce Baldwin: Kontabiliteti financiar.

Following is literature which is recommended during studies

1. William Boyes & Michael Melvin, “Microeconomics”, botimi i pestë.2. Walter Rudin, Principles of mathematical analysis, McGraw Hill, 1976.3. Thomas Albright, Bruce Baldwin: Kontabiliteti financiar.4. Shpëtim Leka: Teoria e probabiliteteve dhe statistika matematike, Tiranë, 2004.5. S. T. Karris, Mathematics for business, science, and technology, Orchard Publications, Premont 2003.6. Robert Ingram: Kontabilitetit financiar..7. Rahmil Nuhiu, Ahmet Shala: Bazat e statistikës, Prishtinë, 2001.8. R. L. Burden, J. D. Faires, Numerical analysis, Brooks/Cole, 2001.9. Prof.Dr.Gazmend Luboteni, Financat e korporatave, Prishtinë, 2007.10. Philip Kotler: Marketing Menagment, 200911. Peter Grossman, Discrete Mathematics for computing, Monach University, 1995.12. Paul A. Samuelson, William D. Nordhaus: Econimcs

38

13. Paul A. Samuelson & William D. Nordhaus, “Economics”, botimi i shtatëmbëdhjetë;14. P.DuChateau, D.W. Zachman, Schaum’s outline of Theory and Problems of Partial Differential Equations,McGraw Hill, New york, 107615. P. Mizori Oblak: Matematika za študente tehnike in naravoslovja I, Fakulteta za strojništvo, Ljubljana,2001.16. P. Mizori‐Oblak: Matematika za študente tehnike in naravoslovja II, Fakulteta za strojništvo, Ljubljana,2003.17. Nail Reshidi & Bardhyl Ceku: Marketingu, 200618. N. Braha dhe I. Shehu, Analiza matematike I, Prishtine, 200619. Murray R. Spiegel: Theory and problems of statistiks, 2/ed., McGraw‐Hill Company, New York, 1992.20. Mancellari,A.,Haderi,S.,Kule , Dh ., Qiriqi, S..(2000):Hyrje ne Ekonomi: shtepia botuese PEGI, Tiranë21. M. Efendija, Q. Haxhibeqiri, R. Limani: Matemtika 12 Analiza me teori të gjasës, gjimnazi MatematikëInformatikë, 2008.22. M. Efendija, Analiza Matematike III & IV, Prishtinë, 2005.23. M. Efendija, Analiza Matematike II, në botim të UP.24. M. Dobovišek, D. Kobal, B. Magajna: Naloge iz algebre I, DMFA‐založništvo, Ljubljana, 2005.25. M. Berisha dhe R.Zejnullahu, Permbledhje detyrash te zgjidhura nga analiza matematike I, Prishtine,1991.26. Ligjerata te autorizuara,Prof. Dr.Sinan Ademaj,Prishtinë,200027. Laurence D. Hoffman; Gerald L. Bradly: Finte Mathematics with Calculus, McGraw‐Hill, INC.28. L. N. Trefethen, D. Bau, Numerical Linear Algebra, SIAM, Philadelphia, 1997.29. L. D. Hoffmann, G. L. Bradley, Calculus for business, economics, and the social and life sciences,McGraw Hill, 2000.30. Kontabiliteti financiar (pjesa e parë), Prof. dr. Skënder Ahmeti,31. Kontabiliteti financiar – nga Robert Ingram, Thomas Albright dhe Bruce Baldwin (teksti i përkthyer nëshqip – vazhdim i kapitujve të dedikuar për vitin e II)32. Kontabiliteti financiar nga prof.ass. Sotiraq Dhamo.33. Keneth Rosen: Discrete Mathematics and Its Applications, McGraw Hill, 2003.34. Kansas State University, 2003.2735. K.Bogart, C.Stein: Discrete Mathematics in Computer Sciences, (Botim Interneti).36. K. Bukuroshi, Analiza Matematike I, Tiranë , 1977.

