Graduate Seminar
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: second degree study
Type of study: full time
discipline specialities : Applications of Mathematics in Economics
The degree after graduating from university: master
The name of the module department : Departament of Discrete Mathematics
The code of the module: 4056
The module status: mandatory for teaching programme with the posibility of choice Applications of Mathematics in Economics
The position in the studies teaching programme: sem: 3, 4 / P90 / 6 ECTS / Z,Z
The language of the lecture: Polish
The name of the coordinator 1: Prof. Józef Banaś, DSc, PhD
office hours of the coordinator: podane w harmonogramie pracy jednostki.
The name of the coordinator 2: Prof. Dov Bronisław Wajnryb, DSc, PhD
office hours of the coordinator: podane w harmonogramie pracy jednostki.
The name of the coordinator 3: Iwona Włoch, DSc, PhD
office hours of the coordinator: podane w harmonogramie pracy jednostki.
The name of the coordinator 4: Andrzej Włoch, DSc, PhD
office hours of the coordinator: podane w harmonogramie pracy jednostki.
The name of the coordinator 5: Leszek Olszowy, DSc, PhD
office hours of the coordinator: podane w harmonogramie pracy jednostki.
semester 3: Bohdan Datsko, DSc, PhD
semester 4: Liliana Rybarska-Rusinek, DSc, PhD
semester 4: Tomasz Zając, PhD
The aim of studying and bibliography
The main aim of study: Preparation for solving tasks related to the diploma thesis.
The general information about the module: sem: 3, 4 / P60 / 6 ECTS / Z,Z
Bibliography required to complete the module
| 1 | R. Engelking | Topologia ogólna | Wydaw.Nauk.PWN. | 2012. |
| 2 | F. Leja | Rachunek różniczkowy i całkowy | Warszawa : Wydaw.Nauk.PWN. | 2012 |
| 3 | S. Łojasiewicz | Wstęp do teorii funkcji rzeczywistych | Warszawa : PWN. | 1976 |
| 4 | J. Musielak | Wstęp do analizy funkcjonalnej | Warszawa : PWN. | 1989 |
| 5 | M. Startek | Podstawy rachunku prawdopodobieństwa z elementami statystyki matematycznej | Oficyna Wydawnicza Politechniki Rzeszowskiej. | 2005 |
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: Knowledge of the maths sections presented during the semesters 1-3.
Basic requirements in category skills: Ability to use the fundamental mathematical tools in the area of the studies in mathematics.
Basic requirements in category social competences: Ability to comprehensively present mathematical content.
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 |
|---|---|---|---|---|---|
| 01 | Student can write a diploma thesis. | seminar, individual project | written report, oral presentation |
K_W01+ K_W02+ K_W04+++ K_W05+ K_W06+++ K_U01+++ K_U02+++ K_U03++ K_U04++ K_U13++ K_U14+++ K_U16+ K_K01++ K_K02+++ K_K04+++ K_K05++ K_K06+++ K_K07++ |
P7S_KK P7S_KO P7S_KR P7S_UK P7S_UO P7S_UU P7S_UW P7S_WG P7S_WK |
| 02 | He can prepare the presentation of the diploma thesis and prepare a paper on the topic of work. | seminar | written report, oral presentation |
K_W04+++ K_U01+++ K_U02+++ K_U03+++ K_U15+ |
P7S_UK P7S_UO P7S_UU P7S_UW P7S_WG |
| 03 | Student is able to present basic definitions and main theorems of the basic branches of mathematics from the course of study. | seminar | oral presentation |
K_W04+++ K_U14+++ K_K03+ |
P7S_KO P7S_KR P7S_UW P7S_WG |
Attention: Depending on the epidemic situation, verification of the achieved learning outcomes specified in the study program, in particular credits and examinations at the end of specific classes, can be implemented remotely (real-time meetings).
