Accesibility Adjustments

Choose the right accessibility profile for you
OFF ON
Highlight Links Highlights all the links on the site!
OFF ON
Pause Animations Animations will be paused on the site!
OFF ON
Dyslexia Font Dyslexia Font will be applied on the site!
OFF ON
Hide Images All images will be hidden on the site!
Choose the right accessibility profile for you
Adjust Font Sizing
Default
High Saturation
High Contrast
Light Contrast
Dark Contrast
Adjust Letter Spacing
Default
Adjust Line Height
Default
Speak Mode
Align Center
Align Left
Align Right

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / INTRODUCTION TO MATHEMATICAL LOGIC

Course:INTRODUCTION TO MATHEMATICAL LOGIC/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
3979Obavezan142+1+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises
Student workload
Per weekPer semester
4 credits x 40/30=5 hours and 20 minuts
2 sat(a) theoretical classes
0 sat(a) practical classes
1 excercises
2 hour(s) i 20 minuts
of independent work, including consultations 		Classes and final exam:
5 hour(s) i 20 minuts x 16 =85 hour(s) i 20 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
5 hour(s) i 20 minuts x 2 =10 hour(s) i 40 minuts
Total workload for the subject:
4 x 30=120 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
24 hour(s) i 0 minuts
Workload structure: 85 hour(s) i 20 minuts (cources), 10 hour(s) i 40 minuts (preparation), 24 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / ENGLISH LANGUAGE 1

Course:ENGLISH LANGUAGE 1/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
5545Obavezan142+1+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites There are no pre-requisites for the course. However, the students should command intermediate English in order to be able to follow the classes.
Aims To master the basic grammar structures and use the English language in everyday situations.
Learning outcomes After passing this exam, the students will be able to: - Understand the English discourse messages on topics commonly encountered (family, professions, hobbies, etiquette, customs), as well as the basic messages of the more complex English texts and audio recordings on various concrete and abstract topics (art, travel, media, school systems, weather), - Speak English relatively fluently on familiar topics using simple structures, exchange information and participate in conversation on familiar topics as well as those covered in classes, - Describe experience, events, plans, provide explanation and arguments in the English language, - Command the English grammar at the lower-intermediate level, - Write a short essay in English on a familiar topic, - Be aware of the connection between the foreign language and culture, and be familiar with some traditions in the English-speaking countries.
Lecturer / Teaching assistantMilica Vuković Stamatović, Savo Kostić
MethodologyA short introduction to the topics covered, with the focus on the participation of students in various types of exercises - conversation and writing, pairwork, groupwork, presentations, discussions etc.
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesIntroduction to the course, Present Simple vs Present Continuous
I week exercisesPresent Simple vs Present Continuous
II week lecturesPast Simple (regular/irregular verbs); Used to
II week exercises Past Simple (regular/irregular verbs); Used to, exercises
III week lecturesPast Continuous (Past Simple vs Past Continuous)
III week exercisesPast Continuous (Past Simple vs Past Continuous), exercises
IV week lecturesPresent Perfect Simple (Past Simple vs Present Perfect Simple)
IV week exercisesPresent Perfect Simple (Past Simple vs Present Perfect Simple), exercises
V week lecturesFuture (Future simple – Be going to – Present Continuous)
V week exercisesFuture (Future simple – Be going to – Present Continuous), exercises
VI week lecturesMidterm test
VI week exercisesMidterm test
VII week lecturesRevision and error correction
VII week exercisesRevision and error correction
VIII week lecturesPronouns; Infinitives
VIII week exercisesPronouns; Infinitives, exercises
IX week lecturesAdjectives
IX week exercisesAdjectives, exercises
X week lecturesModal Verbs
X week exercisesModal Verbs, exercises
XI week lecturesPast Perfect Simple; Past Perfect Continuous
XI week exercisesPast Perfect Simple; Past Perfect Continuous, exercises
XII week lecturesPassive Voice
XII week exercisesPassive Voice, exercises
XIII week lecturesReported Speech
XIII week exercisesReported Speech, exercises
XIV week lecturesConditionals - Wishes
XIV week exercisesConditionals - Wishes, exercises
XV week lecturesPreparation for the exam
XV week exercisesPreparation for the exam
Student workload
Per weekPer semester
4 credits x 40/30=5 hours and 20 minuts
2 sat(a) theoretical classes
0 sat(a) practical classes
1 excercises
2 hour(s) i 20 minuts
of independent work, including consultations 		Classes and final exam:
5 hour(s) i 20 minuts x 16 =85 hour(s) i 20 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
5 hour(s) i 20 minuts x 2 =10 hour(s) i 40 minuts
Total workload for the subject:
4 x 30=120 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
24 hour(s) i 0 minuts
Workload structure: 85 hour(s) i 20 minuts (cources), 10 hour(s) i 40 minuts (preparation), 24 hour(s) i 0 minuts (additional work)
Student obligations Attendance, doing homework, active participation in classes
Consultations
LiteratureLiteratura: Grammarway 3
Examination methodsLiteratura: Grammarway 3
Special remarksAdopted on 21-7-2016: http://senat.ucg.ac.me/data/1469020997-Akreditacija%20PMF%202017%20final.pdf
Comment/
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / COMPUTERS AND PROGRAMMING

Course:COMPUTERS AND PROGRAMMING/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
495Obavezan163+3+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises
Student workload
Per weekPer semester
6 credits x 40/30=8 hours and 0 minuts
3 sat(a) theoretical classes
0 sat(a) practical classes
3 excercises
2 hour(s) i 0 minuts
of independent work, including consultations 		Classes and final exam:
8 hour(s) i 0 minuts x 16 =128 hour(s) i 0 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
8 hour(s) i 0 minuts x 2 =16 hour(s) i 0 minuts
Total workload for the subject:
6 x 30=180 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
36 hour(s) i 0 minuts
Workload structure: 128 hour(s) i 0 minuts (cources), 16 hour(s) i 0 minuts (preparation), 36 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / LINEAR ALGEBRA 1

Course:LINEAR ALGEBRA 1/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
3967Obavezan184+3+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims Standard course of Linear algebra for students of mathematics. Includes theory of finite-dimensional vector spaces, matrices, systems of linear equations and linear mappings in finite-dimensional vector spaces (including spectral theory).
Learning outcomes
Lecturer / Teaching assistantVladimir Jaćimović, Dušica Slović
Methodologylectures, seminars, consultations
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesGroups and fields. Vector spaces. Definition. Examples. Vector subspaces. Linear span.
I week exercisesGroups and fields. Fields of real and complex numbers. Geometric vectors in the plane.
II week lecturesLinearly dependent and independent vectors. Base and dimension of vector spaces. Isomorfism of vector spaces.
II week exercises Vector spaces. R^n and C^n. Vector subspaces. Linear span.
III week lecturesMatrices. Gauss method for solving linear systems of equations. Matrices of elementary transforms.
III week exercisesLinearly dependent and independent vectors. Base and dimension of vector spaces. Problems and examples in R^n. Subspaces in R^n. Systems of linear equations.
IV week lecturesDeterminants of square matrices. Rank of matrix.
IV week exercisesGauss method for solving systems of linear equations. Matrices. Matrices of elementary transforms.
V week lecturesInverse matrix. Regular and singular matrices. Matrices of change of bases. Equivalent matrices.
V week exercisesDeterminant and rank of matrix.
VI week lecturesSystems of linear equations. Existence and uniqueness of solution. General solution. Kronecker Capelli theorem. Cramers' rule.
VI week exercisesInverse matrix. Regular and singular matrices. Matrices of coordinate change.
VII week lectures1st test
VII week exercises1st test
VIII week lecturesEmpty week
VIII week exercisesEmpty week
IX week lecturesLinear mappings in vector spaces. Definition. Examples. Kernel and image of linear mapping.
IX week exercisesHomogeneous and nonhomogeneous systems of linear equations. Methods of solving. Existence and uniqueness of solution. Cramers' rule.
X week lecturesMatrix of linear mapping. Similar matrices. Inverse mapping. Rank of linear mapping.
X week exercisesLinear mappings in vector spaces. Kernel and image of linear mapping. Examples: operators of projection, rotation and differentiation of polynomials.
XI week lecturesInvariant subspaces of linear mapping. Eigenvalues and eigenvectors. Eigenspaces.
XI week exercisesMatrix of linear mapping. Inverse mapping. Rank of linear mapping.
XII week lecturesFundamental theorem of algebra. Characteristic polynomial of linear mapping. Polynomials of matrices/operators. Hamilton-Cayley theorem.
XII week exercisesEigenvalues and eigenvectors of linear mapping. Characteristic polynomial of linear mapping.
XIII week lecturesJordan form and cannonical base of nilpotent linear mapping.
XIII week exercisesMethod of calculation of eigenvectors. Eigenspaces.
XIV week lecturesJordan form of linear mapping. Examples.
XIV week exercisesJordan form of linear mapping. Similar matrices.
XV week lectures2nd test
XV week exercises2nd test
Student workload4 hours/week lectures + 3 hours/week seminars + 4 hours/week homework = 11 hours/week. Total: 11 hours/week x 16 weeks = 176 hours
Per weekPer semester
8 credits x 40/30=10 hours and 40 minuts
4 sat(a) theoretical classes
0 sat(a) practical classes
3 excercises
3 hour(s) i 40 minuts
of independent work, including consultations 		Classes and final exam:
10 hour(s) i 40 minuts x 16 =170 hour(s) i 40 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
10 hour(s) i 40 minuts x 2 =21 hour(s) i 20 minuts
Total workload for the subject:
8 x 30=240 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
48 hour(s) i 0 minuts
Workload structure: 170 hour(s) i 40 minuts (cources), 21 hour(s) i 20 minuts (preparation), 48 hour(s) i 0 minuts (additional work)
Student obligations
Consultations1 hour/week (lectures) + 1 hour/week (seminars)
LiteratureM. Jaćimović, I. Krnić „Linearna algebra, teoreme i zadaci“ (skripta) E. Shikin „Lineinie prostranstva i otobrazheniya“, Moskva 1987. S. Friedberg, A. Insel, L. Spence „Linear algebra, 4th edition“ Pearson, 2002.
Examination methodsattendance (5 points), homework (5x1 points), 2 tests (2x30 points), one corrective test, final exam (30 points), corrective final exam, 2 brief oral exams (optional – 2x5 points)
Special remarksThe language of instruction is Serbo-Croat. Lectures can be given in English or Russian language.
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / ANALYSIS 1

Course:ANALYSIS 1/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
3977Obavezan184+3+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites None.
Aims The aim of the course is for students to adopt and master the basics of mathematical analysis: limit theory, elements of differential and integral calculus and the theory of series.
Learning outcomes On successful completion of this course students will be able to: 1. Define the basic notions of Mathematical analysis 1: the set of real numbers, the limit of a sequence and function, differentiability of functions, derivatives and antiderivatives on segments. 2. Define the basic properties of the set of real numbers. 3. Derive basic propositions of limit theory and differential calculus, establish when a sequence or function has a limit or the property of continuity or differentiability. 4. Examine and relate properties of functions of one variable using differential calculus. 5. Apply the acquired knowledge to solving different tasks related to the stated content of mathematical analysis. 6. Apply the acquired knowledge to solving real tasks and problems.
Lecturer / Teaching assistantProf. dr Žarko Pavićević - lecturer, Nikola Konatar - teaching assistant
MethodologyLectures, exercises, homework assignments, consultations, written exams.
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesIntroducing students to basic topics covered by the course.
I week exercisesIntroducing students to basic topics covered by the course.
II week lecturesThe set of real numbers – axiomatic construction.
II week exercises The set of real numbers – axiomatic construction.
III week lecturesCompleteness principles of the set of real numbers.
III week exercisesCompleteness principles of the set of real numbers.
IV week lecturesConvergent sequence theory.
IV week exercisesConvergent sequence theory.
V week lecturesBolzano’s and Cauchy’s theorem for sequences. Banach fixed-point theorem.
V week exercisesBolzano’s and Cauchy’s theorem for sequences. Banach fixed-point theorem.
VI week lecturesTopology on the set of real numbers.
VI week exercisesTopology on the set of real numbers.
VII week lecturesLimit of a function. Continuity of a function at a point.
VII week exercisesLimit of a function. Continuity of a function at a point.
VIII week lecturesGlobal properties of functions continuous on segments.
VIII week exercisesGlobal properties of functions continuous on segments.
IX week lecturesUniform continuity of functions.
IX week exercisesUniform continuity of functions.
X week lecturesReview. First midterm exam.
X week exercisesReview. First midterm exam.
XI week lecturesDifferentiability of functions at a point. Derivative of a function.
XI week exercisesDifferentiability of functions at a point. Derivative of a function.
XII week lecturesDerivatives of higher order.
XII week exercisesDerivatives of higher order.
XIII week lecturesMean value theorems of differential calculus. Bernouli – L’Hopital’s rule. Taylor formulas.
XIII week exercisesMean value theorems of differential calculus. Bernouli – L’Hopital’s rule. Taylor formulas.
XIV week lecturesMonotonicity and extrema of differentiable functions. Convexity of functions. Inflection points.
XIV week exercisesMonotonicity and extrema of differentiable functions. Convexity of functions. Inflection points.
XV week lecturesExamining properties and sketching graphs of functions. Second midterm exam.
XV week exercisesExamining properties and sketching graphs of functions. Second midterm exam.
Student workload
Per weekPer semester
8 credits x 40/30=10 hours and 40 minuts
4 sat(a) theoretical classes
0 sat(a) practical classes
3 excercises
3 hour(s) i 40 minuts
of independent work, including consultations 		Classes and final exam:
10 hour(s) i 40 minuts x 16 =170 hour(s) i 40 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
10 hour(s) i 40 minuts x 2 =21 hour(s) i 20 minuts
Total workload for the subject:
8 x 30=240 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
48 hour(s) i 0 minuts
Workload structure: 170 hour(s) i 40 minuts (cources), 21 hour(s) i 20 minuts (preparation), 48 hour(s) i 0 minuts (additional work)
Student obligations Students are required to attend classes, do the homework assignments and take all exams.
ConsultationsAs agreed with students.
LiteratureV. I. Gavrilov,,Ž. Pavićević, Matematička analiza I, I.M. Lavrentjev, R. Šćepanović, Zbirka zadataka iz mat. analize I, B.P. Demidovič: Zbirka zadataka iz matematičke analize (Prevod)
Examination methodsTwo homeworks or tests are graded with 8 points (4 points for each homework or test). 2 points are awarded for attendance to lectures and exercises. Two midterm exams are graded with 20 points each (40 points in total). Final exam - 50 points. A passing grade is awarded to students who accumulate at least 50 points.
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / ENGLISH LANGUAGE 2

