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Faculty of Science and Mathematics / MATHEMATICS / GEOMETRY

Course:GEOMETRY/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
12061Obavezan153+1+0
ProgramsMATHEMATICS
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 / RANDOM PROCESSES

Course:RANDOM PROCESSES/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
12062Obavezan153+1+0
ProgramsMATHEMATICS
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 / METHODS OF OPTIMIZATION

Course:METHODS OF OPTIMIZATION/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
12063Obavezan153+1+0
ProgramsMATHEMATICS
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 / FINANCIAL MATHEMATICS I

Course:FINANCIAL MATHEMATICS I/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
12064Obavezan153+1+0
ProgramsMATHEMATICS
Prerequisites There is none
Aims To acquire the basic concepts of financial mathematics and to be able to apply the theory in solving specific problems of financial mathematics.
Learning outcomes Understanding of stock market functioning and the ability to implement mathematical models that describe stock market operations.
Lecturer / Teaching assistantDarko Mitrovic
MethodologyLectures, exercises, consultations, homework.
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesIntroduction to the subject. Multi period model.
I week exercisesIntroduction to the subject. Multi period model.
II week lecturesPortfolio and trading strategy.
II week exercises Portfolio and trading strategy.
III week lecturesReachability and replication. Linear price functionals.
III week exercisesReachability and replication. Linear price functionals.
IV week lecturesNon-arbitrage and functional strictly positive prices.
IV week exercisesNon-arbitrage and functional strictly positive prices.
V week lecturesCompleteness and extensions.
V week exercisesCompleteness and extensions.
VI week lecturesThe first colloquium
VI week exercisesSolving the first colloquium
VII week lecturesLectures - recapitulation of material.
VII week exercisesExercises - recapitulation of the material
VIII week lecturesMartingales and asset pricing.
VIII week exercisesMartingales and asset pricing.
IX week lecturesThe Fundamental Theorem on Asset Pricing.
IX week exercisesThe Fundamental Theorem on Asset Pricing.
X week lecturesCox-Ross-Rubinstein economics.
X week exercisesCox-Ross-Rubinstein economics.
XI week lecturesCox-Ross-Rubinstein model and its parameterization.
XI week exercisesCox-Ross-Rubinstein model and its parameterization.
XII week lecturesEquivalent martingale measures, uniqueness and existence.
XII week exercisesEquivalent martingale measures, uniqueness and existence.
XIII week lecturesPrices and hedging in the Cox-Ross-Rubinstein model.
XIII week exercisesPrices and hedging in the Cox-Ross-Rubinstein model.
XIV week lecturesSecond colloquium.
XIV week exercisesSolving the second colloquium.
XV week lecturesEuropean options model
XV week exercisesEuropean options model
Student workloadClasses and final exam: 6 hours and 40 minutes. 16=106 hours and 40 minutes. Necessary preparations 2 6 hours and 40 min. =13 hours and 20 minutes. Total workload for the subject: 5 30=150 Overtime: 0-30 hours Load structure 106 hours and 40 minutes (teaching) + 13 hours and 20 minutes (preparation) + 30 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
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 and do colloquiums.
ConsultationsMonday 14:00-16:00
LiteratureP. Medina, S. Merino. Mathematical Finance and Probability, Birkhauser, 2005.
Examination methodsThe maximum number of points on each colloquium is 30, and on the final exam it is 40. The minimum number of points for the passing grade is 51.
Special remarksNone
CommentNone
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 / TEACHING MATHEMATICS I

Course:TEACHING MATHEMATICS I/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
12065Obavezan153+1+0
ProgramsMATHEMATICS
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 / PHYSICS

Course:PHYSICS/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
12066Obavezan152+2+0
ProgramsMATHEMATICS
Prerequisites No prerequisites
Aims Introduction to the basic laws of physics that apply at the level of atoms and their nuclei
Learning outcomes Upon completion of this course the student will be able to: 1. know how to solve the simplest examples of one-dimensional Schrödinger equation 2. understand the statistical interpretation of wave function and measurement 3. interpret the uncertainty relation 4. know the basic properties of momentum in quantum mechanics 5. reproduce basic properties spectra of hydrogen atoms
Lecturer / Teaching assistantPredrag Miranović
Methodologylectures, exercises, consultations
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesWave function. Schrödinger equation. Statistical interpretation. Probability.
I week exercises
II week lecturesNormalization
II week exercises
III week lecturesMomentum. Uncertainty principle
III week exercises
IV week lecturesTime independent Schrödinger equation. Stationary states.
IV week exercises
V week lecturesInfinite square well
V week exercises
VI week lecturesHarmonic oscillator
VI week exercises
VII week lecturesFinite depth potential well
VII week exercises
VIII week lecturesFree particle
VIII week exercises
IX week lecturesDelta-function potential
IX week exercises
X week lecturesMathematical formalism. Linear algebra
X week exercises
XI week lecturesHilbert space. Generalized statistical interpretation
XI week exercises
XII week lecturesSchrödinger and Heisenberg picture
XII week exercises
XIII week lecturesQuantum mechanics in three dimensions. Schrödinger equation in spherical coordinates
XIII week exercises
XIV week lecturesHydrogen atom
XIV week exercises
XV week lecturesAngular momentum
XV week exercises
Student workload5 ECTS
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 regularly.
Consultations
Literature1. Introduction to quantum mechanics, D. J. Griffiths, Prentice Hall, New Jersey 2005
Examination methodsTests (40 points), homework (10 points), final exam (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 / DIFFERENTIAL GEOMETRY

