Introduction to Computational Mathematics A Field of study: Mathematics
Programme code: W4-S1MT19.2024

Module name: Introduction to Computational Mathematics A
Module code: W4-MT-S1-24-WMObA
Programme code: W4-S1MT19.2024
Semester: summer semester 2025/2026
Language of instruction: Polish
Form of verification: exam
ECTS credits: 5
Purpose and description of the content of education:
Celem przedmiotu jest poznanie i zrozumienie podstaw matematyki obliczeniowej oraz zasad działania programów typu CAS (ang. Computer Algebra System): reprezentacji obiektów matematycznych, symbolicznych oraz numerycznych algorytmów obliczeniowych. Program wykładu obejmuje takie zagadnienia jak: - reprezentacja wybranych obiektów matematycznych (np. wielomiany, macierze) oraz algorytmy obliczeniowe pozwalające na nich operować; - równania wielomianowe jednej zmiennej oraz układy równań wielomianowych wielu zmiennych; - inne aspekty matematyki obliczeniowej - w zależności od dostępnego czasu i zainteresowań studentów.
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]
Student zna podstawowe zasady działania programów matematycznych oraz ich ograniczenia. [WMObA_1]
 K_W06 [4/5] K_W07 [1/5] K_U07 [1/5]
Student zna reprezentacje podstawowych obiektów matematycznych (takich jak: liczby całkowite, liczby zmiennoprzecinkowe, macierzy, wielomiany) oraz podstawowe algorytmy pozwalające na nich operować. [WMObA_2]
 K_W06 [2/5] K_W07 [1/5] K_U04 [2/5] K_U07 [2/5] K_U08 [1/5] K_U09 [1/5]
Student zna pojęcie błędów zaokrągleń i reprezentacji dla liczb zmiennoprzecinkowych oraz ma świadomość różnych rodzajów błędów występujących w obliczeniach numerycznych. [WMObA_3]
 K_W06 [1/5] K_W07 [1/5] K_U07 [1/5]
Student zna podstawowe algorytmy używane do rozwiązywania równań (i układów równań) wielomianowych. [WMObA_4]
 K_W06 [2/5] K_W07 [1/5] K_U03 [1/5] K_U04 [1/5] K_U07 [2/5] K_U08 [1/5] K_U09 [1/5]
Student potrafi rozwiązywać równania wielomianowe jednej zmiennej oraz układy równań wielomianowych dwóch i więcej zmiennych. [WMObA_5]
 K_W06 [2/5] K_W07 [1/5] K_U03 [1/5] K_U04 [1/5] K_U07 [2/5] K_U08 [1/5] K_U09 [1/5]
Form of teaching Number of hours Methods of conducting classes Assessment of the learning outcomes Learning outcomes
lecture [WMObA_fs_1] 30 Formal lecture/ course-related lecture [a01] 
Explanation/clarification [a05]  		exam WMObA_1 WMObA_2 WMObA_3 WMObA_4 WMObA_5
laboratory classes [WMObA_fs_2] 30 Working with a computer [d01] 
Project scheduling [e04]  		course work WMObA_1 WMObA_2 WMObA_3 WMObA_4 WMObA_5
The student's work, apart from participation in classes, includes in particular:
Name Category Description
Search for materials and review activities necessary for class participation [a01] Preparation for classes
reviewing literature, documentation, tools and materials as well as the specifics of the syllabus and the range of activities indicated in it as required for full participation in classes
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
Production/preparation of tools, materials or documentation necessary for class participation [a05] Preparation for classes
developing, preparing and assessing the usefulness of tools and materials (e.g. aids, scenarios, research tools, equipment, etc.) to be employed in class or as an aid when preparing for classes
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
Implementation of an individual or group assignment necessary for course/phase/examination completion [c03] Preparation for verification of learning outcomes
a set of activities aimed at performing an assigned task, to be executed out of class, as an obligatory phase/element of the verification of the learning outcomes assigned to the course
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)