Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / THEORY OF ALGORITHM COMPLEXITY
| Course: | THEORY OF ALGORITHM COMPLEXITY/ |
| Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
| 5755 | Obavezan | 2 | 5 | 3+1+0 |
| Programs | MATHEMATICS AND COMPUTER SCIENCE |
| Prerequisites | |
| Aims | |
| Learning outcomes | |
| Lecturer / Teaching assistant | |
| Methodology |
| Plan and program of work | |
| Preparing week | Preparation 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 week | Per 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: | F | E | D | C | B | A |
| Number of points | less than 50 points | greater than or equal to 50 points and less than 60 points | greater than or equal to 60 points and less than 70 points | greater than or equal to 70 points and less than 80 points | greater than or equal to 80 points and less than 90 points | greater than or equal to 90 points |
Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / METHODS OF OPTIMIZATION
| Course: | METHODS OF OPTIMIZATION/ |
| Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
| 5761 | Obavezan | 1 | 5 | 3+1+0 |
| Programs | MATHEMATICS AND COMPUTER SCIENCE |
| Prerequisites | |
| Aims | |
| Learning outcomes | |
| Lecturer / Teaching assistant | |
| Methodology |
| Plan and program of work | |
| Preparing week | Preparation 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 week | Per 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: | F | E | D | C | B | A |
| Number of points | less than 50 points | greater than or equal to 50 points and less than 60 points | greater than or equal to 60 points and less than 70 points | greater than or equal to 70 points and less than 80 points | greater than or equal to 80 points and less than 90 points | greater than or equal to 90 points |
Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / MATHEMATICAL MODELING
| Course: | MATHEMATICAL MODELING/ |
| Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
| 5762 | Obavezan | 1 | 5 | 3+1+0 |
| Programs | MATHEMATICS AND COMPUTER SCIENCE |
| Prerequisites | Three years of mathematical education (bachelor level) completed. |
| Aims | Students are introduced into methods and aims of mathematical modeling. Some well-known simple ("toy") models are analysed. Students are expected to obtain some understanding mathematical modeling while working on their projects. |
| Learning outcomes | |
| Lecturer / Teaching assistant | Vladimir Jaćimović |
| Methodology | lectures, consultations, projects, presentations |
| Plan and program of work | |
| Preparing week | Preparation and registration of the semester |
| I week lectures | Methods and aims of mathematical modeling. Achievements and limits of mathematical modeling. Steps in elaboration of mathematical model. Modeling hypotheses. Calibration and validation of the model. Example: model exponential population growth and Verhuls |
| I week exercises | Solving logistic equation. |
| II week lectures | Models from classical mechanics: small pendulum oscillations and the particle in bistable potential field. Models of population dynamics (continuation): two models of harvesting. Models of chemical reaction of first and second order. |
| II week exercises | Studying harvesting model. |
| III week lectures | Concept of equilibrium in dynamical systems. Stability after Lyapunov. Lyapunov theorem on linear stability and Lyapunov function. Classification of equilibrium points. Phase portraits. |
| III week exercises | Solving ODE systems in Matlab. Visualization of solutions. |
| IV week lectures | Models of population dynamics: Lotka-Volterra models of two interacting species. |
| IV week exercises | Studying stability of equilibrium points in Lotka-Volterra models. |
| V week lectures | Mathematical economy: consumers' preference problems. Constrained and unconstrained optimization problems. Necessary and sufficient conditions of optima. Method of Lagrange multipliers. |
| V week exercises | Solving constrained optimization problems by Lagrange multiplier approach. |
| VI week lectures | Resource allocation problems: Game theory and equilibrium after Nash. Example: transportation problems and optimal rooting problem. |
| VI week exercises | Seminar on homeworks and projects. |
| VII week lectures | test |
| VII week exercises | test |
| VIII week lectures | Empty week. |
| VIII week exercises | Empty week. |
| IX week lectures | Stochastic models. Stochastic processes, Brownian motion, Langevin equation. |
| IX week exercises | Stochastic simulations. |