Course:ENGLISH LANGUAGE 2/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
5546Obavezan222+1+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites None
Aims To understand and be able to use ESP (English for Mathematics)
Learning outcomes After passing this exam, the students will be able to: - Differentiate, understand and use the most basic mathematical English terminology in the field of number theory, applied mathematics, combinatorics and discrete mathematics, - Read simple mathematical expressions in English, - Understand the basic messages of popular-professional English texts in the field of mathematics, - Communicate in English independently, both orally and in writing, at the intermediate level, - Orally present in English on the mathematical topic chosen, - Write a summary of a popular-professional text or audio recording in English.
Lecturer / Teaching assistantMilica Vuković Stamatović, Savo Kostić
MethodologyLectures and exercises. Preparation of a presentation on a topic related to the content covered in the course. Studying for the test and the exam. Consultations.
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesIntroduction to the course. Reading: My Future Profession; Basic mathematical terms
I week exercisesVocabulary and grammar exercises
II week lecturesMathematical terms – algebra and geometry
II week exercises Vocabulary and grammar exercises
III week lecturesReading: A Genius Explains; Conditionals
III week exercisesConditionals, exercises
IV week lecturesReading: Number Theory; Active and Passive
IV week exercisesActive and Passive, exercises
V week lecturesRevision
V week exercisesRevision
VI week lecturesReading: Applied Mathematics; Articles; Transformations
VI week exercisesTransformations, exercises
VII week lecturesPreparation for the mid-term test
VII week exercisesPreparation for the test
VIII week lecturesMid-term test
VIII week exercisesMid-term test
IX week lecturesReading: Combinatorics; Modal verbs
IX week exercisesModal verbs, exercises
X week lecturesReading: Discrete Mathematics; The Language of Proof
X week exercisesVocabulary exercises
XI week lecturesReading: An Interview with Leonardo Fibonacci; Vocabulary Revision
XI week exercisesVocabulary revision
XII week lecturesGrammar Revision
XII week exercisesGrammar Revision
XIII week lecturesMid-term test (2nd term)
XIII week exercisesMid-term test (2nd term)
XIV week lecturesTranslation exercises
XIV week exercisesTranslation exercises
XV week lecturesPreparation for the final exam
XV week exercisesPreparation for the final exam
Student workload
Per weekPer semester
2 credits x 40/30=2 hours and 40 minuts
2 sat(a) theoretical classes
0 sat(a) practical classes
1 excercises
-1 hour(s) i 40 minuts
of independent work, including consultations 		Classes and final exam:
2 hour(s) i 40 minuts x 16 =42 hour(s) i 40 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
2 hour(s) i 40 minuts x 2 =5 hour(s) i 20 minuts
Total workload for the subject:
2 x 30=60 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
12 hour(s) i 0 minuts
Workload structure: 42 hour(s) i 40 minuts (cources), 5 hour(s) i 20 minuts (preparation), 12 hour(s) i 0 minuts (additional work)
Student obligations Students have to attend the classes, do a presentation on a given topic and take the mid-term test and the final exam.
Consultations
LiteratureTextbook: English 2 (ESP - English for students of theoretical and applied mathematics)
Examination methods
Special remarksAdopted on 21-7-2016: http://senat.ucg.ac.me/data/1469020997-Akreditacija%20PMF%202017%20final.pdf
Comment/
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / INTRODUCTION TO COMBINATORICS

Course:INTRODUCTION TO COMBINATORICS/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
3981Obavezan242+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises
Student workload
Per weekPer semester
4 credits x 40/30=5 hours and 20 minuts
2 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
1 hour(s) i 20 minuts
of independent work, including consultations 		Classes and final exam:
5 hour(s) i 20 minuts x 16 =85 hour(s) i 20 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
5 hour(s) i 20 minuts x 2 =10 hour(s) i 40 minuts
Total workload for the subject:
4 x 30=120 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
24 hour(s) i 0 minuts
Workload structure: 85 hour(s) i 20 minuts (cources), 10 hour(s) i 40 minuts (preparation), 24 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / ANALYTIC GEOMETRY

Course:ANALYTIC GEOMETRY/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
1341Obavezan242+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites Attending and taking this course is not conditioned by other courses.
Aims The aim of this course is to introduce students to elements of vector algebra and the method of coordinates for investigation of geometrical objects and for solving of geometrical problems.
Learning outcomes On successful completion of the course, students will be able to: 1. Describe Cartesian, polar and sphere coordinate system and explain how basic geometric objects: point, line, plane, circle, ellipse, parabola and hyperbola can be presented in these coordinate systems. 2. Explain how the equations of a geometric object can be used establish their relation and position in plane and space. 3. Study the properties of geometric objects by using the equations they are described with. 4. Using the method of coordinates, solve some geometric tasks. 5. Using the equation of the second order of two and three variables, classify curves and surfaces of the second order.
Lecturer / Teaching assistantProf. dr Milojica Jaćimović – lecturer, Mr. Dušica Slović, assistant
MethodologyLectures and exercises with active participation of students, individual homework assignments, group and individual consultations.
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesCartesian coordinate systems in plane and in space. Polar and spherical coordinate systems.
I week exercisesCartesian coordinate systems in plane and in space. Polar and spherical coordinate systems.
II week lecturesVectors in coordinate system. Linear operations. Scalar, vector and mixed products.
II week exercises Vectors in coordinate system. Linear operations. Scalar, vector and mixed products.
III week lecturesCurves and surfaces and their equations. Examples.
III week exercisesCurves and surfaces and their equations. Examples.
IV week lecturesLine in the plane, plane in the space, line in the space, different equations of the line and the plane.
IV week exercisesLine in the plane, plane in the space, line in the space, different equations of the line and the plane.
V week lecturesRelations of lines and planes in space. Examples. Distance from a point to a plane and line.
V week exercisesRelations of lines and planes in space. Examples. Distance from a point to a plane and line.
VI week lecturesPlane in the n-dimensional Euclidean space. Dimension of the plane. Parallel planes.
VI week exercisesPlane in the n-dimensional Euclidean space. Dimension of the plane. Parallel planes.
VII week lecturesTest.
VII week exercisesTest.
VIII week lecturesLine and hyperplane. Distance from a point to the hyperplane. Plane as a intersection of hyperplanes.
VIII week exercisesLine and hyperplane. Distance from a point to the hyperplane. Plane as a intersection of hyperplanes.
IX week lecturesConvex set in a n-dimensional space. Segment, ray, half-space. Linear programming. Conic section. Classification. Canonical equations.
IX week exercisesConvex set in a n-dimensional space. Segment, ray, half-space. Linear programming. Conic section. Classification. Canonical equations.
X week lecturesProperties of the ellipse, hyperbola, parabola.
X week exercisesProperties of the ellipse, hyperbola, parabola.
XI week lecturesIsometric transformations of the Euclidean space. The group of isometric transformations.
XI week exercisesIsometric transformations of the Euclidean space. The group of isometric transformations.
XII week lecturesQuadric surfaces. Reduction to canonical form. Theorem of inertia.
XII week exercisesQuadric surfaces. Reduction to canonical form. Theorem of inertia.
XIII week lecturesSecond-order curves. Invariants. Properties, classification.
XIII week exercisesSecond-order curves. Invariants. Properties, classification. Correctional test.
XIV week lecturesSecond-order surfaces. Canonical form.
XIV week exercisesSecond-order surfaces. Canonical form.
XV week lecturesInvariants and second order surfaces.
XV week exercisesInvariants and second order surfaces.
Student workload2 hours of lectures 2 hours of exercises 1 hour 20 minutes of individual activity, including consultations
Per weekPer semester
4 credits x 40/30=5 hours and 20 minuts
2 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
1 hour(s) i 20 minuts
of independent work, including consultations 		Classes and final exam:
5 hour(s) i 20 minuts x 16 =85 hour(s) i 20 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
5 hour(s) i 20 minuts x 2 =10 hour(s) i 40 minuts
Total workload for the subject:
4 x 30=120 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
24 hour(s) i 0 minuts
Workload structure: 85 hour(s) i 20 minuts (cources), 10 hour(s) i 40 minuts (preparation), 24 hour(s) i 0 minuts (additional work)
Student obligations Students are required to attend classes.
ConsultationsAs agreed with the professor or teaching assistant.
LiteratureN. Elezović, Linearna algebra, Element, Zagreb, 2001; P.S. Modenov: Analiticka geometrija, Moskovski univerzitet; M. Jaćimović, I. Krnić: Linearna algebra – teoreme i zadaci, skripta, Podgorica
Examination methodsActivities on classes up to 10 points, Test ( up to 40 points), and the final exam (up to 50 points). Grading: 51-60 points- E; 61-70 points- D; 71-80 points- C; 81-90 points- B; 91-100 points- A.
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / GEOMETRY OF SPACE LEVELS

Course:GEOMETRY OF SPACE LEVELS/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
10106Obavezan242+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises
Student workload
Per weekPer semester
4 credits x 40/30=5 hours and 20 minuts
2 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
1 hour(s) i 20 minuts
of independent work, including consultations 		Classes and final exam:
5 hour(s) i 20 minuts x 16 =85 hour(s) i 20 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
5 hour(s) i 20 minuts x 2 =10 hour(s) i 40 minuts
Total workload for the subject:
4 x 30=120 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
24 hour(s) i 0 minuts
Workload structure: 85 hour(s) i 20 minuts (cources), 10 hour(s) i 40 minuts (preparation), 24 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / PRINCIPLES OF PROGRAMMING

Course:PRINCIPLES OF PROGRAMMING/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
1335Obavezan263+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises
Student workload
Per weekPer semester
6 credits x 40/30=8 hours and 0 minuts
3 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
3 hour(s) i 0 minuts
of independent work, including consultations 		Classes and final exam:
8 hour(s) i 0 minuts x 16 =128 hour(s) i 0 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
8 hour(s) i 0 minuts x 2 =16 hour(s) i 0 minuts
Total workload for the subject:
6 x 30=180 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
36 hour(s) i 0 minuts
Workload structure: 128 hour(s) i 0 minuts (cources), 16 hour(s) i 0 minuts (preparation), 36 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / LINEAR ALGEBRA 2

