Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-02-12-K-1

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 8.0 CP 156 h
4 V Lecture 56 h
2 U Exercise class (in small groups) 28 h
(4V+2U) 8.0 CP 84 h 156 h

Basedata

SWS 4V+2U 8.0 CP = 240 h 1 Sem. in SuSe [1] Bachelor (General) [DE] German Böhm, Janko, Dr. (WMA | DEPT: MAT) Kunte, Michael, Dr. (WMA | DEPT: MAT) [MAT-Service] Mathematics for other Departments [NORM] Active

Possible Study achievement

• Verification of study performance: proof of successful participation in the exercise classes (ungraded)
• Details of the examination (type, duration, criteria) will be announced at the beginning of the course.

Contents

Combinatorics:
• Binomial coefficients,
• applications (e.g. complete brackets),
• sieve formula, application: counting prime numbers,
• counting mappings, words,
• counting injective mappings, permutations,
• counting surjective mappings, applications (e.g. partitions of sets), equivalence relations,
• partitions of numbers,
• multisets,
• equivalence classes of mappings.

Stochastics:

• probability spaces,
• discrete distributions (e.g. binomial, Poisson),
• continuous distributions (e.g. normal, exponential),
• conditional probability, Bayesian formula, independence,
• random variables, expected value and variance,
• independence of random variables, covariance and correlation,
• applications (for example, runtime analysis of Mergesort and Quicksort),
• Markov inequality, Hoeffding inequality,
• weak and strong law of large numbers,
• central limit theorem,
• Markov chains, hidden Markov models,
• Monte Carlo simulation, simulation of distributions, application (e.g. Monte Carlo ray tracing).

Statistics:

• estimating parameters,
• confidence interval,
• testing hypotheses,
• tests for expected value,
• application (e.g. pseudo-random numbers),
• linear regression.

Literature

• B. Kreußler, G. Pfister: Mathematik für Informatiker: Algebra, Analysis, Diskrete Strukturen,
• M. Wolff, P. Hauck, W. Küchlin: Mathematik für Informatik und Bioinformatik,
• M. Aigner: Diskrete Mathematik,
• U. Krengel: Einführung in die Wahrscheinlichkeitstheorie und Statistik.

Materials

Further literature will be announced in the lecture; exercise material will be provided.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

None

References to Course [MAT-02-12-K-1]

Module Name Context
[MAT-02-12-M-1] Mathematics for Computer Science Students: Combinatorics, Stochastics, and Statistics P: Obligatory 4V+2U, 8.0 LP
[MAT-12-10P-M-3] Build-Up Module Mathematics (for Students of Physics) WP: Obligation to choose 4V+2U, 8.0 LP