Computational Mathematics Field of study: Mathematics
Programme code: W4-N2MT19.2023

Module name: Computational Mathematics
Module code: W4-MT-N2-23-MObl
Programme code: W4-N2MT19.2023
Semester: winter semester 2023/2024
Language of instruction: Polish
Form of verification: course work
ECTS credits: 3
Purpose and description of the content of education:
Celem przedmiotu jest pogłębione zapoznanie studentów z algorytmami i strukturami danych używanymi w matematyce obliczeniowej. Oś przedmiotu jest paralelna do kursowego wykładu "Wstęp do matematyki obliczeniowej" odbywającego się na studiach 1. stopania, jednakże celem bieżącego kursu jest przedstawienie studentom bardziej zaawansowanych metod obliczeniowych. Program wykładu obejmuje następujące zagadnienia: - szybka transformata Fouriera i jej zastosowania, w tym szybkie algorytmy mnożenia za pomocą FFT; - rozkład bezkwadratowy i jego zastosowania do rozkładu funkcji wymiernych na ułamki proste oraz całkowania symbolicznego funkcji wymiernych; - zaawansowane algorytmy rozwiązywania równań wielomianowych jednej zmiennej; - porządki jednomianowe, bazy Gröbnera, rozwiązywanie układów równań wielomianowych wielu zmiennych za pomocą baz Gröbnera, inne zastosowania baz Gröbnera.
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 potrafi zastosować wybrany system CAS rozwiązywania problemów z różnych działów matematyki. [MObl_1]
 K_U07 [1/5]
Student zna podstawowe i zaawansowane algorytmy używane do rozwiązywania równań wielomianowych jednej zmiennej a także układów równań wielomianowych wielu zmiennych. [MObl_2]
 K_W04 [1/5] K_W05 [1/5] K_U07 [1/5]
Student zna zasady działania programów matematycznych oraz ich ograniczenia. [MObl_3]
 K_W01 [1/5]
Student potrafi zastosować rozkład bezkwadratowy wielomianu do symbolicznego obliczania całek z funkcji wymiernych. [MObl_4]
 K_W01 [1/5] K_W04 [1/5] K_W05 [1/5]
Student zna wybrane zastosowania baz Gröbnera. [MObl_5]
 K_W04 [1/5] K_W05 [1/5]
Form of teaching Number of hours Methods of conducting classes Assessment of the learning outcomes Learning outcomes
lecture [MObl_fns_1] 15 Formal lecture/ course-related lecture [a01] 
Explanation/clarification [a05]  		course work MObl_1 MObl_2 MObl_3 MObl_4 MObl_5
laboratory classes [MObl_fns_2] 15 Working with a computer [d01] 
Project scheduling [e04]  		course work MObl_1 MObl_2 MObl_3 MObl_4 MObl_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)
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
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
Attachments
Module description (PDF)
Information concerning module syllabuses might be changed during studies.
Syllabuses (USOSweb)
Semester Module Language of instruction
(no information given)