Symbolic C++: An Introduction to Computer Algebra Using Object-Oriented Programming

Rating:
Summary: Eclectic but rich
Review: A mixture of C++, group theory, and mathematical physics. Far from a polished treatment, but maybe worth perusing if these are topics of interest to you.

Rating:
Summary: a great object-oriented application
Review: You will find this book fascinating if you are a computer science student intrigued by symbolic calculation systems such as Mathematica and Maple, and if you would like to see how such systems would be implemented in C++ (Mathematica and Maple are actually implemented in plain old C).

The C++ level required is just after CS2, the second C++ class that comprises data structures. If I were a CS2 instructor, I guess I would require students to read some parts of this book since it is a great means of reinforcing about all the concepts learned in C++, while building a nontrivial application; although some examples are taken from physics, physics knowledge is by no means required and the general math level called for reading this book remains comfortably low, and one can always skip the things one does not know or does not care about (such as quaternions, but hey, some people might be turned on by that stuff...).

It shows how to build classes that actually perform calculations using integers of arbitrary length, rational numbers of the a/b form, vectors, matrices, quaternions, symbolic variables, differentiation, integration, etc.

The system described in the book, SymbolicC++, can be used as a FREE alternative to Mathematica or Maple, less of course the graphing capabilities these great software products offer (less also zillions of functions available). SymbolicC++ may nevertheless be connected to Gnuplot to produce graphs. SymbolicC++ may also be of interest to the professional developer having to struggle with complex calculations, since its classes can be included in any C++ environment.

So in short, this book is great if you have the right background and the right interests.

I should also point out that Dr Steeb has written another great book that shows the system at work in problems from the physical sciences and finance ("The Nonlinear Workbook")