Item card
Probability
Some basic information about the module
Cycle of education:
2019/2020
The name of the faculty organization unit:
The faculty Mathematics and Applied Physics
The name of the field of study:
Mathematics
The area of study:
sciences
The profile of studing:
The level of study:
first degree study
Type of study:
full time
discipline specialities :
Applications of Mathematics in Economics
The degree after graduating from university:
bachelor's degree
The name of the module department :
Departament of Mathematical Modelling
The code of the module:
1066
The module status:
mandatory for teaching programme Applications of Mathematics in Economics
The position in the studies teaching programme:
sem: 4 / W30 C30 / 6 ECTS / E
The language of the lecture:
Polish
The name of the coordinator 1:
Mariusz Startek, PhD
office hours of the coordinator:
Podane na stronie domowej.
The name of the coordinator 2:
Liliana Rybarska-Rusinek, DSc, PhD
The aim of studying and bibliography
The main aim of study:
Explore the basic messages and methods of probability.
The general information about the module:
Probability, random variable, parameters of random variable, independence, sequences of random variables, limit theorems.
Bibliography required to complete the module
| 1 | M. Fisz | Rachunek prawdopodobieństwa i statystyka matematyczna | PWN, Warszawa. | 1969 |
| 2 | M. Startek | Podstawy rachunku prawdopodobieństwa z elementami statystyki matematycznej | Oficyna Wydawnicza Politechniki Rzeszowskiej. | 2005 |
| 3 | J. Stankiewicz, K. Wilczek | Elementy rachunku prawdopodobieństwa i statystyki matematycznej. Teoria, przykłady, zadania | Oficyna Wydawnicza Politechniki Rzeszowskiej. | 2000 |
| 1 | M. Startek | Podstawy rachunku prawdopodobieństwa z elementami statystyki matematycznej | Oficyna Wydawnicza Politechniki Rzeszowskiej. | 2005 |
| 2 | W. Krysicki, J. Bartos, W. Dyczka, K. Królikowska, M. Wasilewski | Rachunek prawdopodobieństwa i statystyka matematyczna w zadaniach | WNT, Warszawa. | 2003 |
| 1 | A. i E. Plucińscy | Probabilistyka | WNT, Warszawa. | 2003 |
Basic requirements in category knowledge/skills/social competences
Formal requirements:
The student satisfies the formal requirements set out in the study regulations
Basic requirements in category knowledge:
Knowing the analysis.
Basic requirements in category skills:
Ability to use basic mathematical apparatus for the analysis.
Basic requirements in category social competences:
The student is prepared to take substantially justified mathematical operations in order to solve the posed exercise.
Module outcomes
| MEK | The student who completed the module | Types of classes / teaching methods leading to achieving a given outcome of teaching | Methods of verifying every mentioned outcome of teaching | Relationships with KEK | Relationships with PRK |
|---|---|---|---|---|---|
| MEK01 | use the concept of probability space, is able construct and analyze the mathematical model of random experiment; | lecture, classes | test, written exam |
K-W01+ K-W03+ K-U30++ |
P6S-UW P6S-WG P6S-WK |
| MEK02 | is able to give examples of discrete and continuous probability distributions and discuss selected random experiment and mathematical models in which these distributions ocur; know the practical application of elementary distributions; | lecture, classes | test, written exam |
K-W05+ K-U31++ |
P6S-UK P6S-UO P6S-UU P6S-UW P6S-WG |
| MEK03 | is able to use the formula of total probability and Bayes formula; | lecture, classes | test, written exam |
K-W04+ K-U32++ |
P6S-UW P6S-WG P6S-WK |
| MEK04 | is able to count the parameters of distributions of random variables; is able to use limit theorems and the laws of large numbers. | lecture, classes | test, written exam |
K-W02+ K-U33++ K-K01+ |
P6S-KK P6S-UW P6S-WG P6S-WK |
The syllabus of the module
| Sem. | TK | The content | realized in | MEK |
|---|---|---|---|---|
| 4 | TK01 | wykład, ćwiczenia | MEK01 MEK02 MEK03 MEK04 |
The student's effort
| The type of classes | The work before classes | The participation in classes | The work after classes |
|---|---|---|---|
| Lecture (sem. 4) | contact hours:
30.00 hours/sem. |
complementing/reading through notes:
15.00 hours/sem. Studying the recommended bibliography: 15.00 hours/sem. |
|
| Class (sem. 4) | The preparation for a Class:
15.00 hours/sem. The preparation for a test: 10.00 hours/sem. Others: 5.00 hours/sem. |
contact hours:
30.00 hours/sem. |
Finishing/Studying tasks:
20.00 hours/sem. |
| Advice (sem. 4) | The participation in Advice:
1.00 hours/sem. |
||
| Exam (sem. 4) | The preparation for an Exam:
10.00 hours/sem. |
The written exam:
2.00 hours/sem. |
The way of giving the component module grades and the final grade
| The type of classes | The way of giving the final grade |
|---|---|
| Lecture | Written exam. The obvious exercises and the extra exercises. The obvious exercises must be solved. Only the obvious exercises - 3.0. Exam only after the credit of classes. |
| Class | Written test. The obvious exercises must be solved. Only the obvious exercises - 3.0. |
| The final grade | After the credit of all types of classes the final grade is the average of grade of classes and grade of exam. |
Sample problems
Required during the exam/when receiving the credit
(-)
Realized during classes/laboratories/projects
(-)
Others
(-)
Can a student use any teaching aids during the exam/when receiving the credit : no
The contents of the module are associated with the research profile: yes
| 1 | A. Linkov; E. Rejwer-Kosińska; L. Rybarska-Rusinek | Enhanced Upward Translations for Systems with Clusters | 2024 |
| 2 | A. Linkov; E. Rejwer-Kosińska; L. Rybarska-Rusinek | Modeling Hydraulic Fracture Entering Stress Barrier: Theory and Practical Recommendations | 2024 |
| 3 | A. Linkov; E. Rejwer-Kosińska; L. Rybarska-Rusinek | The Study of Options for Identification Stress Contrasts via Pumping History | 2023 |
| 4 | A. Linkov; E. Rejwer-Kosińska; L. Rybarska-Rusinek | Evaluation of Rockburst Hazard by Accelerated Numerical Modeling of Stressed State and Induced Seismicity | 2022 |
| 5 | A. Linkov; E. Rejwer-Kosińska; L. Rybarska-Rusinek | On accuracy of translations by kernel independent fast multipole methods | 2022 |
| 6 | A. Linkov; E. Rejwer-Kosińska; L. Rybarska-Rusinek | On evaluation of local fields by fast multipole method employing smooth equivalent/check surfaces | 2021 |
| 7 | A. Linkov; E. Rejwer; L. Rybarska-Rusinek | On speeding up nano- and micromechanical calculations for irregular systems with long-range potentials | 2020 |