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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 01.10.2011
Module code: PIB315
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.
4V+2U (6 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.
6
Semester: 3
Mandatory course: yes
Language of instruction:
German
Assessment:
Written examination

[updated 08.05.2008]
Applicability / Curricular relevance:
All study programs (with year of the version of study regulations) containing the course.

PIB315 (P221-0003) Applied Informatics, Bachelor, ASPO 01.10.2011 , 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).
90 class hours (= 67.5 clock hours) over a 15-week period.
The total student study time is 180 hours (equivalent to 6 ECTS credits).
There are therefore 112.5 hours available for class preparation and follow-up work and exam preparation.
Recommended prerequisites (modules):
PIB215 Mathematics 2


[updated 01.04.2006]
Recommended as prerequisite for:
PIBWI19 Machine Learning
PIBWI37
PIBWI83 Computer Vision


[updated 02.03.2017]
Module coordinator:
Prof. Dr. Rainer Lenz
Lecturer:
Prof. Dr. Rainer Lenz


[updated 06.10.2010]
Learning outcomes:
Students will acquire a fundamental understanding of numerical methods. They will also be taught the basic mathematical skills required to understand and apply the mathematical tools of probability calculus and statistics.

[updated 08.05.2008]
Module content:
1        Introduction
Computer representation of numbers, rounding errors, error propagation
 
2        Numerical root finding
2.1        Bisection method
2.2        Iterative methods, special case of Banach’s fixed-point theorem, a priori estimates
2.3        Newton’s method
 
3        Interpolation and approximation
3.1        Lagrange interpolation polynomials
3.2        Newton interpolation polynomial
3.3        Aitken-Neville interpolation
3.4        Spline interpolation
3.5        Discrete least-squares approximation, method of least-squares
 
4        Numerical integration / Quadrature
4.1        Trapezoidal rule
4.2        Kepler’s rule, Simpson’s rules
4.3        Newton’s 3/8 rule
 
5        Probability spaces
5.1        The statistical perspective
5.2        The concept of probability
5.3        Conditional probability and independent events
5.4        Urn models
 
6        Random variables
6.1        Random variables and distribution functions
6.2        Expectation values and variance
 
7        Distributions
7.1        Discrete distributions
7.2        The Poisson distribution
7.3        Continuous distributions, normal distributions
 
8        Statistical methods
8.1        Estimating parameters
8.2        Confidence intervalsHypothesis testing


[updated 08.05.2008]
Teaching methods/Media:
Use of the Maple software package via video projector, group problem-solving using PCs

[updated 08.05.2008]
Recommended or required reading:
Hartmann, P.:  Mathematik für Informatiker, Vieweg 3. Aufl. 2004
Brill, M.:  Mathematik für Informatiker, Hanser 2. Aufl. 2005


[updated 08.05.2008]
Module offered in:
WS 2017/18, WS 2016/17, WS 2015/16, WS 2014/15, WS 2013/14, ...
[Mon May 29 19:57:04 CEST 2023, CKEY=pmathe3, BKEY=pi, CID=PIB315, LANGUAGE=en, DATE=29.05.2023]