The aim of studying and bibliography

The main aim of study: To familiarize students with the important examples of finite and infinite dimensional linear spaces. To familiarize students with the concept of linear transformation and matrix of linear transformation. Acquiring the ability to find eigenvalues and eigenvectors of a linear transformation

The general information about the module: This course consists of 30 hours of lectures and 30 hours of exercises. It ends with an exam.

Bibliography required to complete the module

Bibliography used during lectures

1	Banaszak G., Gajda W.	Elementy algebry liniowej	Wydawnictwa Naukowo-Techniczne, Warszawa.	2002
2	Białynicki-Birula A.	Algebra liniowa z geometrią	Państwowe Wydawnictwo Naukowe, Warszawa.	1976
3	Jurlewicz T., Skoczylas Z.	Algebra liniowa. Definicje, twierdzenia, wzory	Oficyna Wydawnicza GiS, Wrocław.	2005
4	Klukowski J., Nabiałek I.	Algebra dla studentów	Wydawnictwa Naukowo-Techniczne, Warszawa.	2009
5	Gancarzewicz J.	Algebra liniowa i jej zastosowania	Wydawnictwo Uniwersytetu Jagiellońskiego.	2004
6	Stewart F.M.	Introduction to linear algebra	Princeton: D. Van Nostrand Company.	1963

Bibliography used during classes/laboratories/others

1	Fogiel M. (ed.)	Linear algebra, A complete solution guide for any textbook	Piscataway, New Jersey, Research and Education Association.	1999
2	Jurlewicz T., Skoczylas Z.	Algebra liniowa. Przykłady i zadania	Oficyna Wydawnicza GiS, Wrocław.	2005
3	Przybyło S., Szlachtowski A.	Algebra i geometria afiniczna w zadaniach	Wydawnictwa Naukowo-Techniczne, Warszawa.	1983
4	Rutkowski J.	Algebra liniowa w zadaniach	Państwowe Wydawnictwo Naukowe, Warszawa.	2008
5	Strang G.	Linear algebra and its applications, Fourth Edition	Thomson Brooks/Cole.	2006

Bibliography to self-study

1	Demidowič B.P., Effimow A.V.	Higher mathematics, Worked examples and problems with elements of theory, linear algebra and fundamentals of mathematical analysis	Mir Publishers, Moscow.	1986
2	Jurlewicz T.	Algebra liniowa. Kolokwia i egzaminy.	Oficyna Wydawnicza GiS, Wrocław.	2010
3	Kostrikin A. I.	Zbiór zadań z algebry	Państwowe Wydawnictwo Naukowe, Warszawa.	2005
4	Mostowski A., Stark M.	Algebra liniowa	Państwowe Wydawnictwo Naukowe, Warszawa.	1975
5	Nabiałek I.	Zadania z algebry liniowej	Wydawnictwa Naukowo-Techniczne, Warszawa.	2006

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 basic concepts of the matrices, systems of linear equations and basic algebraic structures.

Basic requirements in category skills: Skill to calculate the rank of a matrix and the determinant of a square matrix. Skill to solve the systems of linear equations.

Basic requirements in category social competences: Student is prepared to undertake objective and justified actions 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
01	can use the notion of a linear space (and linear subspace)	lecture, exercises	written test, written exam	K_W01+ K_W02+ K_W03+ K_W04+ K_W05+ K_U16++ K_K01+	P6S_KK P6S_UW P6S_WG P6S_WK
02	can check the linear independence of the set of the vectors, find generators and a basis of the linear space	lecture, exercises	written test, written exam	K_W01+ K_W02+ K_W04++ K_W05+ K_U16++ K_K01+	P6S_KK P6S_UW P6S_WG P6S_WK
03	can use the notion of a linear transformation	lecture, exercises	written test, written exam	K_W01+ K_W03+ K_W05++ K_U16+++ K_K01+	P6S_KK P6S_UW P6S_WG P6S_WK
04	can find a kernel and an image of the linear transformation	lecture, exercises	written test, written exam	K_W01+ K_W05+ K_U16+++ K_K01+	P6S_KK P6S_UW P6S_WG P6S_WK
05	can find the matrices of linear transformations with respect to various bases, can find the eigenvalues and eigenvectors of the endomorphisms, can check if the eigenvectors are the basis	lecture, exercises	written test, written exam	K_W01+ K_U16++ K_U20+++ K_U21++ K_K01+	P6S_KK P6S_UW 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
2	TK01	Definition and examples of linear spaces and linear subspaces. Operations on subspaces.	W01 - W05, C01 - C05	MEK01
2	TK02	The linear combination of vectors, the span of a set. Linear independence and linear dependence of vectors.	W06 - W10, C06 - C10	MEK01 MEK02
2	TK03	The basis and the dimension of a linear space. The Steinitz exchange lemma. Coordinates of a vector in a basis.	W11 - W16, C11 - C16	MEK01 MEK02
2	TK04	Written test concerning the material learned at the lectures and the exercises.	C17 - C18	MEK01 MEK02
2	TK05	Linear transformations: the definition and examples, the kernel and the image of a linear transformation, the matrix of a linear transformation, the change of basis matrix, the notion of a monomorphism, epimorphism and isomorphism.	W17 - W22, C19 - C23	MEK03 MEK04 MEK05
2	TK06	Endomorphisms: invariant subspaces, eigenvalues and eigenvectors of an endomorphism, diagonalizability of an endomorphism.	W23 - W30, C24 - C28	MEK03 MEK05
2	TK07	Written test concerning the material learned at the lectures and the exercises.	C29 - C30	MEK03 MEK04 MEK05

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 2)		contact hours: 30.00 hours/sem.	complementing/reading through notes: 20.00 hours/sem. Studying the recommended bibliography: 15.00 hours/sem.
Class (sem. 2)	The preparation for a Class: 15.00 hours/sem. The preparation for a test: 20.00 hours/sem.	contact hours: 30.00 hours/sem.	Finishing/Studying tasks: 15.00 hours/sem.
Advice (sem. 2)
Exam (sem. 2)	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	A credit for the lecture is based on the exam.
Class	The grade from the exercises is the arythmetic mean of the grades of MEKs, rounded to obligatory scale Activity during exercises can raise a grade.
The final grade	The final grade is the weighted mean of grades of the exercises (with weight 2) and the exam ( with weight 1), rounded to the obligatory scale (with restriction that student have passed both the exercises and the 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	J. Appell; A. Chlebowicz; S. Reinwand; B. Rzepka	Can one recognize a function from its graph?	2023
2	J. Banaś; A. Chlebowicz; M. Taoudi	On solutions of infinite systems of integral equations coordinatewise converging at infinity	2022
3	A. Chlebowicz	Existence of solutions to infinite systems of nonlinear integral equations on the real half-axis	2021
4	A. Chlebowicz	Solvability of an infinite system of nonlinear integral equations of Volterra-Hammerstein type	2020
5	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
6	J. Banaś; A. Chlebowicz	On solutions of an infinite system of nonlinear integral equations on the real half-axis	2019