| X week lectures | Poisson process. Queuing theory. |
| X week exercises | Simulation of Poisson process and Poisson distribution. |
| XI week lectures | From stochastic towards deterministic model: the idea on Fokker-Planck equation. Heat transfer equation. The probabilistic concept of entropy. Thermodynamic concept of equilibrium. |
| XI week exercises | Calculus of variations. Isoperimetric problem. Probabilistic distributions with maximal entropy. |
| XII week lectures | Mathematical models of stock markets. Options. Black-Scholes equation. Problems of mathematical modeling. Reaction-diffusion equations. |
| XII week exercises | Solving reaction-diffusion equations using deterministic and stochastic methods. |
| XIII week lectures | Entropy. Problem of maximal likelihood estimation of transport flows. Inverse problem: estimation of departures based on transportation flows. |
| XIII week exercises | Algorithms of optimal rooting. Genetic algorithms. Random search. |
| XIV week lectures | Basic concepts of bifurcation theory. Neuronal networks as dynamical systems. Hopfield model. Associative memories. Synchronization of oscillations. |
| XIV week exercises | Stochastic resonance. Stochastic simulations. |
| XV week lectures | Presentations of projects. |
| XV week exercises | Presentations of projects. |
| Student workload | 3 hours lectures + 1 hour seminars + 3 hours homework = 7 hours/week. Total: 16 weeks x 7 hours = 112 hours. |
| Per week | Per 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 | 1 hour/week |
| Literature | J.D.Logan, W.Wolesensky "Mathematical Methods in Biology", John Wiley & Sons, NYC, 2009. J.D.Logan "Applied Mathematics, 4th edition", John Wiley & Sons, NYC, 2013. |
| Examination methods | attendance (6 points), 2 small seminar works (2x5 points), test (32 points), project (50 points), presentation (12 points). |
| Special remarks | The language of instruction is Serbo-Croat. The instruction can also be given in English or Russian language. |
| Comment |
| Grade: | F | E | D | C | B | A |
| Number of points | less than 50 points | greater than or equal to 50 points and less than 60 points | greater than or equal to 60 points and less than 70 points | greater than or equal to 70 points and less than 80 points | greater than or equal to 80 points and less than 90 points | greater than or equal to 90 points |
Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / PARALLEL ALGORITHMS
| Course: | PARALLEL ALGORITHMS/ |
| Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
| 5776 | Obavezan | 1 | 5 | 3+1+0 |
| Programs | MATHEMATICS AND COMPUTER SCIENCE |
| Prerequisites | |
| Aims | |
| Learning outcomes | |
| Lecturer / Teaching assistant | |
| Methodology |
| Plan and program of work | |
| Preparing week | Preparation 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 week | Per 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: | F | E | D | C | B | A |
| Number of points | less than 50 points | greater than or equal to 50 points and less than 60 points | greater than or equal to 60 points and less than 70 points | greater than or equal to 70 points and less than 80 points | greater than or equal to 80 points and less than 90 points | greater than or equal to 90 points |
Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / RANDOM PROCESSES
| Course: | RANDOM PROCESSES/ |
| Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
| 6904 | Obavezan | 1 | 5 | 3+1+0 |
| Programs | MATHEMATICS AND COMPUTER SCIENCE |
| Prerequisites | |
| Aims | |
| Learning outcomes | |
| Lecturer / Teaching assistant | |
| Methodology |
| Plan and program of work | |
| Preparing week | Preparation 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 week | Per 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: | F | E | D | C | B | A |
| Number of points | less than 50 points | greater than or equal to 50 points and less than 60 points | greater than or equal to 60 points and less than 70 points | greater than or equal to 70 points and less than 80 points | greater than or equal to 80 points and less than 90 points | greater than or equal to 90 points |
Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / ACTUARIAL MATHEMATICS
| Course: | ACTUARIAL MATHEMATICS/ |
| Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
| 6905 | Obavezan | 1 | 5 | 3+1+0 |
| Programs | MATHEMATICS AND COMPUTER SCIENCE |
| Prerequisites | Information about the course can be found within the course ACTUARIAL MATHEMATICS, masters studies, program MATHEMATICS |
