The aim of studying and bibliography

The main aim of study:

The general information about the module: Basic schemes of selection and the main methods of solving recursive equations.

Bibliography required to complete the module

Bibliography used during lectures

1	Z. Palka, A. Ruciński	Wykłady z kombinatoryki. Przeliczanie	Warszawa, WNT.	2004
2	H. Levy, F. Lessman	Równania różnicowe skończone	Warszawa, PWN.	1966
3	S. Kanas	Podstawy ekonomii matematycznej	Warszawa, PWN.	2011
4	V. Bryant	Aspekty kombinatoryki	Warszawa, WNT.	1997

Bibliography used during classes/laboratories/others

1

Z. Palka, A. Ruciński

Wykłady z kombinatoryki. Przeliczanie

Warszawa, WNT.

2004

Bibliography to self-study

1

S. Elaydi

An introduction to difference equations

New York, Springer.

2005

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: Student should know operations on matrices and theory of complex numbers.

Basic requirements in category skills: The student should know the methods of solving polynomial equations in a set of real and complex numbers.

Basic requirements in category social competences: Consciousness of necessity of permanent self-studying.

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	Knows basic methods of selection schemes with restrictions.	lecture, laboratory	reports, exam	K_W01++ K_K01++	P6S_KK P6S_WG
02	Is able to solve linear homogeneous and heterogeneous recurrence equations, can create a recursive relationship.	lecture, laboratory	reports, exam	K_W02++ K_U01++ K_U03++	P6S_UW P6S_WG
03	Knows basic properties of Stirling numbers.	lecture, laboratory	reports, exam	K_W01++	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
3	TK01	The basic methods of counting of combinatorial objects. Selection schemes with restrictions.	W1-W2, L1-L2	MEK01
3	TK02	Linear recursive equations, non-linear recursive equations applicable to linear ones.	W3-W5, L3-L5	MEK02
3	TK03	Systems of recursive equations, methods of solving them.	W6-W8, L6-L8	MEK02
3	TK04	Creation of recursive relationships, application of equations and systems of recursive equations in economics (eg market model without stocks, market model with stocks).	W9-W11, L9-L11	MEK02
3	TK05	Stirling numbers of the first and second kind. Sets partially ordered. Counting of graphs (Cayley theorem, Polyi theorem).	W12-W15, L12-L14	MEK03
3	TK06	-	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. 3)	The preparation for a test: 20.00 hours/sem.	contact hours: 15.00 hours/sem.	complementing/reading through notes: 6.00 hours/sem. Studying the recommended bibliography: 8.00 hours/sem.
Laboratory (sem. 3)	The preparation for a Laboratory: 24.00 hours/sem. The preparation for a test: 4.00 hours/sem.	contact hours: 15.00 hours/sem.
Advice (sem. 3)	The preparation for Advice: 4.00 hours/sem.	The participation in Advice: 4.00 hours/sem.
Exam (sem. 3)	The preparation for an Exam: 6.00 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	Passing the lecture is based on the exam.
Laboratory	Reports and practical test at the computer using software such as CAS Maxima.
The final grade	The final grade is the grade from laboratory and 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: no