Mathematics has many branches: there are the pure, the applied, and the applicable; the theoretical and the practical. There is mathematics for school, for college, and for industry. All these belong to the same family and are bound together by a "mathematical way of thinking." Some mathematicians devote themselves entirely to the well being of this family by preserving it, developing it, and teaching it to the next generation. Others use the familial attributes to help outsiders by taking up their problems and transforming them into mathematical questions in order to solve them. The work of these mathematicians is thus problem driven, based on mathematical models, and oriented on the goal of offering practicable solutions. This second group is sizeable; its members include almost all college graduates working in industry, in the private sector, or in the Fraunhofer Institutes, for example. This group is hardly visible, however, and one seldom hears its voices either. This book remedies this situation by relating how the scientists of the first Fraunhofer Institute for Mathematics, the ITWM in Kaiserslautern, go about their daily work. In so doing, it illustrates how extraordinarily successful today's mathematics is in helping solve industrial problems and reveals what lies behind this success. Finally, it describes how this exciting field of problem-driven mathematics can be integrated into classroom instruction, thus helping to bring it the recognition it so richly deserves.