Short description

This module covers the topics of linear equations, matrix algebra and 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, Günter M. (2014): Lineare Algebra. Eine Einführung. 4. Aufl. München: Carl Hanser Verlag.
Sachs, Michael (2018): Wahrscheinlichkeitsrechnung und Statistik: für Ingenieurstudenten an Fachhochschulen. 5. Aufl. München: Carl Hanser Verlag.
Papula, Lothar (2017): Mathematische Formelsammlung. Für Ingenieure und Naturwissenschaftler. 12. Aufl. Wiesbaden: Springer Vieweg. 
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) 
written 

Grade 
10% 
Endofsemester 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. 