Faculty of Science and Mathematics / MATHEMATICS / GEOMETRY
Course: | GEOMETRY/ |
Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
12061 | Obavezan | 1 | 5 | 3+1+0 |
Programs | MATHEMATICS |
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 / RANDOM PROCESSES
Course: | RANDOM PROCESSES/ |
Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
12062 | Obavezan | 1 | 5 | 3+1+0 |
Programs | MATHEMATICS |
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 / METHODS OF OPTIMIZATION
Course: | METHODS OF OPTIMIZATION/ |
Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
12063 | Obavezan | 1 | 5 | 3+1+0 |
Programs | MATHEMATICS |
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 / FINANCIAL MATHEMATICS I
Course: | FINANCIAL MATHEMATICS I/ |
Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
12064 | Obavezan | 1 | 5 | 3+1+0 |
Programs | MATHEMATICS |
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 assistant | Darko Mitrovic |
Methodology | Lectures, exercises, consultations, homework. |
Plan and program of work | |
Preparing week | Preparation and registration of the semester |
I week lectures | Introduction to the subject. Multi period model. |
I week exercises | Introduction to the subject. Multi period model. |
II week lectures | Portfolio and trading strategy. |
II week exercises | Portfolio and trading strategy. |
III week lectures | Reachability and replication. Linear price functionals. |
III week exercises | Reachability and replication. Linear price functionals. |
IV week lectures | Non-arbitrage and functional strictly positive prices. |
IV week exercises | Non-arbitrage and functional strictly positive prices. |
V week lectures | Completeness and extensions. |
V week exercises | Completeness and extensions. |
VI week lectures | The first colloquium |
VI week exercises | Solving the first colloquium |
VII week lectures | Lectures - recapitulation of material. |
VII week exercises | Exercises - recapitulation of the material |
VIII week lectures | Martingales and asset pricing. |
VIII week exercises | Martingales and asset pricing. |
IX week lectures | The Fundamental Theorem on Asset Pricing. |
IX week exercises | The Fundamental Theorem on Asset Pricing. |
X week lectures | Cox-Ross-Rubinstein economics. |
X week exercises | Cox-Ross-Rubinstein economics. |
XI week lectures | Cox-Ross-Rubinstein model and its parameterization. |
XI week exercises | Cox-Ross-Rubinstein model and its parameterization. |
XII week lectures | Equivalent martingale measures, uniqueness and existence. |
XII week exercises | Equivalent martingale measures, uniqueness and existence. |
XIII week lectures | Prices and hedging in the Cox-Ross-Rubinstein model. |
XIII week exercises | Prices and hedging in the Cox-Ross-Rubinstein model. |
XIV week lectures | Second colloquium. |
XIV week exercises | Solving the second colloquium. |
XV week lectures | European options model |
XV week exercises | European options model |
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 | Students are required to attend classes and do colloquiums. |
Consultations | Monday 14:00-16:00 |
Literature | P. Medina, S. Merino. Mathematical Finance and Probability, Birkhauser, 2005. |
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 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 / TEACHING MATHEMATICS I
Course: | TEACHING MATHEMATICS I/ |
Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
12065 | Obavezan | 1 | 5 | 3+1+0 |
Programs | MATHEMATICS |
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 / PHYSICS
Course: | PHYSICS/ |
Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
12066 | Obavezan | 1 | 5 | 2+2+0 |
Programs | MATHEMATICS |
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 assistant | Predrag Miranović |
Methodology | lectures, exercises, consultations |
Plan and program of work | |
Preparing week | Preparation and registration of the semester |
I week lectures | Wave function. Schrödinger equation. Statistical interpretation. Probability. |
I week exercises | |
II week lectures | Normalization |
II week exercises | |
III week lectures | Momentum. Uncertainty principle |
III week exercises | |
IV week lectures | Time independent Schrödinger equation. Stationary states. |
IV week exercises | |
V week lectures | Infinite square well |
V week exercises | |
VI week lectures | Harmonic oscillator |
VI week exercises | |
VII week lectures | Finite depth potential well |
VII week exercises | |
VIII week lectures | Free particle |
VIII week exercises | |
IX week lectures | Delta-function potential |
IX week exercises | |
