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

Module name: Algebra A
Module code: W4-MT-S1-24-AlgA
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:
Moduł „Algebra A” ma na celu wykształcenie umiejętności swobodnego posługiwania się podstawowymi pojęciami i narzędziami algebry w zakresie grup, pierścieni i ciał. 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 [EAAbA_1]
 K_W04 [3/5] K_U04 [3/5]
potrafi dowodzić podstawowe własności poznanych struktur algebraicznych [EAAbA_2]
 K_W02 [3/5] K_W03 [3/5] K_U01 [2/5]
zna schematy dowodów kluczowych twierdzeń dotyczących grup, pierścieni i ciał [EAAbA_3]
 K_W02 [3/5] K_W03 [3/5]
potrafi konstruować podstruktury poznanych struktur algebraicznych, grupy i pierścienie ilorazowe oraz potrafi zadawać strukturę grupy/pierścienia na produkcie kartezjańskim grup/pierścieni [EAAbA_4]
 K_W04 [3/5] K_U01 [3/5]
potrafi zweryfikować czy dane zbiory, spotykane w różnych działach matematyki, spełniają aksjomatykę grupy, pierścienia lub ciała [EAAbA_5]
 K_W04 [3/5] K_U04 [3/5]
potrafi sprawdzać czy dana funkcja jest morfizmem struktur algebraicznych oraz konstruować morfizmy o zadanych własnościach [EAAbA_6]
 K_W04 [3/5] K_U01 [3/5]
Form of teaching Number of hours Methods of conducting classes Assessment of the learning outcomes Learning outcomes
lecture [EAAbA_fs_1] 30 Formal lecture/ course-related lecture [a01]  exam EAAbA_1 EAAbA_2 EAAbA_3 EAAbA_4 EAAbA_5 EAAbA_6
discussion classes [EAAbA_fs_2] 30 Laboratory exercise / experiment [e01]  course work EAAbA_1 EAAbA_2 EAAbA_3 EAAbA_4 EAAbA_5 EAAbA_6
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)