Introduction to Mathematics Field of study: Mathematics
Programme code: W4-S1MT19.2025

Module name: Introduction to Mathematics
Module code: W4-MT-S1-25-WMat
Programme code: W4-S1MT19.2025
Semester: winter semester 2025/2026
Language of instruction: Polish
Form of verification: exam
ECTS credits: 5
Purpose and description of the content of education:
The aim of the classes is to familiarize students with concepts in the field of mathematical logic and the foundations of mathematics. The module will cover the following content: 1. The language of classical propositional logic, Boolean semantics, predicate logic. 2. Algebra of sets. 3. Relations -- equivalence and order . 4. Functions. 5. Cardinality of sets.
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]
student dobrze rozumie przedstawioną na zajęciach teorię i znaczenie dowodu w matematyce, a także pojęcie istotności założeń, zna podstawowe przykłady zarówno ilustrujące konkretne pojęcia matematyczne omawiane podczas zajęć, jak i pozwalające obalić błędne hipotezy lub nieuprawnione rozumowania [WMat_1]
 K_W03 [3/5] K_W05 [1/5]
student zna wybrane pojęcia i metody logiki matematycznej, teorii mnogości i matematyki dyskretnej zawarte w podstawach innych dyscyplin matematyki [WMat_2]
 K_W04 [2/5]
student potrafi w sposób zrozumiały w mowie i na piśmie, przedstawiać poprawne rozumowania matematyczne, formułować twierdzenia i definicje z zakresu tematyki modułu [WMat_3]
 K_U01 [2/5]
student potrafi posługiwać się językiem teorii mnogości, interpretując zagadnienia z różnych obszarów matematyki, potrafi posługiwać się rachunkiem zdań i predykatów oraz stosować język logiki do precyzyjnego opisu, modelowania i formalizacji problemów matematycznych pochodzących z różnych działów matematyki [WMat_4]
 K_U02 [3/5]
Form of teaching Number of hours Methods of conducting classes Assessment of the learning outcomes Learning outcomes
lecture [WMat_fs_1] 30 Formal lecture/ course-related lecture [a01] 
Lecture-discussion [b02]  		exam WMat_1 WMat_2 WMat_3 WMat_4
discussion classes [WMat_fs_2] 30 Explanation/clarification [a05] 
Working with a programmed textbook [d02] 
Reconstruction / reproduction [d04] 
Laboratory exercise / experiment [e01]  		course work WMat_1 WMat_2 WMat_3 WMat_4
The student's work, apart from participation in classes, includes in particular:
Name Category Description
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
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
Undertaking, on one’s own initiative and individually, activities aimed at expanding the scope or depth of the teaching content, also beyond the walls of the University [e01] Activities complementary to the classes
a set of activities undertaken independently and on the student's own initiative, aimed at expanding the depth and scope of knowledge and skills, their revision and repetition, retention or verification, also activities carried outside the university, e.g., in a culture promoting or educational institution, a laboratory, in the open air, etc.; also self-education
Attachments
Module description (PDF)
Information concerning module syllabuses might be changed during studies.
Syllabuses (USOSweb)
Semester Module Language of instruction
(no information given)