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Discrete mathematics


Some basic information about the module

Cycle of education:
2019/2020
The name of the faculty organization unit:
The faculty Mathematics and Applied Physics
The name of the field of study:
Engineering and data analysis
The area of study:
sciences
The profile of studing:
The level of study:
first degree study
Type of study:
full time
discipline specialities :
The degree after graduating from university:
engineer
The name of the module department :
Departament of Mathematical Modelling
The code of the module:
12296
The module status:
mandatory for teaching programme
The position in the studies teaching programme:
sem: 2 / W15 C15 L15 / 3 ECTS / Z
The language of the lecture:
Polish
The name of the coordinator:
Andrzej Włoch, DSc, PhD
semester 2:
Adrian Michalski, PhD
semester 2:
Paweł Bednarz, PhD

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
MEK01 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
MEK02 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
MEK03 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

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