QUALIFICATION CHARACTERIZATION OF MAJOR … use and apply competently the latest multimedia technologies; to use and apply competently fundamental knowledge in the area of Mathematics

QUALIFICATION CHARACTERIZATION

OF MAJOR FIELD OF STUDY “MATHEMATICS AND INFORMATICS” FOR “BACHELOR OF SCIENCE” DEGREE

WITH PROFESSIONAL QUALIFICATION “TEACHER IN MATHEMATICS,

INFORMATICS AND ICT”

I. Requirements to professional qualities and competences of students, completed this

major field of study South-West University “Neofit Rilski” prepares qualified experts in Mathematics and

Informatics that can apply their knowledge and skills in the area of science, culture,

education and economics in Bulgaria and abroad.

After completion of Bachelor of Science (BSc) degree in Mathematics and Informatics, they

can successfully realize themselves as teachers in Mathematics, teachers in Informatics and

teachers in ICT.

At completion of Bachelor of Science degree in Mathematics and Informatics, students

obtain:

profound knowledge in the area of Mathematics and Informatics;

good knowledge of the latest technologies for multimedia education, the

development of modern educational technologies, trends and strategies for

education;

good preparation in the area of Mathematics and Informatics as well as solid

practical skills conforming to modern European standards and requirements;

good opportunities for realizing as teachers in Mathematics, Informatics and ICT;

opportunity for successful continuation of education in higher degrees (Master of

Science and PhD) in Bulgaria and abroad.

II. Requirements to preparation of students completing this major field of study Students completed BSc degree in Mathematics and Informatics have to possess following

knowledge, skills and competences:

to use the obtained knowledge in the practice;

to use and apply competently the latest multimedia technologies;

to use and apply competently fundamental knowledge in the area of Mathematics and

Informatics;

to posses and apply modern educational technologies.

Qualification characterization of Major field of study “Mathematics and Informatics”

for BSc degree is a basic document that determines rules for developing the

curriculum. This qualification characterization is conformed to legislation in the area

of higher education in Republic of Bulgaria.

CURRICULUM Field of Study: Mathematics and Informatics, 2008, Updated 2012

First Year

First Semester ECTS credits Second Semester ECTS

credits

Compulsory Courses

Linear algebra

Analytical geometry

Mathematical analysis I

Introduction to programming

Sport

7.5

7.5

7.5

7.5

0.0

Compulsory Courses

Foreign language 1

Mathematical analysis II

Algebra

Object-oriented programming

Graph theory

3.5

7.5

7.5

7.5

4.0

Total 30 Total 30

Second Year


credits

Compulsory Courses Differential equations and

applications

Number theory

Foreign language 2

School course of algebra and

analysis

Optional course 1

Sport

Optional Courses (course 1)

Computer architectures

Discrete mathematics

Information technology

7.0

5.0

4.0

9.0

5.0

0.0

5.0

5.0

5.0

Compulsory Courses

School course of geometry

Mathematical optimization

Operating systems

Pedagogy

Optional course 2


Computer models in natural sciences Algorithms for graphs and networks

Separable sets of variables of functions

VBA programming

8.0

7.0

5.5

5.5

4.0

4.0

4.0

4.0

4.0

Total 30 Total 30

Third Year


credits

Compulsory Courses Numerical analysis

Differential geometry

Psychology

Optional course 3

Optional course 4

Sport


Development of interactive

multimedia educational content

Operational research

Programing with Object Pascal

and Delphi


Mathematical structures

Descriptive geometry

Fundamentals of arithmetic

8.0

8.0

5.0

4.5

4.5

0.0

4.5

4.5

4.5

4.5

4.5

4.5

Compulsory Courses

Probability and statistics - methodology and

technology

Database

Didactics of mathematics – I

School courses of informatics and ICT

8.0

8.0

5.5

8.5

Total 30 Total 30

Fourth Year


credits

Compulsory Courses Didactics of informatics and ICT

Didactics of mathematics – II

Optional course 5

Optional course 6

Observation of lessons in

mathematics at school

Observation of lessons in

informatics and ICT at school

Sport


Geometry of the circles

Fundamentals of geometry

Methods of extra-curricular work

in mathematics

Fundamentals of computer

graphics


Expert systems

Object-oriented and distributed

databases

Applied statistic

Computer networks and

communications

Internet programming

7.0

7.0

5.0

5.0

2.0

4.0

0.0

5.0

5.0

5.0

5.0

5.0

5.0

5.0

5.0

5.0

Compulsory Course

Audiovisual and information technologies in

teaching

Pedagogical practice in mathematics

Pedagogical practice in informatics

Pre-graduation pedagogical practice in

mathematics

Pre-graduation pedagogical practice in

informatics

Optional course 7

Education and development of special needs

pupils

State examination or thesis


Problem solving practicum for school

course in mathematics

Comparative education /integrative aspects/

History of mathematics

2.5

2.5

2.5

3.0

2.5

3.0

4.0

10.0

3.0

3.0

3.0

Total 30 Total 30

TOTAL FOR 4 ACADEMIC YEARS: 240 CREDITS

COURSES DESCRIPTION

COMPULSORY COURSES

LINEAR ALGEBRA

Semester: 1 semester

Course Type: Lectures and tutorials

Hours per week: 3 lecture hours and 2 tutorial hours / Fall Semester

ECTS credits: 7,5 credits

Lecturer: Assoc. Prof. Dr. Ilinka Dimitrova

Department: Department of Mathematics, Faculty of Mathematics and Natural Sciences,

South-West University “Neofit Rilski” – Blagoevgrad,

tel. +35973588532, e-mail: [email protected]

Course Status: Compulsory course in the B.S. Curriculum of Mathematics and Informatics.

Short Description: The education of that discipline includes some of the basic notations in

combinatory and complex numbers. Students study matrices, determinants, systems linear

equations and methods for their solving, linear spaces, linear transformations, and quadratic

forms.

Course Aims: The students have to obtain knowledge and skills to apply the learned theory

for modeling and solving real practical tasks, to do basic operations with matrices, to solving

determinants and systems linear equations using the methods of Gauss and Kramer, to be

able to distinguish the correspondence between algebraic objects, to determine their

characteristics and to transfer them on others – difficult to examine.

Teaching Methods: lectures, tutorials, homework, and problem solving tests.

Requirements/Prerequisites: The students should have basics knowledge from school

mathematics.

Assessment: permanent control during the semester including homework and two written

exams, and written exam in the semester’s end on topics from tutorials and on topics from

lectures.

Registration for the exam: coordinated with the lecturer and student Service Department

References:

Basic Titles

1. Borisov, A., Il. Guidzhenov, Il. Dimitrova. Linear Algebra. University Press, South-West

University “Neofit Rilski”, Blagoevgrad, 2009 /in Bulgarian/.

2. Borisov, A., M. Kacarska. Handbook on Linear Algebra and Analytic geometry.

University Press, South-West University “Neofit Rilski”, Blagoevgrad, 2011 /in

Bulgarian/.

3. Yordzhev, K., Il. Dimitrova, A. Markovska, Il. Gyudzhenov. Variants for Exams on

Linear Algebra and Analytic Geometry, University Press, South-West University “Neofit

Rilski”, Blagoevgrad, 2007 /in Bulgarian/.

Additional Titles

1. Aslanski, M., B. Giurov. Handbook on Linear Algebra. University Press, South-West


2. Denecke, K., K. Todorov. Lectures on Linear Algebra. University Press, South-West

University “Neofit Rilski”, Blagoevgrad, 1992 /in Bulgarian and German/.

mailto:[email protected]

3. Dimitrov, D. Collections of Problems on Linear Algebra. Sofia, 1978 /in Bulgarian/.

4. Dochev, K., D. Dimitrov. Linear Algebra. Sofia, 1977 /in Bulgarian/.

5. Fadeev, D.K., I.S. Sominski. Handbook on Algebra. Moscow, “Nauka”, 1968 /in

Russian/.

6. Ilin, V.A., E.G. Pozniak. Linear Algebra. Moscow, “Nauka”, 1984 /in Russian/.

7. Kurosh, A. Course on Algebra. Sofia, “Nauka i izkustvo”, 1967 /in Bulgarian and

Russian/

8. Proskuriakov, I.V. Handbook on Linear Algebra. Moscow, “Nauka”, 1967 /in Russian/.

ANALYTIC GEOMETRY



Hours per week: 3 lecture hours and 2 tutorial hours /Fall Semester


Lecturer: Prof. Dr. Iliya Guydzhenov, e-mail: [email protected]



tel. +35973588532, e-mail:


Short Description: The education of that discipline includes learning of vector calculus,

affine coordinate systems and analytic representations of straight lines and planes. After

introducing the cross ratio, the projective coordinate systems are used as well. The basic

elements of the projective, of the affine and of the metric theory of the curves and the

surfaces of the second degree are taught.

Course Aims: The students have to obtain knowledge and skills for application of the

analytic apparatus for research of geometric objects.

Teaching Methods: lectures, tutorials, homework, problem solving tests.

Requirements/Prerequisites: Linear Algebra and Mathematical Analysis



lectures.


References:

Basic Titles

1. A. Borisov. “Lectures on Analytic geometry”. University Press, South-West University

“Neofit Rilski”, Blagoevgrad, 2000 /in Bulgarian/.

2. A. Borisov. “Handbook on Analytic geometry”. University Press, South-West University

“Neofit Rilski”, Blagoevgrad, 2011 /in Bulgarian/.

3. G. Stanilov. “Analytic geometry”. Sofia, 2000 г./in Bulgarian/.

Additional Titles

1. A. Borisov. “Analytic geometry”. University Press, South-West University “Neofit


2. A. Gjonov, N. Stoev. “Handbook on Analytic geometry”. Sofia, 1988 /in Bulgarian/.

3. N. Martinov . “Analytic geometry”. Sofia, 1989 /in Bulgarian/.

4. B. Petkanchin. “Analytic geometry”. Sofia, 1961 /in Bulgarian/.

MATHEMATICAL ANALYSIS I


Course Type: lectures and seminars

Hours per Week: 3 lecture hours and 2 seminars hour / Fall Semester

ECTS Credits: 7,5 credits

Lecturers: Assoc. Prof. Visil Grozdanov, Ph.D.




Course Status: Compulsory course in Mathematics and Informatics B.C. Curriculum.

Short Description: The main topics to be considered:

- Numerical sequences

- Numerical series

- Limit, continuity and differentiability of functions

- Integrals of functions of real variables

- Applications of the integral calculation

Course Aims: This course develops in details the problems of numerical sequences,

numerical series, differential and integral calculation of functions of one real variable.

Teaching Methods: Lectures, tutorials, homework, problem-solving tests. During the

lectures students are acquainted with the basic theoretical material- definitions, theorems,

applications, with the methods of theorems proofs. During seminars students solve practical

problems. The knowledge obtained within the theoretical practice is used and it is also used

in the process of problem solving.

Requirements/Prerequisites: Basic knowledge of courses in Elementary Mathematics,

Linear Algebra, Analytical Geometry is necessary.



lectures.


References:

Basic Titles:

1.V. A. Ilin, V. A. Sadovnichi, B. H. Sendov, Mathematical Analysis, V. 1 and 2, Sofia,

Science and Art, 1989.

2. Ia. Tagamlitzky, Differential Calculation, Sofia, Science and Art, 1971.

3. Ia. Tagamlitzky, Integral Calculation, Sofia, Science and Art, 1971.

4. I. Prodanov, N. Hadjivanov, I. Chobanov, Collection of problems of Differential and

Integral Calculation, Sofia, Science and Art, 1976.

5. V. Grozdanov, K. Iordjev, A. Markovska, Guidance for solving of problems of

mathematical analysis- first part, “Neophit Rilsky” publishing house, Blagoevgrad, 2012.

Additional Titles:

1. S. M. Nikol'skii, Course of Mathematical Analysis, V. 1 and 2, Moskow, Science, 1973.

2. L. D. Kudrjavcev, Mathematical Analysis, V. 1 and 2, Moskow, Science, 1976.

3. L. D. Kudrjavcevв, А. D. Кutassov, V. I. Chehlov, М. I. Shabunin, Collection of

problems of mathematical analysis, Science, Moskow, 1984.


INTRODUCTION TO PROGRAMMING


Type of Course: lectures and tutorials in computer lab

Hours per week: 4 hours lecture and 2 hours tutorials in computer lab/ Fall Semester


Lecturers: Assoc. Prof. PhD. Daniela Tuparova

Department: Department of Informatics, Faculty of Mathematics and Natural Sciences,




Course description: Introduction to programming is the first course in scope of

programming for the students of major “Informatics”. The course includes topics of syntax

and semantics of programming languages construct and statements. The course is based on

the C++.

Objectives: The main goal of the course is the students to master principles of programming

and algorithms.

Methods of teaching: lectures, tutorials, discussions, problem passed method, Project based

method.

Pre- requirements: No need.

Assessment and Evaluation Practical work and test- 50%

Final Еxam 50%

The course is successful completed with at least 65% of all scores.

Registration for the Exam: coordinated with the lecturer and the Student Service Office

References:

1. Азълов П., Ф. Златарова, С++ в примери, задачи и приложения, Просвета, 2011

2. Крушков Х., Програмиране на С++, 1 част - въведение в програмирането

3. Тодорова М., Програмиране на С++, 1 част, СИЕЛА, 2010

4. Тодорова М., и колектив, Сборник от задачи по програмиране на С++, Първа част,

Увод в програмирането, Технологика ООД, 2008

5. Интерактивни учебни материали, достъпни в он-лайн курса на адрес

www.e-learning.swu.bg

FOREIGN LANGUAGE 1

Semester: Second semester

Course type: Seminars

Hours per week: 2 hours per week / Summer Semester

ECTS credits: 3,5

Lecturer: Assist. prof. B. Filatov

Department: Faculty of Pedagogy


Course description: Introducing students to the basic components of English phonology,

morphology and syntax. It helps students learn and practice communicating in everyday

situations including asking and answering questions, using the telephone, taking messages,

initiating conversations, asking for directions, making invitations and closing conversations.

Class activities include role-playing, small-group activities and short presentations. It also


develops skills in reading speed and comprehension. Students are introduced to reading

strategies such as skimming, scanning, guessing meaning from context, previewing,

predicting, making inferences and giving opinions. Reading materials include short stories,

news articles, computer passages and a simplified novel.