Course:LINEAR ALGEBRA 2/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
3968Obavezan262+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites Students are expected to have listened course of Linear algebra I.
Aims Standard course of Linear algebra II for students of mathematics. Includes theory of linear mapping in vector spaces with inner product.
Learning outcomes
Lecturer / Teaching assistantVladimir Jaćimović, Dušica Slović
Methodologylectures, seminars, consultations
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesSpaces with inner product. Hilbert and unitary spaces. Cauchy-Schwarz inequality.
I week exercisesInner product. Axiomatic framework, examples. Inner product of geometric vectors. Inner product in R^n and C^n.
II week lecturesOrthogonal vectors. Orthonormal vector system. Orthonormal base in vector space. Gramian matrix. Gram-Schmidt orthogonalization algorithm.
II week exercises Orthogonal vectors. Orthonormal vector system. Orthonormal base in vector space. Gramian matrix. Gram-Schmidt orthogonalization algorithm.
III week lecturesQuadratic forms in Hilbert spaces. Sign of the quadratic form. Sylvester's criterion.
III week exercisesQuadratic forms in Hilbert spaces. Reduction of quadratic form to sum of squares by coordinate change.
IV week lecturesReduction of quadratic form to the sum of squares. Lagrange and Jacobi methods. Index of quadratic form. Law of inertia for quadratic forms.
IV week exercisesIndex of quadratic form. Sign of quadratic form. Law of inertia, Sylvester's criterion.
V week lecturesLinear mappings in unitary spaces. Adjoint operator. Existence and uniqueness. Matrix of adjoint operator.
V week exercisesAdjoint operator. Matrix of adjoint operator.
VI week lecturesKernel and image of adjoint operators. Normal operator.
VI week exercisesNormal operator.
VII week lectures1st test
VII week exercises1st test
VIII week lecturesEmpty week
VIII week exercisesEmpty week
IX week lecturesUnitary operator. Hermitian operator.
IX week exercisesUnitary operator. Examples and problems.
X week lecturesPositive operators. Square root of operators. Decompositions of operators
X week exercisesHermitian operators. Square root of operators. Positive operators.
XI week lecturesLinear operator in Hilbert spaces. Symmetric operator.
XI week exercisesSymmetric operator. Eigenvalues of symmetric operator.
XII week lecturesOrthogonal operator. Reduction of orthogonal operator to the composition of simple rotations and reflections.
XII week exercisesOrthogonal operator. Orthogonal matrix.
XIII week lecturesClassification of hypersurfaces of second order in Hilbert spaces.
XIII week exercisesReduction of equation of second order hypersurface to canonical form.
XIV week lecturesLinear operator equations in unitary spaces. Existence and uniqueness of solution. Fredholm alternative.
XIV week exercisesLinear operator equations in unitary spaces. Fredholm alternative.
XV week lectures2nd test
XV week exercises2nd test
Student workload2 hours/week (lectures) + 2 hours/week (seminars) + 3 hours/week (homework) = 7 hours/week. Total: 7 hour/week x 16 week = 112 hours
Per weekPer semester
6 credits x 40/30=8 hours and 0 minuts
2 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
4 hour(s) i 0 minuts
of independent work, including consultations 		Classes and final exam:
8 hour(s) i 0 minuts x 16 =128 hour(s) i 0 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
8 hour(s) i 0 minuts x 2 =16 hour(s) i 0 minuts
Total workload for the subject:
6 x 30=180 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
36 hour(s) i 0 minuts
Workload structure: 128 hour(s) i 0 minuts (cources), 16 hour(s) i 0 minuts (preparation), 36 hour(s) i 0 minuts (additional work)
Student obligations
Consultations1 hour/week lectures + 1 hour/week seminars
LiteratureM. Jaćimović, I. Krnić „Linearna algebra, teoreme i zadaci“ (skripta) E. Shikin „Lineinie prostranstva i otobrazheniya“, Moskva 1987. S. Friedberg, A. Insel, L. Spence „Linear algebra, 4th edition“ Pearson, 2002.
Examination methodsattendance (5 points), homework (5x1 points), 2 tests (2x30 points), one corrective test, final exam (30 points), corrective final exam, 2 brief oral exams (optional – 2x5 points)
Special remarksThe language of instruction is Serbo-Croat. Lectures can be given in English or Russian language.
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / ANALYSIS 2

Course:ANALYSIS 2/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
3978Obavezan284+3+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites None.
Aims The aim of the course is for students to adopt and master the basics of mathematical analysis: limit theory, elements of differential and integral calculus and the theory of series.
Learning outcomes On successful completion of the course, students will be able to: 1. Define the basic notions of mathematical analysis 2: Riemann integral on a closed interval, area of a curvilinear trapezoid, curve and curve length, volume and area of a solid of revolution, improper integral, convergent series. 2. Derive basic propositions related to the Riemann and improper integral and convergent series. 3. Calculate the Riemann integral as a limit of the sequence of integral sums. 4. Examine and associate the properties of differentiability and integrability of functions of a real variable. 5. Apply some integral formulas. 6. Apply the acquired knowledge to solving different tasks related to the stated content of mathematical analysis. 7. Apply the acquired knowledge to solving real tasks and problems.
Lecturer / Teaching assistantProf. dr Žarko Pavićević - lecturer, Nikola Konatar - teaching assistant
MethodologyLectures, exercises, homework assignments, consultations, written exams.
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesAntiderivative on an open interval. Indefinite integral.
I week exercisesAntiderivative on an open interval. Indefinite integral.
II week lecturesAntiderivative on an interval. Indefinite integral on an interval.
II week exercises Antiderivative on an interval. Indefinite integral on an interval.
III week lecturesDefinition of the Riemann integral. Properties.
III week exercisesDefinition of the Riemann integral. Properties.
IV week lecturesCriteria for the integrability of functions.
IV week exercisesCriteria for the integrability of functions.
V week lecturesProperties of the definite integral and integrable functions.
V week exercisesProperties of the definite integral and integrable functions.
VI week lecturesIntegral and derivative. Some integral functions.
VI week exercisesIntegral and derivative. Some integral functions.
VII week lecturesReview. First midterm exam.
VII week exercisesReview. First midterm exam.
VIII week lecturesFunctions of bounded variation.
VIII week exercisesFunctions of bounded variation.
IX week lecturesApplications of the definite integral.
IX week exercisesApplications of the definite integral.
X week lecturesImproper integral.
X week exercisesImproper integral.
XI week lecturesSeries. Convergence of series.
XI week exercisesSeries. Convergence of series.
XII week lecturesCriteria for the convergence of series with positive terms.
XII week exercisesCriteria for the convergence of series with positive terms.
XIII week lecturesFunctional sequences and series. Uniform convergence.
XIII week exercisesFunctional sequences and series. Uniform convergence.
XIV week lecturesReview. Second midterm exam.
XIV week exercisesReview. Second midterm exam.
XV week lecturesSome applications of Mathematical analysis in natural sciences.
XV week exercisesSome applications of Mathematical analysis in natural sciences.
Student workload
Per weekPer semester
8 credits x 40/30=10 hours and 40 minuts
4 sat(a) theoretical classes
0 sat(a) practical classes
3 excercises
3 hour(s) i 40 minuts
of independent work, including consultations 		Classes and final exam:
10 hour(s) i 40 minuts x 16 =170 hour(s) i 40 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
10 hour(s) i 40 minuts x 2 =21 hour(s) i 20 minuts
Total workload for the subject:
8 x 30=240 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
48 hour(s) i 0 minuts
Workload structure: 170 hour(s) i 40 minuts (cources), 21 hour(s) i 20 minuts (preparation), 48 hour(s) i 0 minuts (additional work)
Student obligations Students are required to attend classes, do the homework assignments and take both midterm exams.
ConsultationsAs agreed with students.
LiteratureV. I. Gavrilov,Ž. Pavićević, Matematička analiza I, D. Adnađević, Z. Kadelburg, Matematička analiza 2, I.M. Lavrentjev, R. Šćepanović, Zbirka zadataka iz mat. analize I, B.P. Demidovič: Zbirka zadataka iz matematičke analize.
Examination methodsTwo homeworks or tests are graded with 8 points (4 points for each homework or test). 2 points are awarded for attendance to lectures and exercises. Two midterm exams are graded with 20 points each (40 points in total). Final exam - 50 points. A passing grade is awarded to students who accumulate at least 50 points.
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / ENGLISH LANGUAGE 3

Course:ENGLISH LANGUAGE 3/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
5547Obavezan332+1+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites No prerequisites
Aims The course has a goal to make students able to use English for specific purposes in the area of mathematics.
Learning outcomes After students pass the exam they will be able to: - understand the messages of expert discourse for the topic they often experience (sets, functions, geometrical figures and solids, plains...), as well as basic messages of more complex mathematical texts with various topics in English. - orally express mathematical topics in a relatively fluent manner, using simple structures, exchange information and participate in conversations with familiar and practices topics in English, - master the English grammar at upper intermediate level, - write a short composition in English using the vocabulary learned in classes - make a presentation for the topic related to English for mathematics Predmet ima za cilj osposobljavanje studenta da razumiju i da se razumiju i da se služe engleskim jezikom struke. Predavanja i vježbanja. Priprema prezentacije na zadatu temu iz jedne od oblasti sadržaja predmeta. Učenje za kolokvijum i završni ispit. Konsultacije.
Lecturer / Teaching assistantMilica Vukovic Stamatovic, Savo Kostic
MethodologyLectures and practice. Presentations in English on a topic studied. Studying for mid term and final exams. Consultations.
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesMathematical Logic and Foundation; grammar: Past simple vs Past continuous;
I week exercisesPast simple vs Past continuous, exercises
II week lecturesCombinatorics: -ing forms and infinitives;
II week exercises -ing forms and infinitives, exercises
III week lecturesOrdered algebraic structures; grammar: modal verbs must and have to ;
III week exercisesmodal verbs must and have to, exercises
IV week lecturesGeneral algebraic systems; grammar: Present perfect passive;
IV week exercisesPresent perfect passive, exercises
V week lecturesField theory; grammar: conditional sentences
V week exercisesconditional sentences, exercises
VI week lecturesMidterm test
VI week exercisesSpeaking exercises
VII week lecturesRevision and error correction
VII week exercisesRevision and error correction
VIII week lecturesPolynomials; grammar: Time clauses
VIII week exercisestime clauses
IX week lecturesNumber theory; grammar: prepositions
IX week exercisesprepositions
X week lecturesCommutative rings and algebras; Present simple vs present continuous
X week exercisesPresent simple vs present continuous, exercises
XI week lecturesAlgebraic geometry; grammar: Reported speech
XI week exercisesReported speech, exercises
XII week lecturesLinear and multilinear algebra; grammar: clauses of contrast
XII week exercisesclauses of contrast
XIII week lecturesAssociative rings and algebras; grammar: Making predictions
XIII week exercisesMaking predictions, exercises
XIV week lecturesNonasociative rings and algebras; grammar: will and would
XIV week exerciseswill and would
XV week lecturesCategory theory; grammar: certainty
XV week exercisesCertainty
Student workload
Per weekPer semester
3 credits x 40/30=4 hours and 0 minuts
2 sat(a) theoretical classes
0 sat(a) practical classes
1 excercises
1 hour(s) i 0 minuts
of independent work, including consultations 		Classes and final exam:
4 hour(s) i 0 minuts x 16 =64 hour(s) i 0 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
4 hour(s) i 0 minuts x 2 =8 hour(s) i 0 minuts
Total workload for the subject:
3 x 30=90 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
18 hour(s) i 0 minuts
Workload structure: 64 hour(s) i 0 minuts (cources), 8 hour(s) i 0 minuts (preparation), 18 hour(s) i 0 minuts (additional work)
Student obligations Students need to regularly attend classes, make a presentation and take a mid term and a final exam.
Consultations2 times a week for 2 hours
Literature"English for Mathematics" reader Headway Intermediate - Liz and John Soars
Examination methods
Special remarksAdopted on 21-7-2016: http://senat.ucg.ac.me/data/1469020997-Akreditacija%20PMF%202017%20final.pdf
Comment/
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / DISCRETE MATHEMATICS

Course:DISCRETE MATHEMATICS/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
503Obavezan342+1+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises
Student workload
Per weekPer semester
4 credits x 40/30=5 hours and 20 minuts
2 sat(a) theoretical classes
0 sat(a) practical classes
1 excercises
2 hour(s) i 20 minuts
of independent work, including consultations 		Classes and final exam:
5 hour(s) i 20 minuts x 16 =85 hour(s) i 20 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
5 hour(s) i 20 minuts x 2 =10 hour(s) i 40 minuts
Total workload for the subject:
4 x 30=120 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
24 hour(s) i 0 minuts
Workload structure: 85 hour(s) i 20 minuts (cources), 10 hour(s) i 40 minuts (preparation), 24 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / OPERATING SYSTEMS

Course:OPERATING SYSTEMS/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
506Obavezan353+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites none
Aims Through this course, students are introduced to the basic concepts of operating systems, their internal structure, methods of implementation, the principles and criteria of the design. In addition, the exercises students are introduced to the major modern operating systems, programming using system calls, as well as to the basics of shell programming.
Learning outcomes After passing this exam , will be able to: 1. understand basic concepts of operating systems and their internal structure; 2. understand ways of realization, principles and criteria for design of operating systems and to use them in the programming; 3. use and understand the major modern operating systems; 4. design and develop programs using system calls; 5. develop programs using shell programming .
Lecturer / Teaching assistantprof.dr Predrag Stanišić, doc.dr Savo Tomović
MethodologyLectures, exercises in computer classroom / laboratory. Learning and practical exercises. Consultations.
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesIntroduction. The notion of operating system. OS as extended machine and resource manager.
I week exercisesIntroduction to operating systems, MS-DOS. MS-DOS commands
II week lecturesHistory of operating systems. Types of operating systems.
II week exercises Batch processing. Batch programs. First homework assignment.
III week lecturesHardware overview. Processors, memory, I / O devices, bus.
III week exercisesModern OS. Windows, Linux (features, multitasking, multiuser, structure, kernel, file system, ...). I test (theory, MS-DOS commands and batch programs).
IV week lecturesBasic concepts of the operating system. System calls. The structure of the OS.
IV week exercisesBasic commands of Linux.
V week lecturesProcesses and threads. Modeling, activation, termination, state of the process, hierarchy, implementation.
V week exercisesAdvanced commands of Linux. Other homework.
VI week lecturesInterprocess communication. Classical IPC problems.
VI week exercisesAdvanced commands in Linux. II test (theory, shell programming and Linux commands).
VII week lecturesColloquium
VII week exercisesColloquium
VIII week lecturesProcess scheduling. Thread scheduling.
VIII week exercisesShell Programming. Bash shell, structure and run a shell script from the command line. Third homework
IX week lecturesDeadlocks.
IX week exercisesControl structures in shell programming (do, for, while, until).
X week lecturesMemory management.
X week exercisesTrap signal, export variable, writing and reading from file.
XI week lecturesInput/output management.
XI week exercisesC programs, compiling an running from command line (gcc). System calls for memory and I/O management. Fourth homework
XII week lecturesFile systems.
XII week exercisesSystem calls for working with files.
XIII week lecturesSecurity.
XIII week exercisesSystem calls (fork, exec, pipe). Fifth homework
XIV week lecturesMultimedia OS.
XIV week exercisesIII test C programs with system calls
XV week lecturesMultiprocessor and distributed OS.
XV week exercisesC programs with system calls
Student workloadweekly 7 credits x 40/30 = 8 hours Lectures: 3 hours Exercises: 3 hours Other teaching activities: 0 Individual work of students: 2 hours. semester Teaching and the final exam: 8 hours x 16 = 128 hours Preparation before the beginning of the semester (administration, enrollment, etc) 2 x (8 hours) = 16 hours Total hours for the course 6x30 = 180 hours Additional work for exams preparing correction of final exam, including the exam taking 0-36 hours (the remaining time of the first two items to the total work hours for the course, 180 hours) Structure: 128 hours (lectures) + 16 hours (preparation) 36 hours (additional work)
Per weekPer semester
5 credits x 40/30=6 hours and 40 minuts
3 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
1 hour(s) i 40 minuts
of independent work, including consultations 		Classes and final exam:
6 hour(s) i 40 minuts x 16 =106 hour(s) i 40 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
6 hour(s) i 40 minuts x 2 =13 hour(s) i 20 minuts
Total workload for the subject:
5 x 30=150 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
30 hour(s) i 0 minuts
Workload structure: 106 hour(s) i 40 minuts (cources), 13 hour(s) i 20 minuts (preparation), 30 hour(s) i 0 minuts (additional work)
Student obligations Students are required to attend lessons, fulfill tasks and home exercises, and attend colloquium.
ConsultationsCabinet
LiteratureTanenbaum: Modern Operating Systems, Prentice Hall International Silberchatz, Galvin: opearting Systems Concepts, Willey
Examination methodsThe forms of knowledge testing and grading: - 5 home exercises carry 5 points total (1 point each), - 3 tests of 10 points - First test of 30 points - Final exam 35 points.
Special remarksLectures are conducted for a group of about 40-60 students, exercises in groups of about 20 students. Lectures may be taught in English and Russian.
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / ALGEBRA 1

