Mathematical Analysis 1 Field of study: Data Science and Artificial Intelligence
Programme code: W4-S1DS25.2025

Module name: Mathematical Analysis 1
Module code: W4_DSAI_S1_AMat1
Programme code: W4-S1DS25.2025
Semester: 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 zapoznanie studenta z podstawowymi pojęciami i metodami analizy matematycznej. Treści programowe obejmują również typowe zastosowania metod analizy matematycznej. W czasie zajęć będą poruszane zagadnienia dotyczące m.in. własności funkcji, własności zbioru liczb rzeczywistych i jego podzbiorów, podstawowych informacji o przestrzeniach metrycznych, ciągów liczbowych i ich granic, szeregów, granic funkcji, funkcji ciągłych i ich własności, pochodnej funkcji jednej zmiennej, wzoru Taylora, ekstremów lokalnych, całki nieoznaczonej oraz całki Riemanna.
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]
Dostrzega znaczenie wiedzy matematycznej w rozwiązywaniu problemów poznawczych i praktycznych w obszarze analizy danych i sztucznej inteligencji oraz potrafi rozpoznać potrzebę konsultacji z ekspertami w przypadku trudności z ich samodzielnym rozwiązaniem [K01]
 DSAI_1S_K01 [3/5]
Potrafi rozwiązywać zadania z zakresu analizy matematycznej funkcji jednej zmiennej [U01]
 DSAI_1S_U01 [3/5]
Zna podstawowe pojęcia z zakresu analizy matematycznej funkcji jednej zmiennej oraz jej zastosowań [W01]
 DSAI_1S_W01 [3/5]
Zna metody związane z zastosowaniem analizy matematycznej do rozwiązywania problemów przyrodniczych i technicznych [W02]
 DSAI_1S_W01 [3/5]
Rozumie potrzebę ścisłości matematycznej i potrafi przeprowadzać poprawne rozumowania [W03]
 DSAI_1S_W01 [3/5]
Form of teaching Number of hours Methods of conducting classes Assessment of the learning outcomes Learning outcomes
discussion classes [fs_01] 75 Explanation/clarification [a05] 
Lecture-discussion [b02] 
Laboratory exercise / experiment [e01]  		course work K01 U01 W01 W02 W03
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.
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)