Module MAT101M2
Fundamentals of Mathematics (M, 28.0 LP)
Module Identification
Module Number  Module Name  CP (Effort) 

MAT101M2  Fundamentals of Mathematics  28.0 CP (840 h) 
Basedata
CP, Effort  28.0 CP = 840 h 

Position of the semester  2 Sem. from WiSe/SuSe 
Level  [2] Bachelor (Fundamentals) 
Language  [DE] German 
Module Manager  
Lecturers 
Lecturers of the department Mathematics

Area of study  [MATGRU] Mathematics (B.Sc. year 1 and 2) 
Reference course of study  [MAT82.105SG] B.Sc. Mathematics 
LivecycleState  [NORM] Active 
Module Part #A "Fundamental of Mathematics I" (Obligatory, 15.0 LP)
Type/SWS  Course Number  Title  Choice in ModulePart  PresenceTime / SelfStudy  SL  SL is required for exa.  PL  CP  Sem.  

2V+2U  MAT1011BK2  Fundamentals of Mathematics I: Linear Algebra
 P  56 h  124 h 
SL1
 ja  PL1  6.0  WiSe/SuSe 
4V+2U+2T  MAT1011AK2  Fundamentals of Mathematics I: Analysis
 P  112 h  158 h 
SL1
 ja  PL1  9.0  WiSe/SuSe 
 About [MAT1011BK2]: Title: "Fundamentals of Mathematics I: Linear Algebra"; PresenceTime: 56 h; SelfStudy: 124 h
 About [MAT1011BK2]: The study achievement must be obtained. It is a prerequisite for the examination for PL1 .
 About [MAT1011AK2]: Title: "Fundamentals of Mathematics I: Analysis"; PresenceTime: 112 h; SelfStudy: 158 h
 About [MAT1011AK2]: The study achievement must be obtained. It is a prerequisite for the examination for PL1 .
Module Part #B "Fundamentals of Mathematics II" (Obligatory, 13.0 LP)
Type/SWS  Course Number  Title  Choice in ModulePart  PresenceTime / SelfStudy  SL  SL is required for exa.  PL  CP  Sem.  

6V+2U+1T  MAT1012K2  Fundamentals of Mathematics II
 P  126 h  264 h 
qUSchein
   PL1  13.0  WiSe/SuSe 
 About [MAT1012K2]: Title: "Fundamentals of Mathematics II"; PresenceTime: 126 h; SelfStudy: 264 h
 About [MAT1012K2]: The study achievement [qUSchein] proof of successful participation in the exercise classes (incl. written examination) 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")
The proof of successful participation in the exercise classes (incl. written examination) for "Fundamentals of Mathematics I" can be obtained in two parts (proof of successful participation in the exercise classes of [MAT1011BK2] Fundamentals of Mathematics I: Linear Algebra and proof of successful participation in the exercise classes of [MAT1011AK2] Fundamentals of Mathematics I: Analysis).
Examination achievement PL1
 Form of examination: oral examination (3045 Min.)
 Examination Frequency: each semester
 Examination number: 82017
("Fundamentals of Mathematics I/II")
Instead of the proof of successful participation in the exercise classes for "Fundamentals of Mathematics I" (SL1), the prerequisite for the examination PL1 can also be fulfilled in form of the proof of successful participation in the exercise classes for "Fundamentals of Mathematics II" (incl. written examination).
Evaluation of grades
The grade of the module examination is also the module grade.
Contents
 real and complex numbers (axiomatic),
 sequences, limit values, and series; power series; elementary functions,
 continuity,
 differentiation (especially: Taylor expansion, curves, implicit function theorem, inverse function theorem, extrema under constraints),
 integration (one and multidimensional; in particular: Fubini's theorem, variable transformation),
 basic topological terms (metric spaces, connection, compactness),
 vector spaces; linear mappings, matrices and linear systems of equations; dual space; determinants,
 geometry of the Euclidean space (especially: orthogonal transformations, projections),
 eigenvalues, diagonalisability, principal axis transformation, calculation of the Jordan normal form.
In particular, the respective courses treat the following contents:
A.1 Fundamentals of Mathematics I: Analysis
real and complex numbers; sequences, limit values, and series; power series; elementary functions; continuity and differentiation in the onedimensional case; integration in the onedimensional case;
A.2 Fundamentals of Mathematics I: Linear Algebra
vector spaces; linear mappings, matrices and linear systems of equations;
B. Fundamentals of Mathematics II:
metric spaces; differentiation and integration in the multidimensional case; geometry of Euclidean space; diagonalisability, principal axis transformation, calculation of the Jordan normal form.
Competencies / intended learning achievements
In the exercise classes they have acquired a confident, precise and independent handling of the terms, statements and methods from the lectures.
In the exercise classes and tutorials, the students' presentation and communication skills were trained through written work and presentations held by themselves; the students are able to acquire knowledge through selfstudy and at the same time their ability to work in a team was promoted by working in small groups.
Literature
 O. Forster: Analysis 1, Analysis 2,
 H. Heuser: Lehrbuch der Analysis, Teil 1 und Teil 2,
 M. Barner, F. Flohr: Analysis I, Analysis II,
 K. Königsberger: Analysis 1, Analysis 2,
 G. Fischer: Lineare Algebra,
 H.J. Kowalsky, G.O. Michler: Lineare Algebra,
 S. Bosch: Lineare Algebra,
 K. Jänich: Linear Algebra.
Requirements for attendance (informal)
Requirements for attendance (formal)
References to Module / Module Number [MAT101M2]
Course of Study  Section  Choice/Obligation 

[MAT82.105SG] B.Sc. Mathematics  Fundamentals of Mathematics  [P] Compulsory 
[MAT82.276SG] B.Sc. Business Mathematics  Fundamentals of Mathematics  [P] Compulsory 
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