Mathematics Made Simple: Mathematical Modeling

This book explains what mathematical modeling is about, what considerations lead to established models, and how you can develop your own mathematical models.

It covers applications from mechanics, population dynamics, microeconomics, and other fields of knowledge. At the same time, we reflect on what we do and what we often without realizing it assume when we model observed phenomena mathematically.

People with scientific curiosity have always considered phenomena to be truly understood only when mathematical models have been established that provide accurate predictions. This curiosity persists today, leading to new insights, the development of modern approaches such as machine learning, and thus to ever new models.

This book is a translation of the original German edition. The translation was done with the help of an artificial intelligence machine translation tool. A subsequent human revision was done primarily in terms of content, so that the book may read stylistically differently from a conventional translation.

Dirk Langemann studied mathematics at the University of Rostock and has been professor at Technische Universität Braunschweig since 2009. His work focuses on questions of mathematical modeling, and he is responsible for the core undergraduate mathematics courses in engineering degree programs.

Cordula Reisch studied mathematics as well as mathematics and physics for the teaching profession at upper secondary schools at Technische Universität Braunschweig. In 2019, she obtained her doctorate on reaction-diffusion equations with applications in the life sciences. Since 2025 she is professor at Roskilde University. She conducts research on applications of mathematical modeling and teaches courses in these areas.