Currents in Industrial Mathematics. From Concepts to Research to Education

Editors: Neunzert, Helmut, Prätzel-Wolters, Dieter, Springer 2015

 

An accolade to the legacy of IM

This book is a voyage of discovery for readers who are curious to know what modern mathematics, armed with a computational toolbox can ultimately do – especially when one has a trained team equipped with a proper basis in applied mathematics, skills of computing and with a sound understanding of the application area. The book is inspiring reading for both educators and industrial managers, R&D persons and researchers in applied sciences who are working with models, quantitative methods, demanding data sets and measurements.

In the recent decade, rich collection of literature has appeared about the art and science of mathematical modelling, featuring pedagogical expositions about modern applied mathematics and also informative scientific reports about industrial projects containing modeling and scientific computing. The two streams, educational literature and R&D reporting, are in general separate. This book tells the whole story in a way that binds together the essential pieces in a transparent and logical way. The chapters take the reader through the educational realm from high school classroom to university mathematics, fundaments of modelling, learning via real world projects, and finally to the professional field of industrial mathematics, real R&D challenges and the role of mathematical technology in facilitating innovation.

Helmut Neunzert has long time ago formulated the vision and so to speak coined the claim “Mathematics is the next technology”. This book is a proof. It also brings home another important point. It has been traditionally difficult to get scientific credit for work where existing mathematical knowledge, even non-trivial and sophisticated, but already known, is applied to real world problems in a way that produces an impact. The book demonstrates the process how industrial problems can offer a challenge for new mathematics and novel computational approaches. The research on mathematics (both applied and fundamental) often finds real applications after a long delay. The book demonstrates how technological development and hardcore applied mathematics are sometimes fermenting concurrently.

The book celebrates the success story of the Fraunhofer Institut für Techno- und Wirtshaftsmathematik ITWM. The introduction capsulates nicely how the spirit of the Fraunhofer Gesellshaft and the vision of ECMI are well aligned by the characterization of mathematics as “a discipline that is indispensable for maintaining economic competitiveness and meeting the challenges faced by society. It has evolved from being a key to basic research to being an enabling force for virtually every economically significant key technology”.

The chapters of the book mark a path of exploration into the scenery of industrial mathematics. After the titillating Introduction about “Somewhat Different Mathematics” the trail continues to Modeling, Numerics, Data Analysis and Optimization in Practice, each chapter presenting a substantial tutorial of a key area. The next part gives five substantial and well-elaborated examples of industrial projects where the charm and impact of IM is proved beyond reasonable doubt.

Finally the book ends with a chapter about applications and school mathematics, an extremely timely topic and a very nice way to close the story. The articles in part III have been authored by a team of researchers from ITWM. This opens a real shop-floor perspective to industrial mathematics. The book was edited by Helmut Neunzert, a pioneering figure within ECMI and the founder of ITWM and Dieter Prätzel-Wolters who is the present director of the dynamic and flourishing institute.

To those who have followed the growth of the European community of industrial mathematics and the amicable family history of ECMI can recognize some interesting comments across the slightly varying traditions among the hotspots of IM in Europe. Resorting to a joke about words one can say that in addition to currents of industrial mathematics the book contains also subtle “potential differences” that make ideas and discussion to flow. Helmut refers to the Oxford tradition where asymptotic analysis, by recognition of small parameters, is often done in an effort of model reduction and search for transparency and qualitative understanding of model complexity. As contrast the Fraunhofer mathematics at ITWM is proud for its determined pursuit for actual quantitative forecasts where small parameters cannot be smoothed out. The deep ideal of Europe can be celebrated here. It is necessary and a great fortune that the European scene contains all these key centers of excellence with various focus points. The book adds credit to every one of the letters E, C, M, and I.

 

Matti Heilio

Lappeenranta University of Technology

Finland