Gary R. Jensen - Böcker

The theory of exterior differential systems provides a framework for systematically addressing the typically non-linear, and frequently overdetermined, partial differential equations that arise in differential geometry. Adaptation of the techniques of microlocalization to differential systems have led to recent activity on the foundations of the theory; in particular, the fundamental role of the characteristic variety in geometric problems is now clearly established. In this book the general theory is explained in a relatively quick and concrete manner, and then this general theory is applied to the recent developments in the classical problem of isometric embeddings of Riemannian manifolds.

Excellent teaching of mathematics at the elementary school level requires teachers to be experts in school mathematics. This textbook helps prospective teachers achieve the necessary expertise by presenting topics from the K-6 mathematics curriculum at a greater depth than is found in most classrooms. The knowledge that comes from this approach gives prospective teachers essential insight into how topics interrelate and where difficulties may lie. Information is presented at a pace that makes it interesting, rewarding, and enjoyable.With the deeper mathematical preparation inherent in this book, prospective teachers will come away knowing how to explain concepts, demonstrate computational procedures, and lead students through problem-solving techniques. Both students and teachers will find this book key to learning the necessary material and knowing how to express it at the right level. The primary focus is on the foundations of arithmetic, along with a selection of topics from geometry, and a wide range of applications. The number line is used throughout to visualize concepts and to tie them to solutions. The book emphasizes explanations of concepts, of how to solve problems, and of how the concepts relate to the solutions of the problems. This is a textbook for a college course in mathematics for prospective elementary school teachers. It will also be an excellent reference source for instructors of such courses.