Mathematical Foundations of Computer Science Field of study: Mathematics
Programme code: W4-N2MT19.2023

Module name: Mathematical Foundations of Computer Science
Module code: W4-MT-N2-23-MPInf
Programme code: W4-N2MT19.2023
Semester: winter semester 2023/2024
Language of instruction: Polish
Form of verification: course work
ECTS credits: 2
Purpose and description of the content of education:
Celem modułu Matematyczne podstawy informatyki jest wykształcenie umiejętności swobodnego posługiwania się podstawowymi pojęciami informatycznymi w działalności matematycznej. W ramach zajęć przewiduje się realizację następujących treści programowych: 1. Podstawy teorii informacji; pojęcie entropii, kodowanie Huffmana oraz kodowanie Shannona-Fano. 2. Elementy analizy algorytmów. Rozmiar danych, złożoność obliczeniowa. Typy złożoności: pesymistyczna, optymistyczna, średnia. Notacja asymptotyczna, rzędy wielkości funkcji. Algorytmy rekurencyjne. 3. Wybrane metody numeryczne. 4. Matematyczne podstawy kryptografii i jej zastosowania.
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 pojęcie entropii oraz kodowania optymalnego; zna kodowanie Huffmana oraz kodowanie Shannona-Fano [MPIn_1]
 K_W04 [3/5]
zna i rozumie pojęcie złożoności obliczeniowej (czasowej i pamięciowej) oraz notacji asymptotycznej [MPIn_2]
 K_W04 [3/5]
potrafi wyznaczać złożoność obliczeniową prostych algorytmów, w tym algorytmów rekurencyjnych [MPIn_3]
 K_U05 [3/5]
zna podstawowe algorytmy numeryczne [MPIn_4]
 K_W05 [3/5]
zna matematyczne podstawy kryptografii i jej wybrane zastosowania [MPIn_5]
 K_W05 [4/5]
Form of teaching Number of hours Methods of conducting classes Assessment of the learning outcomes Learning outcomes
lecture [MPIn_fns_1] 15 Formal lecture/ course-related lecture [a01] 
Screen presentation [c07]  		course work MPIn_1 MPIn_2 MPIn_4 MPIn_5
laboratory classes [MPIn_fns_2] 15 Activating method – peer learning [b08] 
Working with a computer [d01]  		course work MPIn_1 MPIn_2 MPIn_3 MPIn_4 MPIn_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)
Consulting materials complementary to those indicated in the syllabus [a04] Preparation for classes
agreeing on materials complementary to those indicated in the syllabus, supporting the implementation of tasks resulting from or necessary 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)