| Aims | Information about the course can be found within the course ACTUARIAL MATHEMATICS, masters studies, program MATHEMATICS |
| 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 assistant | Information about the course can be found within the course ACTUARIAL MATHEMATICS, masters studies, program MATHEMATICS |
| Methodology | Information about the course can be found within the course ACTUARIAL MATHEMATICS, masters studies, program MATHEMATICS |
| Plan and program of work | |
| Preparing week | Preparation 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 week | Per 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: | F | E | D | C | B | A |
| Number of points | less than 50 points | greater than or equal to 50 points and less than 60 points | greater than or equal to 60 points and less than 70 points | greater than or equal to 70 points and less than 80 points | greater than or equal to 80 points and less than 90 points | greater than or equal to 90 points |
Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / FINANCIAL MATHEMATICS 1
| Course: | FINANCIAL MATHEMATICS 1/ |
| Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
| 6906 | Obavezan | 1 | 5 | 3+1+0 |
| Programs | MATHEMATICS AND COMPUTER SCIENCE |
| Prerequisites | |
| Aims | |
| Learning outcomes | |
| Lecturer / Teaching assistant | |
| Methodology |
| Plan and program of work | |
| Preparing week | Preparation 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 week | Per 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: | F | E | D | C | B | A |
| Number of points | less than 50 points | greater than or equal to 50 points and less than 60 points | greater than or equal to 60 points and less than 70 points | greater than or equal to 70 points and less than 80 points | greater than or equal to 80 points and less than 90 points | greater than or equal to 90 points |
Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / CRYPTOGRAPHY
| Course: | CRYPTOGRAPHY/ |
| Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
| 6907 | Obavezan | 2 | 5 | 3+1+0 |
| Programs | MATHEMATICS AND COMPUTER SCIENCE |
| Prerequisites | |
| Aims | |
| Learning outcomes | |
| Lecturer / Teaching assistant | |
| Methodology |
| Plan and program of work | |
| Preparing week | Preparation 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 week | Per 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: | F | E | D | C | B | A |
| Number of points | less than 50 points | greater than or equal to 50 points and less than 60 points | greater than or equal to 60 points and less than 70 points | greater than or equal to 70 points and less than 80 points | greater than or equal to 80 points and less than 90 points | greater than or equal to 90 points |
Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / RISK THEORY
| Course: | RISK THEORY/ |
| Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
| 6908 | Obavezan | 2 | 5 | 3+1+0 |
| Programs | MATHEMATICS AND COMPUTER SCIENCE |
| Prerequisites | |
| Aims | |
| Learning outcomes | |
| Lecturer / Teaching assistant | |
| Methodology |
| Plan and program of work | |
| Preparing week | Preparation 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 week | Per 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: | F | E | D | C | B | A |
| Number of points | less than 50 points | greater than or equal to 50 points and less than 60 points | greater than or equal to 60 points and less than 70 points | greater than or equal to 70 points and less than 80 points | greater than or equal to 80 points and less than 90 points | greater than or equal to 90 points |
Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / MARKOV CHAINS
| Course: | MARKOV CHAINS/ |
| Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
| 6909 | Obavezan | 2 | 5 | 3+1+0 |
| Programs | MATHEMATICS AND COMPUTER SCIENCE |
| Prerequisites | Statistics. |
| Aims | Adopt the basic concepts of the theory of Markov chains and identify practices that can be modeled by Markov chains. |
| Learning outcomes | After passing this exam will be able to: 1. Precisely define the Markov chain. 2. Formulate basic concepts and state the basic classes Markov chains. 3. Explain the relationship between stationarity and limit distribution. 4. Formal and descriptive explained ergodicity. 5. Resolves tasks of medium difficulty. |
| Lecturer / Teaching assistant | Sinisa Stamatovic and Goran Popivoda. |
| Methodology | Attending lectures and exercises, doing the homework, preparing essay, final exam. |
| Plan and program of work | |
| Preparing week | Preparation and registration of the semester |
