t.BA.XXM6.AS1.19HS (Algebra und Statistik 1) Module: Algebra and Statistics 1
This information was generated on: 14 July 2020
No.
t.BA.XXM6.AS1.19HS
Title
Algebra and Statistics 1
Organised by
T IAMP
Credits
4

### Description

Version: 1.0 start 01 August 2019

#### Short description

The topics of this module are systems of linear equations, matrix algebra, vector geometry as well as elementary probability theory and discrete random variables.

#### Module coordinator

Ines Stassen Böhlen (sses)

#### 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 the solution set of a system of linear equations.
- determine the number of solutions of a given system of linear equations using suitable criteria.
F,M K2, K3
You are able to
- calculate the sum, product, transpose, inverse and determinant of given matrices.
- determine whether a square matrix is invertible, i.e. whether its columns are linearly independent using suitable criteria.
F,M K2, K3
You are able to
- calculate the sum, a certain linear combination, the dot and cross products of given vectors.
- describe lines, planes, circles and spheres using equations.
- determine intersections of lines, planes, circles and spheres.
- determine whether two given vectors are orthogonal or collinear using suitable criteria.
F,M K2, K3
You are able to
- define the sample space, the event space, the probability distribution and the probability mass function for discrete probability spaces and calculate probabilities of events.
- build basic stochastic models, define random variables, derive their probability density functions (PDFs) and their cumulative distribution functions (CDFs) and calculate probabilities.
- explain the meaning of measures of center and variability for random variables.
- calculate the expected value, the variance and the standard deviation of discrete random variables.
- calculate conditional probabilities.
- build event and probability tree diagrams.
- formulate and apply Bayes' theorem, the theorem of total probability and the multiplication theorem for probability tree diagrams.
F,M K2, K3
 You are able to use the competencies listed above to solve more complex problems.
F,M K3

#### Module contents

Systems of linear equations
Matrix algebra

Vector geometry
Elementary probability theory
Discrete random variables

#### 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) written 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. Course: Algebra und Statistik 1 - Vorlesung
No.
t.BA.XXM6.AS1.19HS.V
Title
Algebra und Statistik 1 - Vorlesung

### Note

• No module description is available in the system for the cut-off date of 01 August 2099.