t.BA.MIM.MA1.23HS (Mathematics 1) 
Module: Mathematics 1
This information was generated on: 26 April 2024
No.
t.BA.MIM.MA1.23HS
Title
Mathematics 1
Organised by
T IAMP
Credits
4

Description

Version: 3.0 start 01 August 2023
 

Short description

 The basics of discrete mathematics and linear algebra are covered.

Module coordinator

 Karl Reiner Lermer (Irka)

Learning objectives (competencies)
Objectives Competences Taxonomy levels
You acquire the mathematical tools needed in engineering subjects. You familiarise yourself with the mathematical way of thinking. You train your ability to think abstractly. F,M K2,K3
You are familiar with the basics of set theory and the rules of set algebra.
You are able to calculate averages, unions, complements, power sets, partitions and Cartesian products and visualise them with the help of diagrams.		 F,M K2,K3
You can
- define the number systems of the natural, whole, rational, real and complex numbers and perform calculations in them.
- calculate modulo and perform division with remainder.
- apply Euclid's algorithm to calculate the ggT.
- apply Heron's algorithm to approximate roots.
- understand and make recursive definitions.
- determine maxima, minima, suprema and infima.
- create and perform calculations using the sum and product sign.		 F,M K2,K3
You can
- interpret and create statements and predicates with conjunctors and quantifiers.
- Interpret and make truth tables.
- apply the rules of predicate logic to prove logical equivalences.		 F,M K2,K3
You can
- decide whether a relation is reflexive, transitive, symmetrical, antisymmetrical or asymmetrical.
- Interpret relations with sets, arrow diagrams and tables.
- decide whether a relation is an equivalence relation.
- determine the equivalence classes of equivalence relations and interpret them as partitions.
- add and multiply residue classes in Z modulo m.
- perform calculations with modular arithmetic.
- determine multiplicative inverses.
- decide and justify whether a relation is pre-order, semi-order, strict order or total order.
- decide and justify whether a relation is a function.
- decide and justify whether a function is surjective, injective or bijective.
- determine whether a function is invertible and determine the inverse.
- perform the concatenation of functions.		 F,M K2,K3
You can
- decide whether sets are vector spaces.
- define and explain n-tuple spaces and polynomial spaces and their vector space operations.
- form linear combinations
- determine the span.
- apply the subspace criteria.
- prove linear independence.
- Identify generating end systems.
- identify and determine bases.
- determine the dimension.
- calculate component vectors.
- identify abstract vector spaces with tuple spaces.		 F,M K2,K3

Module contents

 Subject areas are sets, logic, numbers, relations, functions, vector calculation, vector geometry.

Teaching materials

  

Supplementary literature

 Gerald Teschl. Susanne Teschl. Mathematik für Informatiker. Band 1: Diskrete Mathematik und Lineare Algebra. 4. Aufl., Springer-Vieweg.
Gramlich, Günter M. (2014): Lineare Algebra. Eine Einführung. 4. Aufl. München: Carl Hanser Verlag.
Papula, Lothar (2017): Mathematische Formelsammlung. Für Ingenieure und Naturwissenschaftler. 12. Aufl. Wiesbaden: Springer Vieweg.

Prerequisites

  

Teaching language

 (X) German ( ) English

Part of International Profile

 ( ) Yes (X) No

Module structure

 (Is filled in by the administration)
  For more details please click on this link: T_CL_Modulauspraegungen_SM2025

Exams
Description Type Form Scope Grade Weighting
Graded assignments during teaching semester Regular assessment (e.g. online tests) written   Grade 10%
End-of-semester exam Exam written 90 min Grade 90%

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: Mathematik 1 - Praktikum
No.
t.BA.MIM.MA1.23HS.P
Title
Mathematik 1 - Praktikum

Note

  • No module description is available in the system for the cut-off date of 02 August 2099.
Course: Mathematik 1 - Vorlesung
No.
t.BA.MIM.MA1.23HS.V
Title
Mathematik 1 - Vorlesung

Note

  • No module description is available in the system for the cut-off date of 02 August 2099.