| I week lectures | Marcov property. Examples. |
| I week exercises | |
| II week lectures | Classification of states of Markov chain. |
| II week exercises | |
| III week lectures | |
| III week exercises | Limit and stationary distribution. |
| IV week lectures | Homogeneous Markov chains with a finite number of states. |
| IV week exercises | |
| V week lectures | Strictly Markovski property and ergodic theorem. |
| V week exercises | |
| VI week lectures | First colloquium. |
| VI week exercises | |
| VII week lectures | Free. |
| VII week exercises | |
| VIII week lectures | Monte Carlo method. |
| VIII week exercises | |
| IX week lectures | Examples of applications of Markov chains. |
| IX week exercises | |
| X week lectures | Markov chains in continuous time. Examples. |
| X week exercises | |
| XI week lectures | Chepman Kolmogorov equations. |
| XI week exercises | |
| XII week lectures | Birth and death processes. |
| XII week exercises | |
| XIII week lectures | Stationarity and reversibility. |
| XIII week exercises | |
| XIV week lectures | Training for using of statistical software in the analysis of Markov chains |
| XIV week exercises | |
| XV week lectures | Presentation of second homework. |
| XV week exercises |
| Student workload | |
| Per week | Per 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 | Attending lectures and exercises, presentation of the essaz, a final exam. |
| Consultations | |
| Literature | J. R. Norris: Markov Chains, Cambridge. |
| Examination methods | Two homeworks, the maximum number of points is 15. Final exam, the maximum number of points is 20, essay, maximum score is 40. The rating E: 50 D0 59 points, grade D: from 60 to 69 points, grade C: 70 to 79 points, score B: from 80 to 89 points, a score f |
| Special remarks | |
| Comment |
| Grade: | F | E | D | C | B | A |
| Number of points | less than 50 points | greater than or equal to 50 points and less than 60 points | greater than or equal to 60 points and less than 70 points | greater than or equal to 70 points and less than 80 points | greater than or equal to 80 points and less than 90 points | greater than or equal to 90 points |
Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / FINANCIAL MATHEMATICS 2
| Course: | FINANCIAL MATHEMATICS 2/ |
| Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
| 6910 | Obavezan | 2 | 5 | 3+1+0 |
| Programs | MATHEMATICS AND COMPUTER SCIENCE |
| 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 assistant | Darko Mitrovic |
| Methodology | Lectures. Exercises. Independent creation of tasks through homework and colloquiums. Consultations. |
| Plan and program of work | |
| Preparing week | Preparation and registration of the semester |
| I week lectures | Financial derivatives |
| I week exercises | Financial derivatives |
| II week lectures | Portfolio of assets |
| II week exercises | Portfolio of assets |
| III week lectures | Binomial option pricing model |
| III week exercises | Binomial option pricing model |
| IV week lectures | Geometric Brownian motion. Choice of binomial model parameters. |
| IV week exercises | Geometric Brownian motion. Choice of binomial model parameters. |
| V week lectures | Trinomial model. Recombining the Trinomial Model with Variable Volatility |
| V week exercises | Trinomial model. Recombining the Trinomial Model with Variable Volatility |
| VI week lectures | Modeling option prices in the trinomial model. |
| VI week exercises | Modeling option prices in the trinomial model. |
| VII week lectures | Parameters of model risk protection |
| VII week exercises | Parameters of model risk protection |
| VIII week lectures | Real options, concept and types. |
| VIII week exercises | Real options, concept and types. |
| IX week lectures | Options to delay, extend and abandon the project. |
| IX week exercises | Options to delay, extend and abandon the project. |
| X week lectures | A continuous market model |
| X week exercises | A continuous market model |
| XI week lectures | Black-Scholes option pricing model |
| XI week exercises | Black-Scholes option pricing model |
| XII week lectures | Black Scholes model as limes binomial model |
| XII week exercises | Black Scholes model as limes binomial model |
| XIII week lectures | Colloquium |
| XIII week exercises | Solving tasks from the colloquium |
| XIV week lectures | Remedial colloquium |
| XIV week exercises | Solving tasks from the remedial colloquium |
| XV week lectures | Defense of the seminar paper |