Goal: The goals of the course is to enable students to speak and write effectively and

confidently in their professional and personal lives. Students become acquainted with the

basic terminology in the specific field.

Teaching methods: Seminars

Prerequisites: The knowledge acquired at high school is useful.

Examination and assessment procedures: The estimation of the acquired knowledge is

based on a written exam

Registration for examination: coordinated with the lecturer and the academic affairs

department

References: 1. Soars, John & Liz, New Headway Elementary - fourth edition, Oxford University Press,

2011

2. Soars, John & Liz, New Headway Pre-Intermediate - fourth edition, Oxford University

Press, 2012

3. Raymond Murphy, English Grammar in Use, fourth edition with answers, Cambridge

University Press, 2012

4. Дончева, Лилия , Английски глаголни времена, Skyprint, 2009

5. Ранкова, М., Иванова, Ц., Английска граматика, Наука и изкуство, София, 2010

6. Carter, R., McCarty, M., Mark, G., O’Keeffe, A., English Grammar Today: An A-Z of

Spoken and Written Grammar, Cambridge University Press, 2011

MATHEMATICAL ANALYSIS II

Semester: second semester


Hours per Week: 3 lecture hours and 2 seminars hour / Summer Semester







Course Description: The course in Mathematical Analysis II includes basic concepts of

mathematical analysis: improper integral, functions of two and more variables; continuity of

functions of several variables; partial derivatives, local and relative extrema; implicit

functions; double and triple Riemanm integral, and their applications for finding arias and

volumes; line integrals of first and second type; surface integrals of first and second type;

basic formulas for integrals of Mathematical Physics.

Course Aims: Students should obtain knowledge for Mathematical Analysis II, which is a

basic mathematical discipline. This knowledge is necessary for studying, Mathematical

Analysis III, Ordinary Differential Equations, Numerical Methods, Optimization.

Teaching Methods: lectures and seminars

Requirements/Prerequisites: Mathematical Analysis I




lectures.


References: 1. Yaroslav Tagamlitski – Differential Calculus, Nauka and Izkustvo Publishing House,

Sofia, 1971 (in Bulgarian).

2. Yaroslav Tagamlitski – Integral Calculus, Nauka and Izkustvo Publishing House, Sofia,

1978 (in Bulgarian).

3. V. A. Ilin, V.A. Sadovnichi, B.H. Sendov – Mathematical Analysis, Vol. 1, Vol.2, Nauka

and Izkustvo Publishing House, Sofia, 1989 (in Bulgarian).

4. I. Prodanov, N. Hadjiivanov – Problem book in Differential and Integral Calculus, Nauka

and Izkustvo Publishing House, Sofia, 1976 (in Bulgarian).

5. Е. Varbanova, Lectures on Mathematical Analysis – I, Publishing house of Technical

university Sofia, Sofia, 2009.

6. V. Grozdanov, К. Jordjev, A. Markovska, Methodological conduire for solving of

problems of Mathematical Analysis – part I, Publishing house “Neophit Rilsky”

Blagoevgrad, 2012.

7. V. Grozdanov, К. Jordjev, Ts. Mitova, Methodological conduire for solving of problems

of Mathematical Analysis – part II, Publishing house “Neophit Rilsky” Blagoevgrad, 2013.

8. V. Grozdanov, К. Jordjev, Ts. Mitova, Methodological conduire for solving of problems

of Mathematical Analysis – part III, Publishing house “Neophit Rilsky” Blagoevgrad, 2013.

ALGEBRA

Semester: 2-nd semester


Hours per week: 3 lecture hours and 2 tutorial hours /Summer Semester







Short Description: The education of that discipline includes some of the main notations of

the semigroup and group theory, ring and field theory, algebraic polynomials. The

definitions are introduced in an abstract way and explained with many examples. The Cayley

theorem, the Lagrange theorem and the main theorem for the cyclic groups are proved. The

main tools for investigations of the symmetric group are described and the importance of the

symmetric group is underlined in applications. Characteristic of field and simple fields are

introduced. There is detailed analysis of certain important rings. In the last part the classical

polynomial questions like quotient/remainder theorem, Euklid’s algorithm, Horner’s scheme,

roots of polynomials, symmetric polynomials are considered.

Course Aims: The students have to obtain knowledge and skills for the theoretical

foundations of the semigroup and group theory, ring and field theory, and polynomials as

well as the applications of this apparatus for solving some practical tasks, related to other


mathematical and informatical subjects. The obtained knowledge on this fundamental

discipline are directed to be used by students in their education on other subjects.


Requirements/Prerequisites: The students should have basics knowledge from Number

theory and Linear algebra.



lectures.


References:

Basic Titles

1. Bojilov, А., P. Siderov, K. Chakaryan. Problems in Algebra, Vedi Press, Sofia, 2006 /in

Bulgarian/.

2. Denecke, K., K. Todorov. Foundations of Algebra. University Press, South-West


3. Genov, G., S. Mihovski, T. Mollov, Algebra, University Press, “Paisii Hilendarski”,

Plovdiv, 2006 /in Bulgarian/.

4. Mihailov, I., N. Zyapkov. Algebra and Galois Theory, Faber Press, Veliko Tarnovo,

2004 /in Bulgarian/.

5. Siderov, P., K. Chakaryan. Notes on Algebra, Vedi Press, Sofia, 2006 /in Bulgarian/.

Additional Titles

1. Dochev, K., D. Dimitrov, V. Chukanov. Handbook on Algebra. Sofia, 1976 /in

Bulgarian/.

2. Dodunekov, S., K. Chakaryan. Problems in Number Theory. Regalia Press, 1999 /in

Bulgarian/.

3. Fadeev, D.K., I.S. Sominski. “Handbook on Algebra”. Moscow, “Nauka”, 1968 /in

Russian/.

4. Kurosh, А. Course on Algebra. Sofia, “Nauka I izkustvo”, 1967 /in Bulgarian/.

5. Okunev, L. Ya. Algebra, Moscow, 1949 /in Russian/.

6. Proskuriakov, I.V., “Handbook on Linear Algebra”. Moscow, “Nauka”, 1967 /in

Russian/.

7. Skornyakov, L.A., Elements of Algebra. Moscow, 1986 /in Russian/.

OBJECT-ORIENTED PROGRAMMING


Type of Course: lectures and labs

Hours per week: 2 lectures + 2 labs / Summer Semester


Lecturers: Assoc. Prof. Ph.D. Krasimir Yankov Yordzhev





Course description: In the course students are introduced with methods and means of

Object-oriented programming. The course is providing basic knowledge in development of

algorithms, their programming using particular programming language and running and

http://mce_host/[email protected]

testing of the programs under certain operation system. The structure and the main

operational principles of the computer systems are given. The means and accuracy of

information presentation are also considered. Some of the key classes of algorithms and data

structures are studied. The main techniques of the structural approach of programming and

their application using C++ programming language are introduced. The aim of the course is

to teach the students with the techniques in development of algorithms and programs using

C++ programming language. The knowledge will be used in the general theoretical,

technical and some special courses.

Objectives:

Basic objectives and tasks:

The students give knowledge for algorithum thinking;

to give knowledge for methods and skils in Object-oriented programming in

integrated development environment for visual programming;

to give knowledge for Data structures, that can process with computer;

to give knowledge for methods and skills in programming.

to give knowledge for good style in programming;

to give knowledge for basic principles when develop applications

Methods of teaching: lectures, tutorials, group seminars or workshop, projects, other

methods

Pre- requirements: The course is continued of the course “Introduction in programming”.

Basic knowledge in Mathematics.

Exam: Written examination and discussion at the end of the semester, individual tasks and

the general student’s work during the semester.

Registration for the Exam: Coordinated with the lecturer and the Student Service Office

References: 1. Магдалина Тодорова Програмиране на C++. Част І, Сиела, 2002.

2. Herbert Schildt Teach Yourself C++, McGraw-Hill, 1998.

3. Cay S. Horstmann Computing Consepts with C++ Essentials, John Wiley & Sons, 1999.

4. Steve Donovan C++ by Example. Que/Sams,2002.

5. Tan Kiat Shi, Wili-Hans Steeb, Yorick Hardi Symbolic C++: An Introduction to

Computer Algebra using Object-Oriented Programming. Springer, 2000.

6. Димитър Богданов Обектно ориентирано програмиране със C++. София,

Техника, 2002.

7. Христо Крушков Програмиране на C++. Пловдив, Макрос, 2006.

8. Брайън Овърленд C++ на разбираем език. АлексСофт, 2003.

9. Преслав Наков, Панайот Добриков Програмиране = ++ алгоритми. София, 2005.

10. Г. С. Иванова, Т. Н. Ничушкина, Е. К. Пугачев Объектно-ориентированное

программирование. Москва, МГТУ, 3003.

11. Кент Рейсдрф, Кен Хендерсон Borland C++ Builder. Освой самостоятелно

GRAPH THEORY


Type of Course: lectures and seminars

Hours per week: 2 lecture hours + 1 seminar hour / Summer Semester


Lecturers: Prof. Ivan Mirchev, DSc





Course description: The 1970s ushered in an exciting era of research and applications of

networks and graphs in operations research, industrial engineering, and related disciplines.

Graphs are met with everywhere under different names: "structures", "road maps" in civil

engineering; "networks" in electrical engineering; "sociograms", "communication structures"

and "organizational structures" in sociology and economics; "molecular structure" in

chemistry; gas or electricity "distribution networks" and so on.

Because of its wide applicability, the study of graph theory has been expanding at a very

rapid rate during recent years; a major factor in this growth being the development of large

and fast computing machines. The direct and detailed representation of practical systems,

such as distribution or telecommunication networks, leads to graphs of large size whose

successful analysis depends as much on the existence of "good" algorithms as on the

availability of fast computers. In view of this, the present course concentrates on the

development and exposition of algorithms for the analysis of graphs, although frequent

mention of application areas is made in order to keep the text as closely related to practical

problem-solving as possible. Although, in general, algorithmic efficiency is considered of

prime importance, the present course is not meant to be a course of efficient algorithms.

Often a method is discussed because of its close relation to (or derivation from) previously

introduced concepts. The overriding consideration is to leave the student with as coherent a

body of knowledge with regard to graph analysis algorithms, as possible.

In this course are considered some elements of the following main topics:

Introduction in graph theory (essential concepts and definitions, modeling with

graphs and networks, data structures for networks and graphs, computational

complexity, heuristics).

Matching and assignment algorithms (introduction and examples, maximum-

cardinality matching in a bipartite graph).

The chinesse postman and related arc routing problems (Euler tours and Hamiltonian

tours, the postman problem for undirected graphs, the postman problem for directed

graphs).

The traveling salesman and related vertex routing problems (Hamiltonian tours, basic

properties of the traveling salesman problem, lower bounds, optimal solution

techniques, heuristic algorithms for the TSP).

Course Aims: Students should obtain basic knowledge in Graph theory and skills for solving

optimization problems for graphs and networks.

Teaching Methods: lectures, tutorials, individual student’s work

Requirements/Prerequisites: Graphs, Discretion Programming

Assessment: 3 homework D1,D2,D3; 2 tests K1, K2 (project); written final exam


Rating: = 0,2.(D1+D2+D3)/3 + 0,5.(K1+K2)/2 + 0,3.(Exam)

Registration for the Exam: coordinated with the lecturer and Students Service Department

References:

Basic:

1. Ив.Мирчев, "Графи. Оптимизационни алгоритми в мрежи", Благоевград, 2001 г.

2. Ив.Мирчев, "Математическо онтимиране", Благоевград, 2000 г.

3. Minieka, Е., Optimization Algorithms for Networks and Graphs, Marcel Dekker, Inc.,

New York and Basel, 1978 (Майника, 3. Алгоритми оптимизации на сетях и графах, М.,

"Мир", 1981).

Additional:

1. Keijo Ruohonen. GRAPH THEORY. math.tut.fi/~ruohonen/GT_English.pdf, 2008

2. Ronald Gould. Graph Theory (Dover Books on Mathematics. 2012. US Cafifornia.

3. Lih-Hsing Hsu , Cheng-Kuan Lin, Graph Theory and Interconnection Networks.

1420044818, 2008,

4. Team DDU.Christofides, N., Graph Theory. An Algorithmic approach, Academic Press

lnc (London) Ltd. 1975, 1977 (Крисгофидес, И. Теория графов. Алгоритмический

подход, М., "Мир", 1978 ).

5. Swamy, М., К. Thulasirman, Graphs, Networks and Algorithms, John Wiley & Sons,

1981 (Сваами M., K. Тхуласирман. Графм, сети и алгоритми, М., "Мир", 1984).

DIFFERENTIAL EQUATIONS AND APPLICATIONS



Hours per week: 2 lecture hours and 2 tutorial hours /Fall Semester


Lecturer: Assoc. Prof. Nikolaj Kitanov,




Course Status: Compulsory course from Mathematics and Informatics B.C. Curriculum.

Course Description: Mathematical methods of investigation are used in every field of

science and technology. Differential Equations are the foundations of the mathematical

education of scientists and engineers. The main topics are: First-order Linear equations with

constant coefficients: exponential growth, comparison with discrete equations, series

solutions; modeling examples including radioactive decay and time delay equation. Linear

equations with non-constant coefficients: solution by integrating factor, series solution.

Nonlinear equation: separable equations, families of solutions, isoclines, the idea of a flow

and connection vector fields, stability, phase-plane analysis; examples, including logistic

equation and chemical kinetics. Higher-order Linear equations: complementary function and

particular integral, linear independence, reduction of order, resonance, coupled first order

systems. Examples and PC-models of nonlinear dynamics, order and chaos, attractors. etc.

Course Aims: The main goal is the students to master the instruments and methods of

modeling in science.

Teaching Methods: lectures, tutorials, homework, tests, etc.

Requirements/Prerequisites: Calculus I and II, Linear Algebra and Analytical Geometry.

Exam: tests, homework, final exam


Registration for the exam: Coordinated with lecturer and Students Service Department

References:

1. Differential Equations, 2008, http://www.sosmath.com/diffeq/diffeq.html (наш превод -

в ЮЗУ -2011 г)

2. Попиванов П., П.Китанов, Обикновени диференциални уравнения. ЮЗУ

Благоевград, 2000.

