Kiselev's Geometry Book Ii. Stereometry

This book discusses the changing conceptions about the relationship between geometry and arithmetic within the Euclidean tradition that developed in the British context of the sixteenth and seventeenth century. Its focus is on Book II of the Elements and the ways in which algebraic symbolism and methods, especially as recently introduced by François Viète and his followers, took center stage as mediators between the two realms, and thus offered new avenues to work out that relationship in idiosyncratic ways not found in earlier editions of the Euclidean text.

In discussion with Ramsar’s Max Finlayson and Nick Davidson, and several members of the Society of Wetland Scientists, Springer is proposing the development of a new Encyclopedia of Wetlands, a comprehensive resource aimed at supporting the trans- and multidisciplinary research and practice which is inherent to this field. Aware both that wetlands research is on the rise and that researchers and students are often working or learning across several disciplines, we are proposing a readily accessible online and print reference which will be the first port of call on key concepts in wetlands science and management. This easy-to-follow reference will allow multidisciplinary teams and transdisciplinary individuals to look up terms, access further details, read overviews on key issues and navigate to key articles selected by experts.

Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment.
Book II deals with more advanced material than Book I and is aimed at the graduate level. Chapter 4 deals with additional topics in Riemannian geometry. Properties of real analytic curves given by a single ODE and of surfaces given by a pair of ODEs are studied, and the volume of geodesic balls is treated. An introduction to both holomorphic and Kähler geometry is given. In Chapter 5, the basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincaré duality, and the Künneth formula are proved, and a brief introduction to the theory of characteristic classes is given.