In a recent series of articles and books, Menger has raised grave doubts about the meaning, if any, which can be attached to the phrase "a function f (x) of the real variable x". He proposes to talk instead of "a function f whose domain is the set of real numbers", claiming that on this basis he can develop the calculus without the use of variables at all; his book 'Calculus: A modern approach' is a triumphant vindication of this claim. By denying himself the use of the variable x, Menger is no longer able to use the phrase "as x tends to a" in discussing limits; he boldly returns to a usage similar to that of the nineteenth century ... To drop the phrase "as x tends to a" may be held by some to be a tragedy; certainly its introduction, and that of the arrow notation, were hailed as a great improvement. But the word "tends" inevitably conjures up a picture of x (whatever x is) moving towards a; and as Frege pointed out in an early discussion of the meaning of variables and functions, movement can take place only in time, while pure mathematics has nothing to do with time.

Amid all the current interest in modern algebra, field theory has been rather neglected - most of the recent textbooks in algebra have been concerned with groups or vector spaces. But field theory is a very attractive branch of algebra, with many fascinating applications; and its central result, the 'Fundamental Theorem of Galois Theory', is by any standards one of the really "big" theorems of mathematics. This book aims to bring the reader from the basic definitions to important results and to introduce him to the spirit and some of the techniques of abstract algebra. It presupposes only a little knowledge of elementary group theory and a willingness on the reader's part to remember definitions precisely and to engage in close argument.

This is an attractive book on field theory and Galois theory ... The text is very clearly written, with many examples, and the exercises are good ... All told this is an excellent introduction to field theory.

The presentation is clear and convincing. It is perhaps a hard-headed rather than an exciting presentation, but the author, an ardent Scotsman writing in the Edinburgh series, would presumably wish to have it that way.

The presentation is very clear, detailed and complete, only rarely a proof or even a small argument is left to the reader. This should be particularly useful for students reading the book on their own.

I enjoyed reading the work. The author's style makes the pages and the time fly.

This book is called a 'Workbook' to make it clear from the start that it is not a conventional textbook. Conventional textbooks proceed by giving in each section or chapter first the definitions of the terms to be used, the concepts they are to work with, then some theorems involving these terms (complete with proofs) and finally some examples and exercises to test the readers' understanding of the definitions and the theorems. Readers of this book will indeed find all the conventional constituents - definitions, theorems, proofs, examples and exercises - but not in the conventional arrangement.

In the first part of the book will be found a quick review of the basic definitions of general topology interspersed with a large number of exercises, some of which are described as theorems. ... The exercises are deliberately not "graded" - after all the problems we meet in mathematical "real life" do not come in order of difficulty; some of them are very simple illustrative examples; others are in the nature of tutorial problems for a conventional course, while others are quite difficult results. No solutions of the exercises, no proofs of the theorems are included in the first part of the book - this is a 'Workbook' and readers are invited to try their hand at solving the problems and proving the theorems for themselves. I have been persuaded, with some reluctance, to offer suggestions about how to tackle the exercises which are not entirely straightforward; really dedicated 'Workbook'-ers should ignore these!. The second part of the book contains complete solutions to all but the most utterly trivial exercises and complete proofs of the theorems.

The book is written in an informal and friendly way specifically to appeal to students.

Iain had a long involvement as an Elder and Session Clerk in the Church of Scotland and when he decided to partly retire from his University teaching he undertook a course of training to equip him to become an Auxiliary Ordained Minister of the Church of Scotland. When he completed this training he was appointed to assist in a parish on the outskirts of Dundee where the incumbent minister had four congregations to serve. Iain quickly became a well known and well respected Minister, especially in regard to pastoral care where his willingness to be a listener rather than a speaker endeared him to people with problems.

Iain had a great love of classical music, including opera and studied Italian at the University of Western Australia - no doubt to help him understand some of the operas he attended. He had a great appreciation of art, attended as many concerts as he could and also loved to travel.