39

37. John Sloman: Ecomics, edicioni i peste 2003.38. James C. Van Horne: Finacial Managment and Policy, 1998.39. J.A. Anderson, Disscrete Mathematics with Combinatorics, Pearson Education,INC,2004.40. J. Slater, R. Ponticelli, Business mathematics for college, Irwin, 1997.41. J. Grasselli: Linearna algebra, 1. pogl. v I. Vidav: Višja matematika II, DZS, Ljubljana, 1981.i. Vidav: Algebra, DMFA‐založništvo, Ljubljana, 2003.42. I. I. Ljasko e të tjerë, Matematiceskij analiz II vprimerah i zadacah, Kiev, 1974.43. Halit Xhafa dhe Beshir Ciceri: Drejtimi financiar I dhe II, Shtëpia Botuese Libri Universitar, Tiranë 2001.44. Gregory Mankiw, “Principles of economics”, botimi i tretë;45. G. N. Berman: A Problem Book in Mathematical Analysis, Moskva, Mir Publ., 1980.46. F. Rizvanolli, M. Dema, Matematika për ekonomistët, Prishtinë, 1995.47. F. Križanič: Linearna algebra in linearna analiza, DZS, Ljubljana, 1993.48. Eugene F. Brighman, Joel F. Huston: Fundamentals of Finacial Managment, ninth edition 2001.49. E. Kreyszig: Advanced Engineering Mathematics, Huboken, J. Wiley, 2006.50. E. Hamiti, Matematika III, Prishtinë51. Dornbusch, r.,& Fischer , S.,(1994): Macroeconomics; McGraë Hill,INC (Prts 1 and 2). Ky tekst ështëpërkthyer në shqip nga Marta Muco dhe Sulo Hadëri.52. Demodar Gujarati: Esentials of econometrics, McGraw‐Hill Company, New York, 1999.53. D. Veljan, Kombinatorika I diskretna matematika, Algoritam Zagreb, 2001.54. D. Schmidt, Programming principles in Java: architectures and interfaces, Kansas State University,2003.55. C. F. Gerald, P. O. Wheatley, Applied numerical analysis, Addison Wesley, 1994.56. Brian S. Thomson, Judith B. Bruckner, Andrew M. Bruckner: Elementary real analysis,thomson・bruckner, 2001.57. Brealey, Myers: Principles of Corporate Finance, McGraw Hill, New York, Boston, 2001.58. B. Gazidede, Analiza matematike II, ushtrime dhe probleme të zgjidhura. Tiranë, 2006.59. Ali Jakupi: Marketingu, Prishtine, 200660. Adnadevic.D dhe Kadelburg .Z, Analiza matematike I, Beograd, 1998.

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Presentation of actual implementation by external exsperts

Plan for implementation of recommendations – Financial Mathematics in Banking and Insurance

Recommendations Implementing plan for recommendations

Responsible for implementation of recommendations and needed resources

Dates for implementation of recommendations

Notes/Comment

1. Promotion of the existing teaching staff and bringing new cadres

- Curriculum review- Sending the staff from the department for doctoral studies abroad- Sending teachers to exchange experiences in several European universities- Recruitment of new needed staff

RectorateDeanHead of Department

July 2012

2. Investing in new scientific literature and in infrastructure

- Equip of additional laboratory with computers and accompanying equipment for direction of Computer Science- Academic personnel from department will propose professional literature to be provided

DeanHead of Department September 2011 Financial assets

(FMNS in cooperation with UP)

3. Review of the master program for direction Pure Mathematics

- Syllabuses of the subjects and ECTS credits in master studies will be reviewed also and duration of studies will be one academic year.

DeanHead of Department September 2011

Implementation depends on the decision of the Senate of UP

4. Electronic access to international journals

- Within the UP and FMNS will be arise issue of electronic literature

RectorDeanHead of Department

September 2012

Decisions are made by Dean’s Office and Rectorate

41

Anex 2: Scientific work done in FACULTY OF MATHEMATICAL AND NATURAL SCIENCES

Nr.

Author/s Title of paper Name of journalYear, volume, pages

Sent, in assesmnet, accepted

Scientific work

1 Q.Haxhibeqiri, S.NovakDuality between stable strong shape morphisms and stalle homotopy classes

Glasnik Matematicki, Zagreb2001, Vol. 36(56), pp. 297-310

2Q.Haxhibeqiri

Vargu ekzakt i fibracionit Bul. Shkencor , SHLP “B.Curri”,Gjakovë

1997, No. 4-5, pp.59 – 70.

3Q.Haxhibeqiri

The product and pullback of fibrations

Bul. i pun. Shkenc. I FSHMN, Prishtinë

1996, No. 11, pp.19 – 26.

4Q.Haxhibeqiri

Limitet e vargut të përgjithsuar të nënbashkësive të një hapësire topologjike

Bul. Shkencor,SHLP “B.Curri”, Gjakovë

1995, N0. 3, pp.117-136

5Q.Haxhibeqiri, S.Novak

Stable Strong ShapeGlasnik Matematicki, Zagreb

1989, Vol. 24(44), pp. 149-160

6Q.Haxhibeqiri

Kategorija Inj C Bul. Shkencor,SHLP “B.Curri”, Gjakovë

1987, No. 2, pp.166 – 173.

7Q.Haxhibeqiri

On resolutions for maps of pairs of spaces

Punime matematike, Prishtinë,1986, No. 1, pp. 3-11

42

8Q.Haxhibeqiri

On the surjectivity of shape fibration Matem.Vesnik,Beograd

1985,Knjiga 37,sv. 4, pp.379-384

9Q.Haxhibeqiri

The exact sequence of a shape fibration

Glas. Matem. Zagreb1983, Vol.18 (38), pp.157-177

10Q.Haxhibeqiri

10. Shape fibrations for compact Hausdorff spaces

Publ. De L’Institut Mathemat., Beograd

1982, Tom 31 (45), pp. 33-49.

11Q.Haxhibeqiri

Resolutions of maps of pairs Bul. i pun. Shkenc.i FSHMN, Prishtinë

1982,

12Q.Haxhibeqiri

Shape fibrations for topological spaces Glas. Matem. Zagreb

1982, Vol 17(37), pp. 381-401.

