The aim of studying and bibliography

The main aim of study: The aim of the course is to familiarize students with the basic concepts of logic and set theory. Students should understand these concepts and gain practical ability to solve related tasks.

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	Wojciech Guzicki, Piotr Zakrzewski	Wykłady ze wstępu do matematyki	PWN Warszawa.	2005
2	K. Kuratowski	Wstęp do teorii mnogości i topologii	PWN Warszawa.	1980
3	H. Rasiowa	Wstęp do matematyki współczesnej	PWN Warszawa.	1990
4	Jarosław Górnicki	Elementy teorii mnogości	Oficyna Wyd. Pol. Rzesz..	2006

Bibliography used during classes/laboratories/others

1	W. Marek, J. Onyszkiewicz	Elementy logiki i teorii mnogości w zadaniach.	PWN Warszawa.	1972
2	Wojciech Guzicki, Piotr Zakrzewski	Wstęp do matematyki, Zbiór zadań	PWN.	2006

Bibliography to self-study

1

A. Grzegorczyk

Zarys logiki matematycznej

PWN Warszawa.

1984

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 in secondary school.

Basic requirements in category skills: Showing ability to think and express one's thoughts in a logical way

Basic requirements in category social competences: He feels the need to complement his knowledge.

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	One can apply principle of induction in proofs of equations, inequalitites and arithmetical theorems.	exarcises with calculations, lectures	colloqium or exam.	K_W02++ K_W04+ K_W06+ K_U02+ K_K01+	P6S_KK P6S_UU P6S_UW P6S_WG P6S_WK
02	Knows main features of actions in algebra of sets. Understands principle notions of the set theory.	exarcises with calculations, lectures	colloqium or written exam.	K_W06+ K_U02+ K_K01+	P6S_KK P6S_UU P6S_UW P6S_WG
03	Uses quantifiers in logical calculus with the help of zero-one method.	exarcises with calculations, lectures	colloqium or exam.	K_W01+ K_W03+ K_W05++ K_U02++ K_U04+ K_K01+	P6S_KK P6S_UK P6S_UU P6S_UW P6S_WG P6S_WK
04	Understands realtion of equivalence, order relations, classes of abstractions.	exarcises with calculations, lectures	colloqium or exam.	K_U02+ K_U05+ K_U07++ K_K01+	P6S_KK P6S_UK P6S_UU P6S_UW
05	Knows properties of cardinal numbers.	exarcises with calculations, lectures	collocvium or exam	K_U07++ K_K01+	P6S_KK P6S_UW

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	Logical sentences, alternative, implication, conjunction, functors, zero-one method, tautologies, formulas.	W01,W02, C01, C02	MEK03
1	TK02	Aksioms of the set theorz, actions on sets, algebra of sets, kartesian product.	W03,W04, C03, C04	MEK02
1	TK03	Quantifiers and its applications, tautologies of the calculus of quantifiers.	W05,W06, C05, C06	MEK03
1	TK04	Binarz relations, realotion of equivalnce, classes of abstraction.	W07,W08, C08, C09	MEK04
1	TK05	Functions as realtions. Actions on functions. Monotonic, surjectiv and one-by-one functions.	W09,W10, C10, C11	MEK04
1	TK06	Natural numbers and the principle of mathematical induction.	W11, C12	MEK01
1	TK07	Cardinal numbers. Cantor-Bernstein Theorem. Uncountable sets in examples. Cantor Theorem.	W13,W14, C13	MEK04
1	TK08	Ordered sets. Linear order. Zermelo Theorem. Kuratowski-Zorn Lemma. Continuum hypothesis.	W15,C15	MEK05

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 1)	The preparation for a test: 20.00 hours/sem.	contact hours: 30.00 hours/sem.	complementing/reading through notes: 10.00 hours/sem.
Class (sem. 1)	The preparation for a Class: 30.00 hours/sem. The preparation for a test: 20.00 hours/sem.	contact hours: 30.00 hours/sem.	Finishing/Studying tasks: 10.00 hours/sem.
Advice (sem. 1)	The preparation for Advice: 2.00 hours/sem.	The participation in Advice: 1.00 hours/sem.
Exam (sem. 1)	The preparation for an Exam: 20.00 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	written exam. .
Class	Based on the activity and colloquium
The final grade	The mean of the grades of the class and the lecture

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	M. Nunokawa; K. Piejko; J. Sokół	Applications of Jack’s lemma	2024
2	K. Piejko; J. Sokół; K. Trąbka-Więcław	Coefficient bounds in the class of functions associated with Sakaguchi\'s functions	2023
3	K. Piejko; J. Sokół; K. Trąbka-Więcław	On q-starlike functions	2023
4	K. Piejko; J. Sokół	On convolution and q-calculus	2020
5	K. Piejko; J. Sokół; K. Trąbka Więcław	On q-Calculus and Starlike Functions	2019