The syllabus of the module
| Sem. | TK | The content | realized in | MEK |
|---|---|---|---|---|
| 3 | TK01 | C01-C45 | MEK02 MEK03 | |
| 3 | TK02 | C01-C45 | MEK01 MEK02 MEK03 | |
| 3 | TK03 | C01-C45 | MEK01 MEK03 |
The student's effort
| The type of classes | The work before classes | The participation in classes | The work after classes |
|---|---|---|---|
| Project/Seminar (sem. 3) | The preparation for projects/seminars:
5.00 hours/sem. |
contact hours:
45.00 hours/sem.. |
Doing the project/report/ Keeping records:
20.00 hours/sem. The preparation for the presentation: 5.00 hours/sem. |
| Advice (sem. 3) | The preparation for Advice:
2.00 hours/sem. |
The participation in Advice:
2.00 hours/sem. |
|
| Credit (sem. 3) | The oral credit:
2.00 hours/sem. Others: 8.00 hours/sem. |
||
| Project/Seminar (sem. 4) | The preparation for projects/seminars:
5.00 hours/sem. |
contact hours:
45.00 hours/sem.. |
Doing the project/report/ Keeping records:
20.00 hours/sem. The preparation for the presentation: 5.00 hours/sem. |
| Advice (sem. 4) | The preparation for Advice:
2.00 hours/sem. |
The participation in Advice:
2.00 hours/sem. |
|
| Credit (sem. 4) | The oral credit:
2.00 hours/sem. Others: 8.00 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 |
|---|---|
| Project/Seminar | The final grade is the average of the mark for the presentation of the thesis and the degree of preparation for the final exam |
| The final grade | The final grade is the same as the grade of the project/seminar. |
| Project/Seminar | The final grade is the average of the mark for the presentation of the thesis and the degree of preparation for the final exam |
| The final grade | The final grade is the same as the grade of the project/seminar. |
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 | E. Özkan; D. Strzałka; A. Włoch; N. Yilmaz | On Doubled and Quadrupled Fibonacci Type Sequences | 2024 |
| 2 | J. Banaś; J. Madej | Asymptotically Stable Solutions of Infinite Systems of Quadratic Hammerstein Integral Equations | 2024 |
| 3 | J. Banaś; J. Madej | On solutions vanishing at infinity of infinite systems of quadratic Urysohn integral equations | 2024 |
| 4 | J. Banaś; J. Ochab; T. Zając | On the smoothness of normed spaces | 2024 |
| 5 | L. Olszowy; T. Zając | On Darbo- and Sadovskii-Type Fixed Point Theorems in Banach Spaces | 2024 |
| 6 | A. Ali; J. Banaś; . Mahfoudhi; B. Saadaoui | (P,Q)–ε-Pseudo Condition Spectrum for 2×2 Matrices. Linear Operator and Application | 2023 |
| 7 | A. Kosiorowska; A. Michalski; I. Włoch | On minimum intersections of certain secondary dominating sets in graphs | 2023 |
| 8 | A. Kosiorowska; I. Włoch | On the Existence of Independent [j,k]-Dominating Sets in the Generalized Corona of Graphs | 2023 |
| 9 | D. Bród; A. Szynal-Liana; I. Włoch | One-Parameter Generalization of Dual-Hyperbolic Jacobsthal Numbers | 2023 |
| 10 | D. Bród; A. Szynal-Liana; I. Włoch | One-parameter generalization of the bihyperbolic Jacobsthal numbers | 2023 |
| 11 | J. Banaś; R. Taktak | Measures of noncompactness in the study of solutions of infinite systems of Volterra-Hammerstein-Stieltjes integral equations | 2023 |
| 12 | J. Banaś; V. Erturk; P. Kumar; A. Manickam; S. Tyagi | A generalized Caputo-type fractional-order neuron model under the electromagnetic field | 2023 |
| 13 | N. Paja; A. Szynal-Liana; I. Włoch | On Some Combinatorial Properties of Oresme Hybrationals | 2023 |
| 14 | P. Jaśkiewicz; B. Kozicki; A. Włoch; J. Zieliński | The Impact of the Covid-19 Pandemic and the War Between Russia and Ukraine on Electricity Prices in Selected European Countries in 2022 in Terms of Economic Security | 2023 |
| 15 | A. Szynal-Liana; I. Włoch | A study on Fibonacci and Lucas bihypernomials | 2022 |
| 16 | A. Szynal-Liana; I. Włoch | Dziesięć wykładów z teorii kwaternionów | 2022 |
| 17 | A. Szynal-Liana; I. Włoch | Generalized commutative quaternions of the Fibonacci type | 2022 |
