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## Discrete Mathematics

 Module name (EN): Discrete Mathematics Degree programme: Computer Science and Communication Systems, Master, ASPO 01.10.2017 Module code: KIM-DM Hours per semester week / Teaching method: 3V+1U (4 hours per week) ECTS credits: 6 Semester: 1 Mandatory course: yes Language of instruction: German Assessment: Written exam [updated 26.02.2018] Curricular relevance: KI873 Computer Science and Communication Systems, Master, ASPO 01.04.2016, semester 2, optional course, informatics specific KIM-DM Computer Science and Communication Systems, Master, ASPO 01.10.2017, semester 1, mandatory course PIM-DM Applied Informatics, Master, ASPO 01.10.2011, semester 2, mandatory course PIM-DM Applied Informatics, Master, ASPO 01.10.2017, semester 1, mandatory course Workload: 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): None. Recommended as prerequisite for: KIM-CE Cryptography Engineering [updated 19.10.2020] Module coordinator: Prof. Dr. Peter Birkner Lecturer: Prof. Dr. Gerald Kroisandt [updated 08.07.2018] 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 principlesto 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. Basics1.1. Sets and set operations1.2. Mathematical induction 2. Counting2.1. Basic principles2.2. Subsets2.3. Partitions2.4. Catalan numbers2.5. Polynomials2.6. Generating functions2.7. Asymptotic counting 3. Graph theory3.1. Introduction3.2. Discrete optimization3.2.1. Shortest paths3.2.2. Minimum spanning tree3.3. Eulerian path3.4. Hamiltonian cycle3.5. 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 2021/22, WS 2020/21, WS 2019/20, WS 2018/19, WS 2017/18
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