13.Q.Haxhibeqiri

Fibracije oblika za topoloske prostore, (Phd. Thesis)

PMF, Zagreb,1981, pp. I-X + 1-153

14

Q.Haxhibeqiri

Retrakti u topoloskoj kategoriji i u kategoriji oblika Retrakti u topoloskoj kategoriji i u kategoriji oblika (Mgr. Thesis)

PMF, Zagreb,

1974

Summary (Abstract) from internacional scientific conferences

1Q.Haxhibeqiri

The product of Shape fibrations. Intern. Confer. on Geometric Topology, Dubrovnik

2007

2Q.Haxhibeqiri

Stable strong shape theory Intern. Confer. “Topology and its applications”, Dubrovnik,

1990

43

3Q.Haxhibeqiri

Fibracije oblika topoloskih prostora

The VIII-th Congess of Mathematicians, Physicians and

Astronomers of Yugoslavia.

1985

4Q.Haxhibeqiri

On the surjectivity of Shape Fibrations

Internat. Conf. “Topology and its applications”, Dubrovnik

1985

5

Q.Haxhibeqiri

The pullback of shape fibration The VII-nth Congress of Mathematician, Physician and

Astronomer of Yugoslavia Budva-Becic

1980

6Q.Haxhibeqiri

A generalization of a theorem due to S.Mardesic

The VI-nth Balcanic Congress of Mathematicians, Varna (Bulgaria)

1975

7

Q.Haxhibeqiri

Retrakti u kategoriji oblika The VI-nthCongr. of Mathem., Physi. and Astronom. of Yugoslavia,

Novi Sad

1975

Summary (Abstract) from nacional scientific conferences

1

2

Other publications

44

1Q.Haxhibeqiri

Vërtetimi i disa pabarazimeve “Plus”, Tetovë

2010, No. 70

2Q.Haxhibeqiri

Dy kuriozitete matematike“Plus”, Tetovë,

2010, No.70

3

Q.Haxhibeqiri

Ndërtimi i përafërt i n-këdëshit të rregullt. Syprina e sipërfaqes n- këndëshe të rregullt; teorema e përgjithsuar e Pitagorës

“Plus”, Tetovë,

2008, No. 64

4Q.Haxhibeqiri

Disa detyra që zgjidhen me anën e pabarazimeve

“Plus”, Tetovë2007, No.57, 58

5Q.Haxhibeqiri

Vërtetimi i disa teoremave të rralla për katërkëndëshat

“Plus”, Tetovë206, No.55, 56

6 Q.Haxhibeqiri Marrëveshja fitimprurëse “Plus”, Tetovë 2003, No. 447 Q.Haxhibeqiri Teorema e Napoleonit “Plus”, Tetovë 2003, No. 438 Q.Haxhibeqiri Një detyrë interesante “Plus”, Tetovë 2002, No. 369 Q.Haxhibeqiri Pjestueshmëria me 11 “Plus”, Tetovë 2001, No. 3510

Q.Haxhibeqiri Numri më i madh me katër shifra të njëjta

“Plus”, Tetovë2001, No. 33

11 Q.Haxhibeqiri Kush e ka unazën ? “Plus”, Tetovë 2000, No. 3212 Q.Haxhibeqiri Cila thyesë është më e madhe? “Plus”, Tetovë 1999, No. 2613

Q.HaxhibeqiriDisa vërtetime të teoremës së Pitagorës


14Q.Haxhibeqiri

Vërtetimi i disa teoremave të arithmetikës me metodat gjeometrike


45

15 Q.Haxhibeqiri Për mendjemprehtët ! “Plus”, Tetovë 1998, No. 2316 Q.Haxhibeqiri Disa sofizma matematikore “Plus”, Tetovë 1996, No. 1617

Q.Haxhibeqiri Mesi arithmetik, mesi gjeometrik dhe mesi harmonik

“Plus”, Tetovë1995, 1996, No. 12, 13

18 Q.Haxhibeqiri Zgjidhja e disa detyrave logjike “Plus”, Tetovë 1995, No. 10, 1119 Q.Haxhibeqiri Aritmatika e ores “Plus”, Tetovë 1995, No. 1020 Q.Haxhibeqiri Funksioni invers “Matematika- Fizika”, Prishtinë 1982, No. 221

Q.HaxhibeqiriMbi përkufizimin e funksionit dhe relacionit

“Matematika- Fizika”, Prishtinë1982, No. 1

22Q.Haxhibeqiri

Disa elemente të logjikës matematike

“Dituria”, Prishtinë1971/72, No. 2, 2, pp.141-153

23 M.Efendija, Q.Haxhibeqiri, R.Limani

Matematika 12 – për drejtimin Matematikë- Informatikë (Gjimnaz)

