German website

study programs: Bachelor of Computer Science (B_Inf), Computer Engineering (B_Tinf), IT Engineering (B_ITE), Media Computer Science (B_Minf), Computer Games Technology (B_CGT), Business and Computer Science (B_Winf), e-Commerce (B_ECom), Smart Technology (B_STec), IT-Management Consulting & Auditing (B_IMCA), Data Science & Artificial Intelligence (B_DSAI), 1st semester

ECTS credits: 5

lecture term: summer and winter semester

prerequesites: precalculus mathematics of secondary school

language: This lecture is given in German in both semesters and in English in winter semester only when it is part of the preparatory block for the Master IT engineering programme.

This lecture gives the mathematical fundamentals for further study in all IT related programs. The contents are highly related to a lot of parallel and subsequent courses. This lecture does not require any knowledge of programming.

This lecture covers standard material such as logics and proof concepts, set theory, number theory, combinatorics, and graph theory. Furthermore, we give an introduction in group and field theory which highlights in the construction algorithm for arbitrary finite fields. For exercises, some construction programs implemented by students of FH Wedel in a software project may be downloaded here  (instructions in German).

This lecture is complemented by exercises lead by teaching assistants.

The following links show the latest slides and the assignments of the course. Updates in a current winter semester may occur continuously and will be indicated by a red update information.

 1. Fundamentals of mathematics
    1.1 Motivation
    1.2 Propositional logic (Proof of Modus Tollens)
    1.3 Predicate logic (Predicate logic exercises)

3. Proof concepts
    3.1 Glossary of mathematical structures
    3.2 Mathematical induction (3-divisability, bee ancestors, grammar example)
    3.3 Other proof strategies

4. Number theory
    4.1 Divisibility
    4.2 Dividing with remainders
    4.3 Prime numbers
    4.4 Modular arithmetic

(Examples for gcd and lcm, PrimeFactorisation with Maxima)
Note for the factorisation file: You must store this with the extension .wxm (not .txt). This file can the be executed and altered by the open-source tool Maxima (download here for all operating systems or here an older but still functioning version on the handout server for Windows). Warning: The file should not be altered by any editor other than Maxima's!

6. Combinatorics
    6.1 Enumeration formulae for sets
    6.2 Permutations

7. Graph theory (updated 2023-01-20)
    7.1 Terminology und representation
    7.2 Path problems in graphs (including Dijkstra's algorithm) (Königsberg, Dijkstra graph examples, algorithm example for Dijkstra)
    7.3 Trees (including Kruskal's algorithm) (spanning tree graph example)
    7.4 Planar graphs (platonic solids, example for graph containing a subdivision of C3,3)
    7.5 Graph colouring (Asia map)

Text book (in German)

Norman L. Biggs: Discrete Mathematics, Oxford University Press 2002 (2. edition), ISBN 0-19-850717-8
This book covers nearly all material of this lecture in a slightly more mathematical manner except for some graph algorithms. This book also covers a a lot of material not discussed in this lecture.

Neville Dean: The Essence of Discrete Mathematics, Prentice Hall 1997, ISBN 0-1334-5943-8
This book covers the first 2 chapters of this lecture entirely on a more elementary level.

Susanna S. Epp: Discrete Mathematics with Applications, Brooks/Cole 1995 (2. edition), ISBN 0-534-94446-9
This book covers most of this lecture (Chapter 5 not at all), some on a more elementary level, and lays a strong focus in algorithmic applications.

Jiri Matousek / Jaroslav Nesetril: An Invitation to Discrete Mathematics, Oxford University Press 2008 (2. edition), ISBN 0-1985-7042-2
This book covers some of the material of this lecture on a more scientific level and a lot of other issues for broadening the horizon. 

Kenneth H. Rosen: Discrete Mathematics and its Applications, McGraw-Hill 2003, ISBN 0-07-242434-6
This book covers a big part of this lecture.

literature for broadening the mathematical horizon:

Martin Aigner / Günter Ziegler: Proofs from THE BOOK, Springer-Verlag 2010 (4. edition), ISBN 978-3-642-00855-9
Martin Aigner is my teacher of Discrete Mathematics.

In WS 2016/17, proofs of this book were presented in my seminar.