3. Борисов А., Ил.Гюдженов. Математика, част 3. Елементи на интегралното смятане.

Елементи на обикновените диференциални уравнения.Б-д .2003г

4. Босс. В. Лекции по математике. Дифференциальные уравнения. М. 2004г.

5. Живков А, Е. Хорозов, О. Христов http://debian.fmi.uni-

sofia.bg/~horozov/DifferentialEquations/book.pdf (Х.2007- 2008)

6. http://www.exponenta.ru/educat/class/courses/ode/theme1/theory.asp 2013.

7. Ordinary Differential Equation http://www.mat.univie.ac.at/~gerald/ftp/book-ode/ode.pdf

8. Байнов Д., К.Чимев, Ръководство за решаване на задачи по обикновени

диференциални уравнения. ЮЗУ, Благоевград, 1992г. (учебник и ръководство на

Д.Байнов от ПУ се намира в ЮЗУ библиотеката в голям брой екземпляри).

9. Пушкаров. Д. Математически методи на физиката.Ч. I., ЮЗУ, Бл.1993г.

10. Эльсгольц. Л.Дифференциальные уравнения и вариационное вычисление. М. 2000.

11. Дорозов, А. Т.Драгунов. Визуализация и анализ инвериантных множеств

динамических систем. Москва, 2003г.

12. Ризниченко. Г.Математические модели в биофизике и экологии..М, 2003г.

13. Stewart J. Calculus. III ed. (AUBG). 1996.

14. Сп.Манолов, А.Денева и др. Висша математика, част 3. Техника, 1977г.

15. Методическо ръководство за решаване на задачи по математика, ч. 4, Техника,

София, 1975г.- файловете от ръководството са достъпни за студентите в зала 1-115)

NUMBER THEORY


Type of the course: Lectures and tutorial

Hours per week: 2 lecture hours and 1 tutorial hour / Fall Semester


Lecturer: Prof. Dr.Sc. Oleg Mushkarov





Short Description: Main topics:

- Divisibility

- Primes and the Fundamental theorem of Arithmetic

- Congruences

- Fermat’s, Euler’s and Wilson’s theorems

- Quadratic residues

- Diophantine equations

- Arithmetic functions

http://www.sosmath.com/diffeq/diffeq.html

http://debian.fmi.uni-sofia.bg/~horozov/DifferentialEquations/book.pdf

http://debian.fmi.uni-sofia.bg/~horozov/DifferentialEquations/book.pdf

http://www.exponenta.ru/educat/class/courses/ode/theme1/theory.asp%20%20%20%20%202013

http://www.mat.univie.ac.at/~gerald/ftp/book-ode/ode.pdf


Course Aims: To develop in details the basic notions and methods of elementary Number

theory and their applications for solving problems of divisibility, linear and quadratic

congruences and Diophantine equations.

Teaching Methods: Lectures, tutorials, homework, problem-solving tests. During the

lectures students are acquainted with the basic theoretical material- definitions, theorems and

applications. During seminars students solve practical problems. The knowledge obtained

within the theoretical practice is used in the process of problem solving.

Requirements/Prerequisites: Basic knowledge of the courses in Elementary Mathematics,

Linear and Abstract Algebra.

Assessment: Written exam on problem solving and on the theoretical material from the

lectures.

Registration for the exam: Students and the lecturer agree on the convenient dates within

the announced calendar schedule of examination session.

References:

Basic Titles

1. S. Dodunekov, K. Tchakarjan, Number theory problems, Regalia, 1999.

2. Lecture notes (www.moi.math.bas.bg/~peter).

3. T. Andreescu, D. Andrica, Number Theory, Birkhauser, 2009.

Additional Titles

1. J. Silverman, A Friendly Introduction to Number Theory, Prentice-Hall, Inc., 1997

2. P. Boivalenkov, E. Kolev, O. Mushkarov, N. Nikolov, Bulgarian Mathematical

Competirions 2006 – 2008, UNIMATH, Sofia, 2008.


Competirions 2009 – 2011, UNIMATH, Sofia, 2012.

FOREIGN LANGUAGE 2


Course type: Seminars

Hours per week: 2 hours per week / Fall Semester

ECTS credits: 4.0

Lecturer: Assist. prof. B.Filatov

Department: Faculty of Pedagogy


Course description: Introducing students to the basic components of English phonology,

morphology and syntax. It helps students learn and practice communicating in everyday

situations including asking and answering questions, using the telephone, taking messages,

initiating conversations, asking for directions, making invitations and closing conversations.

Class activities include role-playing, small-group activities and short presentations. It also

develops skills in reading speed and comprehension. Students are introduced to reading

strategies such as skimming, scanning, guessing meaning from context, previewing,

predicting, making inferences and giving opinions. Reading materials include short stories,

news articles, computer passages and a simplified novel.

Goal: The goals of the course is to enable students to speak and write effectively and

confidently in their professional and personal lives. Students become acquainted with the

basic terminology in the specific field.

Teaching methods: Seminars

http://www.moi.math.bas.bg/~peter

Prerequisites: The knowledge acquired at high school is useful.

Examination and assessment procedures: The estimation of the acquired knowledge is

based on a written exam

Registration for examination: coordinated with the lecturer and the academic affairs

department

References: 1. Soars, John & Liz, New Headway Elementary - fourth edition, Oxford University Press,

2011

2. Soars, John & Liz, New Headway Pre-Intermediate - fourth edition, Oxford University

Press, 2012

3. Raymond Murphy, English Grammar in Use, fourth edition with answers, Cambridge

University Press, 2012

4. Дончева, Лилия , Английски глаголни времена, Skyprint, 2009

5. Ранкова, М., Иванова, Ц., Английска граматика, Наука и изкуство, София, 2010

6. Carter, R., McCarty, M., Mark, G., O’Keeffe, A., English Grammar Today: An A-Z of

Spoken and Written Grammar, Cambridge University Press, 2011

SCHOOL COURSE OF ALGEBRA AND ANALYSIS

Semester: 3 semesters

Course Type: lectures and tutorials

Hours per Week: 3 lecture hours, 3 tutorials hours / Fall Semester

ECTS Credits: 9.0 credits

Lecturers: Assoc. professor Kostadin Samardzhiev, PhD




Course Status: Compulsory course in the Mathematics and Informatics B.S. Curriculum.

Course Description: The construction and development of the notion “number” is a difficult

process not only for its mathematical and philosophical character, but for its educative

character, too. The course “Scholar course of education in Algebra and analysis” for the

students from second course in specialty “mathematics and Informatics” follow the

development of the4 notion “number”, which is known from the course “Bases of the

Arithmetic”. This course formulates the basic principles of Algebra – commutative,

associative and distributive; idempotents (neutral elements); the operations addition and

multiplication of natural numbers H. on the base of the operations addition and

multiplication, the course defines the respective orders. It lists the basic properties of the

linear order – each set of natural numbers is limited from below, Archimedean principle, the

method of the mathematical order and etc. the course considers the question about the

division of the natural numbers and the notion “prime number”. All of this illustrated by

concrete examples. The number in different cardinal (countable) systems.

In this course we show that each two natural numbers a, b אthe equations a+x=b and a

x=b do not have solutions in the semiring of the natural numbers א. This lead to the necessity

of enlargement of the semiring א to the ring of the integer numbers Z, to the semifield of the

fraction Qt, and finally to the field rational numbers Q. The course makes clear the validation

of the basic properties of the introduced orders in the semiring of the natural numbers, for


each of mentioned above structures. All of this is illustrated by appropriate example and

problems. The most of the school hours is spared for the field of the real numbers and

respective problems, such as quadratic equations and inequality, systems of equations and

inequality, some of them with irrational expressions, some equivalent expressions with the

collaboration of a special function like exponential, logarithmic, trigonometric and etc. out

auditorium work for this course include homework, course tasks, work in library and

computer room, consultation, preparation for test-paper, assimilation of the lection materials

and etc. the proportion between auditorium and out auditorium work is 90:135.

Course Aims: The introduced course of lections and tutorials shows the status of the

mentioned above material, which is taught in a school course in Mathematics. It is developed

on the base of well-known algebraic structures. Students should learn this basic structures

and problems which can be solved in them. With the help of the obtained knowledge and

skills students should receive a complete canonical form of an algebraic equation or system

of algebraic equations, using possible equivalent transformations.

Teaching Methods: lectures and tutorials.

Requirements / Prerequisites: Higher Algebra, Bases of the Arithmetic.

Assessment: written final exam

Registration for the Exam: coordinated with lecturer and Student Service Department

References:

Basic Titles

1. Денеке, Кл., Тодоров, К., Основи на аритметиката, Благоевград, 1999

2. С. Е. Ляпин, М. И. Баранова, Сборник задачи по элементарной математике,

Учпендгиз, 1963г.

3. Л. Чакалов и др. Сборник задачи по алгебра.

4. Ил.Гюдженов, К.Самарджиев Методическо ръководство за решаванене на задачи по

математика.,1994г.Благоевград

5. Ярослав Тагамлицки, Диференциално смятане, наука и изкуство София 1978г.

6. Божоров Е. Висша математика Държавно издателство Техника-София 1975г.

7.Чимев К.,А.Петрова-Денева Математика Благоевград 1985г.

8.Чимев К.,Тасев М.и др. Методическо ръководство за решаване на задачи по

математика Издателство Благоевград 1988г.

9.Ларичев П.А. Сборник задач по Алгебре част първа Учпедгиз 1961г. Москвы

Additional Titles

1.Чимев К.,Мирчев И.,Щраков Сл. Математика Благоевград 1995г.

2.Киркоров И.,Недев А. Сборник задачи по висша математика част втора Издателство

Наука и изкуство София-1975г.

3.Миланов С.,Стоянов Н.,Денева А. и др. Висша математика 1,2,3,4,5 част Държавно

Издателство Техника София-1977г.

SCHOOL COURSE OF GEOMETRY

Semester: IV semester




Lecturer: Assoc.prof. Georgi Ganchev



tel. +35973588532, e-mail:

Course Status: Compulsory course in the B.S. Curriculum of Mathematics and Informatics

Short Description: The course includes studying of the basic geometrical transformations:

congruence, similarity, affinity. Some principal topics, connected with the area of polygon

and volume of tetrahedron, are considered.

Course Aims: Students should obtain theoretical and practical knowledge, necessary for

teaching High School Geometry.

Teaching Methods: lectures, tutorials, homeworks, problem solving tests.

Requirements/Prerequisites: High School Geometry

Assessment: written exam on topics from tutorials and on topics from lectures.


References:

Basic Titles

1. Borisov, A., A. Langov. School course of Geometry. Blagoevgrad, 2007.

2. A. Borisov, A. Langov. “Handbook on School course of Geometry”. University Press,

South-West University “Neofit Rilski”, Blagoevgrad, 2011 /in Bulgarian/.

3. Lozanov, Ch.; G.Eneva, A.Langov. Synthetic Geometry.Sofia, 1994.

Additional Titles

1. Adamar. J. Elementary Geometry,1,2. Moskow, 1979.

2. Bankov,K.; T.Vitanov. Geometry. Sofia, 2003.

3. Perepolkin.D. I. Course of Elementary Geometry,1,2. Sofia, 1965.

4. Hilbert. D. Foundations of Geometry.Sofia, 1978.

MATHEMATICAL OPTIMIZATION

Semester: IV semester




Lecturer: Assoc. Prof. Stefan Stefanov, PhD





Short Description: The course in Optimization (Mathematical Programming) includes basic

results and methods for solving various types optimization problems and related topics:

nonlinear optimization problems, linear optimization problems (simplex method, duality in

linear optimization, transportation problem, assignment problem), matrix games (John von

Neumann minimax theorem, graphical method for solving 2 х 2, 2 х n, and m х 2 games,

relation between matrix games and linear optimization), convex analysis (convex sets, sum

of sets and product of a set with a real number, projection of a point onto a set, separation of

convex sets, extreme points, cones, polar cones, representation of convex cones,

representation of convex sets, polyhedrons, convex functions, directional derivatives,

subgradients and subdifferentials), convex optimization problems (Kuhn-Tucker theorem),

quadratic optimization problems.


Course Aims: Students should obtain basic knowledge and skills for solving optimization

problems under consideration.

Teaching Methods: lectures and tutorials

Requirements/Prerequisites: Mathematical Analysis, Linear Algebra, Analytic Geometry.

Assessment: written final exam


References: Basic Titles:

1. P. Kenderov, G. Hristov, A. Dontchev – “Mathematical Programming”, Kliment Ohridski

Sofia University Press, Sofia, 1989 (in Bulgarian).

2. “Mathematical Programming Problem Book”, Kliment Ohridski Sofia University Press,


3. Stefan M. Stefanov – “Quantitative Methods of Management”, Heron Press, 2003 (in

Bulgarian).

Additional Titles:

4. Stefan M. Stefanov – “Separable Programming. Theory and Methods”, Kluwer Academic

Publishers, Dordrecht – Boston – London, 2001.

5. Hamdy A. Taha – „Operations Research. An Introduction”, 9-th ed., Prentice Hall, USA,

2010.

OPERATION SYSTEMS



Hours per week: 2 hours lecture and 2 hours tutorials in computer lab/ Summer Semester


Lecturers: Prof. Nina Sinyagina





Course description: The course is introduction in area of operation systems. Basic

knowledge and skills in Linux and Microsoft Windows are covered.

Objectives:

The student should obtain knowledge of:

Basic principles of operation systems.

Basic administration skills in area of operation systems.

Methods of teaching: lectures, tutorials, discussions, project based method.

Pre- requirements: Database systems (core course)

Assessment and Evaluation Pre-exam test – 30%

Final Test- 70%



References 1. Лилян Николов, Операционни системи, ИК "Сиела", София, 1998.


2. William Stallings, Operating Systems: Internals and Design Principles, Prentice Hall,

Third Edition 1998; Fifth Edition 2005.