Course:ALGEBRA 1/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
3973Obavezan352+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites Prerequisities do not exist.
Aims Introduction to the basic algebraic structures.
Learning outcomes After successful completion of this course the student will be able to: 1. Define the basic algebraic structures: groupoid, semigroup, monoid,group, ring and the field. 2. Describe algebra of sets,the algebra of functions and the algebra of natural numbers. 3. Explain and transmit the notion of lattice and complemented lattice. 4. Explain and transmit the basic notions of group theory such as the notions of subgroup, normal subgroup, factor group, cyclic groups, derived subgroup, group homomorphism and inner automorphism. 5. Prove and apply in practice Lagrange”s theorem and the fundamental theorem of group homomorphisms.
Lecturer / Teaching assistant Sanja Jančić-Rašović
MethodologyLectures, exercises,consultations.
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesThe notion of operation. Properties of operations.The notion of algebraic structure (algebra).
I week exercisesThe notion of operation. Properties of operations.The notion of algebraic structure (algebra).
II week lecturesSubalgebra. Congruence relation. Factor algebra.
II week exercises Subalgebra. Congruence relation. Factor algebra.
III week lecturesGroupoid. Homomorphism of groupoids.Fundamental theorem of groupoid homomorphisms.
III week exercisesGroupoid. Homomorphism of groupoids.Fundamental theorem of groupoid homomorphisms.
IV week lecturesSemigroup. Some classes of semigroups.
IV week exercisesSemigroup. Some classes of semigroups.
V week lecturesAlgebra of natural numbers.Peano axioms.Algebra of sets, relation algebra and the algebra of functions.
V week exercisesAlgebra of natural numbers.Peano axioms.Algebra of sets, relation algebra and the algebra of functions.
VI week lecturesLattices. Boolean algebras.
VI week exercisesLattices. Boolean algebras.
VII week lecturesInterim exam.
VII week exercisesInterim exam.
VIII week lecturesGroups. The basic properties and examples.
VIII week exercisesGroups. The basic properties and examples.
IX week lecturesSubgroups. The basic properties of subgroups. Lagrange's theorem (group theory).
IX week exercisesSubgroups. The basic properties of subgroups. Lagrange's theorem (group theory).
X week lecturesNormal subgroups. Factor group.
X week exercisesNormal subgroups. Factor group.
XI week lecturesGroup homomorphism.Fundamental theorem of group homomorphisms.
XI week exercisesGroup homomorphism.Fundamental theorem of group homomorphisms.
XII week lecturesIsomorphism theorems for groups. Inner automorphisms.
XII week exercisesIsomorphism theorems for groups. Inner automorphisms.
XIII week lecturesCyclic groups. Commutator (derived) subgroup.
XIII week exercisesCyclic groups. Commutator (derived) subgroup.
XIV week lecturesCorrectional exam for interim exam.
XIV week exercisesCorrectional exam for interim exam.
XV week lecturesFree groups.
XV week exercisesFree groups.
Student workloadA week 2 hours of lectures 2 hours of exercise 2 hours and 40 minutes of student work, including consultations During the semester Teachig and the final exam: 16x(5h 20min)=85h i 20 min Necessery preparation (before semester administration, enrollment and verification): 2x5h 20min=10h 40min. Total hours for the course::4x30 =120 hours Additional work : 0 to 24 hours Structure:: 85h 40min(lecture)+10h40min(preparation)+24h (additional work)
Per weekPer semester
5 credits x 40/30=6 hours and 40 minuts
2 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
2 hour(s) i 40 minuts
of independent work, including consultations 		Classes and final exam:
6 hour(s) i 40 minuts x 16 =106 hour(s) i 40 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
6 hour(s) i 40 minuts x 2 =13 hour(s) i 20 minuts
Total workload for the subject:
5 x 30=150 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
30 hour(s) i 0 minuts
Workload structure: 106 hour(s) i 40 minuts (cources), 13 hour(s) i 20 minuts (preparation), 30 hour(s) i 0 minuts (additional work)
Student obligations Students have to attend lectures and exercises, take interim exam and final exam.
ConsultationsAfter the lectures.
Literature Introduction to Algebra ,A.I.Kostrikin, Uvod u opstu algebru,V. Dasic, Zbirka rijesenih zadataka iz Algebre,(I dio),B.Zekovic,V..A..Artimonov Zbirka zadataka iz Algebre, Z.Stojakovic,Z.Mijajlovic
Examination methodsPlaned form of assesment : - Interim exam 50 points - Final exam 50 points Grade A B C D E 91-100 81-90 71-80 61-70 51-60
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / DISCRETE MATHEMATICS 1

Course:DISCRETE MATHEMATICS 1/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
6593Obavezan353+1+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises
Student workload
Per weekPer semester
5 credits x 40/30=6 hours and 40 minuts
3 sat(a) theoretical classes
0 sat(a) practical classes
1 excercises
2 hour(s) i 40 minuts
of independent work, including consultations 		Classes and final exam:
6 hour(s) i 40 minuts x 16 =106 hour(s) i 40 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
6 hour(s) i 40 minuts x 2 =13 hour(s) i 20 minuts
Total workload for the subject:
5 x 30=150 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
30 hour(s) i 0 minuts
Workload structure: 106 hour(s) i 40 minuts (cources), 13 hour(s) i 20 minuts (preparation), 30 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / ANALYSIS 3

Course:ANALYSIS 3/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
3969Obavezan363+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises
Student workload
Per weekPer semester
6 credits x 40/30=8 hours and 0 minuts
3 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
3 hour(s) i 0 minuts
of independent work, including consultations 		Classes and final exam:
8 hour(s) i 0 minuts x 16 =128 hour(s) i 0 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
8 hour(s) i 0 minuts x 2 =16 hour(s) i 0 minuts
Total workload for the subject:
6 x 30=180 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
36 hour(s) i 0 minuts
Workload structure: 128 hour(s) i 0 minuts (cources), 16 hour(s) i 0 minuts (preparation), 36 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / PROGRAMMING 1

Course:PROGRAMMING 1/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
3983Obavezan363+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises
Student workload
Per weekPer semester
6 credits x 40/30=8 hours and 0 minuts
3 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
3 hour(s) i 0 minuts
of independent work, including consultations 		Classes and final exam:
8 hour(s) i 0 minuts x 16 =128 hour(s) i 0 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
8 hour(s) i 0 minuts x 2 =16 hour(s) i 0 minuts
Total workload for the subject:
6 x 30=180 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
36 hour(s) i 0 minuts
Workload structure: 128 hour(s) i 0 minuts (cources), 16 hour(s) i 0 minuts (preparation), 36 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / ENGLISH LANGUAGE 4

Course:ENGLISH LANGUAGE 4/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
5548Obavezan422+1+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites No prerequisites
Aims Students need to regularly attend classes, make a presentation and take a mid term and a final exam.
Learning outcomes After students pass the exam they will be able to: -distinguish, understand and use complex mathematical terminology in English from the areas of differential geometry, topology, vector products, mathematical analysis, -read more complex mathematical expressions in English, -understand basic messages of popular and expert texts, -carry out oral and written conversation in English at an intermediate level -present orally a topic in English
Lecturer / Teaching assistantMilica Vukovic Stamatovic, Savo Kostic
MethodologyLectures and practice. Presentations in English on a topic studied. Studying for mid term and final exams. Consultations.
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesHomological algebra; grammar: Past simple vs Past continuous;
I week exercisesPast simple vs Past continuous;
II week lecturesGroup theory and generalizations: -ing forms and infinitive
II week exercises ing forms and infinitives;
III week lecturesTopological groups; grammar: modal verbs
III week exercisesmodal verbs exercises
IV week lecturesReal functions; grammar: Present perfect passive;
IV week exercisesPresent perfect passive;
V week lecturesMeasure and integrations; grammar: conditional sentences
V week exercisesvocabulary exercises
VI week lecturesMid-term test
VI week exercisesMid-term test
VII week lecturesRevision and error correction
VII week exercisesRevision and error correction
VIII week lecturesFunctions of a complex variable;
VIII week exercisesgrammar: revision of clauses
IX week lectures"Potential theory; grammar: prepositions
IX week exercisesrevision of prepositions
X week lecturesCommutative rings and algebras; Present simple vs continuous Grammar - modal verbs of probability
X week exercisesrevision of present tenses
XI week lecturesComplex variables and analytic spaces; grammar: Reported speech
XI week exercisesrevision of indirect speech
XII week lecturesSpecial functions; grammar: expressing contrast
XII week exercises expressing contrast
XIII week lecturesOrdinary differential equations; grammar: Making predictions
XIII week exercisesvocabulary exercises
XIV week lecturesPartial differential equations;
XIV week exercisesrevision of all texts
XV week lecturesPreparation for the final exam
XV week exercisesPreparation for the final exam
Student workload
Per weekPer semester
2 credits x 40/30=2 hours and 40 minuts
2 sat(a) theoretical classes
0 sat(a) practical classes
1 excercises
-1 hour(s) i 40 minuts
of independent work, including consultations 		Classes and final exam:
2 hour(s) i 40 minuts x 16 =42 hour(s) i 40 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
2 hour(s) i 40 minuts x 2 =5 hour(s) i 20 minuts
Total workload for the subject:
2 x 30=60 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
12 hour(s) i 0 minuts
Workload structure: 42 hour(s) i 40 minuts (cources), 5 hour(s) i 20 minuts (preparation), 12 hour(s) i 0 minuts (additional work)
Student obligations Students need to regularly attend classes, make a presentation and take a mid term and a final exam.
Consultationsonce a week for 2 hours
Literature"English for Mathematics" reader
Examination methods
Special remarksAdopted on 21-7-2016: http://senat.ucg.ac.me/data/1469020997-Akreditacija%20PMF%202017%20final.pdf
Comment/
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / ALGEBRA 2

