Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-64-15-M-7

Module Identification

Module Number Module Name CP (Effort)
MAT-64-15-M-7 High-Dimensional Integration 4.5 CP (135 h)

Basedata

CP, Effort 4.5 CP = 135 h 1 Sem. irreg. [7] Master (Advanced) [EN] English Ritter, Klaus, Prof. Dr. (PROF | DEPT: MAT) Ritter, Klaus, Prof. Dr. (PROF | DEPT: MAT) [MAT-SPAS] Analysis and Stochastics [MAT-88.105-SG] M.Sc. Mathematics [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.
2V+1U MAT-64-15-K-7
High-Dimensional Integration
P 42 h 93 h - - PL1 4.5 irreg.
• About [MAT-64-15-K-7]: Title: "High-Dimensional Integration"; Presence-Time: 42 h; Self-Study: 93 h

Examination achievement PL1

• Form of examination: oral examination (20-30 Min.)
• Examination Frequency: each semester
• Examination number: 86248 ("High-Dimensional Integration")

Contents

Algorithms and Complexity of high and infinite-dimensional integration problems:
• Monte Carlo Method,
• discrepancy of point sequences and quasi Monte Carlo Method,
• randomisation,
• lower error bound and complexity of continuous problems,
• curse of dimension,
• quadrature problems for stochastic differential equations.

Competencies / intended learning achievements

Upon successful completion of this module, the students know and understand the basic principles of the construction and analysis of algorithms for high-dimensional integration. They can apply the algorithms to solve practical problems, and they can critically analyze the possibilities and limitations of those. They understand how to develop important results and methods of complexity theory of continuous problems. They understand proofs presented in the lecture and are able to reproduce and explain them.

By solving the given exercises, they have gained a precise and independent handling of the terms, propositions and methods of the lecture. In addition, they have learned to apply the methods to new problems, analyze them and develop solution strategies independently or by team work.

Literature

• E. Novak, H. Wozniakowski: Tractability of Multivariate Problems, Vol. I-III.

Registration

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

Requirements for attendance of the module (informal)

Knowledge on stochastic differential equations is useful but not necessarily required.

None

References to Module / Module Number [MAT-64-15-M-7]

Module-Pool Name
[MAT-70-MPOOL-7] Specialisation Stochastic Analysis (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)
[MAT-RM-MPOOL-7] Pure Mathematics (Advanced Modules M.Sc.)