Lecture1: What is Mathematical Modelling? скачать в хорошем качестве

Lecture1: What is Mathematical Modelling?

MA4J5, Introduction: Week 1: Mathematical Modelling, Past, Present and Future • What is Mathematical Modelling? • Why Complex Systems?.. • Philosophy of Science, Empirical Data and Prediction. • About this course. Overview: This should be one of the world's most sophisticated courses on mathematical modelling, combined with applications on complex systems. The current crisis, the global pandemic, economic transitions and climate change have brought complex systems theory once more into the spotlight, and their mathematical modelling is key to their understanding and possible management. We keep also this year the partition of the lecture into three parts, structural modelling, dynamic modelling and learning/data analysis. All of these parts have proven to be necessary for any complex systems modelling, sich as models in the Life Sciences, in the Social Sciences, in Economy & Finance or Ecology and Infectious Diseases. In this lecture will learn how to start the modelling process by thinking about the model's static structure, which then in a dynamic model gives rise to the choice of variables. Finally, with the dive into mathematical learning theories, the students will understand that a mathematical model is never finished, but needs recursive learning steps to improve its parametrisation and even structure. A very important aspect of the lecture is the smooth transition from static to dynamic stochastic models with the help of rule-based system descriptions which have evolved from the modelling of chemical reactions.