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

( ) Yes (X) No

Type 2b

#### 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%

#### 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: 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.