PEDAGOGY



Hours per week: 2 hours lecture and 2 hours seminars/ Summer Semester


Lecturers: Assoc. prof. D.Sc. Lidiya Tsvetanova - Churukova

Department: Department of Pedagogy, Faculty of Pedagogy, South-West University

“Neofit Rilski” – Blagoevgrad, tel. 0888492612, e-mail: [email protected]


Course description: The purpose of the preparation of this course is for students to master

the scientific bases of institutional organized training. It is important to develop their

theoretical thinking, their ability to penetrate into the essence of didactic phenomena and

processes, to analyze the legitimate links between tradition and innovation in education,

navigate the changing pedagogical reality. Their attention will be offered to current

theoretical issues and concepts arising from practice, the system of organized and targeted

training in Bulgaria and the world. By modern interpretation of the problems students will be

able to master thoroughly the nature, regularities, technology and training.

Scientific status of pedagogy. Personal development - biological and social factors. Role and

importance of education and self-education. Family as an educational factor. Educational

process. Methods, forms and principles of education. Didactics in the system of scientific

knowledge. Learning as a comprehensive educational system. Didactic research and

innovations. Learning process. Problem - evolving learning and the formation of higher

intellectual skills. Content of the training. Theory of textbooks and academic literature.

Principles of training. Methods, approaches and techniques . Assessment and evaluation in

education. Organizational systems and training forms. Today's lesson - structuring and

typing. Individualisation and differentiation of training. Failure of students in learning and

their overcoming.

Methods of teaching: The training uses, as traditionally established and interactive methods

(multimedia presentations, case studies, etc.). Examination grade is based on the successful

completion of the written examination and protection of training portfolio. Practical

exercises thematically follow lectures. Continuous assessment during the semester grade is

based on the fulfilled independent work by students and the verification tests in modules or

tests. The share of current assessment is 60% in the final grade of the student.

Assessment and Evaluation: written exam


References:

1. Kuzovlev V.P, Gerasimova E. H. , Ovchinnikova A.Z. , Tsvetanova - Churukova

L.Z. , Popkochev T.A. Pedagogy . - Blagoevgrad : Publishing SWU " N.Rilski " Publishing

EGU " I.A.Bunin " , 2010, 2011.

2. Experience in usage of integrated forms of training in primary grades in the Bulgarian

schools (Text) / LZ Cvetanova - Churukova / / Educational psychology in the multicultural

space - Elets, 2010 № 3 . - V.1 -2.


3. Tsvetanova - Churukova L.Z. Integrated education in primary grades. Monograph. -

Blagoevgrad: SWU "N.Rilski", 2010 + CD; Toihurst, W. & Group Using The Internet,

Yndianopols, 1996 .

4. Education trends in perspective: Analysis of the world education indicators. - 2005 ed. -

Paris: UNESCO, 2005. - 229 p.

5. The encyclopedia of comparative education and national systems of education /

Ed. By T. Neville Post lethwaite. - Oxford: Pergamon Press, 1988. - XXVIII, 778 p.

6. Global education digest 2004: Comparing education statistics across the world. -

Montreal: UNESCO inst. for Statistics, 2004. - 153 p.

7. Bruner, Jerome Seymour The culture of education. - Cambridge, Mass: Harvard Univ

Press, 1996. - XVI, 224 p.

8. E-LEARNING and training in Europe: A survey into the use of e-learning in training and

professional development in the European Union. - Luxembourg: Office for office. Publ. of

the Europ. Communities, 2002. VI, 65 p.

9. INTERNATIONAL mobility of the highly skilled: OECD proceedings. - Paris: OECD,

2002. - 348 p.

10. NATIONAL action to implement lifelong learning in Europe. - Brussels: Eurydice, 2001.

- 151 p.

11. WHAT schools for the future? Schooling for tomorrow. - Paris: OECD, 2001. 250 p.

12. CHANG, Gwand-Chol et al. Educational planning through computer simulation /

G. - C.Chang, M.Radi - Paris: UNESCO, 2001. - [VIII], 85 p.

13. Learning to bridge the digital divide: schooling for tomorrow. Paris: OECD, 2000. 137p.

14. LEARNING to change: the experience of transforming education in South East Europe,

Ed. By Terrice Bassler. - Budapest etc.; Centr. Europ. Univ. Press, 2005. - XIX, 220 p.

14. Marty Nicole Informatique et nouvelles pratiques d ecriture. Paris: Nathan, 2005. - 256p.

15 . Charlier Bernadette, Peraya Daniel Technologie et innovation en pedagogie. - Bruxelles:

De Boeck & Larcier sa; Editions De Boeck Universite, 2003. - 230 p.

NUMERICAL ANALYSIS

Semester: V semester

Course Type: Lectures and labs

Hours per week: 3 lecture hours and 2 lab hours /Fall Semester


Lecturer: Assoc. Prof. Stefan Stefanov, PhD





Course Description: The course in Numerical Analysis includes basic numerical methods of

mathematical analysis, algebra, and differential equations: interpolation and least squares

data fitting as methods for approximating functions given by tabulated data; numerical

differentiation; numerical integration – Newton-Cotes and Gauss quadrature formulas;

numerical solution of nonlinear equations; numerical solution of linear systems of algebraic

equations; numerical solution of the initial-value problem for ordinary differential equations

of first order; numerical solution of the boundary value problem for ordinary differential


equations of second order; and variational methods for solving operator equations (including

differential equations).

Course Objectives: Students should obtain knowledge and skills for numerical solutions of

problems in the area of mathematical analysis, algebra and differential equations, which are

applicable for solving various problems.

Teaching Methods: lectures, tutorials and lab exercises

Requirements/Prerequisites: Mathematical Analysis, Linear Algebra, Analytic Geometry,

Differential Equations

Assessment: written final exam covering problems /omitted in case the average grade of two

current problem tests is higher than Very Good 4.50/ (grade weight is 30 %) and theory on

two topics (grade weight is 30 %); two homework (grade weight is 20 %) and two projects

(grade weight is 20 %)


References: Basic Titles:

1. Бл. Сендов, В. Попов – “Числени методи”, I част, Университетско издателство “Св.

Климент Охридски”, София, 1996; II част, “Наука и изкуство”, 1978.

2. Б. Боянов – “Лекции по числени методи”, София, 1995.

3. Колектив – “Сборник от задачи по числени методи”, 2-ро изд., Университетско

издателство “Св. Климент Охридски”, София, 1994.

4. М. Касчиев – “Ръководство по числени методи”, изд. “Мартилен”, София, 1994.

Additional Titles:

1. R. L. Burden, J. D. Faires – “Numerical Analysis”, ”, 9-th ed., Cengage Learning,

Stamford, CT, USA, 2010.

2. J. D. Faires, R. L. Burden – “Numerical Methods”, Brooks/Cole Publishing Company,

Pacific Grove, CA, USA, 2002.

3. S.M. Stefanov – “Numerical Analysis”, MS4004-2203, Limerick, 1998.

GEOMETRY





Lecturer: Assoc.Prof. Dr. Georgi Ganchev



tel. +35973588532, e-mail:


Short Description: The course includes: studying of basic themes of the classical

differential geometry of the curves, the one-parametric sets of straight lines and the surfaces

in the three-dimensional real Euclidean space.

Course Aims: The students have to obtain knowledge and skills for application of the

differential-geometric methods for learning of geometric objects.

Teaching Methods: Lectures, tutorials, home works, problem solving tests.

Requirements/ Prerequisites: Analytic Geometry, Mathematical Analysis, Differential

Equations.


Registration for the Exam: coordinated with the lecturer and Student Service Department.

References: Basic Titles

1. Borisov, A. Differential Geometry. University Press, South-West University “Neofit

Rilski” Blagoevgrad, 1994(in Bulgarian).

2. Gjonov, A. Handbook on Differential Geometry. Sofia, 1999 (in Bulgarian).

Additional Titles:

1. Ivanova-Karatopraklieva, I. Differential Geometry. University Press “St. Kl. Ohridski”,


2. Petkanchin, B. Differential Geometry. Sofia, 1964 (in Bulgarian).

3. Stanilov, G. Differential Geometry. Sofia, 1997 (in Bulgarian).

PSYCHOLOGY

Semester: V semester


Hours per week: 2 hours lectures and 1 hour seminar / Fall Semester


Lecturers: Assoc. Prof. Maria Mutafova, PhD

Department: Department of Psychology, Faculty of Philosophy, South-West University

“Neofit Rilski” – Blagoevgrad, e-mail: [email protected]


Course description: Bachelors acquire specialized theoretical competence in Psychology

(General, Developmental and Educational psychology) course. The purpose of the proposed

training is students to benefit from advances in world practice in General, Developmental

and Educational psychology, and building skills to interpret data from empirical studies for

application of appropriate methods of psychological diagnosis, research design and

psychological characteristics of the interaction between teachers and students of varying

ages. Competence, skills and research culture in Psychology is stimulated.

Methods of teaching: lectures, seminars, tutorials, discussions.

Pre-requirements: No need

Assessment: permanent control during the semester including homework and written exams,

and written exam in the semester’s end on topics from tutorials and on topics from lectures.


References:

PROBABILITY AND STATISTICS - METHODOLOGY AND

TECHNOLOGY

Semester: VI semester


Hours per week: 2 hours lectures and 2 hours tutorials in computer lab / Summer Semester


Lecturers: Assoc. Prof. Elena Karashtranova, PhD






Course description: In this course questions of Probability and Mathematical Statistics are

considered. Algorithms connected with finding structural and numerical characteristics of

graphs are represented. Basic notion of Probability and Statistics are considered connected

with Theory of Estimations and Decision Theory in case of big and small samples, testing of

hypothesis based on models about the probability distributions of the features in the

investigated population.

Objectives: The students should obtain knowledge and understanding that the intercourse

character needs to discover the connection Mathematics- Informatics- Physics- Economics

and much more other sciences:

Methods of teaching: seminars, tutorials, discussions, project based method.

Pre-requirements: It is helpful the students have some knowledge in Analysis and

Information Technology

Assessment and Evaluation: Three semestrials tests witch estimations will have part in the

final estimation (50%)




1. Димитров, Б., Янев, Н., Вероятности и статистика, 2001, София.

2. Каращранова Е., Интерактивно обучение по вероятности и статистика,

Благоевград, 2010

3. Карлберг К., Бизнес анализ с Microsoft Excel, СофтПрес 2003

4. Фелър, У. Теория на вероятностите. “Наука и изкуство”, София, 1985.

5. The Statistics Homepage - http://www.statsoft.com/textbook/stathome.html ©1984-

2008

6. Harrison P.G., Nonparametric density estimation, John Wiley,2002

7. Калинов К.,Статистически методи в поведенческите и социалните науки, НБУ,

2010

8. П. Копанов, В. Нончева, С. Христова, Вероятности и статистика,

ръководство за решаване на задачи,Университетско издателство „Паисий

Хилендарски”, 2012, ISBN 978-954-423-796-7

9. G.Freiman,Exploratory data analysis,J., Isr.Math, 2002

Additional Titles:

1. Байнов, Д., Теория на вероятностите и математическа статистика, Импулс-М,

София, 1990.

2. Въндев Д., Теория на вероятностите и Статистика за Физическия факултет на

СУ - http://stochastics.fmi.uni-sofia.bg/

3. Димитров, Б., Каращранова, Е. Статистика за нематематици, 1993, Благоевград.

4. Калинов К., Статистически методи в поведенческите и социалните науки,

София, 2001


http://stochastics.fmi.uni-sofia.bg/

DATABASE

Semester: VI semester

Course Type: lectures and lab exercises

Hours per week/FS/SS: 2 lecture hours and 2 lab exercise hours / Summer Semester

ECTS credits: 7,0

Lecturer: Prof. Peter Milanov, PhD





Course Description: In this course we will present Database Theory. Course contains

programmer/analyst –oriented in database management, practical training.

Course Aims: Students should obtain knowledge and skills for designing of real database.

Teaching Methods: lectures, demonstrations and work on project

Requirements/Prerequisites: Linear algebra, Computer languages.

Assessment: course project

Registration for the Exam: coordinated with the lecturer and Student Service Department

References: 1. Vidya Vrat Agarwal, Beginning C Sharp 5.0 Databases, 2012 New York Press,

2. Alapati and Bill Padfield, Expert Indexing in Oracle Database, 2011, New York Press,

3. Toby J. Teorey , Sam S. Lightstone , Tom Nadeau, H.V. Jagadish, Database Modeling and

Design Database Modeling and Design, 2012, Morgan Kaufmann Press

4. Henry H. Liu, Oracle Database Performance and Scalability A Quantitative Approach,

2011 A Jon Wiley and Son, US

5. Павел Азълов. Бази от данни. Релационен и обектен подход, техника, 1991 г.

6. Юлиана Пенева, Бази от данни. І част. София, ИК "Регалия " 6, 2002 г.

7. Shepherd J.C. Database management: Theory and Application. Irwin Inc.,USA 1990.

8. Мейер Д.р Теория релационных баз данных. Издательство "Мир". 1987.

DIDACTICS OF MATHEMATICS I


Course Type: Lectures

Hours per week: 2 lecture hours / Summer Semester


Lecturer: Prof. Dr. Iliya Gyudzhenov



tel. ++35973588545, e-mail:


Short Description: The education of that discipline includes some of the General

Methodology of teaching mathematics.

Course Aims: To prepare the students, teach pupil in mathematics at school.

Teaching Methods: lectures, homework, and problem solving tests.


Requirements/Prerequisites: The students should have basics knowledge from school

mathematics.



lectures.


References:

Basic Titles

1. Ganchev Iv. and others, Methodology of teaching mathematics (General Methodology),

Blagoevgrad, 2002.

2. Ganchev Iv. and others, Methodology of teaching mathematics (VIII – XI class), I part,

Sofia, 1998.

SCHOOL COURSES OF INFORMATICS AND ICT



Hours per week: 3 hours lecture and 3 hours tutorials in computer lab / Summer Semester







Course description: The course includes:

State of the art in the secondary school courses of informatics and ICT. State

educational Standards;

Basic modules of informatics and ICT secondary school curriculum

Programming in Pascal

Programming in QBasic

Objectives: The student should obtain knowledge of:

Educational standards in Informatics and ICT.

School’s curriculums in Informatics and ICT

Programming languages used in the secondary schools.


method.

