Mathematics : Geometry

This textbook emphasises fundamentals and the mathematics underlying 3D computer graphics while also covering programming techniques using OpenGL, a platform-independent graphics programming environment. Topics include transformations and viewing, lighting and shading, ray tracing, radiosity, texture mapping and colour theory, and aspects of animation, including quaternions, orientation, and inverse kinematics. more...

Price: $60.00

A.D. Alexandrov's contribution to the field of intrinsic geometry was original and very influential. This text is a classic that remains unsurpassed in its clarity and scope. It presents his core material, originally published in Russian in 1948, beginning wth an outline of the main concepts and then exploring other topics, such as general propositions on an intrinsic metric; angles and curvature; existence of a convex polyhedron with prescribed metric; curves on convex surfaces; and the role of specific curvature. This text provides Adefinitive source for the development of intrinsic geometry and is indispensable for graduate students who want a better understanding of this subject. more...

Price: $125.00

Abstract regular polytopes are highly symmetric combinatorial structures with distinctive geometric, algebraic or topological properties. This comprehensive up-to-date account of the subject meets a critical need for a text in this area; no book has been published in this topic since Coxeter's Regular Polytopes (1948) and Regular Complex Polytopes (1974). more...

Price: $111.00

This book is a compilation of several works from well-recognized figures in the field of Representation Theory. The presentation of the topic is unique in offering several different points of view, which should makethe book very useful to students and experts alike. more...

Price: $70.00

This new-in-paperback edition provides an introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. Clear explanations of both theory and applications, and almost 600 exercises are included in the text. - ;This new-in-paperback edition provides a general introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularisation (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the fundamental theorem of stable reduction of Deligne-Mumford. This book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are few, and including many examples and approximately 600 exercises, the book is ideal for graduate students. - more...

Price: $91.12