Course:ALGEBRA 2/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
3972Obavezan452+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites None
Aims This course is aimed to introduce students with basic notions in algebra and its applications in mathematical and technical sciences
Learning outcomes On successful completion of this course, students will be able to: - describe the group of symmetry and isometry, direct product of groups and the symmetric group with the proof of the Cayley theorem - examine the structure of a ring in detail and define subrings, ideals, maximal and prime, quotient rings and direct products of rings - prove the Fundamental theorem on homomorphisms of rings, the first and second theorem of isomorphisms of rings with applications - define the characteristic of a ring and prove basic theorems related to it - describe the fraction field - describe the ring of polynomials and polynomial functions and prove the basic theorems about the factorization of polynomials with applications - describe the construction of field extensions and Euclidean rings, especially the Euclid’s algorithm of dividing with residue with applications
Lecturer / Teaching assistantProf.dr Biljana Zeković - lecturer, Dragana Borović - teaching assistant
MethodologyLectures and exercises, consultations, doing homework asignments
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesSymmetrical group. Cayley Theorem
I week exercisesSymmetrical group. Cayley Theorem
II week lecturesGroup of symmetries and isometries
II week exercises Group of symmetries and isometries
III week lecturesDirect product of groups. Some properties
III week exercisesDirect product of groups. Some properties
IV week lecturesRing. Field. Basic properties. (first homework assignment)
IV week exercisesRing. Field. Basic properties. (first homework assignment)
V week lecturesIdeal of ring. Factor-ring.
V week exercisesIdeal of ring. Factor-ring.
VI week lecturesCharacteristic of ring. Homomorphism of rings
VI week exercisesCharacteristic of ring. Homomorphism of rings
VII week lecturesHomomorphism-theorem.
VII week exercisesHomomorphism-theorem.
VIII week lecturesI written exam
VIII week exercisesI written exam
IX week lecturesSubdirect product of rings. Isomorphism-theorems of rings.
IX week exercisesSubdirect product of rings. Isomorphism-theorems of rings.
X week lecturesMaximal and prime ideals. Quotient field. (second homework assignment)
X week exercisesMaximal and prime ideals. Quotient field. (second homework assignment)
XI week lecturesPolynomial ring.
XI week exercisesPolynomial ring.
XII week lecturesRing of polynomial functions.
XII week exercisesRing of polynomial functions.
XIII week lecturesII written exam
XIII week exercisesII written exam
XIV week lecturesExtension of a field (basic concepts).
XIV week exercisesExtension of a field (basic concepts).
XV week lecturesEuclidean ring. (third homework assignment)
XV week exercisesEuclidean ring. (third homework assignment)
Student workload2 hours of lectures, 2 hours of exercises, 1 hour 20 minutes of individual work
Per weekPer semester
5 credits x 40/30=6 hours and 40 minuts
2 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
2 hour(s) i 40 minuts
of independent work, including consultations 		Classes and final exam:
6 hour(s) i 40 minuts x 16 =106 hour(s) i 40 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
6 hour(s) i 40 minuts x 2 =13 hour(s) i 20 minuts
Total workload for the subject:
5 x 30=150 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
30 hour(s) i 0 minuts
Workload structure: 106 hour(s) i 40 minuts (cources), 13 hour(s) i 20 minuts (preparation), 30 hour(s) i 0 minuts (additional work)
Student obligations Attendance, doing homework assignments, taking two written and the final exam
Consultations1 hour weekly (lectures), 1 hour weekly (exercises)
LiteratureUVOD U OPŠTU ALGEBRU, V. Dašić, ALGEBRA, G. Kalajdžić ZBIRKA REŠENIH ZADATAKA IZ ALGEBRE ( I deo), B. Zeković, V. A. Artamonov ZBIRKA ZADATAKA IZ ALGEBRE, Z.Stojaković, Ž.Mijajlović
Examination methodsThree homework assignments ( 2 points each), two written exams (21 point each) and the final exam (50 points), regular attendance (2 points) Everything is in written form, with oral examination in case of any unclarity or doubt that cheating devices wer
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / DISCRETE MATHEMATICS 2

Course:DISCRETE MATHEMATICS 2/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
6592Obavezan453+1+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises
Student workload
Per weekPer semester
5 credits x 40/30=6 hours and 40 minuts
3 sat(a) theoretical classes
0 sat(a) practical classes
1 excercises
2 hour(s) i 40 minuts
of independent work, including consultations 		Classes and final exam:
6 hour(s) i 40 minuts x 16 =106 hour(s) i 40 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
6 hour(s) i 40 minuts x 2 =13 hour(s) i 20 minuts
Total workload for the subject:
5 x 30=150 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
30 hour(s) i 0 minuts
Workload structure: 106 hour(s) i 40 minuts (cources), 13 hour(s) i 20 minuts (preparation), 30 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / DIFFERENTIAL EQUATIONS

Course:DIFFERENTIAL EQUATIONS/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
497Obavezan463+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises
Student workload
Per weekPer semester
6 credits x 40/30=8 hours and 0 minuts
3 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
3 hour(s) i 0 minuts
of independent work, including consultations 		Classes and final exam:
8 hour(s) i 0 minuts x 16 =128 hour(s) i 0 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
8 hour(s) i 0 minuts x 2 =16 hour(s) i 0 minuts
Total workload for the subject:
6 x 30=180 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
36 hour(s) i 0 minuts
Workload structure: 128 hour(s) i 0 minuts (cources), 16 hour(s) i 0 minuts (preparation), 36 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / ANALYSIS 4

Course:ANALYSIS 4/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
3971Obavezan463+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises
Student workload
Per weekPer semester
6 credits x 40/30=8 hours and 0 minuts
3 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
3 hour(s) i 0 minuts
of independent work, including consultations 		Classes and final exam:
8 hour(s) i 0 minuts x 16 =128 hour(s) i 0 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
8 hour(s) i 0 minuts x 2 =16 hour(s) i 0 minuts
Total workload for the subject:
6 x 30=180 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
36 hour(s) i 0 minuts
Workload structure: 128 hour(s) i 0 minuts (cources), 16 hour(s) i 0 minuts (preparation), 36 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / PROGRAMMING 2

Course:PROGRAMMING 2/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
3976Obavezan463+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lecturesLogarithms. Grammar: Indirect Speech
VI week exercisesRevision of terminology and grammar
VII week lecturesRevision for the mid-term test
VII week exercisesRevision for the mid-term test
VIII week lecturesMid-term test
VIII week exercisesMid-term test
IX week lecturesEquations. Reading: Applied Mathematics
IX week exercisesReducing and expanding clauses. Articles
X week lecturesInequalities. Reading: Combinatorics
X week exercisesModal verbs. Revision of grammar
XI week lecturesMake-up mid-term test.
XI week exercisesMake-up mid-term test.
XII week lecturesMatrices, matrix solutions of linear systems.
XII week exercisesReading: Discrete Mathematics
XIII week lecturesFunctions. The Language of Proof
XIII week exercisesSpeaking: Selected topics
XIV week lecturesPresentations
XIV week exercisesPresentations
XV week lecturesRevision
XV week exercisesRevision
Student workload3 credits x 40/30 = 4 hours
Per weekPer semester
6 credits x 40/30=8 hours and 0 minuts
3 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
3 hour(s) i 0 minuts
of independent work, including consultations 		Classes and final exam:
8 hour(s) i 0 minuts x 16 =128 hour(s) i 0 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
8 hour(s) i 0 minuts x 2 =16 hour(s) i 0 minuts
Total workload for the subject:
6 x 30=180 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
36 hour(s) i 0 minuts
Workload structure: 128 hour(s) i 0 minuts (cources), 16 hour(s) i 0 minuts (preparation), 36 hour(s) i 0 minuts (additional work)
Student obligations Regular attendance, presenting in class, taking the mid-term and the final exam.
Consultations
LiteratureEnglish for Mathematics. Krukiewicz-Gacek and Trzaska. AGH University of Science and Technology Press: Krakow. 2012. English for Students of Mathematics. Milica Vuković Stamatović - skripta + handouts
Examination methodsMid-term test: 40 points Presentation: 5 points Attendance: 5 points Final exam: 50 points
Special remarksClasses are in English.
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / OBJECT ORIENTED PROGRAMMING

Course:OBJECT ORIENTED PROGRAMMING/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
1358Obavezan532+1+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims Through this course students learn basic and advanced concepts of object-oriented programming, and practical programming in the C++ language.
Learning outcomes Once a student passes the exam, will be able to: i) write computer programs in the C++ language; ii) use the Class concept for software implementation; iii)use inheritance and abstract classes in order to connect different software modules; iv) reuse program code by means of the object-oriented programming concepts; v) create generic classes and operator functions in the C++ language.
Lecturer / Teaching assistantDoc. dr Aleksandar Popović, Mr Igor Ivanović
MethodologyLectures, exercises in computer classroom/laboratory. Learning and practical exercises. Consultations.
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesIntroduction, Basic notions in the object-oriented programming paradigm
I week exercisesIntroduction, Basic notions in the object-oriented programming paradigm
II week lecturesBasics of the C++ language, Overview of concepts inherited from the C language
II week exercises Basics of the C++ language, Overview of concepts inherited from the C language
III week lecturesIntroduction to classes and objects, Interface and implementation of a class
III week exercisesIntroduction to classes and objects, Interface and implementation of a class
IV week lecturesObjects and methods.References. Pointer named this
IV week exercisesObjects and methods.References. Pointer named this
V week lecturesConstructors and destructors
V week exercisesConstructors and destructors
VI week lecturesInline methods, Const methods, Objects as function arguments
VI week exercisesInline methods, Const methods, Objects as function arguments
VII week lecturesStatic attributes of a class, Static methods, Friendship relation between classes
VII week exercisesStatic attributes of a class, Static methods, Friendship relation between classes
VIII week lecturesInheritance
VIII week exercisesInheritance
IX week lecturesCOLLOQUIUM I
IX week exercisesCOLLOQUIUM I
X week lecturesPolymorphism
X week exercisesPolymorphism
XI week lecturesMultiple Inheritance. Abstract classes
XI week exercisesMultiple Inheritance. Abstract classes
XII week lecturesOperator overloading, Operator functions
XII week exercisesOperator overloading, Operator functions
XIII week lecturesException handling
XIII week exercisesException handling
XIV week lecturesGeneric classes and methods
XIV week exercisesGeneric classes and methods
XV week lecturesCOLLOQUIUM I
XV week exercisesCOLLOQUIUM I
Student workloadTeaching and final exam: 5 hours and 20 minutes x 16 = 85 hours and 20 minutes Preparation before the beginning of the semester 2 x (5 hours and 20 minutes) = 10 hours i 40 minutes Total work hours for the course 4x30 = 120 hours Additional work for preparation of the exam in remedial exam period, including final exam from 0 to 24 sati (the remaining time of the first two items to the total work hours for the subject of 120 hours) Structure: 85 hours and 20 minutes(lectures) + 10 hours and 40 minutes (preparation) +24 hours (additional work)
Per weekPer semester
3 credits x 40/30=4 hours and 0 minuts
2 sat(a) theoretical classes
0 sat(a) practical classes
1 excercises
1 hour(s) i 0 minuts
of independent work, including consultations 		Classes and final exam:
4 hour(s) i 0 minuts x 16 =64 hour(s) i 0 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
4 hour(s) i 0 minuts x 2 =8 hour(s) i 0 minuts
Total workload for the subject:
3 x 30=90 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
18 hour(s) i 0 minuts
Workload structure: 64 hour(s) i 0 minuts (cources), 8 hour(s) i 0 minuts (preparation), 18 hour(s) i 0 minuts (additional work)
Student obligations Students are required to attend classes, as well as to do home exercises, and colloquia.
Consultations
LiteratureD. Milićev, Objektno-orijentisano programiranje na jeziku C++, Mikroknjiga, Beograd
Examination methods2 colloquia 70 points total (35 points for each), Final exam 30 points. The passing grade is obtained with at least 45 points
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / NUMERICAL ANALYSIS

Course:NUMERICAL ANALYSIS/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
502Obavezan552+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites None.
Aims The aim of the course is for students to adopt and master the basics of mathematical analysis: limit theory, elements of differential and integral calculus and the theory of series.
Learning outcomes On successful completion of the course, students will be able to: 1. Define the basic notions of mathematical analysis 1: the set of real numbers, limit of a sequence and function, differentiability of a function, derivative and indefinite integral on an interval. 2. State the basic properties of the set of real numbers. 3. Derive basic propositions in limit theory and differential calculus, determine when a sequence or function has a limit, or when the function is continuous or differentiable. 4. Examine and associate properties of functions of a real variable using differential calculus. 5. Apply the acquired knowledge to solving different tasks related to the stated content of mathematical analysis. 6. Apply the acquired knowledge to solving real tasks and problems.
Lecturer / Teaching assistantProf. dr Žarko Pavićević –lecturer, Lazar Obradović – teaching assistant
MethodologyLectures, exercises, homework assignments, consultations, written exams.
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesIntroducing students to basic topics studied in this course.
I week exercisesIntroducing students to basic topics studied in this course.
II week lecturesThe set of real numbers – axiomatic construction.
II week exercises The set of real numbers – axiomatic construction.
III week lecturesCompleteness principles of the set of real numbers.
III week exercisesCompleteness principles of the set of real numbers.
IV week lecturesTheory of convergent sequences.
IV week exercisesTheory of convergent sequences.
V week lecturesBolzano’s and Cauchy’s theorem for sequences. Banach fixed-point theorem.
V week exercisesBolzano’s and Cauchy’s theorem for sequences. Banach fixed-point theorem.
VI week lecturesTopology on the set of real numbers.
VI week exercisesTopology on the set of real numbers.
VII week lecturesStudy break
VII week exercisesStudy break
VIII week lecturesLimit of a function. Continuity of a function at a point.
VIII week exercisesLimit of a function. Continuity of a function at a point.
IX week lecturesBasis of a set. Convergence and continuity of a function with regard to the basis of the set.
IX week exercisesBasis of a set. Convergence and continuity of a function with regard to the basis of the set.
X week lecturesGlobal properties of functions which are continuous on a closed interval. First written exam
X week exercisesGlobal properties of functions which are continuous on a closed interval. First written exam
XI week lecturesUniform continuity of functions
XI week exercisesUniform continuity of functions
XII week lecturesDifferentiability of a function at a point. Derivative. Higher order derivatives.
XII week exercisesDifferentiability of a function at a point. Derivative. Higher order derivatives.
XIII week lecturesMean value theorem of differential calculus. Bernouli – L’Hopital’s rule. Taylor formulas.
XIII week exercisesMean value theorem of differential calculus. Bernouli – L’Hopital’s rule. Taylor formulas.
XIV week lecturesMonotonicity and extrema of differentiable functions. Convexity of functions. Inflection points.
XIV week exercisesMonotonicity and extrema of differentiable functions. Convexity of functions. Inflection points.
XV week lecturesExamining properties and drawing the graph of a function. Second written exam
XV week exercisesExamining properties and drawing the graph of a function. Second written exam
Student workload10 credits x 30 hours = 300 hours
Per weekPer semester
5 credits x 40/30=6 hours and 40 minuts
2 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
2 hour(s) i 40 minuts
of independent work, including consultations 		Classes and final exam:
6 hour(s) i 40 minuts x 16 =106 hour(s) i 40 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
6 hour(s) i 40 minuts x 2 =13 hour(s) i 20 minuts
Total workload for the subject:
5 x 30=150 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
30 hour(s) i 0 minuts
Workload structure: 106 hour(s) i 40 minuts (cources), 13 hour(s) i 20 minuts (preparation), 30 hour(s) i 0 minuts (additional work)
Student obligations Students are required to attend classes, do the homework assignments and take all exams.
Consultations1 hour a week (lectures) + 1 hour a week (exercises)
LiteratureV. I. Gavrilov,,Ž. Pavićević, Matematička analiza I, I.M. Lavrentjev, R. Šćepanović, Zbirka zadataka iz mat. analize I
Examination methods4 homework assignments, 2 points each (8 points in total). 2 points for attendance. 2 written exams, 20 points each (40 points in total). Final exam, 50 points. Students who collect at least 51 points pass the course.
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / COMPLEX ANALYSIS 1