Pre- requirements: Programming, Data structures, Discrete Mathematics, ICT, Operating

Systems

Assessment and Evaluation Practical work-50%

Final Еxam- 50%



References


1. All school books in informatics and ICT, approved by Bulgarian Ministry Of Education

2. Jurnal Mathematics and Informatics, Sofia- In Bulgarian

3. Jurnal Informatics and education- in Russian

DIDACTICS OF INFORMATICS AND ICT



Hours per week: 2 hours lecture and 2 hours tutorials in computer lab / Fall Semester








Methods and principles of instruction in secondary school courses in Informatics and

ICT;

Planning and organization of lessons in Informatics and ICT;

Specific methods of instruction of basic modules in Informatics and ICT at the

secondary school.


Educational objectives in secondary school courses of Informatis and ICT.

Ways of implementation of basic methods and rules of instruction.

Planning and development of school lesons in Informatics and ICT.

Development of problem solving

Analysis of school lessons in Informatics and ICT.


method.

Pre- requirements: psychology, Pedagogy, Operating Systems, Programming Languages,

Data Structures, Word-processing, spreadsheets, Computer’s networks, Database, School

courses of informatics and ICT

Assessment and Evaluation Project- 40%

Practical work-30%

Final Еxam- 30%



References 1. Dureva D., Problems in didactics of informatics and ICT, 2003- in Bulgarian

2. Jurnal Mathematics and Informatics, Sofia- In Bulgarian

3. Jurnal Informatics and education- in Russian


DIDACTICS OF MATHEMATICS II

Semester: 7-th semester

Course type: lectures and seminars

Hours per week: 2 hours lecture and 2 hours seminars / Fall Semester







Description of the course: The subject includes problems of the Special Methodology of

teaching mathematics, that is the themes: functions, relations and operations, equations and

inequations, samenesses (identities) and likenesses, vector, geometric figures (Shapes) in the

plane and in the space.

Purpose (Aim) of the subject: To prepare the students, teach pupil in mathematics at

school.

Methods of teaching: Lectures and practices (exercises)

Precursory conditions: Knowledge in the content of the school course in mathematics, and

also knowledge in psychology and pedagogy.

Appraisement: Examination in written form

Registration for the examination: concerted with the teacher and the school department.

References:

1. Ganchev Ivan and others: “Methodology of teaching mathematics /General

Methodology/, Blagoevgrad, 2002.

2. Ganchev Ivan and others “Methodology of teaching mathematics from 8th to 11th class”

Sofia 1998

OBSERVATION OF LESSONS IN MATHEMATICS AT SCHOOL


Course type: observation in real educational environment

Hours per week: 1 hour observation and discussions in lab / Fall Semester

ECTS credits: 2,0 credits.

Department: Department of Mathematics

Lecturers: Maya Stoyanova - PhD-student

, Faculty of Mathematics and Natural Sciences, South-West University “Neofit Rilski” –

Blagoevgrad,



Course description: The course introduces students to their future profession. The students

observe lessons taught by supervised theachers at school, conferencing observed lessons and

present three analyses of observed lessons in writing.

Course aims: The aim of the course is to give students an idea of the basic requirements for

a lesson in mathematics, the skills to develop various kinds of lessons, to select and

streamline tasks offered to students, to evaluate the performance of the individual student

and the class as a whole.



Methods of teaching: tutorials - observations at school, discussion.

Pre-requirements: Didactics of Mathematics I and II, and School course in Mathematics.

Assessment and Evaluation

Participation in the discussions - 60%

Analysis of the lessons – 40%.


References: 1. School books of Mathematics approved by Ministry of education and used in

cooperated schools by supervised teachers.

OBSERVATION OF LESSONS IN INFORMATICS AND ICT AT

SCHOOL


Course type: observation in real educational environment

Hours per week: 2 hours observation and discussions in lab / Fall Semester


Lecturers: Assoc. Prof. Daniela Dureva





Course description: During the course students observe lessons in school. They participate

in discussions about used methods, interactions etc.

Objectives:

The student should obtain knowledge and skills to:

Evaluate and analysis of lessons carried out in secondary or high schools.

Determinate basic components of observed lessons as methods, structure of lessons,

principles, interactions among teacher and students etc.

Methods of teaching: observation, discussions, project based method.

Pre-requirements: Pedagogy, Pshycology, School courses of informatics and ICT

Assessment and Evaluation Semester’s grading - 100%

Assessment is based on the following components:

Participation in discussions after observation (30%);

Portfolio with collected notes of observations (50%);

Lesson plan for 1 lesson in Informatics (10%);

Lesson plan for 1 lesson in Informatics (10%);



References: 2. School books of ICT and Informatics approved by Ministry of education and used in



AUDIOVISUAL AND INFORMATION TECHNOLOGIES IN

TEACHING



Hours per week: 1 hour lecture and 1 hour tutorials in computer lab / Summer Semester








Tools and technology in education

Basic characteristics of educational software

Multimedia in education

Internet in education

Technologies of E-learning


Rules of using educational software

Development and presentation of learning materials;

Use of Internet services for educational goals

E-learning


method.

Pre-requirements: psychology, Pedagogy, Word-processing, spreadsheets, Computer’s

networks,


Final Еxam- 45%



References: 1. Cassey Doyle, Microsoft Office 97 Step by Step, Microsoft Press, 1998

2. HTML в лесни стъпки, Софтпрес, 2000

3. Елизабет Кастро, HTML за World Wide Web, Инфодар, 2000

4. Даниъл Грей, Професионален дизайн в Web, Софтпрес, 2000

5. Yuval Fisher, Spining the Web, Springer 1996

PEDAGOGICAL PRACTICE IN MATHEMATICS


Course type: Practice in real environment

Hours per week: 2 hours tutorials / Summer Semester






tel. +35973588532, e-mail:


Course description: The course prepares students to their future profession. Each student

taught two lessons – one in the secondary school grades 5-8 and one in the upper grades 8-

12. The other of the students observed lessons.





Methods of teaching: observations at school, discussions, teaching



Presentation of two lessons at school – 60%

Presented analysis of three lessons – 40%.

Registration for the Exam: coordinated with the lecturer and the cooperative teacher.



PEDAGOGICAL PRACTICE IN INFORMATICS



Hours per week: 2 hours practice / Summer Semester







Course description: During the practice students obtain basic competences about lessons

planning, classes organizing, conducting of lessons in real school environment. The practice

is carried out under supervising of cooperative teacher (mentor) and responsible university

lecturer.

Objectives:


Plan activities for lessons and classes management;

Conduct training in real school environment.

Methods of teaching: observation, discussions, teaching.

Pre - requirements: Pedagogy, Pshycology, School courses of informatics and ICT



Semester’s grading - 100%


Lesson’s plans for 2 lessons in Informatics or ICT (25%);

Performance of 2 lessons in real school environment (75%);


Registration for the Exam: coordinated with the lecturer and the cooperative teacher



3. Dureva D. Problems of didactics in informatics and ICT, 2003, Blagoevgrad

PRE-GRADUATION PEDAGOGICAL PRACTICE IN MATHEMATICS








tel. +35973588532, e-mail:


Course description: The course prepares students to their future profession. By Order of the

Rector students are assigned to a school for 10 weeks practice. Each week they presented

three lessons and observed two lessons of their colleagues. For the whole practice they must

present 15 lessons at Secondary school and 15 lessons at High school. The cooperative

teacher (mentor) assists students in the development of the lessons and oversees the work of

trainees in school. If the trainee is not prepared for the lesson, the mentor and the director of

the school may require interruption of the practice.





Methods of teaching: observations at school, discussion, teaching.



Presentation of two or three lessons at school – 60%

Presented papers of the lessons – 40%.

Registration for the Exam: coordinated with the lecturer and the cooperative teacher.



PRE-GRADUATION PEDAGOGICAL PRACTICE IN INFORMATICS










Course description: During the practice student obtain basic competences about lessons

planning, classes organizing, conducting of lessons in real school environment. The practice

is carried out under supervising of cooperative teacher (mentor). Each student has to perform

30 lessons in classes according to schedule of supervised teacher.

Objectives:


Plan activities for lessons and classes management;

Conduct training in real school environment.

Methods of teaching: observation, discussions, teaching.

Pre - requirements: Pedagogy, Pshycology, School courses of informatics and ICT,

Hospetition, Practice in school

Assessment and Evaluation Semester’s grading - 100%


Lesson’s plans for lessons in Informatics or ICT (20%);

Performance of lessons in real school environment (80%);


Registration for the Exam: coordinated with the lecturer and the cooperative teacher



3. Dureva D. Problems of didactics in informatics and ICT, 2003, Blagoevgrad

EDUCATION AND DEVELOPMENT OF SPECIAL NEEDS PUPILS



Hours per week: 2 hour lecture and 1 hour seminar / Summer Semester


Lecturers: Assoc. Prof. Pelagia Terziyska, PhD

Department: Department of Pedagogy, Faculty of Pedagogy, South-West University

“Neofit Rilski” – Blagoevgrad, e-mail: [email protected]


Course description: The course is aimed at training, development and socialization of

children with special educational needs integrated into mainstream schools. Designed for the



acquisition of knowledge about the specifics of working with these students. The main

objective is introduces the students with the most effective methods, approaches and the

pedagogical technologies for teaching, of different groups of pupils with SEN, to clarify the

psychological and pedagogical problems of education and social adaptation in the midst

from their peers in norm.

Content of the course:

The main substantive points were: initial knowledge of the main characteristics of children

and pupils with SEN; specifics of the educational process in the mainstream school in terms

of integrated training; features of academic activities and teaching methods for different

groups of pupils with SEN; specific requirements to the teacher.

Teaching and assessment:

Training includes lectures. Knowledge available in the system, using interactive methods -

case studies, discussions, debates, role-plays, planning and conducting analysis mini-

experiments behavior of children with SEN in different situations and different social and

cultural environment. There were strict criteria for the development of papers, which are

transmitted within a given period for checking. After that all papers will be discussed in

class.


References: 1. Ainscow M., Booth T. (2003) The Index for Inclusion: Developing Learning &

Participation in Schools. Bristol: Center for Studies in Inclusive Education

2. Cortiella, C. (2009). The State of Learning Disabilities. New York, NY: National Center

for Learning Disabilities.

3. Stainback, W., & Stainback, S. (1995). Controversial Issues Confronting Special

Education. Allyn & Bacon.

4. Strully, J., & Strully, C. (1996). Friendships as an educational goal: What we have learned

and where we are headed. In W. Stainback & S.

5. Thomas, G., & Loxley, A. (2007) Deconstructing Special Education and Constructing

Inclusion (2nd Edition). Maidenhead: Open University Press.

6. Terziyska, P. (2012) Children with special educational needs in the mainstream

environment.

7. Trainer, M. (1991). Differences in common: Straight talk on mental retardation, Down

Syndrome, and life. Rockville, MD" Woodbine house.

OPTIONAL COURSES

COMPUTER ARCHITECTURES

Semester: 3-rd semester

Course type: Lectures

Hours per week: 3 lecture hours / Fall Semester


Lecturer: Assoc. Prof. L.Taneva, PhD


South-West University “Neofit Rilski” – Blagoevgrad, tel. +35973588532

Course Status: Optional course in the B.S. Curriculum of Mathematics and Informatics

Description of the course: The course covers the advanced computer systems, their

programming and functional model, introduce information in computer organization and

memory types (major, operational, permanent, outdoor, etc.), system interruptions, features

and technology solutions, conveyor ADP modes, system bus (types and structures), some

problems of modern computer architectures (RISC, parallel and multiprocessor computer

systems).

Scope of the course: Obtaining knowledge of a systematic overview of the modern

computer architecture, systems to form the theoretical and practical basis for better

understanding of the work of computers to acquire skills in programming in assembly

language.

Methods: discussions, practical exercises of the codes under consideration

Preliminary requirements: The students must have basic knowledge from mathematics.

Evaluation: permanent control during the semester (two written exams) and final exam.

Registration for the Course: by request at the end of the current semester


References:

Basic titles

1. Hennessy John L. and David A. Patterson, Computer Architecture, Fifth Edition: A

Quantitative Approach (The Morgan Kaufmann Series in Computer Architecture and

Design) (5th Edition), 2011.

2. Боровска Пламенка, Компютърни системи, второ преработено издание, Сиела,

София, 2007

3. Брадли, Д. “Програмиране на асемблер за персонален компютър IBM/PC” Техника,

София, 1989

4. Иванов Р. “Архитектура и системно програмиране за Pentium базирани компютри”,

Габрово, 1998.

5. J. L. Hennessy, D. A. Patterson. Computer Architecture: A Quantitative Approach (3rd

ed.). Morgan Kaufmann Publishers, 1996.

6. Боровски Б., Боровска П., Архитектура на ЕИМ и микрокомпютри, Техника, 1992.

7. Горслайн Дж., Фамилия ИНТЕЛ, Техника, 1990.

8. Въчовски И., Наръчник по 32-разредни микропроцесори.

9. Скот Мюлер, Компютърна енциклопедия, Част 1, 2, 3, СофтПрес 2002 г.

10. Бари Прес, Компютърна библия I и II част, АлексСофт,1998 г.

11. ШиндлерД., Компютърни мрежи, СофтПрес, 2003 г.

12. Людмила Иванова, Въведение в PC, изд. БАН, 2007 г.

Web

1. http://www.computers.bg

2. http://www.hardwarebg.com

3. http://www.comexgroup.com

4. http://www.webopedia.com

5. http://www.sagabg.net

6. http://benchmarkhq.ru

7. http://csg.csail.mit.edu/6.823/lecnotes.html , достъпни към май 2013

Additional titles

1. Wikipedia.ORG - Internet енциклопедия.

2. 3DNow: Technology Manual

3. S. Bondeli, Divide and conquer: A parallel algorithm for the solution of a tridiagonal

linear system of equations, Parallel Computing, 1991

4. Intel Corp. Intel Pentium 4 and Intel Xeon Processor Optimization Manual 2001

5. David Culler, Parallel Computer Architecture: A hardware software Approach, Morgan

Kaufmann, 1998

6. Брайант Рэндал Э., Дэвид О'Халларон , Компьютерные системы: архитектура и

программирование Computer Systems: A Programmer's Perspective, Издательство: БХВ-

Петербург, ISBN 5-94157-433-9, 0-13-034074-X; 2005.

