Higher Mathematics (in English)
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: 4054
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: 2 / C45 / 2 ECTS / Z
The language of the lecture: English
The name of the coordinator: Iwona Włoch, DSc, PhD
The aim of studying and bibliography
The main aim of study: Knowledge of graph theory and combinatorics
The general information about the module: Classes in English
Bibliography required to complete the module
| 1 | R.Diestel | Graph Theory | Springer-Verlag-Heidelberg. | 2005 |
| 1 | A.Szynal-Liana, I.Włoch | Hypercomplex numbers of the Fibonacci type | Oficyna Wydawnicza PRz. | 2005 |
Basic requirements in category knowledge/skills/social competences
Formal requirements: English B2
Basic requirements in category knowledge: Basic mathematical knowledge
Basic requirements in category skills: English B2
Basic requirements in category social competences: Ability in group work
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 | A student know basic terminology used in graph theory and combinatorics, can wrie and translate a mathematical text | Classes | Wriiten raport and oral presentation |
K_W13+ K_U02+ K_K01+ K_K04+ K_K06+ K_K07+ |
P7S_KK P7S_KO P7S_KR P7S_UK P7S_UO P7S_UW P7S_WK |
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 |
|---|---|---|---|---|
| 2 | TK01 | C01-C45 | MEK01 |
The student's effort
| The type of classes | The work before classes | The participation in classes | The work after classes |
|---|---|---|---|
| Class (sem. 2) | The preparation for a Class:
8.00 hours/sem. The preparation for a test: 5.00 hours/sem. |
contact hours:
45.00 hours/sem. |
|
| Advice (sem. 2) | The participation in Advice:
2.00 hours/sem. |
||
| Credit (sem. 2) |
The way of giving the component module grades and the final grade
| The type of classes | The way of giving the final grade |
|---|---|
| Class | The final degree follows from the written report and its oral presentation |
| The final grade |
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. Kosiorowska; A. Michalski; I. Włoch | On minimum intersections of certain secondary dominating sets in graphs | 2023 |
| 2 | A. Kosiorowska; I. Włoch | On the Existence of Independent [j,k]-Dominating Sets in the Generalized Corona of Graphs | 2023 |
| 3 | D. Bród; A. Szynal-Liana; I. Włoch | One-Parameter Generalization of Dual-Hyperbolic Jacobsthal Numbers | 2023 |
| 4 | D. Bród; A. Szynal-Liana; I. Włoch | One-parameter generalization of the bihyperbolic Jacobsthal numbers | 2023 |
| 5 | N. Paja; A. Szynal-Liana; I. Włoch | On Some Combinatorial Properties of Oresme Hybrationals | 2023 |
| 6 | A. Szynal-Liana; I. Włoch | A study on Fibonacci and Lucas bihypernomials | 2022 |
| 7 | A. Szynal-Liana; I. Włoch | Dziesięć wykładów z teorii kwaternionów | 2022 |
| 8 | A. Szynal-Liana; I. Włoch | Generalized commutative quaternions of the Fibonacci type | 2022 |
| 9 | D. Bród; A. Szynal-Liana; I. Włoch | On some combinatorial properties of generalized commutative Jacobsthal quaternions and generalized commutative Jacobsthal-Lucas quaternions | 2022 |
| 10 | D. Bród; A. Szynal-Liana; I. Włoch | One-parameter generalization of dual-hyperbolic Pell numbers | 2022 |
| 11 | D. Bród; A. Szynal-Liana; I. Włoch | Two generalizations of dual-complex Lucas-balancing numbers | 2022 |