Course:COMPLEX ANALYSIS 1/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
3970Obavezan552+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises
Student workload
Per weekPer semester
5 credits x 40/30=6 hours and 40 minuts
2 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
2 hour(s) i 40 minuts
of independent work, including consultations 		Classes and final exam:
6 hour(s) i 40 minuts x 16 =106 hour(s) i 40 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
6 hour(s) i 40 minuts x 2 =13 hour(s) i 20 minuts
Total workload for the subject:
5 x 30=150 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
30 hour(s) i 0 minuts
Workload structure: 106 hour(s) i 40 minuts (cources), 13 hour(s) i 20 minuts (preparation), 30 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / FUNCTIONAL ANALYSIS

Course:FUNCTIONAL ANALYSIS/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
4099Obavezan553+1+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites None.
Aims The aim of the course is for students to adopt and master the basics of mathematical analysis: limit theory, elements of differential and integral calculus and the theory of series.
Learning outcomes On successful completion of the course, students will be able to: 1. Define the basic notions of mathematical analysis 1: the set of real numbers, limit of a sequence and function, differentiability of a function, derivative and indefinite integral on an interval. 2. State the basic properties of the set of real numbers. 3. Derive basic propositions in limit theory and differential calculus, determine when a sequence or function has a limit, or when the function is continuous or differentiable. 4. Examine and associate properties of functions of a real variable using differential calculus. 5. Apply the acquired knowledge to solving different tasks related to the stated content of mathematical analysis. 6. Apply the acquired knowledge to solving real tasks and problems.
Lecturer / Teaching assistantProf. dr Žarko Pavićević –lecturer, Lazar Obradović – teaching assistant
MethodologyLectures, exercises, homework assignments, consultations, written exams.
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesIntroducing students to basic topics studied in this course.
I week exercisesIntroducing students to basic topics studied in this course.
II week lecturesThe set of real numbers – axiomatic construction.
II week exercises The set of real numbers – axiomatic construction.
III week lecturesCompleteness principles of the set of real numbers.
III week exercisesCompleteness principles of the set of real numbers.
IV week lecturesTheory of convergent sequences.
IV week exercisesTheory of convergent sequences.
V week lecturesBolzano’s and Cauchy’s theorem for sequences. Banach fixed-point theorem.
V week exercisesBolzano’s and Cauchy’s theorem for sequences. Banach fixed-point theorem.
VI week lecturesTopology on the set of real numbers.
VI week exercisesTopology on the set of real numbers.
VII week lecturesStudy break
VII week exercisesStudy break
VIII week lecturesLimit of a function. Continuity of a function at a point.
VIII week exercisesLimit of a function. Continuity of a function at a point.
IX week lecturesBasis of a set. Convergence and continuity of a function with regard to the basis of the set.
IX week exercisesBasis of a set. Convergence and continuity of a function with regard to the basis of the set.
X week lecturesGlobal properties of functions which are continuous on a closed interval. First written exam
X week exercisesGlobal properties of functions which are continuous on a closed interval. First written exam
XI week lecturesUniform continuity of functions
XI week exercisesUniform continuity of functions
XII week lecturesDifferentiability of a function at a point. Derivative. Higher order derivatives.
XII week exercisesDifferentiability of a function at a point. Derivative. Higher order derivatives.
XIII week lecturesMean value theorem of differential calculus. Bernouli – L’Hopital’s rule. Taylor formulas.
XIII week exercisesMean value theorem of differential calculus. Bernouli – L’Hopital’s rule. Taylor formulas.
XIV week lecturesMonotonicity and extrema of differentiable functions. Convexity of functions. Inflection points.
XIV week exercisesMonotonicity and extrema of differentiable functions. Convexity of functions. Inflection points.
XV week lecturesExamining properties and drawing the graph of a function. Second written exam
XV week exercisesExamining properties and drawing the graph of a function. Second written exam
Student workload10 credits x 30 hours = 300 hours
Per weekPer semester
5 credits x 40/30=6 hours and 40 minuts
3 sat(a) theoretical classes
0 sat(a) practical classes
1 excercises
2 hour(s) i 40 minuts
of independent work, including consultations 		Classes and final exam:
6 hour(s) i 40 minuts x 16 =106 hour(s) i 40 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
6 hour(s) i 40 minuts x 2 =13 hour(s) i 20 minuts
Total workload for the subject:
5 x 30=150 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
30 hour(s) i 0 minuts
Workload structure: 106 hour(s) i 40 minuts (cources), 13 hour(s) i 20 minuts (preparation), 30 hour(s) i 0 minuts (additional work)
Student obligations Students are required to attend classes, do the homework assignments and take all exams.
Consultations1 hour a week (lectures) + 1 hour a week (exercises)
LiteratureV. I. Gavrilov,,Ž. Pavićević, Matematička analiza I, I.M. Lavrentjev, R. Šćepanović, Zbirka zadataka iz mat. analize I
Examination methods4 homework assignments, 2 points each (8 points in total). 2 points for attendance. 2 written exams, 20 points each (40 points in total). Final exam, 50 points. Students who collect at least 51 points pass the course.
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / DATABASE SYSTEMS

Course:DATABASE SYSTEMS/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
512Obavezan563+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites None.
Aims The aim of the course is for students to adopt and master the basics of mathematical analysis: limit theory, elements of differential and integral calculus and the theory of series.
Learning outcomes On successful completion of the course, students will be able to: 1. Define the basic notions of mathematical analysis 1: the set of real numbers, limit of a sequence and function, differentiability of a function, derivative and indefinite integral on an interval. 2. State the basic properties of the set of real numbers. 3. Derive basic propositions in limit theory and differential calculus, determine when a sequence or function has a limit, or when the function is continuous or differentiable. 4. Examine and associate properties of functions of a real variable using differential calculus. 5. Apply the acquired knowledge to solving different tasks related to the stated content of mathematical analysis. 6. Apply the acquired knowledge to solving real tasks and problems.
Lecturer / Teaching assistantProf. dr Žarko Pavićević –lecturer, Lazar Obradović – teaching assistant
MethodologyLectures, exercises, homework assignments, consultations, written exams.
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesIntroducing students to basic topics studied in this course.
I week exercisesIntroducing students to basic topics studied in this course.
II week lecturesThe set of real numbers – axiomatic construction.
II week exercises The set of real numbers – axiomatic construction.
III week lecturesCompleteness principles of the set of real numbers.
III week exercisesCompleteness principles of the set of real numbers.
IV week lecturesTheory of convergent sequences.
IV week exercisesTheory of convergent sequences.
V week lecturesBolzano’s and Cauchy’s theorem for sequences. Banach fixed-point theorem.
V week exercisesBolzano’s and Cauchy’s theorem for sequences. Banach fixed-point theorem.
VI week lecturesTopology on the set of real numbers.
VI week exercisesTopology on the set of real numbers.
VII week lecturesStudy break
VII week exercisesStudy break
VIII week lecturesLimit of a function. Continuity of a function at a point.
VIII week exercisesLimit of a function. Continuity of a function at a point.
IX week lecturesBasis of a set. Convergence and continuity of a function with regard to the basis of the set.
IX week exercisesBasis of a set. Convergence and continuity of a function with regard to the basis of the set.
X week lecturesGlobal properties of functions which are continuous on a closed interval. First written exam
X week exercisesGlobal properties of functions which are continuous on a closed interval. First written exam
XI week lecturesUniform continuity of functions
XI week exercisesUniform continuity of functions
XII week lecturesDifferentiability of a function at a point. Derivative. Higher order derivatives.
XII week exercisesDifferentiability of a function at a point. Derivative. Higher order derivatives.
XIII week lecturesMean value theorem of differential calculus. Bernouli – L’Hopital’s rule. Taylor formulas.
XIII week exercisesMean value theorem of differential calculus. Bernouli – L’Hopital’s rule. Taylor formulas.
XIV week lecturesMonotonicity and extrema of differentiable functions. Convexity of functions. Inflection points.
XIV week exercisesMonotonicity and extrema of differentiable functions. Convexity of functions. Inflection points.
XV week lecturesExamining properties and drawing the graph of a function. Second written exam
XV week exercisesExamining properties and drawing the graph of a function. Second written exam
Student workload10 credits x 30 hours = 300 hours
Per weekPer semester
6 credits x 40/30=8 hours and 0 minuts
3 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
3 hour(s) i 0 minuts
of independent work, including consultations 		Classes and final exam:
8 hour(s) i 0 minuts x 16 =128 hour(s) i 0 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
8 hour(s) i 0 minuts x 2 =16 hour(s) i 0 minuts
Total workload for the subject:
6 x 30=180 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
36 hour(s) i 0 minuts
Workload structure: 128 hour(s) i 0 minuts (cources), 16 hour(s) i 0 minuts (preparation), 36 hour(s) i 0 minuts (additional work)
Student obligations Students are required to attend classes, do the homework assignments and take all exams.
Consultations1 hour a week (lectures) + 1 hour a week (exercises)
LiteratureV. I. Gavrilov,,Ž. Pavićević, Matematička analiza I, I.M. Lavrentjev, R. Šćepanović, Zbirka zadataka iz mat. analize I
Examination methods4 homework assignments, 2 points each (8 points in total). 2 points for attendance. 2 written exams, 20 points each (40 points in total). Final exam, 50 points. Students who collect at least 51 points pass the course.
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / ADVANCED DATABASE SYSTEMS