DISCRETE MATHEMATICS

Semester: 3-rd semester

Course type: Lectures

Hours per week: 3 lecture hours / Fall Semester


Lecturer: Assoc. Prof. Dr. Sc. Slavcho Shtrakov





Course description: The course is an introduction in Discrete Structures used as a

mathematical model in different computer science areas: logic, operations and relations in

finite algebraic structures, representations of them as data structures, Boolean algebras,

graphs, complexity of algorithms, combinatorics, finite automata etc.

Course aims: Non-trivial introduction in some important for Computer science areas,

allowing the students to use effectively their knowledge in solving combinatorial problems.

Teaching methods: lectures, tutorials, group seminars or workshop, projects, other methods

Requirements/ Prerequisites: Basic knowledge in Mathematics.

Materials: Textbook and manual of the course are published, instructions for every

laboratory theme and exemplary programs; access to web sites via Internet.

Evaluation: Written examination and discussion at the end of the semester, individual tasks

and the general student’s work during the semester.



References:

1. Денев, Й., С. Щраков, Дискретна математика, Благоевград,1995

2. Павлов, Р., С. Радев, С. Щраков, Математически основи на информатиката,

Благоевград, 1997

3. Денев, Й., Р. Павлов, Я. Деметрович, Дискретна математика, София, 1984

4. Т.Фудзисава, Т.Касами, Математика для радиоинжинеров, Радио и связь, Москва,

1984.

5. К.Чимев, Сл.Щраков, Математика с информатика, Благоевград, 1989.

6. С.В.Яблонски, Введение в дискретную математику, М.,1979.

7. С.В.Яблонски, Г.П.Гаврилов, В.Б.Кудрявцев, Функции алгебры логики и классы

Поста, М.,1966.

8. Z.Manna, Mathematical theory of computation, McGraw-Hill Book Company, NY, 1974.


9. V.J.Rayward-Smith, A first course in formal language theory, Bl.Sc.Publ., London, 1983.

10. A.Salomaa, Jewels of formal language theory, Comp.Sc.Press, Rockville, 1981.

INFORMATION TECHNOLOGY



Hours per week: 2 hour lecture and 1 hour tutorials in computer lab / Fall Semester






Course Status: Optional course in the B.S. Curriculum of Mathematics and Informatics.

Course description: The course is introduction in Information systems and technologies.

The basic concepts and principles in ICT such as Information, Information processes,

operating systems, office software, multimedia and computer graphics, presentation of

information etc. are discussed. The course is an extension of the secondary school course in

ICT

Objectives: The student should obtain knowledge of;

Basic concepts in ICT

Types of system and application software.

Most popular services in Internet;

Information security and ethical and Law Issues of ICT.


method, e-learning technologies

Pre- requirements: No


Formatitive Tests- 30%

Final Test- 5035%

The course is successful completed with at least 65% of all scores. Registration for the Course: by request at the end of the current semester


References:

1. Halversen, M., Yung M., All for Microsoft Office XP, Софтпрес, Sofia, 2001

2. ICT course- http://www.e-learning.swu.bg - after registration of the student.

COMPUTER MODELS IN NATURAL SCIENCES


Course Type: lectures and labs

Hours per week: 2 lecture hours and 1 lab hour / Summer Semester

ECTS Credits: 4,0

Lecturer: Assoc. Prof. M. Kolev, PhD




tel. ++35973588545, e-mail


Course Description: The course “Computer model in science” could be used as a basic or

optional one for all subjects aiming broad university preparation. The course is adapted and

applied in teaching in the departments “Informatics”, “Pedagogy of Teaching of

Mathematics and Computer Science”, “Pedagogy of Teaching of Physics and mathematics”.

To take that course it is enough for the student to have accomplished regular mathematics

and science secondary school courses. Among the main objectives of the course (in times of

information revolution and new information technologies) is the good and timely orientation

and the acquisition of general mathematical and scientific knowledge by students - it is

adapted first of all for non-physics students.

The course comprises of separate modules and mostly of computer experiments. For each

PC-experiment with color computer animation, graphics, numerical results, explanations are

provided. There are experiments in mechanics, thermodynamics and molecular physics,

oscillations and waves, electricity and magnetism; optics, quantum physics, math. ecologies,

biophysics, nonlinear economics, astrophysics, etc. The possibility in the course of

independent work the change the parameters and observe the results of a computer

experiment allows the student to investigate interactively each model in each topic. All that

results in promotion of interest towards scientific knowledge and new information

technologies application along with learning motivation. PC-models in Mathematical

methods of investigation are used in every field of science and technology. Differential

Equations are the foundations of the mathematical education of scientists and engineers.

(PC –models also use a model of exponential growth, comparison with discrete equations,

series solutions; modeling examples including radioactive decay and time delay equation,

integrating factor, series solution. nonlinear equation , separable equations, families of

solutions, isoclines, the idea of a flow and connection vector fields, stability, phase-plane

analysis; examples, including logistic equation and chemical kinetics. resonance, coupled

first order systems, examples and PC-models of nonlinear dynamics, order and chaos,

attractors. etc.)

Course Aims: The main goal is the students to master the instruments and methods of

modeling in science.

Teaching Methods: lectures, tutorials, homeworks, tests, etc.

Requirements/Prerequisites: Calculus I and II, Linear Algebra and Analytical Geometry,

Differential Equations.

Exam: tests, home works, final exam.



References: 1. Kirkpatrick, Wheeler. Physics. A World View. 2-nd ed. 1995.

2. Stewart J. Calculus. III ed. (AUBG). 1996.

3. Фулър. Х., Р. Фулър. Физиката в живота на човека, изд. Наука и изкуство. С.,

1988.

4. Pontryagin L.S., Differential equations and applications, Moscow, 1988 (in Russian).

5. Boss. Lectures in mathematics. Differential equations, Moscow, 2004 (in Russian).

6. Elsgolc. L. Differential equations and variational calculus, Moscow, 2000 (in

Russian)

7. Diacu. An Introduction to Differential Equations: Order and Chaos, Freeman, 2000.

8. Максимов, М., Г. Христакудис. Физика 10.клас, Булвест, С., 2000.

9. Райчев, П., Кр. Иванов и др. Физика за 10 клас (ч. 2. Вълни и частици),

Просвета, С., 1991г.

10. Файнман, Р., Р. Лейтон, М.Сендс. Файнманови лекции по физика.

11. www.exponenta.ru

12. Multimedia course “Open Physics–I and II”

13. WinSet. M-I, 2003 etc.

14. www.mathworld.wolfram.com.

ALGORITHMS FOR GRAPHS AND NETWORKS


Cours Tipe: Lectures

Hours per week: 3 lecture hours / Summer Semester


Lecturer: Prof. Ivan Mirchev, DSc




Course Status: Optional course in the B.S. Curriculum of Mathematics and Informatics. Short Description: The 1970s ushered in an exciting era of research and applications of

networks and graphs in operations research, industrial engineering, and related disciplines.

Graphs are met with everywhere under different names: "structures", "road maps" in civil

engineering; "networks" in electrical engineering; "sociograms", "communication structures" and

"organizational structures" in sociology and economics; "molecular structure" in chemistry; gas

or electricity "distribution networks" and so on.

Because of its wide applicability, the study of graph theory has been expanding at a very rapid

rate during recent years; a major factor in this growth being the development of large and fast

computing machines. The direct and detailed representation of practical systems, such as

distribution or telecommunication networks, leads to graphs of large size whose successful

analysis depends as much on the existence of "good" algorithms as on the availability of fast

computers. In view of this, the present course concentrates on the development and exposition of

algorithms for the analysis of graphs, although frequent mention of application areas is made in

order to keep the text as closely related to practical problem-solving as possible.

Although, in general, algorithmic efficiency is considered of prime importance, the present

course is not meant to be a course of efficient algorithms. Often a method is discussed because of

its close relation to (or derivation from) previously introduced concepts. The overriding

consideration is to leave the student with as coherent a body of knowledge with regard to graph

analysis algorithms, as possible.

In this course are considered some elements of the following main topics:

Introduction in graph theory (essential concepts and definitions, modeling with graphs

and networks, data structures for networks and graphs, computational complexity,

heuristics).

Tree algorithms (spanning tree algorithms, variations of the minimum spanning tree

problem, branchings and arborescences).

Shortest-path algorithms (types of shortest-path problems and algorithms, shortest-paths

from a single source, all shortest-path algorithms, the k- shortest-path algorithm, other

shortest-paths).


Maximum- flow algorithms (flow-augmenting paths, maximum-flow algorithm,

extensions and modifications, minimum-cost flow algorithms, dynamic flow algorithms).

Matching and assignment algorithms (introduction and examples, maximum-cardinality

matching in a bipartite graph, maximum-cardinality matching in a general graph,

maximum-weight matching in a bipartite graph, the assignment problem).

The chinest postman and related arc routing problems ( Euler tours and Hamiltonian

tours, the postman problem for undirected graphs, the postman problem for directed

graphs).

The traveling salesman and related vertex routing problems (Hamiltonian tours, basic

properties of the traveling salesman problem, lower bounds, optimal solution

techniques, heuristic algorithms for the TSP).

Location problems (classifying location problems, center problems, median

problems).

Project networks (constructing project networks, critical path method, generalized

project networks).

Course Aims: Students should obtain basic knowledge and skills for solving optimization

problems for graphs and networks.

Teaching Methods: lectures, individual student’s work

Requirements/Prerequisites: Linear Algebra, Linear optimization

Assessment: 3 homework D1,D2,D3; 2 tests K1, K2 ( project); written final exam

Rating: = 0,2.(D1D2 D3)/3 + 0,5.(K1K2)/2 + 0,3.(Exam)



References:

Basic:

1. Ив.Мирчев, "Графи. Оптимизационни алгоритми в мрежи", Благоевград, 2001 г.

2. Ив.Мирчев, "Математическо оптимиране", Благоевград, 2000 г.

3. Minieka, Е., Optimization Algorithms for Networks and Graphs, Marcel Dekker,

Inc., New York and Basel, 1978 (Майника, 3. Алгоритми оптимизации па сетях и

графах, М., "Мир", 1981).

Additional:

1. Keijo Ruohonen. GRAPH THEORY. math.tut.fi/~ruohonen/GT_English.pdf, 2008

2. A book on algorithmic graph theory, http://code.google.com/p/graph-theoryalgorithms-

book/;

3. Ronald Gould. Graph Theory (Dover Books on Mathematics. 2012. US Cafifornia.

4. Lih-Hsing Hsu , Cheng-Kuan Lin, Graph Theory and Interconnection Networks.

1420044818, 2008, 5. Team DDU.Christofides, N., Graph Theory. An Algorithmic approach, Academic Press lnc

(London) Ltd. 1975, 1977 (Крисгофидес, И. Теория графов. Алгоритмический подход, М.,

"Мир", 1978 ).

6. Swamy, М., К. Thulasirman, Graphs, Networks and Algorithms, John Wiley & Sons, 1981

(Сваами M., K. Тхуласирман. Графм, сети и алгоритми, М., "Мир", 1984).

SEPARABLE SETS OF VARIABLES OF FUNCTIONS


Course Type: Lectures and seminars

Hours per week: 2 lecture hours and 1 hour seminar/ Summer Semester

ECTS credits: 4.0 credits Lecturer: Assoc. Prof. Dimiter St. Kovachev, PhD



tel. ++35973588532, e-mail: [email protected]


Course Description: The study of behavior of discrete functions when they are substituted

by some of their variables by constants, as well as identification of variables, is connected

with the development of mathematical cybernetics, automata theory, it is used in the study of

recursive functions, in some methods for synthesis of control systems, in the synthesis of

contact schemes (the cascade method) and many other parts of the theoretical and applied

informatics. In the proposed course, some topics connected with separable sets of variables

for the functions are considered, whose applied interpretation in the synthesis of contact

schemes and automata make them actual and important. Graphs of functions with respect to

separable pairs of their variables are studied. Great attention is paid to strongly essential and

с-strongly essential variables for the functions.

Course Aims: Students should obtain basic knowledge in the area of Theory of separable

sets of variables for the functions, as well as the ability to apply this theoretical knowledge to

Graph Theory in respect to their separable pairs of variables.

Teaching Methods: lectures, exercises, course works and extracurricular occupation.

Requirements/Prerequisites: Preliminary knowledge of Graph Theory and Discrete

Functions is useful.

Assessment: Current assessment (four homeworks H1, H2, H3, H4; two control works C1,

C2 /course works/) and Exam grade.

Final Grade: FG=0.05(H1+H2+H3+H4)+0.2(C1+C2)+0.4(Exam)

Registration for the Course: by request at the end of the previous semester.



1. Chimev, K. Separable Sets of Arguments of Function. Blagoevgrad, 1983, 1-190.

2. Chimev, K. Functions and Graphs. Blagoevgrad, 1983, 1-195.

3. Chimev, K. Separable Sets of Arguments of Function. Blagoevgrad, 2005.

Additional Titles

1. Chimev, K., Separable Sets of Arguments of Function, MTA Sz TAKI, Budapest,

180, 1986, 1-173

2. Chimev, K. Discrete functions and subfunctions. Blagoevgrad, 1991, 1-258.

3. Chimev, K., Aslanski, Structural characteristics of one class of Boolean Functions,

Koezlemenyck, 31, 1984, 23-31.

4. Chimev, K., Il. Gyudzhenov. Subfunctions and power of some classes of functions.

Blagoevgrad, 1991, 1-220.

5. Chimev, K., Iv. Mirchev. Separable and dominating sets of variables, Blagoevgrad,

1993, 1-131.

6. Shtrakov, Sl. Dominating and annulling sets of variables for the functions.

Blagoevgrad, 1987, 1-180.

7. Shtrakov Sl. and Denecke K., Essential Variables and Separable Sets in Universal

Algebra, 2008

8. Shtrakov Sl and Koppitz J., Finite symmetric functions with non-trivial arity gap, Serdica

J. Computing 6 (2012), 419–436.


VBA PROGRAMMING


Type of Course: Lectures and tutorials in computer lab.

Hours per week: 1 hour lectures and 2 hours tutorials in computer lab / Summer Semester.