Course:DIFFERENTIAL GEOMETRY/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
12069Obavezan253+1+0
ProgramsMATHEMATICS
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 / FINANCIAL MATHEMATICS II

Course:FINANCIAL MATHEMATICS II/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
12070Obavezan253+1+0
ProgramsMATHEMATICS
Prerequisites Financial mathematics 1
Aims Familiarity with financial derivatives: options, future and forward contracts with special reference to the binomial model and Black-Scholes PDJ.
Learning outcomes Students will be able to apply different options pricing models in stock market trading.
Lecturer / Teaching assistantDarko Mitrovic
MethodologyLectures. Exercises. Independent creation of tasks through homework and colloquiums. Consultations.
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesIntroduction to options and markets
I week exercisesThe first colloquium Introduction to options and markets
II week lecturesProperty value as a random walk
II week exercises Property value as a random walk
III week lecturesBlack-Scholes option pricing model
III week exercisesBlack-Scholes option pricing model
IV week lecturesDetermination of parameters and hedging in practice
IV week exercisesDetermination of parameters and hedging in practice
V week lecturesDiffusion equation.
V week exercisesDiffusion equation.
VI week lecturesThe first colloquium
VI week exercisesSolving tasks from the first colloquium
VII week lecturesBlack-Scholes formulas
VII week exercisesBlack-Scholes formulas
VIII week lecturesVariations of the Black-Scholes model
VIII week exercisesVariations of the Black-Scholes model
IX week lecturesForward and Futures contracts and options on them
IX week exercisesForward and Futures contracts and options on them
X week lecturesAmerican options
X week exercisesAmerican options
XI week lecturesBinomial model
XI week exercisesBinomial model
XII week lecturesBlack-Scholes model as limes binomial model
XII week exercisesBlack-Scholes model as limes binomial model
XIII week lecturesInterest rates derivative products
XIII week exercisesInterest rates derivative products
XIV week lecturesSecond colloquium
XIV week exercisesSolving tasks from the second colloquium
XV week lecturesRemedial colloquiums
XV week exercisesSolving remedial colloquium tasks
Student workloadClasses and final exam: 6 hours and 40 minutes. 16=106 hours and 40 minutes. Necessary preparations 2 6 hours and 40 min. =13 hours and 20 minutes. Total workload for the subject: 5 30=150 Overtime: 0-30 hours Load structure 106 hours and 40 minutes (teaching) + 13 hours and 20 minutes (preparation) + 30 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
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 Attendance at lectures and exercises. Doing homework.
ConsultationsMonday 14:00-16:00
LiteratureBlack-Scholes option valuation model, Masters thesis; author: Biljana Rašović The Mathematics of Financial Derivatives: A Student Introduction; by Paul Wilmott, Sam Howison, Jeff Dewynne
Examination methods2 colloquiums of 40 points each (80 points in total). Final exam - 20 points.
Special remarksNone
CommentNone
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 / ACTUARIAL MATHEMATICS

