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 book presents the life and works of one of Germany's most famous computer scientists, Carl Adam Petri. It is written in a vivid and entertaining manner, providing an in-depth discussion of the background behind Petri's best-known contribution to computer science, the Petri net. In this way the book can be read as a first introduction to nets, but it also covers the theoretical, physical and philosophical foundations behind nets, thus facilitating a comprehensive understanding of the wider range of Petri's works. The book is intended for readers with a previous knowledge in computer science, as well as for "interested non-professionals", who want to get to know a remarkable personality of contemporary science.

Der Autorprasentiert Leben, Werk und Wirken eines der weltweit bekanntesten deutschen Informatiker: Carl Adam Petri. Die Stadien seiner Entwicklung sind lebendig und kurzweilig beschrieben, gehen aber so weit in die Tiefe, dass der Leser ein gutes Verstandnis fur die Hintergrunde von Petris wichtigstem Beitrag zur Informatik bekommt, die nach ihm benannten Petrinetze. Das Buch kann so als Einfuhrung in die Petrinetze gelesen werden, erortert aber auch die theoretischen, physikalischen und philosophischen Grundlagen der Netze, die erst einen umfassenden Zugang zu Petris Werk ermoglichen. Das Buch wendet sich dank seiner verstandlichen Darstellung aber auch an Leser, die einfach nur eine bemerkenswerte Personlichkeit der Zeitgeschichte kennenlernen mochten."

The book provides an introduction to common programming tools and methods in numerical mathematics and scientific computing. Unlike widely used standard approaches, it does not focus on any particular language but aims to explain the key underlying concepts. In general, new concepts are first introduced in the particularly user-friendly Python language and then transferred and expanded in various scientific programming environments from C / C ++, Julia and MATLAB to Maple. This includes different approaches to distributed computing. The fact that different languages are studied and compared also makes the book useful for mathematicians and practitioners trying to decide which programming language to use for which purposes.

The book presents the life and works of one of Germany's most famous computer scientists, Carl Adam Petri. It is written in a vivid and entertaining manner, providing an in-depth discussion of the background behind Petri's best-known contribution to computer science, the Petri net. In this way the book can be read as a first introduction to nets, but it also covers the theoretical, physical and philosophical foundations behind nets, thus facilitating a comprehensive understanding of the wider range of Petri's works. The book is intended for readers with a previous knowledge in computer science, as well as for "interested non-professionals", who want to get to know a remarkable personality of contemporary science.

Das Buch f hrt in leicht verst ndlicher und dennoch pr ziser Form in die Grundlagen der Berechenbarkeitstheorie ein. Es richtet sich an Informatikstudenten, ist aber f r alle an der algorithmischen Berechenbarkeit Interessierten geeignet; vom Leser wird nur eine gewisse Vertrautheit mit formaler Argumentation erwartet. Der Darstellung liegt das Modell der Registermaschine zugrunde, das dem Umgang mit realen Computern und Programmiersprachen entlehnt ist. Daneben werden auch die klassischen Berechenbarkeitsmodelle betrachtet und die Gleichwertigkeit der Ans tze untereinander gezeigt. Dar ber hinaus werden nicht-berechenbare Funktionen und unentscheidbare Probleme nachgewiesen. Als weiterf hrendes Thema wird die Unentscheidbarkeit der Pr dikatenlogik und einiger Probleme aus dem Bereich der formalen Sprachen behandelt.