Lecturers: Assoc. Prof. Daniela Tuparova, PhD





Course description: The course is introduction in area of object-oriented and distributed

databases. Transaction processing, Data warehousing and Conceptual and semantic

approaches of data modeling are considered. A short description of corporative DBMS

(Oracle DB) is introduced.


Design and use of object-oriented and distributed databases.

Transaction processing.

Conceptual and semantic approaches of data modeling.




Final Test- 70%




References 1. Peneva J., Tuparov, G., Databases Part II, Regalia 6, Sofia, 2004

2. Peneva J., Databases Part I, Regalia 6, Sofia, 2004

3. Elmasri, R., Navathe, S. Fundamentals of Database Systems, 4-th ed. Addison-Wesley,

2004

4. Connolly, T., Begg, C. Database Systems: A Practical Approach to Design,

Implementation and Management, 4-th ed., Pearson Education, 2004

DEVELOPMENT OF INTERACTIVE MULTIMEDIA EDUCATIONAL

CONTENT


Course Type: lectures, seminars

Hours per week/FS/SS: 2 lecture; 1 seminar exercise / Fall Semester

ECTS credits: 4,5







Course Description: The course covers topics in area of development of interactive

multimedia educational content with MS Power Point and Visual Basic for Application

(VBA).

Objectives:


Design of interactive multimedia for educational purpose.

Develop interactive multimedia content.


Pre - requirements: Information technology

Assessment and Evaluation Semester’s grading - 60%, includes grading of project

Final Test- 40%

The course is successful completed with at least 53% of all scores. Registration for the Course: by request at the end of the current semester


References:

1. Online courses at: www.e-learning.swu.bg и www.leo.swu.bg

2. Иванов И. Интерактивни презентации, Нова Звезда 2011

3. PPT Tools, http://www.pptools.com/index.html?referrer=pptfaq

4. Markoviz d., Powerful PowerPoint for Educators: Using Visual Basic for Application

to Make PowerPoint Interactive,http://www.loyola.edu/edudept/PowerfulPowerPoint/

OPERATIONAL RESEARCH


Course Type: lectures, seminars

Hours per week/FS/SS: 2 lecture; 1 seminar exercise / Fall Semester

ECTS credits: 4,5

Lecturer:. Prof. Peter Milanov, PhD





Course Description: The aim of the research operation is quantitative analysis and finds a

solution by management system.

Course Aims: Students should obtain knowledge and skills to find the optimal solution in the

analyzing problem.

Teaching Methods: lectures, demonstrations and work on project

Requirements/Prerequisites: Linear algebra, Computer languages. optimization theory.

Assessment: course project



References:


http://www.e-learning.swu.bg/

http://www.leo.swu.bg/

http://www.pptools.com/index.html?referrer=pptfaq

http://www.loyola.edu/edudept/PowerfulPowerPoint/


1. H. A. Eiselt, Operations Research: A Model-Based Approach (Springer Texts in Business and

Economics), 2012, Springer Heidelberg NY.

2. Hamdy A. Taha, Operations Research: An Introduction, 2010 Springer,

3. A. Ravi Ravindran, Donald P. Warsing Jr.Supply Chain Engineering: Models and

Applications (Operations Research Series), 2012, Jonson and Son,

4. Венцель И. Исследования операции. Москва, 1970.

5. Vagner G. Operational research Vol I-III 1998.

6. Зайченко Ю. Исследования операции. Москва, 1988

PROGRAMING WITH OBJECT PASCAL AND DELPHI

Semester: 5th semester

Type of Course: lectures and labs

Hours per week: 2 lectures + 2 labs per week / Fall Semester


Lecturers: Assoc. Prof. PhD Krasimir Yankov Yordzhev





Course description: In the course students are introduced with methods and means of

Object-oriented programing in integrated development interface for visual programing -

Delphi. The students should have a basic knowledge on programming with Pascal. Suppouse

that students are successablity passed courses in Programming and Data structures and

Object-oriented programming (in SWU this courses are basic on program language C++) and

students are known for fundamental skils in programming. In the course students develop

programs using different platform and language - Object Pascal and Dlephi.

Objectives: Basic objectives and tasks:

The students give knowledge for algorithum thinking;

to give knowledge for Data stuctures, that can process with computer;

to give knowledge for methods and skils in Object-oriented programming in

integrated development environment for visual programming;

to give knowledge for syntax of another program language (Object Pascal and

Delphi);

to give knowledge for good style in programming;

to give knowledge for basic principles when develop applications.

Methods of teaching: lectures and labs

Pre-requirements: Basic knowledge in "Programming and Data structures".

Exam: two course projects and final exam

Registration for the Course: A request is made by students at the end of the current

semester

Registration for the Exam: Coordinated with the lecturer and the Student Service Office

References: 1. Франк Елер Delphi 6. „ИнфоДАР”, 2001.

2. Христо Крушков Програмиране с Delphi. Пловдив, „Макрос”, 2004.

3. Мартин Гардън Delphi – създаване на компоненти. АмПрес, 1999.


4. Хавиер Пачеко, Стийв Тейхера Delphi 5, т.1, т.2, т.3, „ИнфоДар”, 1999

5. Хавиер Пачеко, Стийв Тейхера Delphi 5 – ръководство за напреднали. „ИнфоДАР”,

1999.

6. Марко Канту, Mastering Delphi 6, т.1, т.2, "Софтпрес", 2002

MATHEMATICAL STRUCTURES










Short Description: The subject education includes the study of basic number system and the

basic algebrical theorem.

Course Aims: The students obtain knowledge and skills in the already mentioned themes

and learn how to use them in their future educational practice.


Requirements/Prerequisites: The students should have basics knowledge from High

algebra, Number theory and Mathematical analysis.



lectures. Registration for the Course: by request at the end of the current semester


References:

1. Petkanchin, B. Fundamentals of Mathematics, Science and art, Sofia, 1963.

2. Davidov, L., S. Dodunekov. Elementary algebra and elementary functions, Narodna

prosveta, Sofia, 1984.

3. Radnev, P. The foundations of the school course of algebra and analysis. University

Press, Plovdiv, 1985.

4. Roussev, R., V. Georgiev. Guidance for solving problems of mathematics for applicants

for universities, Science and art, Sofia, 1973.

DESCRIPTIVE GEOMETRY



Hours per week: 2 lecture hours and 1 tutorial hour /Fall Semester






tel. +35973588532, e-mail:


Short Description: The course includes studying of basic topics in classical Descriptive

Geometry: Monge’s method, acsonometry and perspective.

Course Aims: The students should assimilate and enlarge their knowledge in

Stereometry and to developed their space imagination.


Requirements/Prerequisites: Stereometry , High School Mathematics

Assessment: written exam on topics from tutorials and on topics from lectures. Registration for the Course: by request at the end of the current semester


References:

Basic Titles

1. Dimitrov, St., R. Petrov. Descriptive Geometry. Sofia, 1974 /in Bulgarian/.

2. Dimitrov, St., Handbook on Descriptive Geometry. Sofia, 1969 /in Bulgarian/.

3. Langov, A. Descriptive Geometry. Sofia, 1979 /in Bulgarian/.

Additional Titles

1. Petrov, G. Descriptive Geometry. Sofia, 1958 /in Bulgarian/.

2. Uzunov, N., G. Petrov, S. Dimitrov. Descriptive Geometry. Sofia, 1965 /in Bulgarian/.

3. Tabakov, D. Handbook on Descriptive Geometry. Sofia, 1941 /in Bulgarian/.

FUNDAMENTALS OF ARITHMETIC








tel. ++35973588532, e-mail: [email protected]


Short Description: The optional course in Fundamentals of the Arithmetic has the objective

to make the students familiar with the notation of “number” and connected with it operations

and ordinance relation. The course comprises the natural numbers, the integer numbers, the

rational numbers, and the real numbers and in particular cases the complex numbers. The

course start with the definition of the notation “finite set” and the notation “induction set”,

which was introduced in the beginning of the 20-th century by B. Russell. The course pays

attention to the notation natural number; to the operations addition and multiplication of two

natural numbers; to the laws that they satisfy; to the inequality between two natural numbers.

The students should learn to pass from a decimal system to an arbitrary system. The course

continuing with extensions of the semiring of the natural numbers to the ring of the integer

numbers, also to the semifield of the fractions and their ordinances. The course finishes with

the consideration of the real and the complex numbers.


Course Aims: Students should obtain knowledge and skills for the recent theoretical ideas

and the whole scholar course of education in Algebra.


Requirements/Prerequisites: The students should have basics knowledge from Number

theory and High algebra.



lectures. Registration for the Course: by request at the end of the current semester


References:

Basic Titles

5. Denecke, Kl., K. Todorov, Fundamentals of Arithmetic, Blagoevgrad 1999.

6. Petkov, P. Fundamentals of Arithmetic. Library of the Faculty of mathematics in

University “Kliment Ohridski”, Sofia.

7. Ziapkov, N., N. Yankov, I. Mihailov. Elementary Number Theory. „Faber”, Veliko

Tarnovo, 2008.

Additional Titles

1. Petkanchin, B. Fundamentals of Mathematics, Sofia, 1959.

Липсват от 5 група

GEOMETRY OF THE CIRCLES




ECTS credits: 5.0 credits




tel. +35973588532, e-mail:


Short Description: The course includes studying of the bundle of circles and some

transformations of the circles.

Course Aims: Students should obtain knowledge for the circles.


Requirements/Prerequisites: School course of Geometry.

Assessment: written exam on topics from tutorials and on topics from lectures. Registration for the Course: by request at the end of the current semester


References:

Basic Titles

1. Borisov, A., A. Langov. School course of Geometry. University Press “N. Rilski”,

Blagoevgrad, 2007 /in Bulgarian/.

2. Borisov, A., A. Langov. Handbook on School course of Geometry. University Press “N.


3. Petrov, K. Hendbook on Mathematics. Planimetry. Vol. I and II. Sofia, 1966 /in

Bulgarian/.

Additional Titles

1. Adamar, J. Elementary Geometry. Moscow, 1957 /in Russian/.

2. Perepolkin, D. I. Course of Elementary Geometry. Sofia, 1956 /in Bulgarian/.

FUNDAMENTALS OF GEOMETRY








tel. +35973588532, e-mail:


Short Description: The course includes studying of the following basic topics: Hilbert’s

axiomatic, Kolmogorov’s metric axiomatic and Well’s axiomatic of the Euclidean Geometry

and their equivalence is proved.

Course Aims: Students should obtain knowledge and skills about rigorous construct of a

mathematical discipline.

Teaching Methods: lectures, tutorials, homeworks and tests.

Requirements/Prerequisites: High School Mathematics




References:

Basic Titles

1. Borisov, A., A. Langov. Foundations of geometry. Blagoevgrad, University Press “N.


2. Losanov, Ch., A. Langov, G. Eneva. Synthetic Geometry, University Press “St. Kl.

Ohridski”, Sofia 1994 /in Bulgarian/.

3. Petkanchin, B. Foundations of mathematics. Sofia, “Nauka i Izkustvo”, 1968 /in

Bulgarian/.

Additional Titles

1. Martinov, N. Geometry. Sofia, “Nauka i Izkustvo”, 1968 /in Bulgarian/.

2. Hilbert, D. Foundations of geometry. “Nauka i Izkustvo”, 1978 /in Bulgarian/.

METHODS OF EXTRA-CURRICULAR WORK IN MATHEMATICS





Lecturer: Prof. DSc. Oleg Mushkarov





Short Description: Main topics:

- Bulgarian and International mathematical olympiads

- Geometric problems on maxima and minima

- Algebraic inequalities

- Employing algebraic inequalities

- Employing geometric transformations

- Selected types of geometric problems on maxima and minima

- Complex numbers

Course Aims: To develop the basic principles of teaching extracurricular topics in

mathematics for high school students by using various methods for solving geometric

problems on maxima and minima.

Requirements/Prerequisites: Basic knowledge of the high school courses of Algebra and

Geometry.

Assessment: Written exam on problem solving and on the theoretical material from the

lectures and project developed by the student.


Registration for the exam: Students and the lecturer agree on the convenient dates within

the announced calendar schedule of examination session.

References:

Basic Titles

1. O. Mushkarov, L. Stoyanov, Geometric Extremum Problems , Narodna Prosveta, Sofia,

1989

2. I. Tonov, Applications of complex numbers in geometry Narodna Prosveta, Sofia, 1988

3. T. Andreescu, O. Mushkarov, L. Stoyanov, Geometric Problems on Maxima and Minima,

Birkhauser Boston, 2005

Additional Titles

1. L. Davidov, V. Petkov, I. Tonov, V. Chukanov, Mathematical competitions Narodna

Prosveta, Sopfia, 1977


Competirions 2006 – 2008, UNIMATH, Sofia, 2008 .


Competirions 2009 – 2011, UNIMATH, Sofia, 2012 .

4. Mathematical Journals: Mathematics and Informatics, Mathematics, Mathematics Plus.

FUNDAMENTALS OF COMPUTER GRAPHICS









tel. +35973588532, e-mail:


Short Description: The program a syllabus contains an extension of the subjects:

1. Linear transformations – collineations, affinities, similitudes, identities and their

classifications in the plane and in the space.

2. Fundamental methods of representation of the space on the plane – axonometry

and perspective.

Course Aims: The students have to obtain knowledge and skills for an application of the

transformations in the computer programs of the computer graph.

Teaching Methods: Lectures, tutorials, home works, problem solving tests.

Requirements/ Prerequisites: Analitic Geometry, Linear Algebra and School course of

Geometry.

Assessment: Written exam on topics from tutorials and on topics from lectures.




1. Borisov, A; A.Langov. Geometry. Blagoevgrad, Univ.Publ.”Neofit Rilski”, 2006.

2. Langov, A. Descriptiv Geometry. Sofia, Nauka and Izkustvo, 1979.

Additional Titles:

1.Borisov A; I.Gyudzhenov. Linear Algebra and Analitic Geometry. Blagoevgrad, Univ.

Publ. “Neofit Rilski”, 1999.

2. Losanov, Ch., A. Langov, G. Eneva. Syntetic Geometry. Sofia, Univ. Publ. “S.Kl.

Ohridski”, 1994.

EXPERT SYSTEMS



Hours per week: 2 hours lecture and 1 hour tutorials in computer lab/ Fall Semester


Lecturers: Assoc. Pro Irena Atanasova, PhD



tel. +35973588532, e-mail:


Course description: The course is introduction in area of expert systems.

