Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-02-12-M-1

Mathematics for Computer Science Students: Combinatorics, Stochastics, and Statistics (M, 8.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-02-12-M-1 Mathematics for Computer Science Students: Combinatorics, Stochastics, and Statistics 8.0 CP (240 h)

Basedata

CP, Effort 8.0 CP = 240 h
Position of the semester 1 Sem. in SuSe
Level [1] Bachelor (General)
Language [DE] German
Module Manager
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-Service] Mathematics for other Departments
Reference course of study [INF-82.79-SG] B.Sc. Computer Science
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V+2U MAT-02-12-K-1
Mathematics for Computer Science Students: Combinatorics, Stochastics, and Statistics
P 84 h 156 h
U-Schein
ja PL1 8.0 SuSe
  • About [MAT-02-12-K-1]: Title: "Mathematics for Computer Science Students: Combinatorics, Stochastics, and Statistics"; Presence-Time: 84 h; Self-Study: 156 h
  • About [MAT-02-12-K-1]: The study achievement [U-Schein] proof of successful participation in the exercise classes (ungraded) must be obtained. It is a prerequisite for the examination for PL1.

Examination achievement PL1

  • Form of examination: written exam (Klausur) (120-150 Min.)
  • Examination Frequency: each semester
  • Examination number: 80215 ("Mathematics for Computer Science Students: Combinatorics, Stochastics, and Statistics")

Evaluation of grades

The grade of the module examination is also the module grade.


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.

Competencies / intended learning achievements

Upon successful completion of this module, the students have achieved the following learning outcomes:
  • The students know and understand the fundamental concepts of enumerative combinatorics, stochastics and statistics.
  • On the basis of an application-oriented and computational approach they have learned the fundamental statements and methods of these fields and are able to apply them to problems in computer science.
  • They are trained in analytical thinking and their ability to think abstractly has been promoted.
  • In the exercise classes they have acquired a confident, precise and independent handling of the terms, statements and methods from the lecture.
  • In addition, their presentation skills and ability to work in a team have been promoted.

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.

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 Module / Module Number [MAT-02-12-M-1]

Course of Study Section Choice/Obligation
[INF-82.79-SG] B.Sc. Computer Science Theoretical Foundations [P] Compulsory
[INF-82.B16-SG] B.Sc. Socioinformatics Computer Science [P] Compulsory