“Dukagjini”, Prishtinë2006, pp.1- 274

24 M.Efendija, Q.Haxhibeqiri,R.Limani

“Dukagjini”, Prishtinë2005, pp. 1- 475

25Q.Haxhibeqiri

Përmbledhje detyrash nga topologjia (tekst universitar),

UP, Prishtinë1996, pp. 1 - 516

26 Q.Haxhibeqiri Topologjia (tekst universitar), ETMM, Prishtinë 1989, pp. 1- 46727 Q.Haxhibeqiri,

S.Zdravkovska Uvod u algebarsku topologiju,

FSHMN, Prishtinë,1979, pp. 1- 98

28 Z.Ivkoviq,D.Banjeviq Probabiliteti dhe statistika matematike, (përkthim nga sërbishtja )

ETMM, Prishtinë ,1985

29 S.Kurepa Hyrje në matematikë: Bashkësitë- Strukturat- Numrat, (përkthim nga

ETMM, Prishtinë 1976

46

kroatishtja)

Anex 2: Scientific work done in FACULTY OF MATHEMATICAL AND NATURAL SCIENCES

Nr.



Scientific work

1Minir Efendija

Funksioni i drejtë dhe faktet themelore në lidhje me te

Bul. i pun. shkenc. i FSHMN1976/ IV

2Minir Efendija

C – lëvizshmëria e drejtë, Bul. i pun. shkenc. i FSHMN 1981/ VII

3Minir Efendija

Cp – trivialiteti i drejtë Bul. i pun. shkenc. i FSHMN 1982/ VIII

4

Minir Efendija

Përshkrimi i kuazi-relacioneve të drejta me ndihmën e mutacioneve të drejta

Bul. i pun. shkenc. i SHLP të Gjakovës

1983-86/IX

5Minir Efendija

Prave kvazi-relacije i prava C – pitomost

Kërkime, 4, Akad. e Shkenc.dhe Arteve, Prishtinë;

1986/4

6 Minir Efendija Një invariant i ri i formës së Bul. i pun. shkenc. i SHLP të Gjakovës 1987/2

47

drejtë,

8 Minir Efendija Proper C – calmness Punime Matematike, FSHMN 1990/5

9 Minir Efendija Proper deformation dimension Bul. i pun. shkenc. i FSHMN 1990/ V

10 Minir Efendija Property SUV∞and proper quasi-

relationsBul. i pun. shkenc. i FSHMN

1996/IX

11 Minir Efendija Disa shembuj që tregojnë se kuazi-relacionet e drejta janë më të dobëta se relacionet e formës së drejtë

Bul. i pun. shkenc. i SHLP të Gjakovës1997/5

12 Minir Efendija Proper quasi-relations in the sense of proper mutations,

Kërkime, 4, Akad. e Shkenc. dheArteve, Prishtinë;

2001/9

13 Minir Efendija Proper quasi-relations for locally compact metric ANR spases

Kërkime, 4, Akad. e Shkenc. dheArteve, Prishtinë;

2003/11

14 Minir Efendija, Qefsere Gjonbalaj,

Kuazi-relacionat e drejta të hapësirave

Buletini shkencor, UNIEL (Seria eshkencave të natyrës ), Elbasan

2004/1

15 Minir Efendija Proper movabilty for locally compact metric spaces in terms of ANR systems

preprint2011


1Minir Efendija Proper quassi-relations for locally

compact metric spacesDubrovnik

1981

2Minir Efendija Proper quasi-relations for locally

compact metric ANR spasesBudva

48


1Minir Efendija Funksioni i drejtë dhe faktet themelore

Prishtinë1985

2

Other publications

1Minir Efendija Kuptimet themelore të diferencialit të

funksionit me një variabël, Matematika – Fizika

1983/2

2Minir Efendija Analiza matematike II (tekst

universitar),Universities book, ETMM

1988

3Minir Efendija Homotopija e drejtë,

Bul. i pun. shkenc. i SHLP të Gjakovës1995/3

4 M. Efendija, R.Zejnullahu

M. Efendija, R.Zejnullahu, Përmbledhje detyrash të zgjidhura nga Analiza matematike II

Universities book, University of Prishtina

1995

5 Minir Efendija Një veti e trekëndhshit barakrahësh dhe disa zbatime të saj

Plus, Tetovë1996/13

6 Minir Efendija Një metodë për gjetjen e katrorit të numrit,

Plus, Tetovë1997/20

49

7 M. Efendija, Q. Haxhibeqiri, R. Limani,

Matematika 11 – Drejtimi Matematikë- Informatikë (për Gjimnaze),

Book for Secondary school, “Dukagjini”

2004

8 Minir Efendija Analiza matematike III &IV (tekst universitar , ribotim i tekstit Analiza matematike II (me disa plotësime))

Universities book, UP2005

9 Minir Efendija Analiza matematike I &II (tekst universitar , dorëzuar për botim nëUniversitetin e Prishtinës).

Universities book, UP2009

10 M. Efendija, Ramadan Limani

M. Efendija, Ramadan LimaniMatematika Elementare me zbatime në Ekonomiks dhe Biznes,

Propozuar për botim2010

Anex 2: Scientific work done in FACULTY OF MATHEMATICAL AND NATURAL SCIENCES, PRISHTINA



Scientific workQ. Gashi dhe T.

