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INFB  Mathematics I Course INF
Lecturers : Prof. Dr. Roland Uhl    eMail
Prof. Dr. Rolf Socher    eMail
Term 1
Course Classification : Informatik Bachelor CH 4
Language : Deutsch Type VÜ 
Type of examination : PL  Credits 5 
Method of evaluation : written examination 90 min 
Requirements :
Cross References :  
Previous knowledges :  
Aids and special features :  
Teaching aims : Adoption of mathematical thinking (abstraction, accuracy, logical deduction and argumentation)
Mastery of several proof strategies and techniques, especially induction, counting techniques, methods to compute discrete probabilities
Understanding of essential basic concepts such as sets, relations, functions
Familiarity with several discrete structures such as graphs, and algebras; this includes confident handling of the respective methods like calculation with sets and elements of discrete structures,
diagonal method, isomorphism proofs as well as applicable knowledge of basic properties and results like Kuratowskis lemma and Fermats theorem. 
Contents :

Atomic and complex propositions as building blocks for mathematical reasoning, truth tables, propositions with quantifiers
Set theory: basic concepts, operations on sets , simplification of set representation, powersets, products of sets
Relations: definition, operations on relations, equivalence relations and factorisation, partially ordered sets
Mappings and functions: definitions and examples, surjectivity and injectivity, sequences of sets, cardinality of sets?Cantors diagonal method,
Proof strategies: direcly, by contradiction, case-based reasoning, proofs with quantifiers, proofs in combinatorics,
Complete induction: idea, structure, generalised induction, inductive definition
Counting: combinatorics, calculation with binomial coefficients, Stirling formula
Discrete stochastics: non-deterministic experiments, random variables, conditional probability, expected values, examples for discrete distributions
Boolean algebras: definition and properties, atoms, normal forms, representation theorem
Graphs and trees: directed and undirected graphs, properties and representation of graphs, planary graphs, paths, cycles, incidence- und adjacence matrices isomorphisms, trees
Modular arithmetic: modulo operation, Euklidian algorithm, Fermats theorem
Algebraic structures: definition and signature of algebras, operations and properties, groups, rings and fields, primitive elements, properties of finite groups, cyclic groups, homomorphisms, isomorphisms 

Literature : Hagerty R.: Diskrete Mathematik für Informatiker, Bonn: Addison-Wesley, 2004
Schubert M.: Mathematik für Informatiker. Wiesbaden: Vieweg und Teubner Verlag 2009
Socher R.: Mathematik für Informatiker. München: Hanser 2011
Teschl S. und Teschl G.: Mathematik für Informatiker, Band 1, Diskrete Mathematik und Lineare Algebra. 3. Aufl. Berlin, Heidelberg: Springer 2008 

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