Preface: The exploration on which this work rests was begun towards the end of 1959. The subsequent record of it owes much, in its early stages, to the friendship and encouragement of Lord Russell, who was one of the few men at the beginning who could see a value in what I proposed to do. It owes equally, at a later stage, to the generous help of Dr J C P Miller, Fellow of University College and Lecturer in Mathematics in the University of Cambridge, who not only read the successive sets of printer's proofs, but also acted as an ever-available mentor and guide, and made many suggestions to improve the style and accuracy of both text and context. In 1963 I accepted an invitation of Mr H G Frost, Staff Lecturer in Physical Sciences in the Department of Extra-mural Studies in the University of London, to give a course of lectures on the mathematics of logic. The course was later extended and repeated annually at the Institute of Computer Science in Gordon Square, and from it sprang some of the context in the notes and appendices of this essay. I was also enabled, through the help of successive classes of pupils, to extend and sharpen the text. Others helped, but cannot, alas, all be mentioned. Of these the publishers (including their readers and their technical artist) were particularly cooperative, as were the printers, and, before this, Mrs Peter Bragg undertook the exacting task of preparing a typescript. Finally I should mention the fact that an original impetus to the work came from Mr I V Idelson, General Manager of Simon-MEL Distribution Engineering, the techniques here recorded being first developed not in respect of questions cf logic, but in response to certain unsolved problems in engineering.
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