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The book provides an introduction to common programming tools and methods in numerical mathematics and scientific computing. Unlike standard approaches, it does not focus on any specific language, but aims to explain the underlying ideas. Typically, new concepts are first introduced in the particularly user-friendly Python language and then transferred and extended in various programming environments from C/C  , Julia and MATLAB to Maple and Mathematica. This includes various approaches to distributed computing. By examining and comparing different languages, the book is also helpful for mathematicians and practitioners in deciding which programming language to use for which purposes. At a more advanced level, special tools for the automated solution of partial differential equations using the finite element method are discussed. On a more experimental level, the basic methods of scientific machine learning in artificial neural networks are explained and illustrated.
The core material is essentially the same as in the first edition, but thoroughly revised and updated to the current versions of the programming environments. Based on reader comments and suggestions, several cross-references have been included to facilitate comparison between different programming approaches. In the area of computer algebra systems, we have added a chapter on Mathematica. Here, the presentation is essentially based on that of the Maple chapter and can thus help the reader decide which system to use. Completely new is the chapter on scientific machine learning, a discipline that is currently in a rather experimental stage, but shows emerging potential. In any case, the discussion can help to take a fresh look at the concept of algorithms in general