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 |