| 18 | D. Bród; A. Szynal-Liana; I. Włoch | On some combinatorial properties of generalized commutative Jacobsthal quaternions and generalized commutative Jacobsthal-Lucas quaternions | 2022 |
| 19 | D. Bród; A. Szynal-Liana; I. Włoch | One-parameter generalization of dual-hyperbolic Pell numbers | 2022 |
| 20 | D. Bród; A. Szynal-Liana; I. Włoch | Two generalizations of dual-complex Lucas-balancing numbers | 2022 |
| 21 | D. Bród; A. Szynal-Liana; I. Włoch | Two-parameter generalization of bihyperbolic Jacobsthal numbers | 2022 |
| 22 | J. Banaś; A. Chlebowicz; M. Taoudi | On solutions of infinite systems of integral equations coordinatewise converging at infinity | 2022 |
| 23 | J. Banaś; R. Nalepa | The Space of Functions with Tempered Increments on a Locally Compact and Countable at Infinity Metric Space | 2022 |
| 24 | J. Banaś; R. Nalepa; B. Rzepka | The Study of the Solvability of Infinite Systems of Integral Equations via Measures of Noncompactness | 2022 |
| 25 | M. Dettlaff; M. Lemańska; A. Michalski; I. Włoch | On proper(1,2)-dominating sets in graphs | 2022 |
| 26 | M. Kelemen; Y. Mlavets; V. Polishchuk; O. Tymoshenko; I. Włoch | The hybrid mathematical model for the evaluation and selection of iron ore raw materials in the context of the European Green Deal | 2022 |
| 27 | M. Liana; A. Szynal-Liana; I. Włoch | Generalized commutative quaternion polynomials of the Fibonacci type | 2022 |
| 28 | M. Liana; A. Szynal-Liana; I. Włoch | Jacobsthal Representation Hybrinomials | 2022 |
| 29 | M. Liana; A. Szynal-Liana; I. Włoch | On certain bihypernomials related to Pell and Pell-Lucas numbers | 2022 |
| 30 | R. Grabowski; B. Kozicki; S. Mitkow; A. Włoch | Impact of Covid-19 Pandemic on Economic Security - Multidimensional Analysis of Real Estate Market Across Poland | 2022 |
| 31 | S. Dudek; L. Olszowy | Measures of noncompactness in the space of regulated functions on an unbounded interval | 2022 |
| 32 | S. Dudek; L. Olszowy | Remarks on incorrect measure of noncompactness in BC (R+ x R+) | 2022 |
| 33 | U. Bednarz; A. Włoch; M. Wołowiec-Musiał | New Types of Distance Padovan Sequences via Decomposition Technique | 2022 |
| 34 | B. Datsko; A. Kunynets; M. Kutniv; A. Włoch | New explicit high‐order one‐step methods for singular initial value problems | 2021 |
| 35 | D. Bród; A. Szynal-Liana; I. Włoch | Balancing hybrid numbers, their properties and some identities | 2021 |
| 36 | D. Bród; A. Szynal-Liana; I. Włoch | Bihyperbolic numbers of the Fibonacci type and their idempotent representation | 2021 |
| 37 | D. Bród; A. Szynal-Liana; I. Włoch | On a new generalization of bihyperbolic Pell numbers | 2021 |
| 38 | D. Bród; A. Szynal-Liana; I. Włoch | On a new one-parameter generalization of dual-complex Jacobsthal numbers | 2021 |
| 39 | D. Bród; A. Szynal-Liana; I. Włoch | On a new two-parameter generalization of dual-hyperbolic Jacobsthal numbers | 2021 |
| 40 | D. Bród; A. Szynal-Liana; I. Włoch | On some combinatorial properties of bihyperbolic numbers of the Fibonacci type | 2021 |
| 41 | D. Bród; A. Włoch | (2,k)-Distance Fibonacci Polynomials | 2021 |
| 42 | D. Strzałka; A. Włoch; S. Wolski | Distance Fibonacci Polynomials by Graph Methods | 2021 |
| 43 | D. Wajnryb | The braid group and its presentation | 2021 |
| 44 | E. Özkan; A. Włoch; N. Yilmaz | On F3(k,n)-numbers of the Fibonacci type | 2021 |
| 45 | J. Banaś; W. Woś | Solvability of an infinite system of integral equations on the real half-axis | 2021 |
| 46 | M. Kelemen; Y. Mlavets; A. Polishchuk; V. Polishchuk; M. Sharkadi; I. Włoch | Conceptual Model of Presentation of Fuzzy Knowledge | 2021 |
| 47 | N. Paja; I. Włoch | Some interpretations of the (k, p)-Fibonacci numbers | 2021 |
| 48 | U. Bednarz; I. Włoch | Fibonacci numbers in graphs with strong (1, 1, 2)-kernels | 2021 |
| 49 | A. Michalski; I. Włoch | On the existence and the number of independent (1,2)-dominating sets in the G-join of graphs | 2020 |
