Microchip Mathematics: Number Theory for Computer Users

Number Theory is one of the few areas of modern mathematics which is accessible to the non-expert. (At least, the kind of Number Theory considered here: there is a lot of other material which also goes under the title •Number Theory1, most of which is pretty well inaccessible to the majority of trained mathematicians1.) It is also an area in which there is a genuine two-way flow between man and the computer. Indeed, it was this fascinating interplay of brain power and computer power that awakened my own interest in the subject to a level where I began to give a course on the subject at Lancaster University and, coincidentally, write about it in The Guardian. (Previously my mathematical research work had been in Set Theory, a subject dealing almost exclusively with the mysterious world of the infinite.)
This is a book about (the computational aspects of) Number Theory. Though written for university undergraduates in mathematics, I have tried to present the material in such a way that it can be followed by the keen but largely untrained 'amateur' sitting at home with (or possibly even without) a cheap home computer. I do not pretend to give a complete coverage of the computational aspects of Number Theory. (For instance, no mention is made of Quadratic Reciprocity, a tremendously important part of the subject.) Rather my aim is to cover the (very) basic parts of Number Theory and at the same time give some indication of the way in which Number Theory both feeds off and leads to advances in Computation Theory. Consequently, if the book were used as a text to accompany a university lecture course, the lecturer would presumably deal with additional topics not covered in this book.