Combinatorics Field of study: Mathematics
Programme code: W4-S1MT19.2023

Module name: Combinatorics
Module code: W4-MT-S1-23-Kom
Programme code: W4-S1MT19.2023
Semester: summer semester 2024/2025
Language of instruction: Polish
Form of verification: course work
ECTS credits: 3
Purpose and description of the content of education:
Elementarne metody przeliczania: prawo mnożenia, prawo dodawania, metoda bijektywna. Schematy wyboru: permutacje, kombinacje, wariacje, podziały zbioru, podziały liczb. Liczby Fibonacciego, Catalana, Stirlinga. Współczynniki dwumianowe i ich własności. Dwumian Newtona. Zasada szufladkowa Dirichleta, reguła włączania i wyłączania i zasada podziałowa. Rekurencja, funkcje tworzące. Elementy teorii grafów.
List of modules that must be completed before starting this module (if necessary): not applicable
Learning outcome of the module Codes of the learning outcomes of the programme to which the learning outcome of the module is related [level of competence: scale 1-5]
zna definicje podstawowych obiektów kombinatorycznych i ich własności [Kom_1]
 K_W06 [5/5] K_U29 [5/5]
zna i potrafi rozpoznawać podstawowe obiekty kombinatoryczne w różnych zagadnieniach matematycznych i praktycznych [Kom_2]
 K_W06 [5/5] K_U29 [5/5]
potrafi łączyć różne schematy losowania z odpowiednimi obiektami kombinatorycznymi [Kom_3]
 K_W06 [5/5] K_U29 [5/5]
zna i potrafi swobodnie stosować poznane metody zliczania [Kom_4]
 K_W06 [5/5] K_U29 [5/5]
potrafi rozwiązywać proste równania różnicowe i rekurencyjne [Kom_5]
 K_W06 [5/5] K_U29 [5/5]
zna podstawowe pojęcia i fakty teorii grafów [Kom_6]
 K_W06 [5/5] K_U29 [5/5]
Form of teaching Number of hours Methods of conducting classes Assessment of the learning outcomes Learning outcomes
lecture [Kom_fs_1] 15 Formal lecture/ course-related lecture [a01]  course work Kom_1 Kom_2 Kom_3 Kom_4 Kom_5 Kom_6
discussion classes [Kom_fs_2] 15 Activating method – peer learning [b08] 
Laboratory exercise / experiment [e01]  		course work Kom_2 Kom_3 Kom_4 Kom_5
The student's work, apart from participation in classes, includes in particular:
Name Category Description
Literature reading / analysis of source materials [a02] Preparation for classes
reading the literature indicated in the syllabus; reviewing, organizing, analyzing and selecting source materials to be used in class
Developing practical skills [a03] Preparation for classes
activities involving the repetition, refinement and consolidation of practical skills, including those developed during previous classes or new skills necessary for the implementation of subsequent elements of the curriculum (as preparation for class participation)
Determining the stages of task implementation contributing to the verification of learning outcomes [c01] Preparation for verification of learning outcomes
devising a task implementation strategy embracing the division of content, the range of activities, implementation time and/or the method(s) of obtaining the necessary materials and tools, etc.
Studying the literature used in and the materials produced in class [c02] Preparation for verification of learning outcomes
exploring the studied content, inquiring, considering, assimilating, interpreting it, or organizing knowledge obtained from the literature, documentation, instructions, scenarios, etc., used in class as well as from the notes or other materials/artifacts made in class
Analysis of the corrective feedback provided by the academic teacher on the results of the verification of learning outcomes [d01] Consulting the results of the verification of learning outcomes
reading through the academic teacher’s comments, assessments and opinions on the implementation of the task aimed at checking the level of the achieved learning outcomes
Attachments
Module description (PDF)
Information concerning module syllabuses might be changed during studies.
Syllabuses (USOSweb)
Semester Module Language of instruction
(no information given)