SchedlerProjective normality of toric varieties arising from root systems

2011 Sent for publishing

Q. Gashi, T. Looping of the numbers game and the J. of Combin. Th. - Series A 2012 Accepted

50

Schedler, D. Speyer alcoved hypercubeQ. Gashi and T. Schedler

On dominance and minuscule Weyl group elements J. Algebraic Combin.

2011, Vol. 33, No. 3, 383-399

Published

Q. Gashi On a conjecture of Kottwitz and Rapoport Ann. Sci. de l’E.N.S.

2010, Vol. 43, fasc 6, 1017-1038

Published

Anex 2: Scientific work done in FACULTY OF MATHEMATICAL AND NATURAL SCIENCES, PRISHTINA

Nr.



Scientific work

1 Muhib R. Lohaj,Necessary condition for quasidiagonality of some special nilpotent operators

Rad.Mat, Vol.10(2001)209-217

2Muhib R. Lohaj Necessary condition for

quasidiagonality of certain bounded operators defined in the direct sum H ⊕H⊕H ,

Rad.Mat,

Vol.10(2001) 113-117

M. Lohaj, N.Braha Some properties of μ - approximate l1 Mat. Bilt, Vol.27(2003),

51

http://www.springerlink.com/content/0925-9899/33/3/

http://www.springerlink.com/content/0925-9899/33/3/

3 sequences in Banach spaces 87-94.

4 Muhib R. Lohaj, Quasitriangularity of weighted shift operators with special operator weights,

Mat. Bilt, Vol.28(2004), 67-80.

5 N.Braha, M. Lohaj, F,Marevci, Sh.Lohaj

Some propertis of paranormal and hyponormal operators Bull. Math.. Anal. Apl.

Vol. 1 (2009), 23-35

6 Shqipe I. Lohaj, Muhib R. Lohaj,

Essentially hyponnormal operators with essential spectrum contained in a circle

Le Matematiche

Vol LXIV(2009),81-84.

7 Muhib R.Lohaj, Shqipe I Lohaj,

Quasidiagonal operators,Sarajevo journal of math.

Vol. 6(19)(2010) 1-7


1Muhib R. Lohaj Quasidiagonal operators

Elbasan2006

2 Muhib R.Lohaj, Shqipe I Lohaj,

Quasidiagonal operators in Hilbert spaces

Elbasan 2009

3Shqipe I Lohaj, Muhib R. Lohaj

Quasinormal operatorsElbasan

2009

52


Muhib R. Lohaj Quasinormal and N-quasinormal elements in C*-algebras

Alb-Shkenca2011

Other publications

1Muhib R. Lohaj Quasidiagonal operators

Buletini i Shkencave Elbasan2006

2Shqipe I Lohaj, Muhib R.Lohaj,

Quasinormal operatorsBuletini i Shkencave Elbasan

2009

3Muhib R.Lohaj, Shqipe I Lohaj,

Quasidiagonal operators in Hilbert spaces Buletini i Shkencave Elbasan

2009

Anex 2: Scientific work conducted by one teacher in Department of Mathematics in FMNS

53

Nr. Author/s Title of paper Name of journalYear, volume, pages


Scientific work1 Bujar Fejzullahu A Cohen type inequality for Fourier

expansions of orthogonal polynomials with a non-discrete Gegenbauer-Sobolev inner product

Math. Nachr.

2011/284/240-254

2Bujar Fejzullahu, Francisco Marcellan

A Cohen type inequality for Fourier expansions of orthogonal polynomials with a nondiscrete Jacobi-Sobolev inner product

J. Inequal. Appl.

2010/ID.

128746/22p

3 Bujar Fejzullahu A Cohen-type inequality for Fourier expansions with respect to non-discrete Laguerre-Sobolev inner product

Numer. Funct. Anal. Optim.

2010/31/

1330-1341

4 Bujar Fejzullahu,Ramadan Zejnullahu

Orthogonal polynomials with respect to the Laguerre measure perturbed by the canonical transformations

Integral Transforms Spec. Funct.2010/21/

569-580

5 Bujar Fejzullahu, Francisco Marcellan

Asymptotic properties of orthogonal polynomials with respect to a non-discrete Jacobi- Sobolev inner product

Acta Appl. Math.2010/110/

1309-1320

6 Bujar Fejzullahu Asymptotic properties and Fourier expansions of orthogonal polynomials with a non-discrete Gegenbauer-

J. Approx. Theory 2010/162/

397-406

54

Sobolev inner product

7 Bujar Fejzullahu Asymptotics for orthogonal polynomials with respect to the Jacobi measure modified by a rational factor

Math. Balkanica2010/24/

41-50


On convergence and divergence of Fourier expansions with respect to some Gegenbauer-Sobolev type inner product

Commun. Anal. Theory Contin. Fract.

2009/16/

1-11

9 Bujar Fejzullahu,Ramadan Zejnullahu

Lebesgue constants for polynomial expansions associated with weight function

(1−x )α(1+x )β dx+Mδ−1+Nδ1

Int. Journal of Math. Analysis

2009/3/

1701-1709


A Cohen type inequality for Laguerre–Sobolev expansions J. Math. Anal. Appl.

