Module MAT-10-1-M-2
Fundamentals of Mathematics (M, 28.0 LP)
Module Identification
Module Number | Module Name | CP (Effort) |
---|---|---|
MAT-10-1-M-2 | 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 | |
Area of study | [MAT-GRU] Mathematics (B.Sc. year 1 and 2) |
Reference course of study | [MAT-82.105-SG] B.Sc. Mathematics |
Livecycle-State | [NORM] Active |
Module Part #A "Fundamental of Mathematics I" (Obligatory, 15.0 LP)
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.
Module Part #B "Fundamentals of Mathematics II" (Obligatory, 13.0 LP)
Type/SWS | Course Number | Title | Choice in Module-Part | Presence-Time / Self-Study | SL | SL is required for exa. | PL | CP | Sem. | |
---|---|---|---|---|---|---|---|---|---|---|
6V+2U+1T | MAT-10-12-K-2 | Fundamentals of Mathematics II
| P | 126 h | 264 h |
qU-Schein
| - | PL1 | 13.0 | WiSe/SuSe |
- About [MAT-10-12-K-2]: Title: "Fundamentals of Mathematics II"; Presence-Time: 126 h; Self-Study: 264 h
- About [MAT-10-12-K-2]: The study achievement "[qU-Schein] 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 [MAT-10-11B-K-2] "Fundamentals of Mathematics I: Linear Algebra" and proof of successful participation in the exercise classes of [MAT-10-11A-K-2] "Fundamentals of Mathematics I: Analysis").
Examination achievement PL1
- Form of examination: oral examination (30-45 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 multi-dimensional; 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 one-dimensional case; integration in the one-dimensional 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 self-study 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 of the module (informal)
None- Notice: Some Courses have informal requirements for attendance:
Requirements for attendance of the module (formal)
NoneReferences to Module / Module Number [MAT-10-1-M-2]
Course of Study | Section | Choice/Obligation |
---|---|---|
[MAT-82.105-SG] B.Sc. Mathematics | [Fundamentals] Fundamentals of Mathematics | [P] Compulsory |
[MAT-82.276-SG] B.Sc. Business Mathematics | [Fundamentals] Fundamentals of Mathematics | [P] Compulsory |
Notice