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t.BA.XXM6.AS2.19HS (Algebra and Statistics 2)
Module: Algebra and Statistics 2
This information was generated on: 29 February 2024
No.
t.BA.XXM6.AS2.19HS
Title
Algebra and Statistics 2
Organised by
T IAMP
Credits
4
Description
Version: 3.0 start 01 August 2019
Short description
This module covers linear transformations, eigenvectors and eigenvalues, continuous probability distributions, the Gaussian distribution, the central limit theorem, deductive statistics and also linear regression.
Module coordinator
Lermer Karl Reiner (lrka)
Learning objectives (competencies)
Objectives
Competences
Taxonomy levels
You become acquainted with the mathematical tools and concepts required for the engineering modules. You familiarize yourself with the mathematical way of thinking and practice your ability to abstract.
You are able to
- determine whether a transformation is linear.
- derive the transformation matrix of a linear transformation.
- calculate and apply the composition of linear transformations as a product of matrices
- define and apply two and three dimensional compressions, rotations, projections and reflections
.
F, M
K2, K3
You are able to
- compute
real eigenvalues and eigenvectors of linear transformations and matrices.
F, M
K2, K3
You are able to
-distinguish discrete and continuous random variables
-calculate the expected value, the variance and the standard deviation of continuous random variables.
- apply the probability density function (PDF) and cumulative distribution function (CDF)
of the Gaussian distribution in examples.
-explain and apply the central limit theorem.
F, M
K2, K3
You are accustomed to basic terms of deductive statistics (point and interval estimate, bias and consistency)
You are able to calculate confidence intervals and derive hypothesis tests.
F, M
K2, K3
You are able to calculate linear regression lines.
F, M
K2, K3
You are able to use the competencies listed
above to solve more complex problems.
F, M
K3
Module contents
Linear transformations
Eigenvectors and eigenvalues
Continuous probability distributions
Gaussian distribution
Central limit theorem
Deductive statistics
Linear regression
Teaching materials
Depending on the lecturer
Supplementary literature
Gramlich, G.,
Lineare Algebra – Eine Einführung
(München: Carl Hanser Verlag, 4. Aufl. 2014), ISBN: 978-3446441408
Sachs, M.,
Wahrscheinlichkeitsrechnung und Statistik: für Ingenieurstudenten an Fachhochschulen
(München: Carl Hanser Verlag, 4. Aufl. 2013), ISBN: 978-3446437975
Papula, L.,
Mathematische Formelsammlung: Für Ingenieure und Naturwissenschaftler
(Wiesbaden: Springer Vieweg, 12. Aufl. 2017), ISBN 978-3658161941
Prerequisites
Mathematics of the technical vocational baccalaureate.
Teaching language
(X) German ( ) English
Part of International Profile
( ) Yes (X) No
Module structure
Type 2b
For more details please click on this link:
T_CL_Modulauspraegungen_SM2025
Exams
Description
Type
Form
Scope
Grade
Weighting
Graded assignments during teaching semester
1 test
written
45 min
grade
20%
regular
assessment (e.g.
online tests)
grade
10%
End-of-semester exam
exam
written
90 min
grade
70%
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
Course: Algebra und Statistik 2 - Vorlesung
No.
t.BA.XXM6.AS2.19HS.V
Title
Algebra und Statistik 2 - Vorlesung
Note
No module description is available in the system for the cut-off date of 01 August 2099.