Item card
Linear Algebra and Analytic Geometry
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 Discrete Mathematics
The code of the module:
1044
The module status:
mandatory for teaching programme Applications of Mathematics in Economics
The position in the studies teaching programme:
sem: 1 / W45 C45 / 6 ECTS / E
The language of the lecture:
Polish
The name of the coordinator:
Małgorzata Wołowiec-Musiał, PhD
office hours of the coordinator:
poniedziałek 10:30-12:00, czwartek 10:30-12:00
semester 1:
Natalia Paja, PhD
The aim of studying and bibliography
The main aim of study:
The aim of the course is to familiarize students with the basics of linear algebra and analytic geometry.
The general information about the module:
The module consists of 45 hours of lectures and 45 hours of classes. It ends with an exam.
Bibliography required to complete the module
| 1 | Banaszak G., Gajda W. | Elementy algebry liniowej, cz. I | WNT Warszawa . | 2002. |
| 2 | Białynicki- Birula A. | Algebra liniowa z geometrią | PWN. | 1976. |
| 3 | Jurlewicz T., Skoczylas Z. | Algebra i geometria analityczna. Definicje, twierdzenia, wzory | Oficyna Wydawnicza GiS, Wrocław. | 2009. |
| 4 | Zakrzewski M. | Markowe wykłady z matematyki - Algebra z geometrią | Oficyna Wydawnicza GiS, Wrocław . | 2015. |
| 1 | Gdowski B., Pluciński E. | Zbiór zadań z rachunku wektorowego i geometrii analitycznej | PWN, Warszawa. | 1995. |
| 2 | Jurlewicz T., Skoczylas Z. | Algebra i geometria analityczna. Przykłady i zadania | Oficyna Wydawnicza GiS, Wrocław. | 2008. |
| 3 | Rutkowski J. | Algebra liniowa w zadaniach | PWN, Warszawa. | 2008. |
| 4 | Stankiewicz J., Wilczek K. | Algebra z geometrią. Teoria, przykłady, zadania | Oficyna Wydawnicza PRz, Rzeszów. | 2006. |
| 1 | Kostrykin, A. I. | Wstęp do algebry cz. I | PWN, Warszawa. | 2004. |
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:
basic knowledge of mathematics at the high school level.
Basic requirements in category skills:
ability to use basic mathematical tools at the high school level.
Basic requirements in category social competences:
preparation for taking substantively justified mathematical actions to solve the posed problem.
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 | can make operations on complex numbers written in various forms, can find roots of complex polynomials | lecture, class | written test, written exam |
K-W01+ K-W05+ K-K01+ |
P6S-KK P6S-WG P6S-WK |
| MEK02 | knows the basics of matrix calculus | lecture, class | written test, written exam |
K-W01+ K-W02+ K-W04++ K-W05+ K-U18+ K-K01+ |
P6S-KK P6S-UW P6S-WG P6S-WK |
| MEK03 | can use knowledge from matrix calculus to solve systems of linear equations | lecture, class | written test, written exam |
K-W01+ K-W02+ K-U18++ K-U19++ K-K01+ |
P6S-KK P6S-UW P6S-WG P6S-WK |
| MEK04 | can describe conic curves, lines and planes in space | lecture, class | written test, written exam |
K-W01+ K-W02+ K-U19+ K-K01+ |
P6S-KK P6S-UW P6S-WG P6S-WK |
The syllabus of the module
| Sem. | TK | The content | realized in | MEK |
|---|---|---|---|---|
| 1 | TK01 | W01-W03, C01-C03 | MEK01 | |
| 1 | TK02 | W04-W12, C04-C15 | MEK01 | |
| 1 | TK03 | W13-W21, C16-C24 | MEK02 | |
| 1 | TK04 | W22- W33, C25-C30 | MEK02 MEK03 | |
| 1 | TK05 | W34- W45, C31-C39 | MEK04 | |
| 1 | TK06 | C40-C45 | 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. 1) | contact hours:
45.00 hours/sem. |
complementing/reading through notes:
15.00 hours/sem. Studying the recommended bibliography: 15.00 hours/sem. |
|
| Class (sem. 1) | The preparation for a Class:
6.00 hours/sem. The preparation for a test: 10.00 hours/sem. |
contact hours:
45.00 hours/sem. |
Finishing/Studying tasks:
30.00 hours/sem. |
| Advice (sem. 1) | The preparation for Advice:
2.00 hours/sem. |
The participation in Advice:
2.00 hours/sem. |
|
| Exam (sem. 1) | The preparation for an Exam:
8.00 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 | A credit for the lecture is based on the written exam. There is a possibility of exemption from the exam based on a good grade of a class. |
| Class | Student is obliged to pass each module outcome defined for the course.The grade from the class is the arythmetic mean of grades of module outcomes (rounded to the obligatory scale). Student's activity during tutorials can raise the grade. |
| 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 | U. Bednarz; M. Wołowiec-Musiał | Generalized Fibonacci–Leonardo numbers | 2024 |
| 2 | U. Bednarz; A. Włoch; M. Wołowiec-Musiał | New Types of Distance Padovan Sequences via Decomposition Technique | 2022 |
| 3 | U. Bednarz; M. Wołowiec-Musiał | Distance Fibonacci Polynomials—Part II | 2021 |
| 4 | U. Bednarz; M. Wołowiec-Musiał | Distance Fibonacci Polynomials | 2020 |