| 12 | D. Bród; A. Szynal-Liana; I. Włoch | Two-parameter generalization of bihyperbolic Jacobsthal numbers | 2022 |
| 13 | M. Dettlaff; M. Lemańska; A. Michalski; I. Włoch | On proper(1,2)-dominating sets in graphs | 2022 |
| 14 | 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 |
| 15 | M. Liana; A. Szynal-Liana; I. Włoch | Generalized commutative quaternion polynomials of the Fibonacci type | 2022 |
| 16 | M. Liana; A. Szynal-Liana; I. Włoch | Jacobsthal Representation Hybrinomials | 2022 |
| 17 | M. Liana; A. Szynal-Liana; I. Włoch | On certain bihypernomials related to Pell and Pell-Lucas numbers | 2022 |
| 18 | D. Bród; A. Szynal-Liana; I. Włoch | Balancing hybrid numbers, their properties and some identities | 2021 |
| 19 | D. Bród; A. Szynal-Liana; I. Włoch | Bihyperbolic numbers of the Fibonacci type and their idempotent representation | 2021 |
| 20 | D. Bród; A. Szynal-Liana; I. Włoch | On a new generalization of bihyperbolic Pell numbers | 2021 |
| 21 | D. Bród; A. Szynal-Liana; I. Włoch | On a new one-parameter generalization of dual-complex Jacobsthal numbers | 2021 |
| 22 | D. Bród; A. Szynal-Liana; I. Włoch | On a new two-parameter generalization of dual-hyperbolic Jacobsthal numbers | 2021 |
| 23 | D. Bród; A. Szynal-Liana; I. Włoch | On some combinatorial properties of bihyperbolic numbers of the Fibonacci type | 2021 |
| 24 | M. Kelemen; Y. Mlavets; A. Polishchuk; V. Polishchuk; M. Sharkadi; I. Włoch | Conceptual Model of Presentation of Fuzzy Knowledge | 2021 |
| 25 | N. Paja; I. Włoch | Some interpretations of the (k, p)-Fibonacci numbers | 2021 |
| 26 | U. Bednarz; I. Włoch | Fibonacci numbers in graphs with strong (1, 1, 2)-kernels | 2021 |
| 27 | A. Michalski; I. Włoch | On the existence and the number of independent (1,2)-dominating sets in the G-join of graphs | 2020 |
| 28 | A. Szynal-Liana; I. Włoch | Generalized Fibonacci-Pell hybrinomials | 2020 |
| 29 | A. Szynal-Liana; I. Włoch | Introduction to Fibonacci and Lucas hybrinomials | 2020 |
| 30 | A. Szynal-Liana; I. Włoch | On generalized Mersenne hybrid numbers | 2020 |
| 31 | A. Szynal-Liana; I. Włoch | On Special Spacelike Hybrid Numbers | 2020 |
| 32 | A. Włoch; I. Włoch | On some multinomial sums related to the Fibonacci type numbers | 2020 |
| 33 | D. Bród; A. Szynal-Liana; I. Włoch | On the combinatorial properties of bihyperbolic balancing numbers | 2020 |
| 34 | D. Bród; A. Szynal-Liana; I. Włoch | Two Generalizations of Dual-Hyperbolic Balancing Numbers | 2020 |
| 35 | M. Liana; A. Szynal-Liana; I. Włoch | Some identities for generalized Fibonacci and Lucas numbers | 2020 |
| 36 | U. Bednarz; I. Włoch | On strong (1,1,2)-kernels in graphs | 2020 |
| 37 | A. Szynal-Liana; I. Włoch | Hypercomplex numbers of the Fibonacci type | 2019 |
| 38 | A. Szynal-Liana; I. Włoch | On Jacobsthal and Jacobsthal-Lucas hybrid numbers | 2019 |
| 39 | A. Szynal-Liana; I. Włoch | The Fibonacci Hybrid Numbers | 2019 |
| 40 | L. Trojnar-Spelina; I. Włoch | On a new type of the companion Pell numbers | 2019 |
| 41 | L. Trojnar-Spelina; I. Włoch | On generalized Pell and Pell-Lucas numbers | 2019 |
| 42 | M. Liana; A. Szynal-Liana; I. Włoch | On Pell hybrinomials | 2019 |
| 43 | M. Liana; A. Szynal-Liana; I. Włoch | On some kind of numbers of the Fibonacci type and their applications for bicomplex numbers | 2019 |