Modulniveau: Master Sprache: Englisch Semesterdauer: Einsemestrig Häufigkeit: Wintersemester Credits*: 9 Gesamt- stunden: 270 Eigenstudiums- stunden: 180 Präsenz- stunden: 90 Prüfungsart: schriftlich Prüfungsdauer (min.): 90 Wiederholungs- möglichkeit: Im Folgesemester: Nein Am Semesterende: Ja Hausaufgaben: Nein Vortrag: Nein Gespräch: Nein Hausarbeit: Nein Modulbeschreibung MA3001: Funktionalanalysis Fakultät für Mathematik * Die Zahl der Credits kann in Einzelfällen studiengangsspezifisch variieren. Es gilt der im Transcript of Records oder Leistungsnachweis ausgewiesene Wert. Beschreibung der Studien-/Prüfungsleistungen: The module examination is based on a written exam (90 minutes). Students have to know theoretical basics and methods to analyze linear functionals and operators in Banach and Hilbert spaces. They can give solutions to application problems in limited time. (Empfohlene) Voraussetzungen: MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Lineare Algebra 1, MA1102 Lineare Algebra 2 Inhalt: Banach and Hilbert spaces; bounded linear operators, open mapping theorem; spectral theory for compact selfadjoint operators; duality, Hahn-Banach theorems; weak and weak* convergence; brief introduction to unbounded operators Lernergebnisse: After successful completion of the module students are able to understand and apply basic theoretical techniques to analyze linear functionals and operators on Banach and Hilbert spaces. Lehr- und Lernmethoden: The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should motivate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress. At the beginning of the module, the practice sessions will be offered under guidance, but during the term the sessions will become more independent, and intensify learning individually as well as in small groups. Medienform: blackboard Literatur: W. Rudin, Functional Analysis, McGraw Hill, 1991. M. Reed/B. Simon, Functional Analysis, Academic Press, 1972. D. Werner: Funktionalanalysis, Springer, 2007. F. Hirzebruch, W. Scharlau: Einführung in die Funktionalanalysis, BI-Hochschulbücher, 1991.

Modulbeschreibung MA3001: Funktionalanalysis · PDF fileMA1001 Analysis 1, MA1002 Analysis 2, MA1101 Lineare Algebra 1, MA1102 Lineare Algebra 2 Inhalt: Banach and Hilbert spaces;

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Page 1: Modulbeschreibung MA3001: Funktionalanalysis · PDF fileMA1001 Analysis 1, MA1002 Analysis 2, MA1101 Lineare Algebra 1, MA1102 Lineare Algebra 2 Inhalt: Banach and Hilbert spaces;

Modulniveau:Master

Sprache:Englisch

Semesterdauer:Einsemestrig

Häufigkeit:Wintersemester

Credits*:9

Gesamt-stunden:270

Eigenstudiums-stunden:180

Präsenz-stunden:90

Prüfungsart:schriftlich

Prüfungsdauer (min.):90

Wiederholungs-möglichkeit:Im Folgesemester: NeinAm Semesterende: Ja

Hausaufgaben:Nein

Vortrag:Nein

Gespräch:Nein

Hausarbeit:Nein

Modulbeschreibung

MA3001: Funktionalanalysis

Fakultät für Mathematik

* Die Zahl der Credits kann in Einzelfällen studiengangsspezifisch variieren. Es gilt der im Transcript of Records oder Leistungsnachweis ausgewiesene Wert.

Beschreibung der Studien-/Prüfungsleistungen:The module examination is based on a written exam (90 minutes). Students have to know theoretical basics andmethods to analyze linear functionals and operators in Banach and Hilbert spaces. They can give solutions toapplication problems in limited time.

(Empfohlene) Voraussetzungen:MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Lineare Algebra 1, MA1102 Lineare Algebra 2

Inhalt:Banach and Hilbert spaces; bounded linear operators, open mapping theorem; spectral theory for compact selfadjointoperators; duality, Hahn-Banach theorems; weak and weak* convergence; brief introduction to unbounded operators

Lernergebnisse:After successful completion of the module students are able to understand and apply basic theoretical techniques toanalyze linear functionals and operators on Banach and Hilbert spaces.

Lehr- und Lernmethoden:The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will bepresented in a talk with demonstrative examples, as well as through discussion with the students. The lectures shouldmotivate the students to carry out their own analysis of the themes presented and to independently study the relevantliterature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions willbe available. In this way, students can deepen their understanding of the methods and concepts taught in the lecturesand independently check their progress. At the beginning of the module, the practice sessions will be offered underguidance, but during the term the sessions will become more independent, and intensify learning individually as wellas in small groups.

Medienform:blackboard

Literatur:W. Rudin, Functional Analysis, McGraw Hill, 1991.M. Reed/B. Simon, Functional Analysis, Academic Press, 1972.D. Werner: Funktionalanalysis, Springer, 2007.F. Hirzebruch, W. Scharlau: Einführung in die Funktionalanalysis, BI-Hochschulbücher, 1991.