X week lectures | Mathematical formalism. Linear algebra |
X week exercises | |
XI week lectures | Hilbert space. Generalized statistical interpretation |
XI week exercises | |
XII week lectures | Schrödinger and Heisenberg picture |
XII week exercises | |
XIII week lectures | Quantum mechanics in three dimensions. Schrödinger equation in spherical coordinates |
XIII week exercises | |
XIV week lectures | Hydrogen atom |
XIV week exercises | |
XV week lectures | Angular momentum |
XV week exercises |
Student workload | 5 ECTS |
Per week | Per 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 | |
Literature | 1. Introduction to quantum mechanics, D. J. Griffiths, Prentice Hall, New Jersey 2005 |
Examination methods | Tests (40 points), homework (10 points), final exam (50 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 / DIFFERENTIAL GEOMETRY
Course: | DIFFERENTIAL GEOMETRY/ |
Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
12069 | Obavezan | 2 | 5 | 3+1+0 |
Programs | MATHEMATICS |
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 / FINANCIAL MATHEMATICS II
Course: | FINANCIAL MATHEMATICS II/ |
Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
12070 | Obavezan | 2 | 5 | 3+1+0 |
Programs | MATHEMATICS |
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 | Introduction to options and markets |
I week exercises | The first colloquium Introduction to options and markets |
II week lectures | Property value as a random walk |
II week exercises | Property value as a random walk |
III week lectures | Black-Scholes option pricing model |
III week exercises | Black-Scholes option pricing model |
IV week lectures | Determination of parameters and hedging in practice |
IV week exercises | Determination of parameters and hedging in practice |
V week lectures | Diffusion equation. |
V week exercises | Diffusion equation. |
VI week lectures | The first colloquium |
VI week exercises | Solving tasks from the first colloquium |
VII week lectures | Black-Scholes formulas |
VII week exercises | Black-Scholes formulas |
VIII week lectures | Variations of the Black-Scholes model |
VIII week exercises | Variations of the Black-Scholes model |
IX week lectures | Forward and Futures contracts and options on them |
IX week exercises | Forward and Futures contracts and options on them |
X week lectures | American options |
X week exercises | American options |
XI week lectures | Binomial model |
XI week exercises | Binomial model |
XII week lectures | Black-Scholes model as limes binomial model |
XII week exercises | Black-Scholes model as limes binomial model |
XIII week lectures | Interest rates derivative products |
XIII week exercises | Interest rates derivative products |
XIV week lectures | Second colloquium |
XIV week exercises | Solving tasks from the second colloquium |
XV week lectures | Remedial colloquiums |
XV week exercises | Solving remedial colloquium tasks |
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 | Monday 14:00-16:00 |
Literature | Black-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 methods | 2 colloquiums of 40 points each (80 points in total). 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 / ACTUARIAL MATHEMATICS
Course: | ACTUARIAL MATHEMATICS/ |
Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
12071 | Obavezan | 2 | 5 | 3+1+0 |
Programs | MATHEMATICS |
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 assistant | Darko Mitrovic |
Methodology | Lectures, exercises, consultations, homework. |
Plan and program of work | |
Preparing week | Preparation and registration of the semester |
I week lectures | Introduction to the subject. Base model. |
I week exercises | Introduction to the subject. Base model. |
II week lectures | Homogeneous Poisson process, intensity function, Kramer-Lundberg model. |
II week exercises | Homogeneous Poisson process, intensity function, Kramer-Lundberg model. |
III week lectures | Markov property. Relation between homogeneous and inhomogeneous Poisson process. |
III week exercises | Markov property. Relation between homogeneous and inhomogeneous Poisson process. |
IV week lectures | Renewal processes. |
IV week exercises | Renewal processes. |
V week lectures | Expectation, dispersion and asymptotics in renewal processes. |
V week exercises | Expectation, dispersion and asymptotics in renewal processes. |
VI week lectures | The first colloquium |
VI week exercises | Solving tasks from the first colloquium |
VII week lectures | Lectures - recapitulation of material. |
VII week exercises | Exercises - recapitulation of material. |
VIII week lectures | Distribution of demand. |