2009/352/

880-889

11 Bujar Fejzullahu On divergence a.e. of Fourier expansions with respect to non-discrete Laguerre-Sobolev inner product

Funct. Anal. Approx. Comput.

2009/1/1-12

12 Bujar Fejzullahu A Cohen type inequality for orthogonal expansions with respect to the generalized Jacobi weight

Results Math.2009/55/

373-381

13 Bujar Fejzullahu On convergence and divergence of Filomat 2009/23/

55

Fourier expansions associated to Jacobi measure with mass pointms

61-68

14 Bujar Fejzullahu A Cohen type inequality for polynomial expansions associated with the measure

(1−x )α(1+x )β dx+Mδ−1+Nδ1

J. Math. Sci. Univ, Tokyo.

2008/15/

243-255

15 Bujar Fejzullahu Divergent Legendre-Sobolev polynomial series

Novi Sad J. Math. 2008/38/

35-41

16 Bujar Fejzullahu A Cohen type inequality for Legendre-Sobolev expansions

Filomat 2008/22/

23-31

17 Bujar Fejzullahu Divergent Cesaro means of Jacobi-Sobolev expansions

Rev. Mat. Complut. 2008/21/

427-433

18 Bujar Fejzullahu A Cohen type inequality for Jacobi-Sobolev expansions

J. Inequal. Appl. 2007/ID 93815/10pp

19 Bujar Fejzullahu Divergent Cesaro means of Fourier expansions with respect to polynomials associated with the

measure (1−x )α(1+x )β dx+MΔ−1

Filomat 2007/ 21/

153-160

20 Bujar Fejzullahu A Riemann-Lebesgue Lemma for Fourier-Jacobi coefficients

Mat. Bilten 2006/ 30/

43-48

56


1Bujar Fejzullahu On Divergence of Fourier expansions

with respect to some Laguerre- Sobolev type inner product

International Workshop on Orthogonal Polynomials and Approximation Theory, Universidad Carlos III de Madrid, Spain

September 8-12, 2008

2Bujar Fejzullahu A Cohen type inequality for Fourier

expansions of orthogonal polynomials with a non-discrete Jacobi-Sobolev inner product

Conference on Approximation Theory, Computer Aided Geometric Design, Numerical Methods and Applications, Ubeda, Spain.

July 4-9, 2010

57

Model of CV

CURRICULUM VITAE

1. Family Name: HAXHIBEQIRI

2. First Name: QAMIL

3. Nationality: Albanian

4. Date of Birth April, 8, 1949

5. Gender: M

6. Contact details: “Mithat Frashëri”, 86, Gjakovë

Email: [email protected]: 044 386 988

7. Education Degree:

Institution: Faculty of Mathematical and Natural Sciences (FMNS)- PrishtinëDegree Date: Jyly, 7, 1971Degree : Professor of mathematics

Institution: Faculty of Mathematical and Natural Sciences (FMNS)- ZagrebDegree Date: November, 25, 1974Degree/ Master : Magister of Mathematical Sciences (Topology)

Institution: Faculty of Mathematical and Natural Sciences (FMNS)- ZagebDegree Date: March, 10, 1981Degree / Doctorate : Doctor of Mathematical Sciences (Topology)

8. Academic Degree: Ordinary Professor

Institution: Faculty of Mathematical and Natural Sciences (FMNS)- PrishtinëDegree Date: Juny, 30,1994

9. Scientific Publications:

Scientific journal

Title of paper Journal name Year / Volume / Pages1. (with S.Novak), Duality between stable strong shape morphisms and Stable homotopy classes

Glasnik Matematicki, Zagreb

2001,

2.Vargu ekzakt i fibracionit Bul. Shkencor , SHLP 1997, No. 4-5, pp.59 – 70.

58

“B.Curri”,Gjakovë3.The product and pullback of fibrations

Bul. i pun. Shkenc. I FSHMN, Prishtinë

1996, No. 11, pp.19 – 26.

4.Limitet e vargut të përgjithsuar të nënbashkësive të një hapësire topologjike

Bul. Shkencor,SHLP “B.Curri”, Gjakovë

1995, N0. 3, pp.117-136

5. (with S. Novak), Stable Strong Shape Glas. Matem. Zagreb 1989, Vol. 24(44), pp. 149-1606. Kategorija Inj C Bul. Shkencor,SHLP

“B.Curri”, Gjakovë1987, No. 2, pp.166 – 173.

7. On resolutions for maps of pairs of spaces

Punime matematike, Prishtinë,

1986, No. 1, pp. 3-11

8. On the surjectivity of shape fibration Matem.Vesnik,Beograd 1985,Knjiga 37,sv. 4, pp.379-3849. The exact sequence of a shape fibration

Glas. Matem. Zagreb 1983, Vol.18 (38), pp.157-177

10. Shape fibrations for compact Hausdorff spaces

Publ. De L’Institut Mathemat., Beograd

1982, Tom 31 (45), pp. 33-49.

