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Mathematica is a powerful computer program for MS-Dos and Macintosh machines. It is widely used in teaching maths in higher education, and there is growing interest in it and similar packages for teaching maths at A level. Neither of the books reviewed here is written for A-level students, but for a school or college that possesses a copy of Mathematica, either of them might be a useful addition to the library for reference by A-level students, or for use by teachers as a source of ideas about how such software can be used at this level.
Exploring Calculus with Mathematica is written to accompany Calculus, a text written by Deborah Hughes-Hallett, Andrew Gleason et al as a result of a project at Harvard University. Effective use of this book really requires access to Calculus. Topics covered are similar to those covered in A-level maths, although the treatment may be a little more advanced. Each chapter starts with a set of problems worked on Mathematica, and a discussion of issues arising, followed by a set of Laboratory exercises. The book illustrates, for example, how the program can be used not only to find derivatives but also to reinforce the concept by looking closely at the steps involved in finding a derivative using Mathematica.
Differential Equations with Mathematica is also written to accompany another text, but it is more flexible, and could be used alongside a standard text on ordinary differential equations. It begins with a simple introduction to the capability of the program, before illustrating how it can be used to solve ordinary differential equations and plot the solutions. The book goes well beyond A- level maths, and the notation used is advanced.
It seems likely there will be more books published within the next few years to make use of software such as this.