Module Handbook

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Module MAT-10-11-M-2

Fundamentals of Mathematics A: Linear Algebra I and Analysis I (M, 15.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-10-11-M-2 Fundamentals of Mathematics A: Linear Algebra I and Analysis I 15.0 CP (450 h)

Basedata

CP, Effort 15.0 CP = 450 h
Position of the semester 1 Sem. in WiSe/SuSe
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-31.105-SG] B.Ed. LaGR Mathematics
Livecycle-State [NORM] Active

Notice

To prepare for the course, it is recommended to participate in the Online Mathematics Bridge Course (OMB+), see https://www.mathematik.uni-kl.de/omb/

The course is also offered as distance learning course as part of the early entrance programme FiMS, see https://fims.mathematik.uni-kl.de

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V+2U MAT-10-11B-K-2
Fundamentals of Mathematics I: Linear Algebra
P 56 h 124 h
SL1
ja PL1 6.0 WiSe/SuSe
4V+2U+2T MAT-10-11A-K-2
Fundamentals of Mathematics I: Analysis
P 112 h 158 h
SL1
ja PL1 9.0 WiSe/SuSe
  • About [MAT-10-11B-K-2]: Title: "Fundamentals of Mathematics I: Linear Algebra"; Presence-Time: 56 h; Self-Study: 124 h
  • About [MAT-10-11B-K-2]: The study achievement SL1 must be obtained.
    • It is a prerequisite for the examination for PL1.
  • About [MAT-10-11A-K-2]: Title: "Fundamentals of Mathematics I: Analysis"; Presence-Time: 112 h; Self-Study: 158 h
  • About [MAT-10-11A-K-2]: The study achievement SL1 must be obtained.
    • It is a prerequisite for the examination for PL1.

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 (30-45 Min.)
  • Examination Frequency: each semester
  • Examination number: 80105 ("Fundamentals of mathematics I: Linear Algebra & Analysis")

Evaluation of grades

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


Contents

Fundamentals of Mathematics I: Linear Algebra:
  • vector spaces,
  • linear mappings,
  • linear systems of equations,
  • matrices,
  • determinants.

Fundamentals of Mathematics I: Analysis:

  • real and complex numbers,
  • sequences, limit values and series; power series,
  • elementary functions; continuity,
  • differentiation (in the one-dimensional case),
  • integration (in the one-dimensional case).

Competencies / intended learning achievements

Upon successful completion of this module, the students
  • have mastered the basic concepts of Linear Algebra and one-dimensional Analysis as a foundation for further scientific studies; through the exercises and the tutorials they have acquired a confident, precise and independent handling of the terms, statements and methods dealt with in the lectures;
  • are trained in analytical thinking; they are able to recognise abstract structures and to work on mathematical problems imaginatively;
  • are able to convey elementary mathematical facts; their teamwork and communication skills have been trained through exercises and tutorials.

Literature

  • G. Fischer: Lineare Algebra,
  • K. Jänich: Lineare Algebra,
  • H.-J. Kowalsky, G.O. Michler: Lineare Algebra,
  • S. Bosch: Lineare Algebra,
  • O. Forster: Analysis 1,
  • H. Heuser: Lehrbuch der Analysis, Teil 1,
  • M. Barner, F. Flohr: Analysis I,
  • K. Königsberger: Analysis 1.

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-10-11-M-2]

Course of Study Section Choice/Obligation
[MAT-31.105-SG] B.Ed. LaGR Mathematics [Section (non-specific)] Compulsory Modules [P] Compulsory
[MAT-47.105-SG] B.Ed. LaBBS Mathematics [Section (non-specific)] Compulsory Modules [P] Compulsory
[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