Algebra Field of study: Mathematics
Programme code: W4-S1MT19.2024

Module name: Algebra
Module code: W4-MT-S1-24-Alg
Programme code: W4-S1MT19.2024
Semester: winter semester 2026/2027
Language of instruction: Polish
Form of verification: exam
ECTS credits: 5
Purpose and description of the content of education:
Celem przedmiotu „Algebra” jest wykształcenie u słuchaczy umiejętności dostrzegania i identyfikowania struktur algebraicznych takich jak grupy, pierścienie i ciała, a także posługiwania się własnościami tych struktur i ich homomorfizmów. W ramach kursu przewiduje się realizację następujących treści programowych: 1. Teoria grup: grupy i podgrupy, podgrupy normalne i grupy ilorazowe, homomorfizmy grup. 2. Teoria pierścieni przemiennych: pierścienie i podpierścienie, ideały i pierścienie ilorazowe, homomorfizmy pierścieni, elementy teorii podzielności w pierścieniach całkowitych. 3. Teoria ciał: ciała, podciała i rozszerzenia ciał, monomorfizmy ciał, elementy algebraiczne nad ciałem.
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 podstawowe pojęcia z zakresu teorii grup, teorii pierścieni i teorii ciał, potrafi się nimi posługiwać oraz dowodzić podstawowych własności poznanych struktur algebraicznych [Alg_1]
 K_W02 [3/5] K_W03 [3/5] K_W04 [3/5] K_U01 [2/5] K_U04 [3/5]
zna schematy dowodów kluczowych twierdzeń algebraicznych poznanych na wykładzie [Alg_2]
 K_W02 [3/5] K_W03 [3/5]
potrafi konstruować struktury algebraiczne, ich podstrukty, struktury ilorazowe oraz produktowe, a także ich morfizmy [Alg_3]
 K_W04 [3/5] K_U01 [3/5]
potrafi weryfikować własności poznanych struktur algebraicznych w konkretnych sytuacjach [Alg_4]
 K_W04 [3/5] K_U04 [3/5]
potrafi zastosować poznane narzędzia algebraiczne w sytuacjach problemowych [Alg_5]
 K_W04 [3/5] K_U01 [3/5] K_U04 [3/5]
Form of teaching Number of hours Methods of conducting classes Assessment of the learning outcomes Learning outcomes
lecture [Alg_fs_1] 30 Formal lecture/ course-related lecture [a01]  exam Alg_1 Alg_2 Alg_3 Alg_4 Alg_5
discussion classes [Alg_fs_2] 30 Laboratory exercise / experiment [e01]  course work Alg_1 Alg_2 Alg_3 Alg_4 Alg_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
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
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)