Mathematics : Geometry

This work is an introduction to the theory of elliptic curves, ranging from its most elementary aspects to current research. This manuscript grew out of Tate's Haverford Lectures. For the second edition, the author has written three new chapters and there are also two new appendices which were written by S. Theisen and O. Forster. more...

Price: $79.95

The book deals with nonlocal elliptic differential operators. These are operators whose coefficients involve shifts generated by diffeomorphisms of the manifold on which the operators are defined. The main goal of the study is to relate analytical invariants (in particular, the index) of such operators to topological invariants of the manifold itself. This problem can be solved by modern methods of noncommutative geometry. To make the book self-contained, the authors have included necessary geometric material (C*-algebras and their K-theory, cyclic homology, etc.). more...

Price: $119.00

The recent revolution in differential topology related to the discovery of non-standard (“exotic”) smoothness structures on topologically trivial manifolds such as R4 suggests many exciting opportunities for applications of potentially deep importance for the spacetime models of theoretical physics, especially general relativity. This rich panoply of new differentiable structures lies in the previously unexplored region between topology and geometry. Just as physical geometry was thought to be trivial before Einstein, physicists have continued to work under the tacit — but now shown to be incorrect — assumption that differentiability is uniquely determined by topology for simple four-manifolds. Since diffeomorphisms are the mathematical models for physical coordinate transformations, Einstein’s relativity principle requires that these models be physically inequivalent. This book provides an introductory survey of some of the relevant mathematics and presents preliminary results and suggestions for further applications to spacetime models. more...

Price: $91.00

This book provides an in-depth discussion of the theory of finite packings and coverings by convex bodies. It contains various new results and arguments and provides a comprehensive treatment of problems whose interplay was not clearly understood before. Two-dimensional and higher-dimensional arrangements are discussed separately, arrangements of congruent convex bodies in Euclidean space are discussed, and the density of finite packing and covering by balls in Euclidean, spherical and hyperbolic spaces is considered. more...

Price: $68.00

Flexagons are paper models that can be flexed in different ways to change their shape. They are easy to make, and work in surprising ways. This book explains the maths behind flexagons and includes instructions to make them. Flexagons will appeal to anyone interested in puzzles or recreational maths. more...

Price: $35.00