Algebra and Geometry Field of study: Mathematics
Programme code: W4-S2MT19.2024

Module name: Algebra and Geometry
Module code: W4-MT-S2-23-AGeo
Programme code: W4-S2MT19.2024
Semester: winter semester 2024/2025
Language of instruction: Polish
Form of verification: exam
ECTS credits: 4
Purpose and description of the content of education:
The aim of the course is to familiarize students with the basic notions of algebra and classical geometry, to the extent necessary to teach mathematics in high school and prepare high school students for participation in competitions and subject olympiads. The course includes the following content: 1. Basic algebraic structures: rings and fields, matrix groups. 2. Spaces, subspaces and linear transformations 3. Fundamentals of affine geometry: space, subspace, affine transformations, systems of points. 4. Two- and three-dimensional analytical geometry. 5. Scalar product, bilinear space. isometries.
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]
The student knows and understands algebra and geometry sufficiently to teach it in high school. [AGeo_1]
 K_W01 [2/5] K_W03 [2/5]
The student knows the relationship between algebra and geometry. He can use algebraic tools to describe and study objects and geometric transformations. [AGeo_2]
 K_U04 [2/5] K_U07 [2/5]
The student knows the schemes of proofs of key theorems learned during the lecture. [AGeo_3]
 K_U01 [2/5] K_U03 [2/5]
The student is able to explain algebraic and geometric problems to a non-specialist and present their applications [AGeo_4]
 K_U07 [2/5] K_U09 [2/5]
Form of teaching Number of hours Methods of conducting classes Assessment of the learning outcomes Learning outcomes
lecture [AGeo_fs_1] 15 Formal lecture/ course-related lecture [a01]  exam AGeo_1 AGeo_2 AGeo_3 AGeo_4
discussion classes [AGeo_fs_2] 30 Problem-based lecture [b01] 
Activating method – peer learning [b08]  		course work AGeo_1 AGeo_2 AGeo_3 AGeo_4
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
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
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.
Consulting the schedule [b03] Consulting the curriculum and the organization of classes
getting acquainted with the class schedule, possibly in the presence of the year tutor, in order to optimize participation in classes, including those supplementary to the core subjects listed in the pursued study programme
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)