| XV week exercises | Defense of the seminar paper |
| Student workload | Classes 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 week | Per 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. |
| Consultations | Mondaz 14:00-16:00 |
| Literature | Introduction to Mathematical Finance: Discrete Time Models, author: S. Pliska Black-Scholes option valuation model, Masters thesis; author: Biljana Rašović Trinomial option price model, Master thesis, author: Marija Milovanovic (University of Niš) Options, Futures, and Other Derivatives, author: J.C. Hull |
| Examination methods | Colloquium of 40 points . Seminar work 40 points. Final exam - 20 points. |
| Special remarks | None |
| Comment | None |
| Grade: | F | E | D | C | B | A |
| Number of points | less than 50 points | greater than or equal to 50 points and less than 60 points | greater than or equal to 60 points and less than 70 points | greater than or equal to 70 points and less than 80 points | greater than or equal to 80 points and less than 90 points | greater than or equal to 90 points |
Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / EQUATIONS OF MATHEMATICAL PHYSICS
| Course: | EQUATIONS OF MATHEMATICAL PHYSICS/ |
| Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
| 6912 | Obavezan | 1 | 5 | 3+1+0 |
| Programs | MATHEMATICS AND COMPUTER SCIENCE |
| Prerequisites | Information about the subject can be found within the subject EQUATIONS OF MATHEMATICAL PHYSICS, specialist studies, program: MATHEMATICS |
| Aims | Information about the subject can be found within the subject EQUATIONS OF MATHEMATICAL PHYSICS, specialist studies, program: MATHEMATICS |
| 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 assistant | Information about the subject can be found within the subject EQUATIONS OF MATHEMATICAL PHYSICS, specialist studies, program: MATHEMATICS |
| Methodology | Information about the subject can be found within the subject EQUATIONS OF MATHEMATICAL PHYSICS, specialist studies, program: MATHEMATICS |
| Plan and program of work | |
| Preparing week | Preparation 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 week | Per 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: | F | E | D | C | B | A |
| Number of points | less than 50 points | greater than or equal to 50 points and less than 60 points | greater than or equal to 60 points and less than 70 points | greater than or equal to 70 points and less than 80 points | greater than or equal to 80 points and less than 90 points | greater than or equal to 90 points |
Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / GEOGRAPHIC INFORMATION SYSTEMS
| Course: | GEOGRAPHIC INFORMATION SYSTEMS/ |
| Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
| 6913 | Obavezan | 1 | 5 | 3+1+0 |
| Programs | MATHEMATICS AND COMPUTER SCIENCE |
| Prerequisites | |
| Aims | |
| Learning outcomes | |
| Lecturer / Teaching assistant | |
| Methodology |
| Plan and program of work | |
| Preparing week | Preparation 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 week | Per 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: | F | E | D | C | B | A |
| Number of points | less than 50 points | greater than or equal to 50 points and less than 60 points | greater than or equal to 60 points and less than 70 points | greater than or equal to 70 points and less than 80 points | greater than or equal to 80 points and less than 90 points | greater than or equal to 90 points |
Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / MATHEMATICAL MODELS IN ECONOMY
| Course: | MATHEMATICAL MODELS IN ECONOMY/ |
| Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
| 6914 | Obavezan | 2 | 5 | 3+1+0 |
| Programs | MATHEMATICS AND COMPUTER SCIENCE |
| Prerequisites | Attending and taking this course as a part of specialist studies is not conditioned by other courses. |
| Aims | The aim of the course is for students to master mathematical methods used in describing and analyzing economic processes. |
| Learning outcomes | After passing this exam the student will be able to: 1. Explain the concept of economic equilibrium 2. Explain the concept of Pareto optimum 3. Explain the Walras model of economy. 4. Explain, formulate and prove Arrow’s impossibility theorem (Arrow’s dictator theorem) 5. Explain the concept of calls and puts options and Black-Scholes equation. |
| Lecturer / Teaching assistant | Milojica Jaćimović, lecturer, Lazar Obradović, assistant |
| Methodology | Lectures, consultations, individual homework assignments, writing papers |
| Plan and program of work | |
