# Difference between revisions of "Algorithms for Scientific Computing - Summer 17"

Term
Summer 2017
Lecturer
Time and Place
Lecture: Mon 8:30-10:00, Fri 10:15-11:45, MI Hörsaal 2 (1st lecture: Mon, Apr 24)
Tutorial: Wed 10:15-11:45, MI 00.13.09A
Audience
see module description (IN2001) in TUMonline
Tutorials
Emily Mo-Hellenbrand, M.Sc., Jean-Matthieu Gallard, M.Sc.
Exam
written exam at the end of the semester
Semesterwochenstunden / ECTS Credits
6 SWS (4V + 2Ü) / 8 Credits
TUMonline
https://campus.tum.de/tumonline/wbLv.wbShowLVDetail?pStpSpNr=950290914

## News & Announcements

• please re-check the solution of exercise 4 on worksheet 7; this has been corrected!
• please re-check the solution of exercise 1 on worksheet 4; this has been corrected!
• as an exception, the lecture on Fri, May 19, will start at 10.30 (until 12.00)

Many applications in computer science require methods of (numerical) mathematics - especially in science and engineering, of course, but also in surprisingly many areas that one might suspect to be directly at the heart of computer science:

Consider, for example, Fourier and wavelet transformations, which are indispensable in image processing and image compression. Similar, numerical methods for approximation have become essential techniques for high-dimensional classification problems in data science. Essentially, these methods come down to the question of how to represent and process information or data as (multi-dimensional) continuous functions. "Algorithms for Scientific Computing" thus provides an algorithmically oriented introduction to the foundations of such mathematical methods.

Topics include:

• The fast Fourier transformation (FFT) and some of its variants:
• FCT (Fast Cosine Transform), real FFT, Application for compression of video and audio data
• Hierarchical and recursive methods in scientific computing
• From Archimedes' quadrature to the hierarchical basis
• Classification problems
• From the hierarchical basis to wavelets
• High-demonsional problems
• Sparse grids and the sparse-grid combination technique
• Octrees and Space filling curves (SFCs):
• Construction and properies of SFCs
• Application for parallelization and to linearize multidimensional data spaces in data bases

## Lecture Slides and Supplementary Materials

Lecture slides are published here successively. For future lectures, the respective slides from summer 2016 will be linked.

## Worksheets and Solutions

Number Topic Worksheet Tutorial Solution
1 Discrete Fourier Transform I Worksheet 1Python Introduction Apr. 26
2 Discrete Fourier Transform II Worksheet 2 Worksheet 2 Notebook template May 3
- - - May 10 tutorial cancelled due to student assembly
3 Discrete Cosine Transform Worksheet 3 Worksheet 3 Notebook template Template Exercise 1 May 17
4 Discrete Fourier Transform III Worksheet 4 May 24
5 Numerical Quadrature 1D Worksheet 5 Worksheet 5 Notebook template May 31
6 Hierarchical Basis Worksheet 6 Jun. 07
7-Part1 Function Approximation and Wavelet Ex1-3: Worksheet 7 Worksheet 7 Notebook template Jun. 14
7-Part2 Function Approximation and Wavelet Ex4-5: See above Jun. 21 See above
8 Multi-dimensional Quadrature Worksheet 8 Worksheet 8 template Jun. 28

### Jupyter Notebook

Books that are labeled as "available as e-book" can be accessed as e-book via the TUM library - see the ebooks website of the library for details on how to access the books.

### Fast Fourier Transform:

The lecture is oriented on: