The aim of studying and bibliography

The main aim of study:

The general information about the module:

Bibliography required to complete the module

Bibliography used during lectures

1	A. Włoch, I. Włoch	Matematyka dyskretna- podstawowe metody i algorytmy teorii grafów	Oficyna Wydawnicza Politechniki Rzeszowskiej, Rzeszów.	2004.
2	K. Ross, Ch. Wright	Matematyka dyskretna	PWN, Warszawa.	1996.
3	P.N. de Souza, R.J. Fateman, J. Moses, C. Yapp	The Maxima Book	http://maxima.sourceforge.net.

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: Basics of linear algebra and mathematical analysis

Basic requirements in category skills:

Basic requirements in category social competences:

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 knows basic combinatorial objects, methods and tools of counting and generating.	lecture, laboratory, exercises	written work	K_W01+ K_U02+ K_U03+ K_K02+	P6S_KK P6S_KO P6S_UW P6S_WG
02	Student is able to calculate the quantity of combinatorial objects using induction, permanent, solving recurrence relations.	lecture, exercises, laboratory	written work	K_W01+ K_W02+ K_U02+ K_U03+ K_K02+	P6S_KK P6S_KO P6S_UW P6S_WG
03	Student is able to apply CAS MAXIMA to generate combinatorial objects and count quantity of such objects.	laboratory	written work	K_W02+ K_U02+ K_U03+ K_K01+ K_K02+	P6S_KK P6S_KO P6S_UW P6S_WG

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	Mathematical induction with applications.	W1-W2, C1-C2	MEK01 MEK02
2	TK02	Combinatorial objects, existence, counting and generating. Counting principle, counting finite sequences, subset counting, Stirling numbers and Bell numbers, number partitions, set partitions, the pigeonhole principle, binomial coefficients, the Pascal triangle.	W3-W8, C3-C8, L1-L5	MEK01 MEK02 MEK03
2	TK03	Recursion, recurrence relations, solving linear recurrence relations, characteristic equation.	W9-W10, C9-C10, L6-L8	MEK01 MEK02 MEK03
2	TK04	Generating functions, exponential generating functions, generating functions of two variables. Solving recurrence relations with generating functions.	W11-W12, C11-C12, L9-L11	MEK01 MEK02 MEK03
2	TK05	Systems of distinct representatives, permanent of a matrix, Hungarian algorithm.	W13-W15, C13-C15, L12-L15	MEK01 MEK02 MEK03

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 2)	The preparation for a test: 5.00 hours/sem.	contact hours: 15.00 hours/sem.
Class (sem. 2)	The preparation for a Class: 5.00 hours/sem. The preparation for a test: 2.00 hours/sem.	contact hours: 15.00 hours/sem.
Laboratory (sem. 2)	The preparation for a Laboratory: 10.00 hours/sem. The preparation for a test: 3.00 hours/sem.	contact hours: 15.00 hours/sem.	Finishing/Making the report: 3.00 hours/sem.
Advice (sem. 2)		The participation in Advice: 2.00 hours/sem.
Credit (sem. 2)	The preparation for a Credit: 3.00 hours/sem.	The written 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
Lecture
Class
Laboratory
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: no