Previous semester

Modellierung I

Instructors: Univ.-Prof. Dr. Michael Wand
Shortname: 08.079.314
Course No.: 08.079.314
Course Type: Vorlesung/Übung

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. Basics of computer graphics are useful, but not required (plan for a bit of extra time, in case).
  2. Knowledge in Python & C++ (or an alternative environment simularly suited for data analysis, numerics and visualization).

Digital teaching

The course can be offered in-person and virtually, depending on circumstances.

Details will be available on the course's web page at:

https://luna.informatik.uni-mainz.de/mod1-2122/
(online at the start of the semester)

Recommended reading list

Will be announced during the lecture.

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.

 

Dates

Date (Day of the week) Time Location
10/19/2021 (Tuesday) 16:00 - 18:00 Newtonraum
10/19/2021 (Tuesday) 16:00 - 18:00 01 122 Newton-Raum
2413 - Neubau Physik/Mathematik
10/26/2021 (Tuesday) 16:00 - 18:00 01 122 Newton-Raum
2413 - Neubau Physik/Mathematik
10/26/2021 (Tuesday) 16:00 - 18:00 Newtonraum
11/02/2021 (Tuesday) 16:00 - 18:00 01 122 Newton-Raum
2413 - Neubau Physik/Mathematik
11/02/2021 (Tuesday) 16:00 - 18:00 Newtonraum
11/09/2021 (Tuesday) 16:00 - 18:00 01 122 Newton-Raum
2413 - Neubau Physik/Mathematik
11/09/2021 (Tuesday) 16:00 - 18:00 Newtonraum
11/16/2021 (Tuesday) 16:00 - 18:00 01 122 Newton-Raum
2413 - Neubau Physik/Mathematik
11/16/2021 (Tuesday) 16:00 - 18:00 Newtonraum
11/23/2021 (Tuesday) 16:00 - 18:00 01 122 Newton-Raum
2413 - Neubau Physik/Mathematik
11/23/2021 (Tuesday) 16:00 - 18:00 Newtonraum
11/30/2021 (Tuesday) 16:00 - 18:00 01 122 Newton-Raum
2413 - Neubau Physik/Mathematik
11/30/2021 (Tuesday) 16:00 - 18:00 Newtonraum
12/07/2021 (Tuesday) 16:00 - 18:00 01 122 Newton-Raum
2413 - Neubau Physik/Mathematik
12/07/2021 (Tuesday) 16:00 - 18:00 Newtonraum
12/14/2021 (Tuesday) 16:00 - 18:00 01 122 Newton-Raum
2413 - Neubau Physik/Mathematik
12/14/2021 (Tuesday) 16:00 - 18:00 Newtonraum
01/04/2022 (Tuesday) 16:00 - 18:00 Newtonraum
01/04/2022 (Tuesday) 16:00 - 18:00 01 122 Newton-Raum
2413 - Neubau Physik/Mathematik
01/11/2022 (Tuesday) 16:00 - 18:00 Newtonraum
01/11/2022 (Tuesday) 16:00 - 18:00 01 122 Newton-Raum
2413 - Neubau Physik/Mathematik
01/18/2022 (Tuesday) 16:00 - 18:00 Newtonraum
01/18/2022 (Tuesday) 16:00 - 18:00 01 122 Newton-Raum
2413 - Neubau Physik/Mathematik
01/25/2022 (Tuesday) 16:00 - 18:00 Newtonraum
01/25/2022 (Tuesday) 16:00 - 18:00 01 122 Newton-Raum
2413 - Neubau Physik/Mathematik
02/01/2022 (Tuesday) 16:00 - 18:00 Newtonraum
02/01/2022 (Tuesday) 16:00 - 18:00 01 122 Newton-Raum
2413 - Neubau Physik/Mathematik