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| Detailed information |
| Original study plan |
Bachelor's programme Computer Science 2025W |
| Learning Outcomes |
Competences |
| Students of the course understand the basics of discrete structures in mathematics and computer science and are familiar with the concepts and mathematical methods presented. They are able to apply and implement these independently in examples and practice-orientated tasks.
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| Skills |
Knowledge |
Students can:
- Understand mathematical formulations and arguments and carry out formal arguments (K3)
- Read and interpret mathematical notation (K4)
- Interpret, use and analyse abstract models such as graphs or algebras (K4)
- Formalize simple facts and apply proof techniques (K3)
- Systematically check the truth of statements using mathematical methods (K5)
- Apply different forms of arithmetic in finite and infinite structures (K4)
- Solve linear (homogeneous) recursion equations and understand their application in computer science (K3)
- Solve elementary counting and enumeration problems (K3)
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- Basics: Fundamentals of logic, deduction rules and proof techniques; set theory; relations and their properties, in particular order and equivalence relations, partitions; functions and their properties (monotonicity, boundedness, injective/surjective/bijective), operations on functions (composition, inverse).
- Basic knowledge of ‘Numbers and enumeration’: Natural, integer, rational and real numbers; (complete) induction, recursion (definition, solution approaches); combinatorics (permutations, binomial coefficients); application examples.
- Fundamentals of algebra: elementary number theory, arithmetic in Z and Zn (greatest common divisor, least common multiple), Euclidean algorithm; prime numbers, congruences and residue class systems, groups, rings and finite fields Application examples.
- Graph theory: Directed and undirected raphs; paths, circles, connections and components, isomorphic graphs; trees; application examples.
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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 |
Slide presentation as well as discussion and examples on the blackboard.
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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.
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| Changing subject? |
No |
| Further information |
This lecture and the corresponding practical form an inseparable didactic unit. The learning outcomes described here are achieved through the interaction of the two courses.
Language of delivery:
German
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| 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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