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t.BA.ITM.HM1.19HS (Higher Mathematics for Computer Scientists 1)
Module: Higher Mathematics for Computer Scientists 1
This information was generated on: 20 April 2021
No.
t.BA.ITM.HM1.19HS
Title
Higher Mathematics for Computer Scientists 1
Organised by
T IAMP
Credits
4
Description
Version: 3.0 start 01 February 2021
Short description
The course Higher Mathematics 1 (together with the follow-up course Higher Mathematics 2) teaches students the basics of numerical mathematics for computer scientists and their applications with Python. Contents are fundamental concepts of computer arithmetic and error estimation, numerical instabilities, algorithms for solving systems of linear equations as well as the computation of eigenvalues and eigenvectors.
Module coordinator
Reto Knaack (knaa)
Learning objectives (competencies)
Objectives
Competences
Taxonomy levels
The students understand the functionality and the basic commands of Python. They are able to use it to write simple scripts and programs to solve typical numerical problems and to implement this in weekly group work. They use the functions provided in Python correctly.
F, M, SO
K2, K3
Students can define the basic concepts of computer arithmetic and correctly apply the associated error estimations. They can explain the possible causes of numerical instabilities.
F, M
K2, K3
Students can explain the principles of the most important solution methods for nonlinear equations and linear systems of equations and apply them to concrete problems. They can numerically calculate real or complex eigenvalues and eigenvectors.
F, M
K2, K3
Module contents
Introduction to Python
Data types
Functions
Programmes
Computer Arithmetic
Machine numbers (floating point and fixed point numbers, single-precision, double-precision, IEEE formats)
Aproximation and rounding errors
Conditioning
Numerical solution of one-dimensional nonlinear problems
Fixed point iterations
Newton method
Numerical solution of linear systems
Gauss algorithm with error propagation and pivoting
Triangular decomposition of matrices
Error calculation and expense estimation
Iterative methods: Jacobi / Gauss-Seidel
Introduction to complex numbers
Numerical calculation of eigenvalues and eigenvectors
Teaching Material
Script and presentations
Numerische Mathematik: Eine beispielorientierte Einführung, Michael
Knorrenschild, 5. Auflage, ISBN 978-3446432338
Supplementary literature
Numerik-Algorithmen, G. Engeln-Müllges, Klaus Niederdrenk, Reinhard Wodicka, 10. Auflage, ISBN 978-3-642-13472-2
Numerische Methoden, T. Huckle, S. Schneider, 2. Auflage, ISBN 978-3540303169
Prerequisites
Analysis 1 & 2
Diskrete Mathematik
Lineare Algebra
Teaching language
(X) German ( ) English
Part of International Profile
( ) Yes (X) No
Module structure
Type 3a
For more details please click on this link:
T_CL_Modulauspraegungen_SM2025
Exams
Description
Type
Form
Scope
Grade
Weighting
Graded assignments during teaching semester
weekly assignements
written
10-12
mark
20%
End-of-semester exam
exam
written
120 min
mark
80%
Remarks
Legal basis
The module description is part of the legal basis in addition to the general academic regulations. It is binding. During the first week of the semester a written and communicated supplement can specify the module description in more detail.
Note
Additional available versions:
1.0 start 01 February 2019
,
2.0 start 01 February 2020
Course: Höhere Mathematik für Informatiker 1 - Praktikum
No.
t.BA.ITM.HM1.19HS.P
Title
Höhere Mathematik für Informatiker 1 - Praktikum
Note
No module description is available in the system for the cut-off date of 01 August 2099.
Course: Höhere Mathematik für Informatiker 1 - Vorlesung
No.
t.BA.ITM.HM1.19HS.V
Title
Höhere Mathematik für Informatiker 1 - Vorlesung
Note
No module description is available in the system for the cut-off date of 01 August 2099.