| Preparing week | Preparation and registration of the semester |
| I week lectures | Optimization tasks with economic content. |
| I week exercises | Examples. |
| II week lectures | Conditional optimization. Duality. The Lagrange function. Kuhn-Tucker theorem. |
| II week exercises | Examples. |
| III week lectures | Economic interpretation of the Kuhn-Tucker theorem. |
| III week exercises | Examples of the applications of the Kuhn-Tucker theorem. |
| IV week lectures | Linear programming problems. Economic and geometric interpretation. |
| IV week exercises | Examples. |
| V week lectures | Simplex method for solving linear programming problems. |
| V week exercises | Examples. |
| VI week lectures | Multicriteria optimization. Pareto optimality. |
| VI week exercises | Examples. |
| VII week lectures | Study break |
| VII week exercises | Study break |
| VIII week lectures | Presentations and the defense of papers. |
| VIII week exercises | Presentations and the defense of papers. |
| IX week lectures | Individual preferences and collective decisions. The theorem of the impossibility of consistent collective decision-making (The theorem of the dictator). |
| IX week exercises | Individual preferences and collective decisions. The theorem of the impossibility of consistent collective decision-making (The theorem of the dictator). |
| X week lectures | Economic equilibrium. Economy of exchange. |
| X week exercises | Analysis of examples. |
| XI week lectures | Walrasian model economics. |
| XI week exercises | Analysis of examples. |
| XII week lectures | Von Neumann’s growth model. |
| XII week exercises | Analysis of examples. |
| XIII week lectures | Derived securities. Optional contracts and options. Call options and put options. |
| XIII week exercises | Analysis of examples. |
| XIV week lectures | American i European options. |
| XIV week exercises | Analysis of examples of optional contracts. |
| XV week lectures | Black-Scholes formula. |
| XV week exercises | Analysis of examples. |
| Student workload | 3 hours of lectures, 1 hour of exercises, 4 hours of individual activity, including consultations |
| Per week | Per 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 papers. |
| Consultations | As agreed with the professor or teaching assistant. |
| Literature | Jean-Pierre Aubin: Optima and Equilibria, Springer-Verlag, Berlin, Heidelberg, New York, 1993 А.А. Васин, П.С. Краснощеков, В.В. Морозов. Исследование операций, АCADEMIA, Moskva 2008. |
| Examination methods | Paper (including the presentation and defense) – up to 50 points, 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: | F | E | D | C | B | A |
| Number of points | less than 50 points | greater than or equal to 50 points and less than 60 points | greater than or equal to 60 points and less than 70 points | greater than or equal to 70 points and less than 80 points | greater than or equal to 80 points and less than 90 points | greater than or equal to 90 points |
Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / NUMERICAL MATHEMATICS
| Course: | NUMERICAL MATHEMATICS/ |
| Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
| 6915 | Obavezan | 2 | 5 | 3+1+0 |
| Programs | MATHEMATICS AND COMPUTER SCIENCE |
| Prerequisites | |
| Aims | |
| Learning outcomes | |
| Lecturer / Teaching assistant | |
| Methodology |
| Plan and program of work | |
| Preparing week | Preparation 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 week | Per 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: | F | E | D | C | B | A |
| Number of points | less than 50 points | greater than or equal to 50 points and less than 60 points | greater than or equal to 60 points and less than 70 points | greater than or equal to 70 points and less than 80 points | greater than or equal to 80 points and less than 90 points | greater than or equal to 90 points |
Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / MATHEMATICAL SOFTWARE PACKAGES
| Course: | MATHEMATICAL SOFTWARE PACKAGES/ |
| Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
| 6916 | Obavezan | 2 | 5 | 3+1+0 |
| Programs | MATHEMATICS AND COMPUTER SCIENCE |
| Prerequisites | |
| Aims | Through this course students learn to use contemporary software tools in the field of mathematics. |
| Learning outcomes | Once a student passes the exam, will be able to: i) use basic functionalities of the MATLAB tool; ii) use more advanced functionalities of the MATLAB tool in order to perform various mathematical calculations iii) use MATLAB functions for data visualization; iv) write MATLAB programs (scripts) including commands found in imperative programming languages v) create GUI in MATLAB vi) use basic functionalities of R software tool. |
