Functional Analysis Field of study: Mathematics
Programme code: W4-S2MT19.2024

Module name: Functional Analysis
Module code: W4-MT-S2-23-AFun
Programme code: W4-S2MT19.2024
Semester: summer semester 2024/2025
Language of instruction: Polish
Form of verification: exam
ECTS credits: 6
Purpose and description of the content of education:
Moduł Analiza funkcjonalna ma na celu wykształcenie umiejętności posługiwania się podstawowymi metodami analizy funkcjonalnej, doboru stosownych przestrzeni i wykorzystania odpowiednich operatorów w szeroko rozumianej analizie. Przewiduje się realizację następujących treści programowych: 1. Przestrzenie unormowane i przestrzenie Banacha. 2. Przestrzenie unitarne i przestrzenie Hilberta. 3. Prostopadłość i rzutowanie prostopadłe. Twierdzenia o zbiorze wypukłym i rzucie prostopadłym. 4. Układy ortonormalne i szeregi Fouriera w przestrzeni Hilberta. 5. Przekształcenia liniowe przestrzeni unormowanych. 6. Przestrzeń sprzężona. Twierdzenie Riesza. 7. Twierdzenia Hahna-Banacha, o odwzorowaniu otwartym, o domkniętym wykresie, Banacha-Steinhausa. 8. Układ trygonometryczny i jego zupełność.
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 klasyczną wiedzę z zakresu analizy funkcjonalnej [AFun_1]
 K_W01 [5/5]
zna i rozumie rolę i znaczenie konstrukcji rozumowań matematycznych z zakresu analizy funkcjonalnej [AFun_2]
 K_W02 [3/5]
zna i rozumie najważniejsze twierdzenia analizy funkcjonalnej [AFun_3]
 K_W03 [5/5]
potrafi konstruować rozumowania matematyczne z zakresu analizy funkcjonalnej i sprawdzać ich poprawność [AFun_4]
 K_U01 [3/5] K_U03 [3/5]
potrafi wyrażać treści matematyczne z zakresu analizy funkcjonalnej w mowie i na piśmie [AFun_5]
 K_U02 [3/5]
Form of teaching Number of hours Methods of conducting classes Assessment of the learning outcomes Learning outcomes
lecture [AFun_fs_1] 30 Formal lecture/ course-related lecture [a01]  exam AFun_1 AFun_2 AFun_3 AFun_4 AFun_5
discussion classes [AFun_fs_2] 30 Activating method – peer learning [b08] 
Working with a programmed textbook [d02] 
Reconstruction / reproduction [d04] 
Laboratory exercise / experiment [e01]  		course work AFun_1 AFun_2 AFun_3 AFun_4 AFun_5
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
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)