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

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.