Monte Carlo Algorithms (4V+2U, 9.0 LP)
|SWS||Type||Course Form||CP (Effort)||Presence-Time / Self-Study|
|-||K||Lecture with exercise classes (V/U)|
|4||V||Lecture||6.0 CP||56 h||124 h|
|2||U||Exercise class (in small groups)||3.0 CP||28 h||62 h|
|(4V+2U)||9.0 CP||84 h||186 h|
|CP, Effort||9.0 CP = 270 h|
|Position of the semester||1 Sem. irreg. SuSe|
|Level|| Master (General)|
+ further Lecturers of the department Mathematics
|Area of study||[MAT-STO] Stochastics/Statistics/Financial Mathematics|
The course is offered at least every second summer semester.
Possible Study achievement
- Verification of study performance: proof of successful participation in the exercise classes (ungraded)
- Examination number (Study achievement): 84037 ("Exercise Class Monte Carlo Algorithms")
- Details of the examination (type, duration, criteria) will be announced at the beginning of the course.
Monte Carlo algorithms are the algorithms which use randomness. The course gives an introduction to this important basic algorithmic technique in mathematics and computer science.
It discusses the topics
- Direct Simulation
- Simulation of distributions
- Variance reduction
- Markov Chain Monte Carlo algorithms
- High-dimensional integration
and applications in physics as well as in financial and actuarial mathematics
Competencies / intended learning achievements
The students have developed a basic understanding of the construction, analysis and applications of Monte Carlo algorithms. They have gained practical experience of using such algorithms and insights into different application fields and they are able to critically assess the applicability and limitations of the algorithms.
- T. Müller-Gronbach, E. Novak, K. Ritter: Monte Carlo-Algorithmen,
- S. Asmussen, P.W. Glynn: Stochastic Simulation,
- E. Behrends: Introduction to Markov Chains,
- P. Brémaud: Markov Chains,
- P. Glasserman: Monte Carlo Methods in Financial Engineering,
- C. Lemieux: Monte Carlo and Quasi-Monte Carlo Sampling,
- R. Motwani, P. Raghavan: Randomized Algorithms,
- J.F. Traub, G.W. Wasilkowski, H. Wozniakowski: Information-based Complexity.
Further literature will be announced in the lecture; Exercise material is provided.
Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de)
Requirements for attendance (informal)
- [MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)
- [MAT-14-14-M-3] Stochastic Methods (M, 9.0 LP)
Requirements for attendance (formal)
References to Course [MAT-60-14-K-6]
|[MAT-60-14-M-6]||Monte Carlo Algorithms||P: Obligatory||4V+2U, 9.0 LP|
|[MAT-50-4V-KPOOL-4]||Elective Courses Optimisation and Stochastics (4V, B.Sc.)|
|[MAT-70-4V-KPOOL-4]||Elective Courses Analysis and Stochastics (4V, B.Sc.)|
|[MAT-70-KPOOL-4]||Specialisation Analysis and Stochastics (B.Sc.)|
|[MAT-80-4V-KPOOL-4]||Elective Courses Modelling and Scientific Computing (4V, B.Sc.)|