The aim of studying and bibliography

The main aim of study: To prepare students for diploma exam.

The general information about the module: This course consists of 30 hours of exercises.

Bibliography required to complete the module

Bibliography used during classes/laboratories/others

1	K. Kuratowski	Wstęp do teorii mnogości i topologii	PWN, Warszawa.	1980
2	A. Białynicki-Birula	Algebra liniowa z geometrią	PWN.	1976
3	F. Leja	Rachunek różniczkowy i całkowy	PWN, Warszawa.	1975

Bibliography to self-study

1

J. Stankiewicz, K. Wilczek

Algebra z geometrią. Teoria, przykłady, zadania.

Oficyna Wydawnicza PRz, Rzeszów.

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 logic, algebra and mathematical analysis.

Basic requirements in category skills: Ability to use the fundamental mathematical tools in the area of the first year of studies in mathematics.

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	Student is able to answer the quastions from the list of the problems for the diploma exam.	seminar	verbal presentation	K_W03+ K_W04+ K_U01+ K_K02+	P6S_KK P6S_KR P6S_UK 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
5	TK01	Binary relations. Equivalence relation. Classes of equivalence. Function as a relation.	C01-C02	MEK01
5	TK02	Equipotent sets. A contable set and an uncontable set. Finite and infinite sets. The infimum and the supremum of a set.	C03-C04	MEK01
5	TK03	A group, a ring, a field, a linear space. Examples.	C05-C07	MEK01
5	TK04	Systems of linear equations. The Kronecker-Capelli theorem and yhe Cramer theorem.	C08-C09	MEK01
5	TK05	A metric space, examples. Basic topological notions in a metric space.	C10-C12	MEK01
5	TK06	Sequences in metric spaces. Convergence of a sequence of numbers. Continuous and uniformly continuous functions.	C13-C15	MEK01

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Class (sem. 5)	The preparation for a Class: 15.00 hours/sem.	contact hours: 30.00 hours/sem.
Advice (sem. 5)	The preparation for Advice: 2.00 hours/sem.	The participation in Advice: 3.00 hours/sem.
Credit (sem. 5)	The preparation for a Credit: 2.00 hours/sem.	The oral credit: 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
Class	The final grade is the average of the grades of oral answers. To receive a positive grade student must attend training classes.
The final grade	The final grade is the average of the grades of oral answers. To receive a positive grade student must attend training classes.

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: no