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

Module name: Geometry A
Module code: W4-MT-S1-24-GeoA
Programme code: W4-S1MT19.2024
Semester: winter semester 2025/2026
Language of instruction: Polish
Form of verification: exam
ECTS credits: 5
Purpose and description of the content of education:
Celem przedmiotu Geometria A jest wykształcenie u słuchaczy umiejętności swobodnego posługiwania się podstawowymi pojęciami i narzędziami geometrii klasycznej i rzutowej. Przewiduje się realizację następujących treści programowych: 1. Euklidesowe przestrzenie współrzędnych ze zwykłym iloczynem skalarnym, rzutowanie prostopadłe, miara kąta. 2. Afiniczne euklidesowe przestrzenie współrzędnych, podprzestrzenie afiniczne: proste, płaszczyzny, hiperpłaszczyzny; metryka euklidesowa, układ współrzędnych, wybrane zagadnienia geometrii elementarnej. 3. Przekształcenia afiniczne, izometrie i podobieństwa. 4.Hiperpowierzchnie stopnia 2, własności wybranych krzywych i powierzchni stopnia 2. 5. Wybrane informacje o geometriach nieeuklidesowych. 6. Elementy geometrii rzutowej, płaszczyzna i przestrzeń rzutowa.
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 pojęcia i fakty z geometrii, potrafi posługiwać się nimi w mowie i piśmie [GeoA_1]
 K_W04 [1/5] K_W05 [2/5] K_U04 [1/5]
zna podstawy geometrii afinicznej i geometrii rzutowej [GeoA_2]
 K_W04 [1/5] K_W05 [2/5] K_U04 [1/5]
zna podstawy geometrii euklidesowej, wie o istnieniu geometrii nieeuklidesowych [GeoA_3]
 K_W04 [1/5] K_W05 [2/5] K_U04 [1/5]
potrafi zastosować wyznacznik i metody rozwiązywania układów równań liniowych w geometrii analitycznej [GeoA_4]
 K_W04 [1/5] K_W05 [2/5] K_U04 [2/5]
potrafi klasyfikować stożkowe i powierzchnie posługując się wyznacznikami macierzy związanych z równaniami tych utworów stopnia 2 [GeoA_5]
 K_W04 [1/5] K_W05 [2/5] K_U04 [1/5]
Form of teaching Number of hours Methods of conducting classes Assessment of the learning outcomes Learning outcomes
lecture [GeoA_fs_1] 30 Formal lecture/ course-related lecture [a01]  exam GeoA_1 GeoA_2 GeoA_3 GeoA_4 GeoA_5
discussion classes [GeoA_fs_2] 30 Activating method – discussion / debate [b04] 
Laboratory exercise / experiment [e01]  		course work GeoA_1 GeoA_2 GeoA_3 GeoA_4 GeoA_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)
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
Verification / adjustment / discussion of syllabus provisions [b02] Consulting the curriculum and the organization of classes
consulting the content of the syllabus, possibly in the presence of the year tutor or members of the class group, and, if necessary, reassessing the provisions concerning special conditions for class participation, e.g., space and time requirements, technical and other requirements, including conditions for participation in classes outside the walls of the university, classes organized in blocks, organized online, 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)