mat950 - Discrete Mathematics (Complete module description)

Module label	Discrete Mathematics
Module code	mat950
Credit points	6.0 KP
Workload	180 h
Institute directory	Department of Mathematics
Applicability of the module	Bachelor's Programme Business Informatics (Bachelor) > Aufbaucurriculum - Pflichtbereich Bachelor's Programme Computing Science (Bachelor) > Aufbaumodule Dual-Subject Bachelor's Programme Computing Science (Bachelor) > Basismodule
Responsible persons	Heß, Florian (module responsibility) Stein, Andreas (module responsibility) Stein, Sandra (module responsibility)
Prerequisites
Skills to be acquired in this module	• Getting to know and to understand the axiomatic structure of mathematics and the importance of mathematical reasoning • Mastering basic mathematical proof techniques and their logical structure • Recognizing the relevance of premises in mathematical theorems: Localization of premises within proofs and possible consequences if premises are not met • Exemplary acquaintance with further mathematical areas and thus expansion of the student's mathematical knowledge • Getting to know applications • Integration and crosslinking of the student’s mathematical knowledge by establishing relationships between different mathematical areas • Learning the essential ideas and methods for discrete structures in mathematics • Knowledge of the fundamental concepts and methods of graph theory • Knowledge of the fundamental concepts and methods of algebra and number theory, such as groups, rings, fields, residue class rings, Euclidean algorithm, Chinese remainder theorem, polynomials. • Knowledge of further concepts and methods for discrete structures, e.g. primality tests, RSA, graph-theoretical algorithms
Module contents	Elements of propositional logic, proof techniques, sets, relations and maps, combinatorics, graphs and applications, the ring of integers and residue class rings, groups and semi groups
Recommended reading	Kreußler, Pfister: Mathematik für Informatiker, Springer 2009. Knauer, Knauer: Diskrete und algebraische Strukturen - kurz gefasst, Springer 2015. Aigner: Diskrete Mathematik, Vieweg 2006. Beutelspacher, Zschiegner: Diskrete Mathematik für Einsteiger, Vieweg 2014. Epp: Discrete Mathematics with Applications, Brooks Cole 2011. Graham, Knuth, Patashnik: Concrete Mathematics, Addison-Wesley 1994. Hartmann: Mathematik für Informatiker, Vieweg 2014. Rosen: Discrete Mathematics and its applications, McGraw-Hill 2018. Steger: Diskrete Strukturen, Band 1, Springer 2007. Teschl, Teschl: Mathematik für Informatiker, Band 1, Springer 2013. Further reading will be announced in the lecture.
Links
Language of instruction	German
Duration (semesters)	1 Semester
Module frequency	annual
Module capacity	unlimited
Reference text	Im Zwei-Fächer Bachelor Informatik ist dieses Modul im Basiscurriculum zu studieren.

Type of course	SWS	Frequency	Workload of compulsory attendance
Lecture	3	WiSe	42
Exercises	1	WiSe	14
Total module attendance time			56 h

Examination	Prüfungszeiten	Type of examination
Final exam of module	after the end of the lecture period	Written exam or oral exam. Bonus points can be earned.