The WAMS-Mathematics and their Interactions was held at the Nesin Mathematics Village in Izmir, Turkey during the period 27 October-3 November, 2019. The objective of this school was to offer a fairly complete offer of courses in the modeling field, ranging from theoretical approaches to concrete developments (modeling and numerical simulations). The implementation and development of numerical approximation methods requires, first and foremost, a good knowledge of mathematical equations (differential equations, partial differential equations), but also the phenomena they account for. Finally, the efficient implementation of the associated approximation algorithms cannot be conceived without an introduction to computer skills. The courses were intended for students, researchers or teaching researchers wishing to acquire an introduction to modern training in the field of mathematics and their applications.

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