Course:ADVANCED DATABASE SYSTEMS/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
1351Obavezan563+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites Introduction to Computer Science, Programming, Operating systems, Database Systems
Aims Through this course students learn advanced concepts of databases, their internal structure, methods of implementation, principles and criteria of their design. In addition, students in exercises learn programming related to databases.
Learning outcomes After passing this exam, student will be able to: 1. understand the advanced concepts of database systems and their internal structure; 2. know theoretical basis of logical database design; 3 3. understand ways of realization, the principles and criteria of the design of the database management and use them in programming; 4. understand the process of execution and query optimization; 5. use at advanced level of main modern systems for database management; 6. design and develop applications using modern programming tools and the SQL language
Lecturer / Teaching assistantprof. dr. Predrag Stanisic, doc. Dr. Aleksandar Popovic
MethodologyLectures, exercises in computer classroom / laboratory. Learning and practical exercises. Consultations.
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesAdministration of database systems. Safety systems. Users. Your rights. Cast. Backup data archiving. Replication.
I week exercisesAdministration database systems. Safety systems. Users. Your rights. Cast. Backup data archiving. Replication.
II week lecturesThe design of a relational database. Design errors and anomalies. Decomposition. Normal forms.
II week exercises The design of a relational database. Design errors and anomalies. Decomposition. Normal forms.
III week lecturesNormalization using functional dependencies. 1NF. 2NF. 3NF. BCNF
III week exercisesNormalization using functional dependencies. 1NF. 2NF. 3NF. BCNF
IV week lecturesNormalization using multivalued dependencies. 4NF. Normalization using depending on the combination. 5NF. Domain-key normal form.
IV week exercisesNormalization using multivalued dependencies. 4NF. Normalization using depending on the combination. 5NF. Domain-key normal form.
V week lecturesQuery processing. Query optimization. Phases. The information in the catalog necessary for the evaluation of the plan. Assessment criteria. Execution of queries.
V week exercisesQuery processing. Query optimization. Phases. The information in the catalog necessary for the evaluation of the plan. Assessment criteria. Execution of queries.
VI week lecturesChoice of execution plan. Assessment and execution of selection. Assessment and execution of joins. Other operations. Evaluation of expression.
VI week exercisesChoice of execution plan. Assessment and execution of selection. Assessment and execution of joins. Other operations. Evaluation of expression.
VII week lecturesColloquium
VII week exercisesColloquium
VIII week lecturesTransaction. ACID properties of transactions. Seriability.
VIII week exercisesTransaction. ACID properties of transactions. Seriability.
IX week lecturesTesting of seriability. Transactions in SQL.
IX week exercisesTesting of seriability. Transactions in SQL.
X week lecturesControl of concurrency. Lock protocols . Timestamp protocols . Protocols based on validation. Granularity. Muliversion schemes. Deadlocks.
X week exercisesControl of concurrency. Lock protocols . Timestamp protocols . Protocols based on validation. Granularity. Muliversion schemes. Deadlocks.
XI week lecturesRecovering from failure. Types of failures. Recovery and Atomicity. Recovery schemes using journal (log). Shadow paging. Recovering from concurrent transactions. Buffer management. Faults with loss of stable memory. Advanced recovery techniques.
XI week exercisesRecovering from failure. Types of failures. Recovery and Atomicity. Recovery schemes using journal (log). Shadow paging. Recovering from concurrent transactions. Buffer management. Faults with loss of stable memory. Advanced recovery techniques.
XII week lecturesParallel databases. Parallelism in databases. Parallelism between queries. Parallelism within queries. Parallelism within operation. Parallelism between operations. Design of parallel systems
XII week exercisesParallel databases. Parallelism in databases. Parallelism between queries. Parallelism within queries. Parallelism within operation. Parallelism between operations. Design of parallel systems
XIII week lecturesDistributed databases. Distributed systems. Network transparency. Fragmentation of data. Catalog management. Distributed query processing
XIII week exercisesDistributed databases. Distributed systems. Network transparency. Fragmentation of data. Catalog management. Distributed query processing
XIV week lecturesNew applications. Systems for decision support. Data analysis. Data mining. Data warehousing.
XIV week exercisesNew applications. Systems for decision support. Data analysis. Data mining. Data warehousing.
XV week lecturesSpatial and geographic databases. Multimedia database. Databases on the Internet. Databases in biology. The genome project. Digital libraries.
XV week exercisesProject presentation
Student workload6 credits x 40/30 = 8 hours Working hours structure: 3 hours for teaching 3 hour for exercises 2 hours for individual work, including consultations per semester Teaching and the final exam: 8 x 16 = 128 hours Necessary preparation (before semester Administration semester): 2 x (8 hours) = 16 hours Total work hours for the course: 6x30 = 180 hours of additional work for exams preparing correction of final exam, including the exam taking from 0 to 36 hours (the remaining time of the first two items to the total work hours for the course, 180 hours) structure: 128 hours (lectures) + 16 hours (preparation) + 36 hours (additional work)
Per weekPer semester
6 credits x 40/30=8 hours and 0 minuts
3 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
3 hour(s) i 0 minuts
of independent work, including consultations 		Classes and final exam:
8 hour(s) i 0 minuts x 16 =128 hour(s) i 0 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
8 hour(s) i 0 minuts x 2 =16 hour(s) i 0 minuts
Total workload for the subject:
6 x 30=180 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
36 hour(s) i 0 minuts
Workload structure: 128 hour(s) i 0 minuts (cources), 16 hour(s) i 0 minuts (preparation), 36 hour(s) i 0 minuts (additional work)
Student obligations Obligations of the students in the course, students are required to attend classes, as well as doing home exercises, and working test.
ConsultationsCabinet
LiteratureSilberchatz, Korth: Database Systems Concepts, McGraw-Hill CJ Date An Introduction to Database Systems, Addison-Wesley
Examination methods5 home exercises 10 points total (2 points for each homework assignment), - tests 20 points - Project 20 points - Final exam 50 points. Minimum 51 points.
Special remarksLectures are conducted for a group of about 40-60 students, exercises in groups of about 20 students.
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / PROBABILITY THEORY

Course:PROBABILITY THEORY/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
3975Obavezan563+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises
Student workload
Per weekPer semester
6 credits x 40/30=8 hours and 0 minuts
3 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
3 hour(s) i 0 minuts
of independent work, including consultations 		Classes and final exam:
8 hour(s) i 0 minuts x 16 =128 hour(s) i 0 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
8 hour(s) i 0 minuts x 2 =16 hour(s) i 0 minuts
Total workload for the subject:
6 x 30=180 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
36 hour(s) i 0 minuts
Workload structure: 128 hour(s) i 0 minuts (cources), 16 hour(s) i 0 minuts (preparation), 36 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / INTRODUCTION TO DIFFERENTIAL GEOMETRY

Course:INTRODUCTION TO DIFFERENTIAL GEOMETRY/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
4291Obavezan642+1+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises
Student workload
Per weekPer semester
4 credits x 40/30=5 hours and 20 minuts
2 sat(a) theoretical classes
0 sat(a) practical classes
1 excercises
2 hour(s) i 20 minuts
of independent work, including consultations 		Classes and final exam:
5 hour(s) i 20 minuts x 16 =85 hour(s) i 20 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
5 hour(s) i 20 minuts x 2 =10 hour(s) i 40 minuts
Total workload for the subject:
4 x 30=120 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
24 hour(s) i 0 minuts
Workload structure: 85 hour(s) i 20 minuts (cources), 10 hour(s) i 40 minuts (preparation), 24 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / VISUALIZATION AND COMPUTER GRAPHICS

Course:VISUALIZATION AND COMPUTER GRAPHICS/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
1349Obavezan642+1+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises
Student workload
Per weekPer semester
4 credits x 40/30=5 hours and 20 minuts
2 sat(a) theoretical classes
0 sat(a) practical classes
1 excercises
2 hour(s) i 20 minuts
of independent work, including consultations 		Classes and final exam:
5 hour(s) i 20 minuts x 16 =85 hour(s) i 20 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
5 hour(s) i 20 minuts x 2 =10 hour(s) i 40 minuts
Total workload for the subject:
4 x 30=120 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
24 hour(s) i 0 minuts
Workload structure: 85 hour(s) i 20 minuts (cources), 10 hour(s) i 40 minuts (preparation), 24 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / INTERNET TECHNOLOGIES

Course:INTERNET TECHNOLOGIES/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
11547Obavezan642+1+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises
Student workload
Per weekPer semester
4 credits x 40/30=5 hours and 20 minuts
2 sat(a) theoretical classes
0 sat(a) practical classes
1 excercises
2 hour(s) i 20 minuts
of independent work, including consultations 		Classes and final exam:
5 hour(s) i 20 minuts x 16 =85 hour(s) i 20 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
5 hour(s) i 20 minuts x 2 =10 hour(s) i 40 minuts
Total workload for the subject:
4 x 30=120 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
24 hour(s) i 0 minuts
Workload structure: 85 hour(s) i 20 minuts (cources), 10 hour(s) i 40 minuts (preparation), 24 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / COMPUTER NETWORKS

Course:COMPUTER NETWORKS/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
1301Obavezan653+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites No prerequisites
Aims The basics of hardware and software structure and basic characteristic of computer networks and their practical implementation.
Learning outcomes On successful completion of this course students should be able to: 1. Explain the impact of network communications on the modern world, and the Internet - basic platform for communication. 2. Describe basic functions, protocols, technologies and architecture used in modern computer networks. 3. Gain the skills necessary for the implementation and use of computer networks and specific Internet services. 4. Individually designs, installs and administers smaller computer networks.
Lecturer / Teaching assistantDr. Stevan Šćepanović - Lectures, M. Sc. Ivana Todorovic - Exercises
MethodologyLectures and seminars with the active participation of students, individual homeworks, group and individual consultations.
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesIntroduction. Basic concepts of computer networks and data transfer. Chronology of the origin and development of computer networks. Communications as an important segment of our lives.
I week exercisesExamples and practical assignments.
II week lecturesNetwork services. Classification of computer networks. Global and local networks. Principles of development of the modern computer networks.
II week exercises Examples and practical assignments.
III week lecturesNetwork architecture layers. ISO OSI and TCP / IP model. Application layer, functions and protocols.
III week exercisesExamples and practical assignments.
IV week lecturesTransport layer. Principles of reliable data transfer and data flow control.
IV week exercisesExamples and practical assignments.
V week lecturesNetwork layer of the OSI model. Commutation and commutation methods. Internetworking.
V week exercisesExamples and practical assignments.
VI week lecturesRouters, basic components and architecture.
VI week exercisesExamples and practical assignments.
VII week lecturesFirst test.
VII week exercisesExamples and practical assignments.
VIII week lecturesThe algorithms and routing protocols. IP addressing.
VIII week exercisesExamples and practical assignments.
IX week lecturesData link layer. Methods, tools and codes for data flow control, as well as data transfer reliability. Data link layer correction protocols. Addressing of Ethernet networks at the data link layer.
IX week exercisesExamples and practical assignments.
X week lecturesPhysical layer. The means and methods for data transfer. The concept and characteristics of the communication channel. Topology of computer networks. Data transfer medium.
X week exercisesExamples and practical assignments.
XI week lecturesCommunication (network) equipment. The principles and means of development of the global computer networks.
XI week exercisesExamples and practical assignments.
XII week lecturesLocal area networks and communication through the mediums with multiple access. Switches and switching.
XII week exercisesExamples and practical assignments.
XIII week lecturesPlanning and network cabling, administration and network management.
XIII week exercisesExamples and practical assignments.
XIV week lecturesSecond test.
XIV week exercisesExamples and practical assignments.
XV week lecturesCorrection of first or second test.
XV week exercisesConsultations.
Student workload4x30 = 120 hours in semester
Per weekPer semester
5 credits x 40/30=6 hours and 40 minuts
3 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
1 hour(s) i 40 minuts
of independent work, including consultations 		Classes and final exam:
6 hour(s) i 40 minuts x 16 =106 hour(s) i 40 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
6 hour(s) i 40 minuts x 2 =13 hour(s) i 20 minuts
Total workload for the subject:
5 x 30=150 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
30 hour(s) i 0 minuts
Workload structure: 106 hour(s) i 40 minuts (cources), 13 hour(s) i 20 minuts (preparation), 30 hour(s) i 0 minuts (additional work)
Student obligations Lessons attendance is mandatory for students, as well as doing home exercises, both tests and laboratory exercises.
ConsultationsMondays after lectures.
Literature1. Alberto Leon-Garcia, Indra Widjaja, “Communication Networks: Fundamental Concepts and Key Architectures”, McGraw-Hill Companies, Inc., New York, San Francisco, St. Louis, Lisabon, London, Madrid, 2004. 2. F. Halsall, - “Data Communications, Computer
Examination methodsWritten exams (3 times in semester), problem solving - homeworks, estimation of individual activity on lectures and seminars.
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / COMPILERS

Course:COMPILERS/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
1348Obavezan652+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites None.
Aims his course covers the design and implementation of translator-oriented systems software, focusing specifically on compilers, with some time spent on related topics such as interpreters and linkers.
Learning outcomes At the end of the course, the participant is expected to be able to: 1. Describe the design of a compiler/interpereter including its phases and components [Familiarity] 2. Use regular expressions and context-free grammars to specify the syntax of languages [Usage] 3. Identify the similarities and differences among various parsing techniques, grammar transformation techniques and type checking methods [Familiarity] 4. Distinguish between methods for scope and binding resolution and parameter passing [Familiarity] 5. Explain how programming language implementations typically organize memory [Familiarity] 6. Design and implement interpreter/compiler for simple language using declarative tools to generate parsers and scanners. [Usage]
Lecturer / Teaching assistantGoran Šuković, Savo Tomović.
MethodologyThe course lasts 14 weeks and consists of two 45-minutes session per week of face-to-face lectures together with a two 45-minute recitation class.
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesIntroduction. Compilers and interpreters.
I week exercisesMIPS intro.
II week lecturesGrammars and languages.
II week exercises MIPS: function call, recursion.
III week lecturesLexical Analysis
III week exercisesRegular Expressions. DFA. NFA.
IV week lecturesSyntax Analysis – "top-down" parsers.
IV week exercisesRE to NFA conversion. NFA to DFA conversion. DFA optimization.
V week lecturesSyntax Analysis – "Bottom-up" parsers. LR(0), SLR(1).
V week exercisesIntro to Flex/Lex.
VI week lecturesSyntax Analysis – LR(1), LALR.
VI week exercisesFlex examples.
VII week lecturesMidterm.
VII week exercisesMidterm.
VIII week lecturesSemantic Analysis.
VIII week exercisesBison/Yacc examples.
IX week lecturesType checking.
IX week exercisesSymbol table.
X week lecturesRuntime environment.
X week exercisesType checking using Bison/YACC.
XI week lecturesTAC
XI week exercisesTAC examples.
XII week lecturesCode generation
XII week exercisesCode generation examples.
XIII week lecturesCode generation (cont.)
XIII week exercisesCode generation with Bison/YACC
XIV week lecturesIntro to dataflow analysis. Loop optimization.
XIV week exercisesOptimization – examples.
XV week lectures
XV week exercises
Student workloadWeekly: 5x40/30 = 6 hours 40 minutes, Lectures: 1 hour 30 minutes, Labs: 1 hour 30 minutes, Other: 0, Individual works: 3 hours 40 minutes
Per weekPer semester
5 credits x 40/30=6 hours and 40 minuts
2 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
2 hour(s) i 40 minuts
of independent work, including consultations 		Classes and final exam:
6 hour(s) i 40 minuts x 16 =106 hour(s) i 40 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
6 hour(s) i 40 minuts x 2 =13 hour(s) i 20 minuts
Total workload for the subject:
5 x 30=150 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
30 hour(s) i 0 minuts
Workload structure: 106 hour(s) i 40 minuts (cources), 13 hour(s) i 20 minuts (preparation), 30 hour(s) i 0 minuts (additional work)
Student obligations
ConsultationsRoom 128.
LiteratureTorczon, Cooper – Engineering a Compiler, 2nd Edition (Morgan Kaufmann, 2011). Appel – Modern Compiler Implementation in Java (2nd edition), Cambridge University Press, 2002. Aho, Sethi, Ullman – Compilers: Principles, Techniques and Tools, 2nd Edition
Examination methods6 Homewoks (3-5% each, programming and pen-and-pencil) = 20% - Midterm 40% - Final exam 40%
Special remarksThe lecturer is able to offer course in English and Russian.
Commentwww.pmf.ac.me, prevodioci@rc.pmf.ac.me
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / INTERNET TECHNOLOGIES

