Discrete mathematics and elements of graph theory Field of study: Data Science and Artificial Intelligence
Programme code: W4-S1DS25.2025

Module name: Discrete mathematics and elements of graph theory
Module code: W4_DSAI_S1
Programme code: W4-S1DS25.2025
Semester: summer semester 2025/2026
Language of instruction: Polish
Form of verification: course work
ECTS credits: 4
Purpose and description of the content of education:
Celem przedmiotu jest zaznajomienie z zagadnieniami związanymi z matematyka dyskretną, które znajdą zastosowanie w kolejnych modułach związanych z analizą danych i sztuczną inteligencją. Realizowane treści: Pojęcia kombinatoryki: wariacje, permutacje, kombinacje; symbole dwumianowe Newtona i ich własności. Algorytmy generujące proste obiekty kombinatoryczne: permutacje, wariacje, podzbiory zbioru; generowanie losowych obiektów kombinatorycznych; przykłady zastosowań takich algorytmów. Metody zliczania obiektów: metoda bijektywna; reguła włączania i wyłączania; rekurencja i funkcje tworzące, liczby Fibonacciego i Catalana. Elementy teorii grafów: podstawowe pojęcia; minimalne drzewo rozpinające; problem minimalnych odległości; grafy Eulera i Hamiltona, problem komiwojażera.
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]
Ma świadomość znaczenia wiedzy w rozwiązywaniu problemów poznawczych i praktycznych oraz uznaje konieczność zasięgania opinii ekspertów w przypadku trudności z samodzielnym rozwiązaniem problemów. [K01]
 DSAI_1S_K01 [3/5]
Potrafi zliczać obiekty kombinatoryczne. [U01]
 DSAI_1S_U01 [3/5] DSAI_1S_U02 [1/5]
Potrafi zastosować właściwe schematy kombinatoryczne do rozwiązywania problemów informatycznych i przeprowadzić konieczne obliczenia przy pomocy poznanych metod i algorytmów [U02]
 DSAI_1S_U01 [3/5] DSAI_1S_U02 [2/5]
Potrafi zastosować terminologię i algorytmy teorii grafów do rozwiązywania problemów informatycznych. [U03]
 DSAI_1S_U01 [3/5] DSAI_1S_U02 [2/5]
Zna wybrane obiekty kombinatoryczne. [W01]
 DSAI_1S_W01 [3/5]
Wymienia najważniejsze metody zliczania obiektów kombinatorycznych. [W02]
 DSAI_1S_W01 [3/5]
Zna pojęcia związane z teorią grafów. [W03]
 DSAI_1S_W01 [3/5]
Form of teaching Number of hours Methods of conducting classes Assessment of the learning outcomes Learning outcomes
discussion classes [fs_01] 45 Description [a03] 
Explanation/clarification [a05] 
Lecture-discussion [b02] 
Activating method – peer learning [b08] 
Screen presentation [c07]  		course work K01 U01 U02 U03 W01 W02 W03
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)
Getting acquainted with the syllabus content [b01] Consulting the curriculum and the organization of classes
reading through the syllabus and getting acquainted with its content
Verification / adjustment / discussion of syllabus provisions [b02] Consulting the curriculum and the organization of classes
consulting the content of the syllabus, possibly in the presence of the year tutor or members of the class group, and, if necessary, reassessing the provisions concerning special conditions for class participation, e.g., space and time requirements, technical and other requirements, including conditions for participation in classes outside the walls of the university, classes organized in blocks, organized online, etc.
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.
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
Development of a corrective action plan as well as supplementary/corrective tasks [d02] Consulting the results of the verification of learning outcomes
reviewing and selecting tasks and activities enabling the elimination of errors indicated by the academic teacher, their verification or correction resulting in completing the task with at least the minimum passing grade
Attachments
Module description (PDF)
Information concerning module syllabuses might be changed during studies.
Syllabuses (USOSweb)
Semester Module Language of instruction
(no information given)