Optional Lecture Field of study: Mathematics
Programme code: W4-S2MT19.2025

Module name: Optional Lecture
Module code: W4-MT-S2-25-WFak
Programme code: W4-S2MT19.2025
Semester:
  • winter semester 2026/2027
  • winter semester 2025/2026
Language of instruction: Polish
Form of verification: course work
ECTS credits: 6
Purpose and description of the content of education:
Celem przedmiotu jest pogłębienie wiedzy i umiejętności studenta z wybranej gałęzi matematyki poprzez wprowadzenie wyspecjalizowanych technik oraz analizę aktualnych zagadnień badawczych. Wykład ma na celu rozwinięcie zainteresowań badawczych oraz przygotowanie do samodzielnej pracy naukowej. W ramach modułu przewidziano realizację następujących zagadnień programowych. 1. Omówienie kluczowych pojęć i twierdzeń charakterystycznych dla danej dziedziny. 2. Wprowadzenie wyspecjalizowanych metod, technik i ich zastosowań. 3. Analiza przykładów ilustrujących zastosowanie wyspecjalizowanych metod. 4. Przedstawienie aktualnych problemów badawczych i wyników w obrębie wybranej gałęzi matematyki. 5. Analiza wybranych zagadnień w kontekście współczesnych badań matematycznych.
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 i rozumie w pogłębionym stopniu kluczowe definicje, twierdzenia oraz ich dowody w obrębie wybranej gałęzi matematyki, zgodnie z zakresem tematycznym realizowanego wykładu fakultatywnego [WFak_1]
 K_W04 [4/5]
rozumie sformułowania problemów otwartych oraz zagadnień badawczych charakterystycznych dla wybranej gałęzi matematyki i jest gotów do ich krytycznej oceny w kontekście treści realizowanego wykładu fakultatywnego [WFak_2]
 K_W05 [5/5] K_K05 [5/5]
umie w pogłębiony sposób stosować i prezentować w mowie oraz piśmie wyspecjalizowane metody charakterystyczne dla wybranej gałęzi matematyki, zgodnie z zakresem tematycznym realizowanego wykładu fakultatywnego [WFak_3]
 K_U05 [5/5]
ma świadomość potrzeby pogłębiania i aktualizowania swojej wiedzy z wybranej gałęzi matematyki poprzez dalsze studiowanie literatury naukowej oraz śledzenie wyników badań związanych z tematyką realizowanego wykładu fakultatywnego [WFak_4]
 K_K01 [5/5]
Form of teaching Number of hours Methods of conducting classes Assessment of the learning outcomes Learning outcomes
lecture [WFak_fs_1] 30 Formal lecture/ course-related lecture [a01]  course work WFak_1 WFak_2 WFak_3 WFak_4
discussion classes [WFak_fs_2] 30 Activating method – peer learning [b08]  course work WFak_1 WFak_2 WFak_3 WFak_4
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)
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
Determining the stages of task implementation contributing to the verification of learning outcomes [c01] Preparation for verification of learning outcomes
devising a task implementation strategy embracing the division of content, the range of activities, implementation time and/or the method(s) of obtaining the necessary materials and tools, 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
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)