It's a little recognised fact, but excellence at mathematics is not particularly common in users of microcomputers or any other computer come to that. Many are much better at languages than sums.

This being so, Terry Shoup's new book, Numerical Methods For The Personal Computer addresses a subject of great importance, virtually for the first time.

I wish I could say it's as usable as it is useful but, sadly, Mr. Shoup is considerably more of a mathematician than most of us, and his book is irritatingly full of bits like: "In the (Rutishauser) method, a matrix A is decomposed into A=LR where L is unit lower triangular and R is upper triangular. Using the similarity transformation, L AL, we see A squared = L raised to the power of -1. AL = L^1(LR)L=RL. Thus A(m-1) = L(m-1)R(m-1) and A(m) = R(m-1), L(m-1). This process is repeated, etc, etc..."

Eh? What? Don't know what he's on about, and couldn't find explanation in the text. Apparently, familiarity with fairly advanced mathematical theories is needed before it's comprehensible.

It is sad that the notations are not explained because they are far from universal. And although this book appears to be for newcomers, it is written for competent mathematicians.

This is not to say you'd get nothing from it. The Basic programs, which apply most of the methods described, are too good to ignore. They are excellently structured, well commented, and apart from the lack of error-traps for invalid, impossible or incomplete data, work correctly.

Unfortunately, there is little or no link between the mathematical text and the program listings.

The best use I could make of the book was to snitch the code, convert it into C and stick it in the library, so I'd have heavy-duty extensions to the mathematical functions. Provided the subroutines work correctly, I'm not bothered exactly how the mathematician arrives at the original equation.

At the back of the book there's a clue to the intended audience... a large glossay of computer terms, but none of mathematical ones.

Thus as a library of complex algorithms for mathematically-incompetent programmers to drag out and use, this book has its uses. Alternatively, is is a good introduction to Basic for non-computer-literate mathematicians.