The volume develops the foundations of differential geometry so as to include finite-dimensional spaces with singularities and nilpotent functions, at the same level as is standard in the elementary theory of schemes and analytic spaces. The theory of differentiable spaces is developed to the point of providing a handy tool including arbitrary base changes, infinitesimal neighbourhoods, sheaves of relative differentials, quotients by actions of compact Lie groups and a theory of sheaves of Frechet modules paralleling the useful theory of quasi-coherent sheaves on schemes.
Filled with FULL COLOR, easy-to-complete projects and sample paintings. The fun and easy way to create beautiful works of art with watercolors. Would you love to paint with watercolors? You can! This friendly guide gives you hands-on instruction and easy-to-follow exercises to help you master the basics. You'll see how to work with color and texture, practice composition, and make smooth changes. And you'll paint a variety of subjects, from animals and still lifes to landscapes and seascapes!
Not another English Book! Indeed, not at all. In this new and exciting text, Dave Hopkins has managed to make the leap from the same old tired textbook filled with the same old tired content, into an important new arena. Smooth Moves is not a text about content, grammar, and language utilization. Smooth Moves is not a "what to teach" textbook, it is an entry into what to do in the classroom, on a daily basis, to facilitate language acquisition.
