Lectures on Modern Mathematics Volume II

Edited by T. L. Saaty London: John Wiley & Sons Ltd. 1963. Pp. vii + 175. Price 45s. This book, the first of a series of three volumes, is an expression of a thoroughgoing attempt to tackle the problem of presenting an integrated outline of modern mathematics, a task which becomes more and more urgent in face of the colossal rate of increase of published mathematical papers and the consequent hopelessness of individual mathematicians' trying to keep up to date, in detail, in more than very few branches of the subject. Although it may seem at first that the idea of a series of expository lectures on a number of substantial research areas, written by leading mathematicians of the various areas, would be only a continuation of the very fragmentation that it is the purpose of the book to overcome, in fact the job has been brilliantly done within the very limited space; the lecturers have on the one hand (through suitable selections), clearly brought out the position of the various fields in mathematical development as a whole, and on the other hand given valuable indications of the nature of deep current problems, together with plenty of references.