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Mathematics 1

Module name (EN): Mathematics 1
Degree programme: Applied Informatics, Bachelor, ASPO 01.10.2011
Module code: PIB125
Hours per semester week / Teaching method: 4V+2U (6 hours per week)
ECTS credits: 7
Semester: 1
Mandatory course: yes
Language of instruction:
German
Assessment:
Written examination

[updated 08.05.2008]
Applicability / Curricular relevance:
PIB125 Applied Informatics, Bachelor, ASPO 01.10.2011, semester 1, mandatory course
Workload:
90 class hours (= 67.5 clock hours) over a 15-week 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 follow-up 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 n-dimensional 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, Cramerís 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, ...
[Sat May 21 00:54:30 CEST 2022, CKEY=pmathe1, BKEY=pi, CID=PIB125, LANGUAGE=en, DATE=21.05.2022]