Course:ACTUARIAL MATHEMATICS/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
12071Obavezan253+1+0
ProgramsMATHEMATICS
Prerequisites There is none
Aims To adopt the basic terms from the theory of non-life insurance and to be able to apply the theory in practice.
Learning outcomes Students will be able to: 1. Explain the basic concepts of financial mathematics and probability theory 2. Derive the basic formulas of actuarial mathematics. 3. Calculate the final and initial values of financial rents 4. Distinguish between financial rents and rents in actuarial mathematics. 5. Solve life insurance problems in different insurance models.
Lecturer / Teaching assistantDarko Mitrovic
MethodologyLectures, exercises, consultations, homework.
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesIntroduction to the subject. Base model.
I week exercisesIntroduction to the subject. Base model.
II week lecturesHomogeneous Poisson process, intensity function, Kramer-Lundberg model.
II week exercises Homogeneous Poisson process, intensity function, Kramer-Lundberg model.
III week lecturesMarkov property. Relation between homogeneous and inhomogeneous Poisson process.
III week exercisesMarkov property. Relation between homogeneous and inhomogeneous Poisson process.
IV week lecturesRenewal processes.
IV week exercisesRenewal processes.
V week lecturesExpectation, dispersion and asymptotics in renewal processes.
V week exercisesExpectation, dispersion and asymptotics in renewal processes.
VI week lecturesThe first colloquium
VI week exercisesSolving tasks from the first colloquium
VII week lecturesLectures - recapitulation of material.
VII week exercisesExercises - recapitulation of material.
VIII week lecturesDistribution of demand.
VIII week exercisesDistribution of demand.
IX week lectures Distributions of total demand.
IX week exercisesDistributions of total demand.
X week lecturesNumerical methods for calculating the distribution of total demand.
X week exercisesNumerical methods for calculating the distribution of total demand.
XI week lecturesRisk processes, probability of bankruptcy and profit.
XI week exercisesRisk processes, probability of bankruptcy and profit.
XII week lecturesLundbergs inequality.
XII week exercisesLundbergs inequality.
XIII week lecturesBayesian estimates. Heterogeneous model.
XIII week exercisesBayesian estimates. Heterogeneous model.
XIV week lecturesSecond colloquium.
XIV week exercises Solving tasks from the second colloquium.
XV week lectures Linear Bayesian model.
XV week exercises Linear Bayesian model.
Student workload Classes and final exam: 20/3 x 16 = 106 hours and 40 minutes Necessary preparations before the beginning of the semester (administration, registration, certification) 2 x 20/3 = 13 hours and 20 minutes Total workload for the course 5x30 = 150 hours Supplementary work for exam preparation in the make-up exam period, including taking the make-up exam from 0 to 30 hours (remaining time from the first two items to the total workload for the course 150 hours) Load structure: 106 hours and 40 minutes (Teaching) + 13 hours and 20 minutes (Preparation) + 30 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
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 and do colloquiums.
Consultations Monday 14:00-16:00
Literature T. Mikosch. Non-Life Insurance Mathematics, Springer, 2006.
Examination methods The maximum number of points on each colloquium is 30, and on the final exam it is 40. The minimum number of points for the passing grade is 51.
Special remarksNone
CommentNone
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 / MATHEMATICAL SOFTWARE PACKAGES

Course:MATHEMATICAL SOFTWARE PACKAGES/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
12072Obavezan253+1+0
ProgramsMATHEMATICS
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 / NUMBER THEORY

Course:NUMBER THEORY/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
12073Obavezan353+1+0
ProgramsMATHEMATICS
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 / ADVANCED ALGEBRA

Course:ADVANCED ALGEBRA/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
12074Obavezan353+1+0
ProgramsMATHEMATICS
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 / EQUATIONS OF MATHEMATICAL PHYSICS

Course:EQUATIONS OF MATHEMATICAL PHYSICS/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
12075Obavezan353+1+0
ProgramsMATHEMATICS
Prerequisites Information about the course can be found within the EQUATIONS OF MATHEMATICAL PHYSICS course, Masters studies, MATHEMATICS AND COMPUTER SCIENCE program.
Aims Information about the course can be found within the EQUATIONS OF MATHEMATICAL PHYSICS course, Masters studies, MATHEMATICS AND COMPUTER SCIENCE program.
Learning outcomes After the student passes this exam, he will be able to: 1. Apply the basic principles of modeling natural and social phenomena with partial differential equations 2. Adjust the coefficients of partial differential equations in accordance with the considered situation 3. Prove the existence and uniqueness of solutions of known nonlinear partial differential equations 4 Recognize the type of partial differential equation and find its numerical solution. 5. Interprets solutions of equations as a description of the natural or social phenomenon it models.
Lecturer / Teaching assistantInformation about the course can be found within the EQUATIONS OF MATHEMATICAL PHYSICS course, Masters studies, MATHEMATICS AND COMPUTER SCIENCE program.
MethodologyInformation about the course can be found within the EQUATIONS OF MATHEMATICAL PHYSICS course, Masters studies, MATHEMATICS AND COMPUTER SCIENCE program.
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 / ALGEBRAIC TOPOLOGY

Course:ALGEBRAIC TOPOLOGY/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
12076Obavezan353+1+0
ProgramsMATHEMATICS
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 / PEDAGOGY WITH DIDACTICS

