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Mathematics 3

Module name (EN): Mathematics 3
Degree programme: Applied Informatics, Bachelor, ASPO 01.10.2017
Module code: PIB-MA3
Hours per semester week / Teaching method: 3V+1U (4 hours per week)
ECTS credits: 5
Semester: 3
Mandatory course: yes
Language of instruction:
German
Assessment:


[still undocumented]
Applicability / Curricular relevance:
PIB-MA3 Applied Informatics, Bachelor, ASPO 01.10.2017, semester 3, mandatory course
Workload:
60 class hours (= 45 clock hours) over a 15-week period.
The total student study time is 150 hours (equivalent to 5 ECTS credits).
There are therefore 105 hours available for class preparation and follow-up work and exam preparation.
Recommended prerequisites (modules):
PIB-MA1 Mathematics 1
PIB-MA2 Mathematics 2


[updated 13.11.2017]
Recommended as prerequisite for:
Module coordinator:
Prof. Dr. Peter Birkner
Lecturer:
Dipl.-Ing. Dirk Ammon
Dipl.-Math. Wolfgang Braun


[updated 13.11.2016]
Learning outcomes:
After successfully completing this module, students will be able to explain the reasons for the inaccuracies that often arise when calculating with computers and know basic methods
  for estimating these inaccuracies.
- Students will know basic iteration techniques for solving application problems using computers.
- They will be able to process and solve elementary combinatorial and probabilistic tasks   
  with the help of an introduction to probability calculus.
- Students will develop the ability to analyze real or planned systems by abstracting practical
  discrete mathematics tasks from the field of IT into mathematical structures.
- Students will be able to use elementary methods of number theory in cryptographic applications
  and coding.


[updated 24.02.2018]
Module content:
Numerical mathematics
  Representation of numbers in computers, errors, rounding errors, error propagation   
  Bisection method
  Iterative methods, Banach fixed-point theorem, a priori estimates
  Newton´s method
Probability calculus
  The concept of "probability"
  Conditional probability and independent events
  Urn experiments
  Random variables and distribution functions
  Expected value and variance
  Discrete distribution, Poisson distribution, normal (or Gaussian) distribution
Discrete Mathematics
  Primitive recursive functions and µ recursive functions
  Elementary number theory
  Finite fields
  Principles of cryptography
  Principles of the coding theory


[updated 24.02.2018]
Teaching methods/Media:
Lecture and use of a computer algebra system. Every two weeks an exercise sheet will be distributed and then discussed in small groups the following week.

[updated 24.02.2018]
Recommended or required reading:
- P. Hartmann, Mathematik für Informatiker (Vieweg); can be downloaded via OPAC as a PDF.
- M. Brill, Mathematik für Informatiker (Hanser).

[updated 24.02.2018]
Module offered in:
WS 2021/22, WS 2020/21, WS 2019/20, WS 2018/19
[Thu Dec  2 02:21:08 CET 2021, CKEY=pm3, BKEY=pi2, CID=PIB-MA3, LANGUAGE=en, DATE=02.12.2021]