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Discrete Mathematics

Module name (EN):
Name of module in study programme. It should be precise and clear.
Discrete Mathematics
Degree programme:
Study Programme with validity of corresponding study regulations containing this module.
Applied Informatics, Master, ASPO 01.10.2017
Module code: PIM-DM
The exam administration creates a SAP-Submodule-No for every exam type in every module. The SAP-Submodule-No is equal for the same module in different study programs.
Hours per semester week / Teaching method:
The count of hours per week is a combination of lecture (V for German Vorlesung), exercise (U for Übung), practice (P) oder project (PA). For example a course of the form 2V+2U has 2 hours of lecture and 2 hours of exercise per week.
3V+1U (4 hours per week)
ECTS credits:
European Credit Transfer System. Points for successful completion of a course. Each ECTS point represents a workload of 30 hours.
Semester: 1
Mandatory course: yes
Language of instruction:
Written exam

[updated 26.02.2018]
Applicability / Curricular relevance:
All study programs (with year of the version of study regulations) containing the course.

DFI-DM (P610-0269) Computer Science, Master, ASPO 01.10.2018 , semester 1, optional course
KI873 Computer Science and Communication Systems, Master, ASPO 01.04.2016 , semester 2, optional course, informatics specific
KIM-DM (P222-0051) Computer Science and Communication Systems, Master, ASPO 01.10.2017 , semester 1, mandatory course
PIM-DM (P222-0051) Applied Informatics, Master, ASPO 01.10.2011 , semester 2, mandatory course
PIM-DM (P222-0051) Applied Informatics, Master, ASPO 01.10.2017 , semester 1, mandatory course
Workload of student for successfully completing the course. Each ECTS credit represents 30 working hours. These are the combined effort of face-to-face time, post-processing the subject of the lecture, exercises and preparation for the exam.

The total workload is distributed on the semester (01.04.-30.09. during the summer term, 01.10.-31.03. during the winter term).
60 class hours (= 45 clock hours) over a 15-week period.
The total student study time is 180 hours (equivalent to 6 ECTS credits).
There are therefore 135 hours available for class preparation and follow-up work and exam preparation.
Recommended prerequisites (modules):
Recommended as prerequisite for:
Module coordinator:
Prof. Dr. Peter Birkner
Prof. Dr. Peter Birkner (lecture/exercise)

[updated 17.06.2024]
Learning outcomes:
After successfully completing this module, students will be able to solve counting problems that have been formulated informally. In doing so, they can either establish a direct link to the principles discussed, or they can use the basic principles
to divide the solution of the counting problem into smaller sub-problems, on which other principles are then used. It is important that the students recognize that simple variations in the formulation of a problem sometimes lead to very complex solution strategies.
For recursive sequences, students will be able to derive a closed representation using generating functions, the validity of which they can prove by means of mathematical induction.
In the field of graph theory, students will learn the concepts of graph theory based on practical exercises. They will be able to identify practical problems with the corresponding mathematical terms. In order to solve these problems, students will learn select graph theory algorithms and will be able to apply them.

[updated 26.02.2018]
Module content:
1. Basics
1.1. Sets and set operations
1.2. Mathematical induction
2. Counting
2.1. Basic principles
2.2. Subsets
2.3. Partitions
2.4. Catalan numbers
2.5. Polynomials
2.6. Generating functions
2.7. Asymptotic counting
3. Graph theory
3.1. Introduction
3.2. Discrete optimization
3.2.1. Shortest paths
3.2.2. Minimum spanning tree
3.3. Eulerian path
3.4. Hamiltonian cycle
3.5. The Traveling Salesman Problem

[updated 26.02.2018]
Recommended or required reading:
Anusch Taraz: Diskrete Mathematik, Birkhäuser, 2012
M.Aigner: Diskrete Mathematik, Verlag Vieweg + Teubner, 6. Auflage 2006
G.Bamberg und A.G.Coenenberg: Betriebswirtschaftliche Entscheidungslehre. Verlag Vahlen, WiSo Kurzlehrbücher, 10. Aufl. 2008
T.Ihringer: Diskrete Mathematik: iene Einführung in Theorie und Anwendungen, Heldermann Verlag 2002
E.Lawler: Combinatorial Optimization: Networks and Matroids, Oxford University Press 1995
C.H.Papadimitriou und K.Steiglitz: Combinatorial Optimization: Algorithms and Complexity, Springer-Verlag, Berlin 2008

[updated 26.02.2018]
Module offered in:
WS 2024, WS 2023/24, WS 2022/23, WS 2021/22, WS 2020/21, ...
[Thu Jun 20 08:06:26 CEST 2024, CKEY=pdm, BKEY=pim2, CID=PIM-DM, LANGUAGE=en, DATE=20.06.2024]