| Lecturer / Teaching assistant | Doc. dr Aleksandar Popović |
| Methodology | Lectures, exercises in computer classroom/laboratory. Learning and practical exercises. Consultations. |
| Plan and program of work | |
| Preparing week | Preparation and registration of the semester |
| I week lectures | The history of mathematical and engineering programming tools (MPT), Contemporary tools and differences between them |
| I week exercises | The history of mathematical and engineering programming tools (MPT), Contemporary tools and differences between them |
| II week lectures | Data types and its' representation in MPTs with an emphasis on matrix and field of numbers |
| II week exercises | Data types and its' representation in MPTs with an emphasis on matrix and field of numbers |
| III week lectures | Basic matrix operations, and graphical representaton of variables |
| III week exercises | Basic matrix operations, and graphical representaton of variables |
| IV week lectures | Programming in MPTs |
| IV week exercises | Programming in MPTs |
| V week lectures | Functions and scripts |
| V week exercises | Functions and scripts |
| VI week lectures | COLLOQUIUM I |
| VI week exercises | COLLOQUIUM I |
| VII week lectures | Working with polynomials, interpolation |
| VII week exercises | Working with polynomials, interpolation |
| VIII week lectures | Working with strings, cells, structures and classes |
| VIII week exercises | Working with strings, cells, structures and classes |
| IX week lectures | Graphical objects |
| IX week exercises | Graphical objects |
| X week lectures | Symbolic mathematics in MAPLE, MATLAB, and MATHEMATICA |
| X week exercises | Symbolic mathematics in MAPLE, MATLAB, and MATHEMATICA |
| XI week lectures | Representation and solving problems in symbolic form |
| XI week exercises | Representation and solving problems in symbolic form |
| XII week lectures | Basic concepts of R tool, Data types, Data visualization |
| XII week exercises | Basic concepts of R tool, Data types, Data visualization |
| XIII week lectures | Functionalities of the R tool aimed at statistical calculations |
| XIII week exercises | Functionalities of the R tool aimed at statistical calculations |
| XIV week lectures | COLLOQUIUM II |
| XIV week exercises | COLLOQUIUM II |
| XV week lectures | Remedial COLLOQUIUM II |
| XV week exercises | Remedial COLLOQUIUM II |
| Student workload | Lecturing and final exam: (5 hours 20 minutes) x 16 = 85 hours 20 minutes Preparation before the beginning of the semester(administrative work) 2 x (5 hours and 20 minutes) = 10 hours and 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 do 24 hours (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. (Lecturing)+10 hours and 40 minutes. (Preparation)+24 hours(Additional work) |
| Per week | Per 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, as well as to do home exercises, and colloquia. |
| Consultations | |
| Literature | Uskoković, LJ. Stanković, I. Djurović: MATLAB for Windows, Univerzitet Crne Gore. |
| Examination methods | 2 colloquia 70 points total (35 points for each), Final exam 30 points. |
| Special remarks | |
| Comment |
| Grade: | F | E | D | C | B | A |
| Number of points | less than 50 points | greater than or equal to 50 points and less than 60 points | greater than or equal to 60 points and less than 70 points | greater than or equal to 70 points and less than 80 points | greater than or equal to 80 points and less than 90 points | greater than or equal to 90 points |
Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / DATA MINING
| Course: | DATA MINING/ |
| Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
| 6918 | Obavezan | 2 | 5 | 3+1+0 |
| Programs | MATHEMATICS AND COMPUTER SCIENCE |
| Prerequisites | |
| Aims | |
| Learning outcomes | |
| Lecturer / Teaching assistant | |
| Methodology |
| Plan and program of work | |
| Preparing week | Preparation 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 week | Per 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: | F | E | D | C | B | A |
| Number of points | less than 50 points | greater than or equal to 50 points and less than 60 points | greater than or equal to 60 points and less than 70 points | greater than or equal to 70 points and less than 80 points | greater than or equal to 80 points and less than 90 points | greater than or equal to 90 points |