Course:PEDAGOGY WITH DIDACTICS/
Course IDCourse statusSemesterECTS creditsLessons (Lessons+Exercises+Laboratory)
12079Obavezan354++0
ProgramsMATHEMATICS
Prerequisites There are no conditions for applying and studying the subject.
Aims o Get to know the basic concepts of pedagogy and didactics o Introduce into pedagogical and didactic thinking o Get to know the phenomenon of education from different points of view o Get to know the basic didactic principles, organization and constitutive elements of teaching o Apply acquired knowledge in solving educational and teaching problems
Learning outcomes o Correct interpretation and interpretation of basic pedagogical terms and aspects/assumptions/concepts of education; o Knowledge and understanding of historical and contemporary definitions of pedagogical science; o Demonstrating knowledge and understanding of the main features of the educational phenomenon, the structure of the educational process, basic educational areas, general principles, educational methods and means, educational communication; o Demonstrating knowledge and understanding of basic didactic principles, organization and constitutive elements of teaching; o Critical analysis of relations and relationships in the environment with primary, secondary, positive and negative influences in the context of modern pedagogical requirements and lifelong education/learning.
Lecturer / Teaching assistantProf. dr Saša Milić
MethodologyLectures, workshops and debates. Preparation of one essay on a given topic from one of the content areas of the course. Studying for tests and final exams. Consultations.
Plan and program of work
Preparing weekPreparation and registration of the semester
I week lecturesSocio-hostorical dimenssion of education
I week exercises
II week lecturesPedagogy - subject and area of ​​research - Constitutive elements, subject, tasks
II week exercises
III week lecturesPedagogical disciplines or branches; Basic pedagogical concepts;
III week exercises
IV week lecturesClassics of Pedagogy
IV week exercises
V week lecturesContemporary requirements of pedagogy - Education for the XXI century / interculturalism
V week exercises
VI week lecturesContemporary requirements of pedagogy - Education for the XXI century / inclusivity
VI week exercises
VII week lecturesI test/colloquium
VII week exercises
VIII week lecturesConcept and types of teaching, Forms of teaching work
VIII week exercises
IX week lecturesPrinciples of teaching work - individualization, differentiation
IX week exercises
X week lecturesPrinciples of teaching work - democratization, cooperative learning
X week exercises
XI week lecturesTeaching planning; Evaluation of student achievements
XI week exercises
XII week lecturesContemporary education models /Reggio Emilia, Waldorf/
XII week exercises
XIII week lecturesContemporary education models /Montessori, Step by Step/
XIII week exercises
XIV week lecturesII test/colloquium
XIV week exercises
XV week lecturesFinal exam
XV week exercises
Student workloadClasses and final exam 2 hours 40 min.x16= 42 hours 40 min. Necessary preparations before the beginning of the semester (administration, enrollment, certification) 2 x 2 hours 40 min. = 5 hours 20 minutes. Total workload for the subject 2x30= 60 hours Supplementary work for exam preparation in the remedial exam period, including taking a make-up exam from 0 to 12 hours (remaining time from the first two items of the total workload for the course) Load structure - 42 hours 40 min. (teaching) + 5 hours 20 min. (preparation) + 12 hours (additional work).
Per weekPer semester
5 credits x 40/30=6 hours and 40 minuts
4 sat(a) theoretical classes
0 sat(a) practical classes
0 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, participate in debates and take two tests. Students prepare one essay each and participate in a debate after the presentation of the essay.
ConsultationsMonday 11:30, room no. 227
Literature 1. Giesecke, H. (1993), Uvod u pedagogiju. Zagreb: Educa.(odabrana poglavlja) 2. Gudjons, H. (1994), Pedagogija-temeljna znanja. Zagreb: Educa.(odabrana poglavlja) 3. Mušanović, M., Lukaš, M (2011), Osnove pedagogije. Rijeka: Hrvatsko futurološko društvo (odabrana poglavlja) 4. Trnavac, N. i Đorđević, J. (1998), Pedagogija. Naučna knjiga. Beograd. 5. Krulj, R. , Kačapor, S. , Kulić, R. , (2002), Pedagogija. Svet knjige. Beograd
Examination methods- Two tests with 20 points (Total 40 points), - Highlighting during lectures and participation in debates 5 points,: Essay with 6 points, - Final exam with 49 points. A passing grade is obtained if at least 51 points are accumulated cumulatively
Special remarksNo
Commenthttp://www.ffri.uniri.hr/files/studijskiprogrami/PED_program_preddipl_1P_2014-2015.pdf
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
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