SoSe 2020

Modellierung I

Univ.-Prof. Dr. Michael Wand

Shortname: 08.079.314
Course No.: 08.079.314

Recommended reading list

Will be announced in the lecture.

Requirements / organisational issues

Requirements:

  1. Basic Mathematics: Core mathematics lectures Calculus 1, Linear Algebra 1 ("for mathematicians"), basic probability theory. Mathematics for Physisists is also well-suited.
  2. Good programming skills („Einführung in die Programmierung“, „Einführung in die Softwareentwicklung“, „Datenstrukturen und Algorithmen“ or equivalent).

Useful:

  1. C++ knowledge: Tutorials will use C++ (other languages are permitted but this might require some additional effort).
  2. Basics of computer graphics are useful, but not required (plan for a bit of extra time, in case).



 

Digitale Lehre

The course will be offered in a digital format involving prerecorded lecture videos and live tutorials.

Further details will be published in the "JGU-Reader": https://reader.uni-mainz.de/

All Info will be made available on or before Friday, April 17 2020 (including an email to all participants via "reader-messages").

 

Contents

The lecture discusses basic concepts of how to model real-world phenomena with a computer. The goal is to give an overview of basic mathematical and theoretical tools for modeling, and (in particular) to bring these concepts into practical implementation and application.

Modeling of real-world phenomena poses a number of questions:

  1. Representation: Which information is constitutes the state of the modeled phenomenon?
  2. Rules/dynamics: How does the phenomenon evolve/behave over time / space?
  3. Simulation: How can we simulate it?
  4. Inverse problems: Can we adjust the model parameter such that the simulation explains real-world measurement data?
  5. Variational modeling and optimization: How can we model problems implicitly through the use of objective functions and constraints?




Bottom Line: Modeling 1 = Linear Modelling
Modelling 1 focusses on linear models (model state is a vector in a linear space). It will discuss representations and sampling issues, and show a number of practical examples (such as global illumination or dynamics of objects). For optimization and inverse problems, we consider simple quadratic variational formulations that can be solved with the nice & easy to use linear algebra tools.

Non-linear and statistical methods are discussed in a subsequent lecture.

Remark: The format in 2020 is the traditional 2h-lecture, 2h-tutorials (V2Ü2) again; the V2Ü2P2-Format from 2019 will be discontinued.

Dates:

Date (Day of the week)TimeLocation
04/21/2020 (Tuesday)16.00 to 18.0004 224
2413 - Neubau Physik/Mathematik
04/28/2020 (Tuesday)16.00 to 18.0004 224
2413 - Neubau Physik/Mathematik
05/05/2020 (Tuesday)16.00 to 18.0004 224
2413 - Neubau Physik/Mathematik
05/12/2020 (Tuesday)16.00 to 18.0004 224
2413 - Neubau Physik/Mathematik
05/19/2020 (Tuesday)16.00 to 18.0004 224
2413 - Neubau Physik/Mathematik
05/26/2020 (Tuesday)16.00 to 18.0004 224
2413 - Neubau Physik/Mathematik
06/02/2020 (Tuesday)16.00 to 18.0004 224
2413 - Neubau Physik/Mathematik
06/09/2020 (Tuesday)16.00 to 18.0004 224
2413 - Neubau Physik/Mathematik
06/16/2020 (Tuesday)16.00 to 18.0004 224
2413 - Neubau Physik/Mathematik
06/23/2020 (Tuesday)16.00 to 18.0004 224
2413 - Neubau Physik/Mathematik
06/30/2020 (Tuesday)16.00 to 18.0004 224
2413 - Neubau Physik/Mathematik
07/07/2020 (Tuesday)16.00 to 18.0004 224
2413 - Neubau Physik/Mathematik

Semester: SoSe 2020