11. Resolutions of maps of pairs Bul. i pun. Shkenc.i FSHMN, Prishtinë

1982,

12. Shape fibrations for topological spaces

Glas. Matem. Zagreb 1982, Vol 17(37), pp. 381-401.

13. Fibracije oblika za topoloske prostore, (Phd. Thesis)

PMF, Zagreb, 1981, pp. I-X + 1-153

14. Retrakti oblika za proizvoljne topoloske prostore

Bul. i pun. Shkenc.i FSHMN, Prishtinë

1975,

15. Retrakti u topoloskoj kategoriji i u kategoriji oblika Retrakti u topoloskoj kategoriji i u kategoriji oblika (Mgr. Thesis)

PMF, Zagreb, 1974

Abstracts from the International and National Conferences

Title of paper Journal name Year / Volume / PagesThe product of Shape fibrations.

Intern. Confer. on Geometric Topology, Dubrovnik

2007

Stable strong shape theory Intern. Confer. “Topology and its applications”, Dubrovnik,

1990

Fibracije oblika topoloskih prostora

The VIII-th Congess of Mathematicians, Physicians and Astronomers of Yugoslavia.

1985

On the surjectivity of Shape Fibrations

Internat. Conf. “Topology and its applications”, Dubrovnik

1985

The pullback of shape fibration The VII-nth Congress of Mathematician, Physician and Astronomer of Yugoslavia

1980

59

Budva-BecicA generalization of a theorem due to S.Mardesic

The VI-nth Balcanic Congress of Mathematicians, Varna (Bulgaria)

1975

Retrakti u kategoriji oblika The VI-nthCongr. of Mathem., Physi. and Astronom. of Yugoslavia, Novi Sad

1975

Other (professional) publications

Title of paper Journal name Year / Volume / Pages1.Vërtetimi i disa pabarazimeve “Plus”, Tetovë 2010, No. 70

2.Dy kuriozitete matematike “Plus”, Tetovë, 2010, No.70Ndërtimi i përafërt i n-këdëshit të rregullt. Syprina e sipërfaqes n- këndëshe të rregullt; teorema e përgjithsuar e Pitagorës

“Plus”, Tetovë, 2008, No. 64

3.Disa detyra që zgjidhen me anën e pabarazimeve

“Plus”, Tetovë 2007, No.57, 58

4. Vërtetimi i disa teoremave të rralla për katërkëndëshat

“Plus”, Tetovë 206, No.55, 56

5. Marrëveshja fitimprurëse “Plus”, Tetovë 2003, No. 446. Teorema e Napoleoni “Plus”, Tetovë 2003, No. 437. Një detyrë interesante “Plus”, Tetovë 2002, No. 368. Pjestueshmëria me 11 “Plus”, Tetovë 2001, No. 359. Numri më i madh me katër shifra të njëjta

“Plus”, Tetovë 2001, No. 33

10. Kush e ka unazën ? “Plus”, Tetovë 2000, No. 3211. Cila thyesë është më e madhe?


12. Disa vërtetime të teoremës së Pitagorës


13. Vërtetimi i disa teoremave të arithmetikës me metodat gjeometrike


14. Për mendjemprehtët ! “Plus”, Tetovë 1998, No. 2315. Disa sofizma matematikore “Plus”, Tetovë 1996, No. 1616. Mesi arithmetik, mesi gjeometrik dhe mesi harmonik

“Plus”, Tetovë 1995, 1996, No. 12, 13

17. Zgjidhja e disa detyrave logjike

“Plus”, Tetovë 1995, No. 10, 11

60

18. Aritmatika e ores “Plus”, Tetovë 1995, No. 1019. Funksioni invers “Matematika- Fizika”, Prishtinë 1982, No. 220.Mbi përkufizimin e funksionit dhe relacionit

“Matematika- Fizika”, Prishtinë 1982, No. 1

21. Disa elemente të logjikës matematike

“Dituria”, Prishtinë 1971/72, No. 2, 2, pp.141-153

Books:1.(with M. Efendia and R. Limani),Matematika 12 – për drejtimin Matematikë- Informatikë (Gjimnaz), Prishtinë, 2005

“Dukagjini”, Prishtinë 2006, pp.1- 274

1.(with M. Efendia and R. Limani),Matematika 11 – për drejtimin Matematikë- Informatikë (Gjimnaz), Prishtinë, 2005

“Dukagjini”, Prishtinë 2005, pp. 1- 475

Përmbledhje detyrash nga topologjia (tekst universitar),

UP, Prishtinë 1996, pp. 1 - 516

Topologjia (tekst universitar), ETMM, Prishtinë 1989, pp. 1- 467(with S. Zdravkovska) Uvod u algebarsku topologiju,

FSHMN, Prishtinë, 1979, pp. 1- 98

Translated boks in Albanian:Z. Ivkoviq, D. Banjeviq, Probabiliteti dhe statistika matematike, (from serbocroatian)

ETMM, Prishtinë , 1985

S. Kurepa, Hyrje në matematikë: Bashkësitë- Strukturat- Numrat, (from serbocroatian)

ETMM, Prishtinë 1976

10. Searching visits:University of Sofia, Bulgaria Teen days 1987University of Warszav, Poland Six months 1986University of Zagreb One year 1979- 1980University of Tirana One month 1977.

