Algebra and Geometry Field of study: Mathematics
Programme code: W4-S2MT19.2025

Module name: Algebra and Geometry
Module code: W4-MT-S2-25-AGeo
Programme code: W4-S2MT19.2025
Semester: winter semester 2025/2026
Language of instruction: Polish
Form of verification: exam
ECTS credits: 4
Purpose and description of the content of education:
The aim of the course "Algebra with Geometry" is to present the interplay between two classical branches of mathematics: algebra and geometry. The course places particular emphasis on demonstrating how algebraic tools can be used to formalize and solve geometric problems, as well as how geometric questions inspire the development of appropriate algebraic techniques. The course content expands and deepens topics introduced in first-cycle (undergraduate) algebra and geometry courses, and includes the following: 1) Linear algebra over rings and module theory. 2) Simplices, simplicial complexes, and polyhedra. 3) Introduction to homological algebra. Applications of module theory to the study of geometric and topological properties of polyhedra. 4) Polyhedral subdivisions and measure-theoretic properties.
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 has a deep knowledge of the relationship between algebra and geometry. [AGeo_1]
 K_W01 [2/5] K_W02 [1/5] K_W03 [2/5]
The student knows the schemes of proofs of key theorems learned during the lecture. [AGeo_2]
 K_W01 [2/5] K_W02 [2/5] K_W03 [2/5]
The student can use algebraic tools to describe and study objects and geometric transformations. [AGeo_3]
 K_U01 [1/5] K_U04 [2/5] K_U07 [2/5]
The student is able to explain algebraic and geometric problems to a non-specialist and present their applications [AGeo_4]
 K_U02 [2/5] K_U07 [1/5] K_U09 [3/5]
The student can use tools from homological algebra to study properties of polyhedra. [AGeo_5]
 K_U01 [2/5] K_U04 [2/5] K_U05 [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 AGeo_5
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 AGeo_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
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)