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Mathematics 3

Module name (EN):
Name of module in study programme. It should be precise and clear.
Mathematics 3
Degree programme:
Study Programme with validity of corresponding study regulations containing this module.
Applied Informatics, Bachelor, ASPO 01.10.2022
Module code: PIB-MA3
SAP-Submodule-No.:
The exam administration creates a SAP-Submodule-No for every exam type in every module. The SAP-Submodule-No is equal for the same module in different study programs.
P221-0003
Hours per semester week / Teaching method:
The count of hours per week is a combination of lecture (V for German Vorlesung), exercise (U for Übung), practice (P) oder project (PA). For example a course of the form 2V+2U has 2 hours of lecture and 2 hours of exercise per week.
3V+1U (4 hours per week)
ECTS credits:
European Credit Transfer System. Points for successful completion of a course. Each ECTS point represents a workload of 30 hours.
5
Semester: 3
Mandatory course: yes
Language of instruction:
German
Assessment:


[still undocumented]
Applicability / Curricular relevance:
All study programs (with year of the version of study regulations) containing the course.

PIB-MA3 (P221-0003) Applied Informatics, Bachelor, ASPO 01.10.2022 , semester 3, mandatory course
Workload:
Workload of student for successfully completing the course. Each ECTS credit represents 30 working hours. These are the combined effort of face-to-face time, post-processing the subject of the lecture, exercises and preparation for the exam.

The total workload is distributed on the semester (01.04.-30.09. during the summer term, 01.10.-31.03. during the winter term).
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 17.06.2024]
Recommended as prerequisite for:
Module coordinator:
Prof. Dr. Peter Birkner
Lecturer:
Prof. Dr. Peter Birkner (lecture)
Dipl.-Ing. Dirk Ammon (exercise)


[updated 17.06.2024]
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 2024/25, WS 2023/24, WS 2022/23, WS 2021/22, WS 2020/21, ... 
[Wed Oct 30 09:27:45 CET 2024, CKEY=pm3, BKEY=pi2, CID=PIB-MA3, LANGUAGE=en, DATE=30.10.2024]