Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-02-12-K-1

Mathematics for Computer Science Students: Combinatorics, Stochastics, and Statistics (4V+2U, 8.0 LP)

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
CP, Effort 8.0 CP = 240 h
Position of the semester 1 Sem. in SuSe
Level [1] Bachelor (General)
Language [DE] German
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-Service] Mathematics for other Departments
Livecycle-State [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,
  • adaptation test, independence test,
  • 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).

Requirements for attendance (informal)

Requirements for attendance (formal)

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