Module Handbook

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Module MAT-10-12L_ERW-M-2

Fundamentals of Mathematics B: Linear Algebra II and Analysis II (M, 15.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-10-12L_ERW-M-2 Fundamentals of Mathematics B: Linear Algebra II and Analysis II 15.0 CP (450 h)

Basedata

CP, Effort 15.0 CP = 450 h
Position of the semester 2 Sem. from WiSe
Level [2] Bachelor (Fundamentals)
Language [DE] German
Module Manager
Lecturers
Area of study [MAT-EDU] Mathematics (B.Ed./M.Ed.)
Reference course of study [MAT-B4.105-SG] ZEP LaG Mathematics
Livecycle-State [NORM] Active

Notice

Dieses Modul ist nur belegbar für Studierende des Lehramts, die das Fach Mathematik im Zertifikatsstudiengang (Erweiterungsprüfung) studieren.

Module Part #A "Exercise Classes Fundamentals of Mathematics I" (Obligatory, 6.0 LP)

In this part of the module the required fundamentals for module part B are developed. The CP awarded do not take into account the self-study time required for working out the contents of the respective lectures.
Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2U MAT-10-11B-K-2
Fundamentals of Mathematics I: Linear Algebra
P 28 h 32 h
SL1
ja no 2.0 WiSe/SuSe
2U+2T MAT-10-11A-K-2
Fundamentals of Mathematics I: Analysis
P 56 h 64 h
SL1
ja no 4.0 WiSe/SuSe
  • About [MAT-10-11B-K-2]: Title: "Fundamentals of Mathematics I: Linear Algebra"; Presence-Time: 28 h; Self-Study: 32 h
  • About [MAT-10-11B-K-2]: The study achievement SL1 must be obtained.
    • It is a prerequisite for the examination.
  • About [MAT-10-11A-K-2]: Title: "Fundamentals of Mathematics I: Analysis"; Presence-Time: 56 h; Self-Study: 64 h
  • About [MAT-10-11A-K-2]: The study achievement SL1 must be obtained.
    • It is a prerequisite for the examination.

Module Part #B "Fundamentals of Mathematics II for Students of Teacher Training Programmes" (Obligatory, 9.0 LP)

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V+2U MAT-10-12L-K-2
Fundamentals of Mathematics II (for Students of Teacher Training Programmes)
P 84 h 186 h
U-Schein
- PL1 9.0 WiSe
  • About [MAT-10-12L-K-2]: Title: "Fundamentals of Mathematics II (for Students of Teacher Training Programmes)"; Presence-Time: 84 h; Self-Study: 186 h
  • About [MAT-10-12L-K-2]: The study achievement "[U-Schein] proof of successful participation in the exercise classes (ungraded)" must be obtained.

Study achievement SL1

  • Verification of study performance: proof of successful participation in the exercise classes (incl. written examination)
  • Study achievement is a prerequisite for the examination.
  • Examination number (Study achievement): 82015 ("Exercise Class Fundamentals of Mathematics I")
    Der qualifizierte Übungsschein kann in Form von zwei Teilleistungen (qualifizierter Übungsschein zu „Grundlagen der Mathematik I: Lineare Algebra“ und qualifizierter Übungsschein zu „Grundlagen der Mathematik I: Analysis“) erbracht werden.

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 80106 ("Fundamentals of mathematics II for Bachelor of education")

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

  • vector spaces,
  • linear mappings,
  • systems of linear equations,
  • matrices,
  • determinants.
  • real and complex numbers (axiomatically),
  • sequences, limits and series, power series; elementary functions,
  • continuity,
  • differentiation (one-dimensional),
  • integration (one-dimensional).
  • basic topological concepts
  • differentiation (multi-dimensional),
  • integration (multi-dimensional),
  • geometry of the Euclidian space,
  • eigenvalues, diagonalisability, principal axis theorem.

Competencies / intended learning achievements

Die Studierenden
  • beherrschen die Grundbegriffe der Linearen Algebra und der Analysis mehrerer Veränderlicher als Fundament für die weiteren fachwissenschaftlichen Studien; sie erkennen die Zusammenhänge zwischen den Gebieten der Linearen Algebra und der Analysis; durch die Übungen und das Tutorium haben sie sich einen sicheren, präzisen und selbständigen Umgang mit den in den Vorlesungen behandelten Begriffen, Aussagen und Methoden erarbeitet;
  • sind im analytischen Denken geschult; sie sind in der Lage, abstrakte Strukturen zu erkennen und mathematische Probleme phantasievoll zu bearbeiten;
  • sind in der Lage, elementare mathematische Sachverhalte zu vermitteln; ihre Team- und Kommunikationsfähigkeit wurde durch Übungen und Tutorium geschult.

Registration

Registration for the exercise classes and tutorials via the online administration system URM (https://urm.mathematik.uni-kl.de).

Requirements for attendance of the module (informal)

None

Requirements for attendance of the module (formal)

None

References to Module / Module Number [MAT-10-12L_ERW-M-2]

Course of Study Section Choice/Obligation
[MAT-B4.105-SG] ZEP LaG Mathematics [Compulsory Elective Modules] Compulsory Elective Modules [WP] Compulsory Elective
[MAT-B2.105-SG] ZEP LaRSP Mathematics [Compulsory Elective Modules] Compulsory Elective Modules [WP] Compulsory Elective
[MAT-B5.105-SG] ZEP LaBBS Mathematics [Compulsory Elective Modules] Compulsory Elective Modules [WP] Compulsory Elective