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

Bibliography used during lectures

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.

Bibliography used during classes/laboratories/others

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.

Bibliography to self-study

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
01	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
02	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
03	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
04	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

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
1	TK01	Basic algebraic structures: a group, a field - definitions and examples.	W01-W03, C01-C03	MEK01
1	TK02	Field of complex numbers, an algebraic form, polar form and exponential form of a complex number, de Moivre's formula, the nth root of a complex number, the fundamental theorem of algebra.	W04-W12, C04-C15	MEK01
1	TK03	Matrices and determinants: operations on matrices, definitions, rules of computation and properties of determinants, the notion of the inverse matrix, definition and properties of the rank of a matrix.	W13-W21, C16-C24	MEK02
1	TK04	Systems of linear equations, Cramer's system, Cramer's Theorem, solvability of a system of linear equations, Theorem of Kronecker-Capelli, Gaussian elimination.	W22- W33, C25-C30	MEK02 MEK03
1	TK05	Analytic geometry in space, conic intersections, vectors in space, inner product, cross product and mixed product, equations of lines and planes, the mutual position of lines and planes	W34- W45, C31-C39	MEK04
1	TK06	Written tests concerning material learned at the lectures and the classes	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	The final grade is the weighted mean of grades of the class (with weight 2) and the exam ( with weight 1), rounded to the obligatory scale (with restriction that student have passed the exam). In case of being exepted from the exam the final grade is the grade of the class.

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
5	U. Bednarz; M. Wołowiec-Musiał	On a new generalization of telephone numbers	2019