Course:INTERNET TECHNOLOGIES/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
1797Obavezan652+1+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites None.
Aims Overview of current web languages and technologies. Ability to compare and contrast web programming with general purpose programming
Learning outcomes At the end of the course, the participant is expected to be able to: 1. Describe the constraints that the web puts on developers. [Familiarity] 2. Discuss how web standards impact software development and review an existing web application against a current web standard [Assessment] 3. Distinguish between content and formatting and use appropriate elements for organizing content and formatting. [Usage] 4. Design and implement client-side data validation [Usage] 5. Use various Application Programming Interfaces (APIs) [Usage] 6. Design and implement a simple web application. [Usage]
Lecturer / Teaching assistantGoran Šuković, Igor Ivanović.
MethodologyTwo face to face 45-minutes lecture sessions and one lab session per week. There are many active learning and problem solving activities integrated into the lecture and lab sessions.
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesIntroduction.
I week exercisesTools and platforms.
II week lecturesIntro to HTML5. Lists, tables, images.
II week exercises Basic HTML examples.
III week lecturesHTML5. Input elements. Semantic web.
III week exercisesHTML tables. Images. Multimedia.
IV week lecturesTest. CSS overview.
IV week exercisesCSS examples.
V week lecturesCSS layout.
V week exercisesCSS examples.
VI week lecturesAdvanced CSS.
VI week exercisesAdvanced CSS examples.
VII week lecturesTest. Intro to JQuery
VII week exercisesPHP intro. PHP control statements
VIII week lecturesJQuery (cont.) - event handling.
VIII week exercisesPHP functions.
IX week lecturesJQuery (cont.)
IX week exercisesPHP – strings and arrays
X week lecturesTest. XML.
X week exercisesPHP – regular expressions
XI week lecturesXML, XMLSchema, XSLT
XI week exercisesPHP – file and database access.
XII week lecturesHTML5 Canvas
XII week exercisesPHP – sessions, cookies, shopping cart.
XIII week lecturesAjax, JSON, Singla page applica
XIII week exercisesCSS frameworks
XIV week lecturesTest. Web security.
XIV week exercisesXSLT-a. XML and PHP: SimpleXML i DOM.
XV week lectures
XV week exercises
Student workloadWeekly: 4x40/30 = 5 hours 20 min, lectures: 1 hour 30 min, Labs: 45 min, Other: 0, Individual work: 2 hours 55 min
Per weekPer semester
5 credits x 40/30=6 hours and 40 minuts
2 sat(a) theoretical classes
0 sat(a) practical classes
1 excercises
3 hour(s) i 40 minuts
of independent work, including consultations 		Classes and final exam:
6 hour(s) i 40 minuts x 16 =106 hour(s) i 40 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
6 hour(s) i 40 minuts x 2 =13 hour(s) i 20 minuts
Total workload for the subject:
5 x 30=150 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
30 hour(s) i 0 minuts
Workload structure: 106 hour(s) i 40 minuts (cources), 13 hour(s) i 20 minuts (preparation), 30 hour(s) i 0 minuts (additional work)
Student obligations
ConsultationsRoom 128
LiteratureBrian P. Hogan - "HTML5 and CSS3, 2nd edition", Pragmatic bookshelf, 2013. Jonathan Chaffer, Karl Swedberg - "Learning jQuery, Fourth Edition", Packt, 2013. Luke Welling, Laura Thompson - "Programming PHP, 3rd Edition", O'Reilly, 2013. Lecture slides and
Examination methods4 in-class test, 5 points each - 5 homeworks, 6 points each - Final project 50 points
Special remarksThe lecturer is able to offer course in English and Russian.
Commentwww.pmf.ac.me, internet@rc.pmf.ac.me
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / PARTIAL EQUATIONS

Course:PARTIAL EQUATIONS/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
3986Obavezan652+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites Enrolling in this course is not conditioned by passing other courses.
Aims The aim of this course is introducing students to basic notions related to partial differential equations
Learning outcomes On successful completion of this course, students will be able to: 1. Solve linear and quasilinear first order partial differential equations 2. Classify second order partial differential equations 3. Know basic methods for solving all three types of second order partial differential equations 4. Understand the notions of uniqueness and continuous dependance on initial conditions 5. Understand the physical meaning of these equations
Lecturer / Teaching assistantProf. dr Oleg Obradović, mr Nikola Konatar
MethodologyLectures, exercises, consultations
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesLinear and quasilinear first order partial differential equations. Method of characteristics.
I week exercisesLinear and quasilinear first order partial differential equations. Method of characteristics.
II week lecturesSolving linear and quasilinear first order partial differential equations.
II week exercises Solving linear and quasilinear first order partial differential equations.
III week lecturesSecond order linear partial differential equations, general notions. Reducing second order linear partial differential equations to canonic form.
III week exercisesSecond order linear partial differential equations, general notions. Reducing second order linear partial differential equations to canonic form.
IV week lecturesClassifying two variable second order partial differential equations with variable coefficients
IV week exercisesClassifying two variable second order partial differential equations with variable coefficients
V week lecturesDeriving the string equation. Existence of solution to the Cauchy problem for infinite string. (DAlembert formula.)
V week exercisesDeriving the string equation. Existence of solution to the Cauchy problem for infinite string. (DAlembert formula.)
VI week lecturesUniqueness of solution to the Cauchy problem. Continuous dependence of the solution to initial conditions.
VI week exercisesUniqueness of solution to the Cauchy problem. Continuous dependence of the solution to initial conditions.
VII week lecturesVibrating of the half-infinite string. Wave equation in space and plane. (Kirchhoff and Poisson formula)
VII week exercisesVibrating of the half-infinite string. Wave equation in space and plane. (Kirchhoff and Poisson formula)
VIII week lecturesFirst midterm exam.
VIII week exercisesFirst midterm exam.
IX week lecturesParabolic equations, general notions. The maximum and minimum theorem. Uniqueness of solution and continuous dependance on initial conditions.
IX week exercisesParabolic equations, general notions. The maximum and minimum theorem. Uniqueness of solution and continuous dependance on initial conditions.
X week lecturesFourier method for parabolic equations. (First boundary value problem. Second boundary value problem.)
X week exercisesFourier method for parabolic equations. (First boundary value problem. Second boundary value problem.)
XI week lecturesSolving one hyperbolic problem using the Fourier method.
XI week exercisesSolving one hyperbolic problem using the Fourier method.
XII week lecturesElliptic equation, general notions.
XII week exercisesElliptic equation, general notions.
XIII week lecturesGreen function for the Dirichlet problem. (three-dimensional case)
XIII week exercisesGreen function for the Dirichlet problem. (three-dimensional case)
XIV week lecturesSolving the Dirichlet problem on a ball.
XIV week exercisesSolving the Dirichlet problem on a ball.
XV week lecturesFourier method for elliptic equations. Second midterm exam.
XV week exercisesFourier method for elliptic equations. Second midterm exam.
Student workload
Per weekPer semester
5 credits x 40/30=6 hours and 40 minuts
2 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
2 hour(s) i 40 minuts
of independent work, including consultations 		Classes and final exam:
6 hour(s) i 40 minuts x 16 =106 hour(s) i 40 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
6 hour(s) i 40 minuts x 2 =13 hour(s) i 20 minuts
Total workload for the subject:
5 x 30=150 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
30 hour(s) i 0 minuts
Workload structure: 106 hour(s) i 40 minuts (cources), 13 hour(s) i 20 minuts (preparation), 30 hour(s) i 0 minuts (additional work)
Student obligations Students must attend lectures, do two midterm exams and the final exam.
ConsultationsAs agreed with students.
LiteratureR. Šćepanović, Diferencijalne jednačine, L. Evans, Weak convergence methods in PDEs, E. Pap, A. Takači, Đ. Takači, D. Kovačević, Zbirka zadataka iz parcijalnih diferencijalnih jednačina
Examination methodsTwo midterm exams, graded with a maximum of 25 points each. Final exam is graded with a maximum of 50 points.
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / THEORY OF MESAURE

Course:THEORY OF MESAURE/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
5889Obavezan652+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises
Student workload
Per weekPer semester
5 credits x 40/30=6 hours and 40 minuts
2 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
2 hour(s) i 40 minuts
of independent work, including consultations 		Classes and final exam:
6 hour(s) i 40 minuts x 16 =106 hour(s) i 40 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
6 hour(s) i 40 minuts x 2 =13 hour(s) i 20 minuts
Total workload for the subject:
5 x 30=150 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
30 hour(s) i 0 minuts
Workload structure: 106 hour(s) i 40 minuts (cources), 13 hour(s) i 20 minuts (preparation), 30 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / SOFTWARE ENGINEERING

Course:SOFTWARE ENGINEERING/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
10153Obavezan653+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises
Student workload
Per weekPer semester
5 credits x 40/30=6 hours and 40 minuts
3 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
1 hour(s) i 40 minuts
of independent work, including consultations 		Classes and final exam:
6 hour(s) i 40 minuts x 16 =106 hour(s) i 40 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
6 hour(s) i 40 minuts x 2 =13 hour(s) i 20 minuts
Total workload for the subject:
5 x 30=150 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
30 hour(s) i 0 minuts
Workload structure: 106 hour(s) i 40 minuts (cources), 13 hour(s) i 20 minuts (preparation), 30 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / PROBABILITY THEORY AND STATISTICS

Course:PROBABILITY THEORY AND STATISTICS/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
504Obavezan663+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises
Student workload
Per weekPer semester
6 credits x 40/30=8 hours and 0 minuts
3 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
3 hour(s) i 0 minuts
of independent work, including consultations 		Classes and final exam:
8 hour(s) i 0 minuts x 16 =128 hour(s) i 0 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
8 hour(s) i 0 minuts x 2 =16 hour(s) i 0 minuts
Total workload for the subject:
6 x 30=180 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
36 hour(s) i 0 minuts
Workload structure: 128 hour(s) i 0 minuts (cources), 16 hour(s) i 0 minuts (preparation), 36 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / STATISTICS

Course:STATISTICS/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
1361Obavezan663+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises
Student workload
Per weekPer semester
6 credits x 40/30=8 hours and 0 minuts
3 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
3 hour(s) i 0 minuts
of independent work, including consultations 		Classes and final exam:
8 hour(s) i 0 minuts x 16 =128 hour(s) i 0 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
8 hour(s) i 0 minuts x 2 =16 hour(s) i 0 minuts
Total workload for the subject:
6 x 30=180 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
36 hour(s) i 0 minuts
Workload structure: 128 hour(s) i 0 minuts (cources), 16 hour(s) i 0 minuts (preparation), 36 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points

Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / COMPLEX ANALYSIS 2

Course:COMPLEX ANALYSIS 2/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
4289Obavezan663+2+0
ProgramsMATHEMATICS AND COMPUTER SCIENCE
Prerequisites
Aims
Learning outcomes
Lecturer / Teaching assistant
Methodology
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lectures
I week exercises
II week lectures
II week exercises
III week lectures
III week exercises
IV week lectures
IV week exercises
V week lectures
V week exercises
VI week lectures
VI week exercises
VII week lectures
VII week exercises
VIII week lectures
VIII week exercises
IX week lectures
IX week exercises
X week lectures
X week exercises
XI week lectures
XI week exercises
XII week lectures
XII week exercises
XIII week lectures
XIII week exercises
XIV week lectures
XIV week exercises
XV week lectures
XV week exercises
Student workload
Per weekPer semester
6 credits x 40/30=8 hours and 0 minuts
3 sat(a) theoretical classes
0 sat(a) practical classes
2 excercises
3 hour(s) i 0 minuts
of independent work, including consultations 		Classes and final exam:
8 hour(s) i 0 minuts x 16 =128 hour(s) i 0 minuts
Necessary preparation before the beginning of the semester (administration, registration, certification):
8 hour(s) i 0 minuts x 2 =16 hour(s) i 0 minuts
Total workload for the subject:
6 x 30=180 hour(s)
Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item)
36 hour(s) i 0 minuts
Workload structure: 128 hour(s) i 0 minuts (cources), 16 hour(s) i 0 minuts (preparation), 36 hour(s) i 0 minuts (additional work)
Student obligations
Consultations
Literature
Examination methods
Special remarks
Comment
Grade:FEDCBA
Number of pointsless than 50 pointsgreater than or equal to 50 points and less than 60 pointsgreater than or equal to 60 points and less than 70 pointsgreater than or equal to 70 points and less than 80 pointsgreater than or equal to 80 points and less than 90 pointsgreater than or equal to 90 points
Mathematica Montisnigri
Mathematica Montisnigri
Ecologica Montenegrina
Ecologica Montenegrina
Digital Herbarium
Digital Herbarium
Publications
Publications
Informator
Informator
EUA
EUA
Bulletins
Bulletins
E-theses
E-theses
Europass
Europass
EURAXESS - network
EURAXESS - network
//