11. Work experience record:

Dates: 1974 –1976Location: PrishtinaName of the Institution: Faculty of Mathematical and Natural Sciences (FMNS)Position: Assistant

61

Description: I was assistant of the courses : Analysis II, Analysis III, Topology

Dates: 1976 - 1982Location: PrishtinaName of the Institution: Faculty of Mathematical and Natural Sciences (FMNS)Position: LecturerDescription: I teach courses: Topology: Functional analysis

Dates: 1982 – 1987Location: PrishtinaName of the Institution: Faculty of Mathematical and Natural Sciences (FMNS)Position: Assistant Professor(Docent)Description: I teach courses: Topology: Functional analysis

Dates: 1987 – 1994Location: PrishtinaName of the Institution: Faculty of Mathematical and Natural Sciences (FMNS)Position: Asociated ProfessorDescription: I teach courses: Topology: Functional analysis

Dates: 1994 – currentLocation: PrishtinaName of the Institution: Faculty of Mathematical and Natural Sciences (FMNS)Position: Ordinary ProfessorDescription: I teach courses: Topology: Analytic Geometry; Linear Algebra and

Analytic Geometry; Metric Spaces

12. Education and training:

Dates: October 1967 – July 1971Title of qualification awarded: Professor of MathematicsPrincipal subjects/occupational skills covered:

Graduate studies

Name and type of institution providing education and training:

Department of Mathematics, FMNS, Prishtina

62

Level of national and international classification:

Dates: September 1971 – Novermber 1974Title of qualification awarded: Magister of Mathematic Sciences

Principal subjects/occupational skills covered:

Topology


Department of Mathematics, FMNS, University of Zagreb;


Dates: September1979 – July 1980Title of qualification awarded:Principal subjects/occupational skills covered:

Advanced studies in Operator Theory


Department of Mathematics, FMNS, University of Zagreb;


Doctor of Mathematic Sciences (PhD)

Principal subjects/occupational skills covered

Shape Theory

12. Additional information:

Organizational skills and competences:

Member of Senate in Uuniversity of Prishtina

Computer skills and competences:

Microsoft Office (Word, Excel, PowerPoint)Microsoft Windows XP, Vista, 7.

Language skills: (1 to 5: 1 lowest - 5 fluent)

Language. Speaking Writing ReadingAlbanian 5 5 5English 4 4 5Russian 3 4 5Serbo-Croatian 5 5 5

Awards and Membership:

63

Questionnaire for subject evaluation

UNIVERSITY OF PRISHTINA Date of filling the questiionnaire: _________________ Semester : _____ Department: ________________________Faculty:____________ Study program: _____________Level ( Bachelor or Master): __________

STUDENT EVALUATION FOR SUBJECT AND TEACHING

Aiming to continuously improve the teaching process, University of Prishtina considers that the student evaluation for subjects in general, quality of teaching and teachers in particular is relevant.

Your assessment is valuable contribute for us.

Assessment is completely confidential and your anonymity will be preserved.

Please fill out carefully the questionnaire and be as objective as you can.

It is important to note that the purpose of this evaluation is to improve the overall quality of studies, including work of teachers and teaching.

For each question answer 1, 2, 3, 4 or 5:

64

( 5 – fully agree, 4 – agree, 3- neutral, 2- disagree, 1- not agree at all)

Questions AnswersSubject Subject 1 Subject 2 Subject 3 Subject 4 Subject 5Name of professor Professor 1 Professor 2 Professor 3 Professor 4 Professor 51 Syllabus of subject including content and the way

of evaluation was presented at the beginning of the semester

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

2 Attendance of teachers was regular during semester 1 2 3 4 5

1 2 3 4 5

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3 Teacher has always been prepared to teach 1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

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4 Activities during the semester have created opportunities for students to engage in discussions, projects and encouraged the interaction of students (work in groups, pairs, etc)

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

5 The teacher has been available to students for consultation

1 2 3 4 5

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6 The teacher encourages students different thoughts and respect them

1 2 3 4 5

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7 The materials offered for long term studies were suitable for acquisition of knowledge and skills specified for this course.

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

8 Evaluation of students for the course is made continuously during the semester and not only the final exam

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

9 Students have been informed in advance of the evaluation criteria of their work in general 1 2 3 4

5 1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

10 Concretization tools and learning spaces have been sufficient and available

1 2 3 4 5

1 2 3 4 5

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11 The course has been successful and benefitial to students

1 2 3 4 5

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66

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Open questions

Professor 1 _________________

Subject 1 ___________________

Impressions for the subject in general: Impressions for teacher in general: Do you have any additional comment or suggestion?

Professor 2; _________________Subject 2; _________________

Impressions for the subject in general:Impressions for teacher in general:Do you have any additional comment or suggestion?






Impressions for the subject in general:Impressions for teacher in general:Do you have any additional commant or suggestion?

Thank you for your cooperation

Office for academic [email protected]

68

One Contract

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