| 50 | A. Szynal-Liana; I. Włoch | Generalized Fibonacci-Pell hybrinomials | 2020 |
| 51 | A. Szynal-Liana; I. Włoch | Introduction to Fibonacci and Lucas hybrinomials | 2020 |
| 52 | A. Szynal-Liana; I. Włoch | On generalized Mersenne hybrid numbers | 2020 |
| 53 | A. Szynal-Liana; I. Włoch | On Special Spacelike Hybrid Numbers | 2020 |
| 54 | A. Włoch; I. Włoch | On some multinomial sums related to the Fibonacci type numbers | 2020 |
| 55 | B. Datsko; A. Kunynets; M. Kutniv; A. Włoch | A new approach to constructing of explicit one-step methods of high order for singular initial value problems for nonlinear ordinary differential equations | 2020 |
| 56 | B. Datsko; M. Kutniv; A. Włoch | Mathematical modelling of pattern formation in activator–inhibitor reaction–diffusion systems with anomalous diffusion | 2020 |
| 57 | D. Bród; A. Szynal-Liana; I. Włoch | On the combinatorial properties of bihyperbolic balancing numbers | 2020 |
| 58 | D. Bród; A. Szynal-Liana; I. Włoch | Two Generalizations of Dual-Hyperbolic Balancing Numbers | 2020 |
| 59 | J. Banaś; A. Chlebowicz; W. Woś | On measures of noncompactness in the space of functions defined on the half-axis with values in a Banach space | 2020 |
| 60 | J. Banaś; B. Krichen; B. Mefteh | Fixed point theorems in WC-Banach algebras and their applications to infinite systems of integral equations | 2020 |
| 61 | J. Banaś; L. Olszowy | Remarks on the space of functions of bounded Wiener-Young variation | 2020 |
| 62 | L. Olszowy; T. Zając | Some inequalities and superposition operator in the space of regulated functions | 2020 |
| 63 | M. Liana; A. Szynal-Liana; I. Włoch | Some identities for generalized Fibonacci and Lucas numbers | 2020 |
| 64 | S. Dudek; L. Olszowy | Measures of noncompactness and superposition operator in the space of regulated functions on an unbounded interval | 2020 |
| 65 | U. Bednarz; I. Włoch | On strong (1,1,2)-kernels in graphs | 2020 |
| 66 | A. Szynal-Liana; I. Włoch | Hypercomplex numbers of the Fibonacci type | 2019 |
| 67 | A. Szynal-Liana; I. Włoch | On Jacobsthal and Jacobsthal-Lucas hybrid numbers | 2019 |
| 68 | A. Szynal-Liana; I. Włoch | The Fibonacci Hybrid Numbers | 2019 |
| 69 | H. Czyż; T. Jasiński; A. Włoch | A Statistical Method for Calculating the Velocity of Acoustic Waves in Extreme Conditions | 2019 |
| 70 | H. Czyż; T. Jasiński; A. Włoch | Separation of Cells from Plasma by Means of Ultrasonics | 2019 |
| 71 | H. Czyż; T. Jasiński; A. Włoch | The Application of the Special Functions to Solving Physical Problems | 2019 |
| 72 | J. Banaś; A. Chlebowicz | On solutions of an infinite system of nonlinear integral equations on the real half-axis | 2019 |
| 73 | J. Banaś; B. Rzepka | Ocena efektywności inwestycji | 2019 |
| 74 | J. Banaś; B. Rzepka | Wykłady matematyki finansowej | 2019 |
| 75 | J. Banaś; L. Olszowy | On the equivalence of some concepts in the theory of Banach algebras | 2019 |
| 76 | J. Banaś; M. Krajewska | On solutions of semilinear upper diagonal infinite systems of differential equations | 2019 |
| 77 | J. Banaś; R. Nalepa | A measure of noncompactness in the space of functions with tempered increments on the half-axis and its applications | 2019 |
| 78 | J. Banaś; T. Zając | On a measure of noncompactness in the space of regulated functions and its applications | 2019 |
| 79 | L. Abadias; E. Alvarez; J. Banaś; C. Lizama | Solvability and uniform local attractivity for a Volterra equation of convolution type | 2019 |
| 80 | L. Olszowy | Measures of noncompactness in the space of regulated functions | 2019 |
| 81 | L. Trojnar-Spelina; I. Włoch | On a new type of the companion Pell numbers | 2019 |
| 82 | L. Trojnar-Spelina; I. Włoch | On generalized Pell and Pell-Lucas numbers | 2019 |
| 83 | M. Liana; A. Szynal-Liana; I. Włoch | On Pell hybrinomials | 2019 |
| 84 | M. Liana; A. Szynal-Liana; I. Włoch | On some kind of numbers of the Fibonacci type and their applications for bicomplex numbers | 2019 |