

Module code: PIB125 

4V+2U (6 hours per week) 
7 
Semester: 1 
Mandatory course: yes 
Language of instruction:
German 
Assessment:
Written examination
[updated 08.05.2008]

PIB125 (P2210001) Applied Informatics, Bachelor, ASPO 01.10.2011
, semester 1, mandatory course

90 class hours (= 67.5 clock hours) over a 15week period. The total student study time is 210 hours (equivalent to 7 ECTS credits). There are therefore 142.5 hours available for class preparation and followup work and exam preparation.

Recommended prerequisites (modules):
None.

Recommended as prerequisite for:
PIB215 Mathematics 2 PIB220 Graph Theory PIB330 Databases PIBWI19 Machine Learning PIBWI83 Computer Vision PIBWI92 Numerical Software
[updated 02.03.2017]

Module coordinator:
Prof. Dr. Rainer Lenz 
Lecturer: Prof. Dr. Rainer Lenz Dipl.Ing. Dirk Ammon (exercise) Dipl.Math. Wolfgang Braun (exercise)
[updated 01.06.2011]

Learning outcomes:
Students will be taught basic skills in general mathematics, they will acquire a basic understanding of algebra and analysis and will become familiar with mathematical terminology.
[updated 08.05.2008]

Module content:
1 Basic mathematical terminology Predicate logic, sets, relations, maps 2 Natural numbers, mathematical induction, recursion 2.1 The axioms of the natural numbers 2.2 Mathematical induction 2.3 Recursive definitions 2.4 Binomial coefficients and binomial formulae 2.5 Basic terminology of combinatorics 3 Elementary vector calculus in Euclidian vector space 3.1 Vector algebra, linear independence, dimension 3.2 Vectors in the Cartesian coordinate system, scalar product, vector product, mixed product 3.3 Geometrical applications 4 Vectors in ndimensional space 4.1 Generating system, basis, subspaces 4.2 Linear maps, range, kernel 4.3 Matrix representation of linear maps 4.4 Geometrical applications: Projections, reflections, rotations 5 Matrices 5.1 Linear systems of equations, Gaussian algorithm 5.2 Matrix algebra 5.3 Quadratic matrices, determining the inverse matrix, determinants, Cramer’s rule, adjoint eigenvalue problems, basis transformation 6 Basic terminology of algebra 6.1 Semigroups, monoids 6.2 Groups, subgroups, normal subgroup, factor groups, homomorphism 6.3 Rings and fields 7 Sequences and series 7.1 Limits, limit theorems, Cauchy sequences 7.2 Series, conditional and absolute convergence, comparison test and ratio test, Cauchy product 7.3 Geometrical series, exponential series 8 Continuity 8.1 Limits of functions 8.2 Properties of continuous functionsInverse functions, logarithms, inverse hyperbolic and inverse trigonometric functions
[updated 08.05.2008]

Recommended or required reading:
Hartmann, P.: Mathematik für Informatiker, Vieweg, 3. Aufl. 2004 Meyberg, K. Vachenauer, P.: Höhere Mathematik 1, Springer
[updated 08.05.2008]

Module offered in:
WS 2016/17,
WS 2015/16,
WS 2014/15,
WS 2013/14,
WS 2012/13,
...
