- vector spaces,
- linear mappings,
- systems of linear equations,
- matrices,
- determinants.
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 |
Lecturers of the department Mathematics
|
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 |
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 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 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
- 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 (informal)
None
Requirements for attendance (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 | [WP] Compulsory Elective |
[MAT-B2.105-SG] ZEP LaRSP Mathematics | Compulsory Elective Modules | [WP] Compulsory Elective |
[MAT-B5.105-SG] ZEP LaBBS Mathematics | Compulsory Elective Modules | [WP] Compulsory Elective |
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