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Algorithms for Scientific Computing - Summer 17

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Term
Summer 2017
Lecturer
Univ.-Prof. Dr. Michael Bader
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
Mon, Aug 7, 10.30 in lecture hall MI HS 1 (F.L. Bauer Hörsaal)
Thu, Oct 5, 16.00 in lecture hall Interim 2
Semesterwochenstunden / ECTS Credits
6 SWS (4V + 2Ü) / 8 Credits
TUMonline
https://campus.tum.de/tumonline/wbLv.wbShowLVDetail?pStpSpNr=950290914



Contents

News & Announcements

  • Review for the repetition exam will be held on 26.10.17 Thursday from 11:00 to 12:00 in room MI 02.05.051 (printer room). Please bring your student ID.
  • Exam review will be held on 24.08.17 at 11AM in room MI 02.05.057. Please bring your Student-ID.
  • As pointed out by some, there are confusions regarding WS6 ex1. Therefore, I reformulated the question and WS6 is updated. Please check.
  • The tutorial on Wednesday 12.07 will include the beginning of the lecture on space-filling curve.
  • The Mock Exam and its solution is now posted in the "Worksheets and Solutions" table. Please note:
    • Disclaimer: this mock exam merely serves the purpose of giving you some ideas/hints on what to expect in the actual exam (e.g., exam format, possible questions, difficulty levels). Please do NOT assume that you will get the same (or very similar) questions in the actual exam, as there are many ways to ask a question on the same subject!
    • Exam coverage: You should prepare for all 4 topics, i.e., FFT, Hier. methods, Sparse grids, SFC. And you should expect questions from all lecture slides (except for Red parts) and worksheet exercises. Pseudo code questions are possible to appear.
    • Preparation hint: Try to solve & understand all the exercises in the worksheets and the mock exam.
  • The supplement material of transforming the regularization formula into a linear system (Lecture July 10, slide 18) is uploaded.
  • Worksheet 9 code template is updated (fixed compatibility issues with Python 3). Please re-download the template zip. NOTE: you need the files supplied in the template zip to run the Worksheet 9 code solution.
  • Worksheet 7 solution is updated (mistake in ex4 corrected). Please re-check the solution!
  • 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)

What's ASC about?

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):
    • Tree-structured (hierarchical) adaptivity
    • 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.

Fast Fourier Transform

Hierarchical Methods

Sparse Grids

Space-Filling Curves

Worksheets and Solutions

Number Topic Worksheet Tutorial Solution
1 Discrete Fourier Transform I Worksheet 1Python Introduction Apr. 26

Ws1 solution Ws1 solution Notebook

2 Discrete Fourier Transform II Worksheet 2 Worksheet 2 Notebook template May 3

Ws2 solution Ws2 solution Notebook Ws2 Ex2 solution code

- - - May 10 tutorial cancelled due to student assembly
3 Discrete Cosine Transform Worksheet 3 Worksheet 3 Notebook template Template Exercise 1 May 17

Ws3 solution Ws3 solution code

4 Discrete Fourier Transform III Worksheet 4 May 24

Ws4 solution

5 Numerical Quadrature 1D Worksheet 5 Worksheet 5 Notebook template May 31

Ws5 solution Notebook

6 Hierarchical Basis Worksheet 6 Jun. 07

Ws6 Ex1-2 solution Notebook Ws6 Ex3 solution

7-Part1 Function Approximation and Wavelet Ex1-3: Worksheet 7 Worksheet 7 Notebook template Jun. 14

Ws7 solution

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

Ws8 solution

9 Multi-dimensional hierarchization and adaptive sparse grids Worksheet 9 Worksheet 9 code template Jul. 05

Ws9 code solution Ws9 Ex2 solution

10 Grammars for space-filling curves Worksheet 10 Worksheet 10 code template Notebook template Jul. 12

Ws10 solution Ws10 solution code Ws10 solution Notebook

11 Arithmetization of space-filling curves Worksheet 11 code template Notebook template Jul. 19

Ws11 solution Ws11 solution code Ws11 solution Notebook

12 Refinement trees and space-filling curves Worksheet 12, Worksheet 12 Notebook template Jul. 26

Ws12 solution Ws12 solution Notebook

13 Q&A session (exercises) Aug. 02
- Mock Exam Mock exam -

Mock exam solution


Jupyter Notebook

Repeat Exam

  • type: written exam, duration: 100 min
  • time, date, room: Thu, Oct 5, 2017, 16.00-17.40 (Interim 2)
    • note that the exam will start precisely on 16.00; please be in the exam room by 15.45, at the latest!
  • helping material:
    • you may use one hand-written sheet of paper (size A4, front and back may be used)
    • no other helping material of any kind is allowed

Literature and Additional Material

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:

Hierarchical Methods and Sparse Grids

Wavelets

Space-filling Curves:

Background Material Concerning Scientific and High Performance Computing