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| Detailed information |
| Original study plan |
Bachelor's programme Computer Science 2013W |
| Objectives |
Students will have knowledge about the foundations of discrete structures in mathematics and computer sciences. They will be familiar with the presented concepts and mathematical models. They will be able to apply them autonomously in examples and case studies.
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| Subject |
Foundations: basic principles of set theory; relations and their properties, in particular orderings and equivalenzes, partitions; functions and properties like monotonicity, boundedness, being injective/surjective/bijective; operations on functions (composition, inverse); real functions, sequences.
Basics from "Numbers and Counting": natural numbers, integers, rational, and real numbers; (complete) induction; recursion (definition, solution strategies); combinatorics (permutations, binomial coefficients); applications.
Elementary Number Theory: computations in Z and Zn (greatest common divisor, least common multiple); Euclidean algorithm; prime numbers, fundamental theorem of number theory (prime decomposition); linear diophantine equations; congruences and modular arithmetics; Fermat's little theorem, Chinese remainder theorem, applications.
Graphs: directed and undirected graphs; paths, cycles, connectivity, connected components; isomorphic graphs; trees; applications.
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| Criteria for evaluation |
General: knowledge, understanding, and application of presented contents;
knowledge, familiarity, and application of proposed concepts and methods.
Specifically: Written exam.
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| Methods |
lecture, discussion
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| Language |
German |
| Study material |
- Kenneth H. Rosen, Discrete Mathematics and Its Applications, McGraw Hill, 5.Auflage, 2003.
- John A. Dossey, Albert D. Otto, Lawrence E. Spence, Charles Vanden Eyden, Discrete Mathematics, Pearson Education, 5. Auflage, 2006.
- Christoph Meinel, Martin Mundhenk, Mathematische Grundlagen der Informatik, Vieweg Teubner, 4. Auflage, 2009.
- Jörg R. Mühlbacher, G. Pilz, M. Widi, Mathematik explorativ, Trauner Verlag, 2006.
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| Changing subject? |
No |
| Corresponding lecture |
(*)ist gemeinsam mit 521THEODISU13: UE Diskrete Strukturen (1,5 ECTS) und einer LVA aus dem Studienfach Vertiefung (1,5 ECTS) im Bachelor Informatik äquivalent zu
INBIPVOMATG: VO Mathematische Grundlagen (3 ECTS) +
INBIPUEMATG: UE Mathematische Grundlagen (3 ECTS)
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