Dynamischer Default-Fachbereich geändert auf MAT

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	Lossen, Christoph, Dr. habil. (WMA \| DEPT: MAT)
Lecturers	The Lecturers of the department Mathematics
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.

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)