Christopher T. J. Dodson Knihy

This treatment of differential geometry and the mathematics required for general relativity makes the subject matter accessible for the first time to anyone familiar with elementary calculus in one variable and with a knowledge of some vector algebra. The emphasis throughout is on the geometry of the mathematics, which is greatly enhanced by the many illustrations presenting figures of three and more dimensions as closely as book form will allow.To maintain the flow of exposition and to develop experience in the reader, the technicalities of many proofs are in the form of carefully programmed exercises rather than endless pages of displayed equations. In this way, the reader is guided through actually doing computations instead of being allowed to skim over a page of ready worked examples.The imaginative text is a major contribution to expounding the subject of differential geometry as applied to studies in relativity, and will prove of interest to a large number of mathematicians and physicists.

We believe that to understand and be comfortable with mathematical con cepts and methods, it is necessary to do mathematics and, traditionally, doing meant with a pencil and paper. Now, a modest home computer can provide a platform for a computer algebra package like Maple, which can perform all of the operations encountered in secondary school mathematics and beyond, and pro vide graphical representations of functions, including animations. The capability of rendering accurate graphics for mathematical functions greatly enhances the learning experience, and helps intuition work in new situations, before beginning to do the algebra and calculus needed to solve a problem. For example, if you can see that a function has a clear minimum from its graph, then you are more likely to be able to identify its location precisely by analysis. This book is designed to support the interactive Maple worksheets that we have developed for the two senior secondary school years and made available via the Internet at the anonymous ftp site ftp. ut irc. utoronto . ca (/pub/ednet/maths/maple). This takes you from basic algebra, functions and sequences, to calculus and its applications. Thus, the book is a hardcopy version of the worksheets, with additional explanatory text, cross-referencing, appen dices containing worked solutions to all exercises, and indexing.