VIII week exercises | Distribution of demand. |
IX week lectures | Distributions of total demand. |
IX week exercises | Distributions of total demand. |
X week lectures | Numerical methods for calculating the distribution of total demand. |
X week exercises | Numerical methods for calculating the distribution of total demand. |
XI week lectures | Risk processes, probability of bankruptcy and profit. |
XI week exercises | Risk processes, probability of bankruptcy and profit. |
XII week lectures | Lundbergs inequality. |
XII week exercises | Lundbergs inequality. |
XIII week lectures | Bayesian estimates. Heterogeneous model. |
XIII week exercises | Bayesian estimates. Heterogeneous model. |
XIV week lectures | Second 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 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 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 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 / MATHEMATICAL SOFTWARE PACKAGES
Course: | MATHEMATICAL SOFTWARE PACKAGES/ |
Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
12072 | Obavezan | 2 | 5 | 3+1+0 |
Programs | MATHEMATICS |
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 / NUMBER THEORY
Course: | NUMBER THEORY/ |
Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
12073 | Obavezan | 3 | 5 | 3+1+0 |
Programs | MATHEMATICS |
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 / ADVANCED ALGEBRA
Course: | ADVANCED ALGEBRA/ |
Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
12074 | Obavezan | 3 | 5 | 3+1+0 |
Programs | MATHEMATICS |
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 / EQUATIONS OF MATHEMATICAL PHYSICS
Course: | EQUATIONS OF MATHEMATICAL PHYSICS/ |
Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
12075 | Obavezan | 3 | 5 | 3+1+0 |
Programs | MATHEMATICS |
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 assistant | Information about the course can be found within the EQUATIONS OF MATHEMATICAL PHYSICS course, Masters studies, MATHEMATICS AND COMPUTER SCIENCE program. |
Methodology | Information 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 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 / ALGEBRAIC TOPOLOGY
Course: | ALGEBRAIC TOPOLOGY/ |
Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
12076 | Obavezan | 3 | 5 | 3+1+0 |
Programs | MATHEMATICS |
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 / PEDAGOGY WITH DIDACTICS
Course: | PEDAGOGY WITH DIDACTICS/ |
Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
12079 | Obavezan | 3 | 5 | 4++0 |
Programs | MATHEMATICS |
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 assistant | Prof. dr Saša Milić |
Methodology | Lectures, 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 week | Preparation and registration of the semester |
I week lectures | Socio-hostorical dimenssion of education |
I week exercises | |
II week lectures | Pedagogy - subject and area of research - Constitutive elements, subject, tasks |
II week exercises | |
III week lectures | Pedagogical disciplines or branches; Basic pedagogical concepts; |
III week exercises | |
IV week lectures | Classics of Pedagogy |
IV week exercises | |
V week lectures | Contemporary requirements of pedagogy - Education for the XXI century / interculturalism |
V week exercises | |
VI week lectures | Contemporary requirements of pedagogy - Education for the XXI century / inclusivity |
VI week exercises | |
VII week lectures | I test/colloquium |
VII week exercises | |
VIII week lectures | Concept and types of teaching, Forms of teaching work |
VIII week exercises | |
IX week lectures | Principles of teaching work - individualization, differentiation |
IX week exercises | |
X week lectures | Principles of teaching work - democratization, cooperative learning |
X week exercises | |
XI week lectures | Teaching planning; Evaluation of student achievements |
XI week exercises | |
XII week lectures | Contemporary education models /Reggio Emilia, Waldorf/ |
XII week exercises | |
XIII week lectures | Contemporary education models /Montessori, Step by Step/ |
XIII week exercises | |
XIV week lectures | II test/colloquium |
XIV week exercises | |
XV week lectures | Final exam |
XV week exercises |
Student workload | Classes 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 week | Per 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. |
Consultations | Monday 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 remarks | No |
Comment | http://www.ffri.uniri.hr/files/studijskiprogrami/PED_program_preddipl_1P_2014-2015.pdf |
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 |