Objectives:

The student should obtain knowledge of:

Expert systems


Pre- requirements: Functional and Logical Programming, Artificial Intelligence (core

courses)

Assessment and Evaluation Tutorials- 20%

Final Test- 80%




References: 1. Stuart Russell, Peter Norvig, Artificial Intelligence: A Modern Approach (3rd ed.),

Prentice Hall, 2009

2. Rajendra Akerkar, Priti Sajja, Knowledge-Based Systems, Jones & Bartlett Publishers,

2009

OBJECT-ORIENTED AND DISTRIBUTED DATABASES



Hours per week: 2 hours lecture and 1 hour tutorials in computer lab/ Fall Semester


Lecturers: Assis. Prof. Velin Kralev, PhD



tel. +35973588532, e-mail: Course Status: Optional course in the B.S. Curriculum of

Mathematics and Informatics.

Course description: The course is introduction in area of object-oriented and distributed

databases. Transaction processing, Data warehousing and Conceptual and semantic

approaches of data modeling are considered. A short description of corporative DBMS

(Oracle DB) is introduced.


Design and use of object-oriented and distributed databases.

Transaction processing.

Conceptual and semantic approaches of data modeling.




Final Test- 70%




References: 1. Peneva J., Tuparov, G., Databases Part II, Regalia 6, Sofia, 2004 (in Bulgarian)

2. Elmasri, R., Navathe, S. Fundamentals of Database Systems, 6-th ed. Addison-Wesley,

2010

APPLIED STATISTIC


Type of Course: seminars and tutorials in computer lab

Hours per week: 2 hours lectures and 1 hour tutorials in computer lab /Fall Semester







Course description: The course is introduction in nonparametric statistic and possibility to

apply new IT in this area.

Objectives: The students should obtain knowledge of:

To apply the methods of nonparametric statistics in practice

To realize concrete applications with tools of IT.

Methods of teaching: seminars, tutorials, discussions, project based method.

Pre- requirements: Probability and Statistics, Information Technology


Final Test- 70%





1. Каращранова Е. Интерактивно обучение по вероятности и статистика, ЮЗУ,

2010

2. Калинов К.,Статистически методи в поведенческите и социалните науки, НБУ,

2010

3. П. Копанов, В. Нончева, С. Христова, Вероятности и статистика,

ръководство за решаване на задачи,Университетско издателство „Паисий

Хилендарски”, 2012, ISBN 978-954-423-796-7

4. G.Freiman,Exploratory data analysis,J., Isr.Math, 2002

Additional Titles:

1. http://www.teststat.hit.bg

2. Мадгерова Р., В. Кюрова, Статистика в туризма, ЮЗУ, 2009.

COMPUTER NETWORKS AND COMMUNICATIONS


Type of Course: seminars and tutorials in computer lab

Hours per week: 2 hours lectures and 1 hour tutorials in computer lab /Fall Semester


Lecturers: Prof. Sinyagina

Department: Department of Computer Systems and Technology, Faculty of Mathematics

and Natural Sciences, South-West University “Neofit Rilski” – Blagoevgrad.



Course description: The course discuses the problems concerning design, building and

application of computer networks. The lectures begin with introduction to computer

networks, principles of building, historical development and their contemporary

classification. Open system interconnection model of ISO is presented. Teaching course

includes basic principles of building and functioning of Local Area Networks (LAN)

illustrated by practical technical solutions in LAN Ethernet. The lectures on the most popular

in the world computer network Internet present its basic characteristics, principles of

functioning and application. The laboratory work helps to better rationalization of lecture

material and contribute to formation of practical skills.

Course Aims: The aim of the course is to acquaint students with the basic principles,

standards and tendencies of development in the field of computer networks. This will help

them in future to professionally solve system tasks in the area of network communications.

Methods of teaching: Lectures (with slides, multimedia projector) and additional text

materials; laboratory work (based on instructions) with a tutorial for every laboratory theme.

Pre- requirements: Basic knowledge in informatics.

Assessment and Evaluation: written exam.




1. Христов В. Киров Н.,“Oснови на компютърните мрежи и интернет”, ЮЗУ

“Н.Рилски” –Благоевград, 2012

2. Христов В. и Стоилов А., „Ръководство за лабораторни упражнения по компютърни

мрежи”, ЮЗУ “Н.Рилски” –Благоевград, 2007

3. Боровска П., Компютърни системи. София, Сиела, 2010 г.

4. Боянов. К. и кол. Компютърни мрежи. Интернет, София, НБУ, 2003.

5. Илиев Г., Д. Атамян , Мрежи за данни и интернет комуникации. София, Нови

Знания, 2009 г.

6. Летников А.И., Наумов В. А. Разработка модели для анализа показателей качества

функционирования сигнализации по протоколу SIP, жур. Электросвязь No 7, 2007 г.,

сс. 44- 47.

7. Мерджанов П., Телекомуникационни мрежи: Част 1 : Нови Знания,2010 г.

8. Zwart B., S. Borst, and M. Mandjes, “Exact queueing asymptotics for multiple heavy-

tailed on-off flows,” in Proc. Conf. Computer Communications (IEEE Infocom), 2001, pp.

279–288.

INTERNET PROGRAMMING


Type of Course: Lectures and tutorials in computer lab.

Hours per week: 2 hours lectures and 1 hour tutorials in computer lab / Fall Semester.


Lecturers: Assoc. Prof. Daniela Tuparova, PhD






Course description: The course is introduction in design and programming of

Internet/Intranet Web-based information systems. Combination of JavaScript, CSS and

MySQL/PHP/Apache technologies is considered in practical aspects.


Design and programming of Internet/Intranet Web-based information systems.

Practical aspects of JavaScript, CSS and MySQL/PHP/Apache technologies.


Pre - requirements: Database systems (core course), Web-design practicum.


Final Test- 70%




References: 1. Castagnetto, J. et all, Professional PHP Programming, Wrox Press, 2000

2. Wilfred, A., et all., PHP Professional Projects, Premier Press, 2002

3. Welling, L., Thompson, L., PHP and MySQL Web Development, Sams Publishing,

2003

4. Kabir, M., Secure PHP Development: Building 50 Practical Application, Willey

Publishing, 2003

5. Allen, J., Homberger, Ch., Mastering PHP 4.1, Sybex, 2002

PROBLEM SOLVING PRACTICUM FOR SCHOOL COURSE IN

MATHEMATICS


Course Type: seminars

Hours per Week: 3 seminar hours / Summer Semester






Course Status: Optional course in Mathematics and Informatics B.C. Curriculum.

Course Description: The course includes: solving problems from corresponding topics of

the school curriculum in mathematics; analyzing and generalizing of the solution methods,

using students’ knowledge in methodology and the courses: School course in algebra and

analysis and School course in geometry.

Course Aims: Course is aiming to acquaint students with the nature of mathematical

problems in School course in mathematics. Moreover in the course are clarified the aims that

school be pursued, when mathematical problems are solved. The course helps students to

systematize and assimilate their knowledge in methodology and in this way they get

profound preparation for their future profession; the students develop problem solving skills

in School coure in mathematics, using knowledge of different age groups.

Methods of teaching: seminars, tutorials, assignments, projects, tests.


Pre-requirements: Some knowledge in Methodology of teaching mathematics and School

course in Mathematics 5 – 12 grade /specialized preparation 8 – 12 grade/, are necessary.

Assessment and Evaluation: It is realized by controlling the attendance of seminar exercise,

2 problem-solving tests and elaborates a project presentation. Problem-solving tests are

holding on as it follows: first – on modulus 1, 2 and 3; second – on modulus 4 and 5. Project

presentation is students’ elaboration on given topic from School course in mathematics –

without any reference to restrictions and with maximum comprehension.

Examination and assessment of students’ knowledge is formed of two problem-solving tests

(first – on modulus 1 and 3, second – on modulus 4 and 5) and defence of a project

presentation. Each problem-solving test is assessed with 20 points, and defense of project

presentation – with 15 points.


Registration for the Exam: coordinated with lecturer and Student Service Office

References:

Basic Titles:

1. Kolarov, K., and al. Geometry problem book for 7 – 10 grade. Prosveta, Sofia, 1991.

2. Kolarov, K., and al. Algebra problem book for 7 – 10 grade. Prosveta, Sofia, 1990.

3. Lazarov, B., and al. Problems in mathematics /for university applicants/, Vol. 1 and

2, Trud Publishing House, Sofia, 1999.

4. Pascalev, G., Problem book in mathematics /Plane geometry/, Regalia, Sofia, 1999.

5. Pascalev, G., Problem book in mathematics /Solid geometry/, Archimedes, Sofia,

2000.

6. School text book in mathematics for 5 – 12 grade.

Additional Titles:

1. Kolarov, K., Hr. Lesov. Geometry problem book for 8 – 12 grade. Integral, Dobrich.

2. Valiov, V.V., and al. Problems in mathematics /Equations and inequalities/, Nauka,

Moscow, 1987.

3. Vasilevski, A.B. Problem solving training in mathematics, Visheisheia Shkola,

Minsk, 1988.

4. Poya, D. How to solve a problem. Narodna prosveta, Sofia, 1972.

5. Fridman, L.M., and al. How to learn to solve problems. Prosveshtenie, Moscow,

1989.

COMPARATIVE EDUCATION /INTEGRATIVE ASPECTS/


Course Type: lectures

Hours per Week: 3 lecture hours / Summer Semester


Lecturers: Department: Philosophy and Political Science, telephone: (073) 8889112

Course Status: Optional course in Mathematics and Informatics B.C. Curriculum.

Short Description: The course includes studying of the following basic topics: The

course includes studying of the following basic topics: It focuses on financing the higher

education, the quality of high school graduates and their selection, and the measures

which the government takes in order to restructure the higher education in conformity

with the qualitative changes in society, the economic, social and political challenges

which the country faces today.

Course Aims: Students should obtain knowledge about Comparative Education and

National Systems of Education.

Teaching Methods: lectures, homeworks and tests.

Requirements/Prerequisites: General Education

Assessment: written exam on topics from lectures.



References:

Basic Titles:

1. Борисов, О. , Право на Европейския съюз, „Аrgo Publishing”, С., 2005 350 с.

2. Вайденфелд, В. Европа от А до Я: Справочник по европейска интеграция,

„Институт за европейска политика”, С., 2002.

3. Динков, Д., България в европейската интеграция. Изд. Къща „96 плюс”, С., 2002

4. Бижков, Г., Н. Попов. Сравнително образование. ІІ изд. Университетско

издателство “Св. Кл. Охридски”, С., 1999

5. Бяла книга за българското образование и наука. МОНТ, С., 1992.

6. Образование в Република България. Години 2003-2006. Национален статистически

институт. София.

7. Попов, Н. Съвременната образователна система в България. Бюро за

педагогически услуги. София, 2004.

8. Попов, Н. Сравнение на структурите на системите на висше образование в 20

европейски страни. Стратегии на научната и образователната политика, 1996, кн.4,

80-87

9. Статистически годишници. Години 1991-2003,Национален статистически

институт, София.

10. UNESCO: 2003,2004,2005,2006. Statistical Yearbooks, Paris,2003-2006

11. The Encyclopedia of Comparative Education and National Systems of Education.

Pergamon Press, Oxford, 1988,p.52 (aspect)

Additional Titles:

1. Програмите на Европейския съюз. Опит и поуки, „Европейски център за обучение

Лактеа”, С.,2005

2. Шрьотер Х., Европа. Актуален справочник, „Рива”, 2002

3. http://www.minedu.government.bg

4. Information Network on Education in Europe (EURIDICE): http://www.euridice.org

5. International Bureau of Education (IBE): http://www.ibe.unesco.org

6. International Institute for Educational Planning: http://www.unesco.org/iiep

7. Organisation for Economic Cooperation and Development (OECD):

http://www.oecd.org/els/stats/edu

8. Statistical Office of the European Communities (EUROSTAT):

http://europa.eu.int/en/comm/eurostat

9. UNICEF: http://www.uniceff.org/statis

10. United Nations Secretariat: http://www.un.org/Depts/unsd/social

11. UNESCO: http://unesco.org/webworld/com

12. U.S. Department of Education: http://www.ed.gov

http://www.minedu.government.bg/

http://www.euridice.org/

http://www.ibe.unesco.org/

http://www.unesco.org/iiep

http://www.oecd.org/els/stats/edu

http://europa.eu.int/en/comm/eurostat

http://www.uniceff.org/statis

http://www.un.org/Depts/unsd/social

http://unesco.org/webworld/com

http://www.ed.gov/

13. U.S. Department of Education,National Center for Educational Statistics:

http://www.nces.ed.gov

14.U.S.Network for Education Information: http://www.ed.gov/NLE/USNEI

15. World Bank: http://www.worldbank.org/data/countrydata

HISTORY OF MATHEMATICS

Semester: 8th semester

Type of Course: lectures

Hours per Week: 3 lecture hours / Summer Semester


Lecturers: Assoc. professor Kostadin Samardjiev, PhD





Course Description: It includes basic steps of the development of mathematical knowledge

until the end of 19th century.

Objectives: basic steps of the development of mathematical knowledge until the end of 19th

century are presented to students and they are given an idea how to use that knowledge in

their future work as teachers in mathematics.

Methods of teaching: lectures and consultations.

Pre-requirements: Knowledge from the School course in Mathematic

Assessment and Evaluation: written exam


Registration for the Exam: coordinated with lecturer and Student Service Office

References:

Basic Titles:

1. Бомарский, Б., Очерки по истории математики, Минск, 1979

2. Ганчев, Ив. История на математиката, 1999

3. Строик, Д. Я. Краткий очерк по истории математики, М. 1988

Additional Titles:

1. Ван дер Ванден, Б. Л. Пробуждаща се наука, С., 1968

2. Денман, И. Я., История Арифметики, М., 1959

http://www.nces.ed.gov/

http://www.ed.gov/NLE/USNEI

http://www.worldbank.org/data/countrydata


Documents

QUALIFICATION CHARACTERIZATION OF MAJOR … use and apply competently the latest multimedia technologies; to use and apply competently fundamental knowledge in the area of Mathematics