Algebraic topology: A first course

establish the true cost of a nuclear power system; and so on. I shall look forward greatly to the second volume. R. T. Severn Reaction Engineering in Direct Coal Liquefaction. By Y. T. Shah. Pp. xiv + 416. Addison-Wesley, Reading, Mass. 1981. $47.50. The first point to make about this book is that it is a book not, as so often these days, a collection of symposium papers. While Professor Shah has co-opted different authors for the various chapters, he has ensured a consistent style and logical account of recent American work on the chemical reactions during liquefaction of coal at high temperatures and pressures, and in the presence of a solvent and hydrogen. The work is presented in relation to American direct liquefaction processes, processes in other countries being only given lip-service or ignored. It is interesting that, though published in 1981, all these American processes have run into trouble since the book was written, mainly. but by no means exclusively, due to lack of funding. Even so, this bringing together and synthesis of the large amount of support work carried out in the States in recent years is valuable to all those still working, or who will, in due course, be working on direct coal liquefaction. As an example. the book is already a useful source of reference to workers on the UK coal liquefaction programme. G. G. Thurlow Algebraic Topology: A First Course. by Marvin J. Greenberg and John R. Harper. Pp. xii + 311. Benjamin/Cummings, Reading, Mass. 198 1. Paperback $19.50, Hardback $31.50. Algebraic topology has some beautiful results. typical theorem A (in meteorological guise): at any time there exists a point on the earth’s surface at which both the temperature and the atmospheric pressure are the same as at its antipodes. The writer of a ‘first course’ must somehow convey these exciting geometrical aspects of the subject without losing readers in the long algebraic and combinatorial calculations needed for their proof. Many authors proceed slowly, their ‘first courses’ doing little more than defining the notions of homotopy and homology. This book, a revision of the first author’s ‘Lectures on Algebraic Topology’ (Benjamin, 1967). moves rapidly, covering a wealth of material: homotopy, singular homology, the cohomology ring, Poincarc duality, and the Lefschetz fixed point theorem. The authors achieve this by omitting technical calculations, but doing so in a way finely judged so that a competent mathematician can easily follow the argument. The result makes delightful reading for someone with a little background in the subject already, but it is questionable whether this level of exposition really is suited to students for

190

whom this is a ‘first course’, even if they have the (fairly substantial) familiarity with point-set topology demanded as a prerequisite. P. G. Dixon Classical Propositional Operators. by Krister Segerberg. Pp. 149. Oxford University Press. 1982. f 12.50. Beginning with an extreme of generality and then gradually and explicitly introducing limiting conditions, this book slowly narrows its attention from whole languages of well-formed formulae down to ‘classical logics’. Successive stages along the way are ‘common’, ‘Boolean’, and ‘pre-classical’; the passage through them is like bringing a field of vision into increasingly sharp focus. The outstanding virtue of the exercise is that the precise role of each axiom in determining the properties of the resultant logics is brought out with complete clarity. The subject matter is highly technical, and the author is to be congratulated on the attractive manner in which he leads the reader through it. The exposition is as clear as such involved matters can be made, adequate attention is paid to motivation, and there are many excellent asides and overviews. The book is entirely self-contained in that every technical term used is explicitly defined; there is a thorough and very necessary index. This is an excellent text-monograph for very advanced students, on the influence of individual axioms and the matching of semantics with syntax. It contains a great deal of original material, and deserves the attention of everyone with an interest in its area. W. Bandler Weather and Climate on Planets. by K. Y. Kondratyev and G. E. Hunt. Pp. 755. Pergamon Press, Oxford. 7981. f50.00. The first successful space-craft, Mariner 2, flew past Venus in 1962. Since then all the planets out as far as Saturn have been studied from close range, and it is fair to say that during the past twenty years we have learned more than we did over the previous twenty centuries. Much is to be gained from studying the climates and atmospheres of the other planets. Nowadays, astronomy has merged not only with physics and mathematics, but with meteorology and climatology as well. In this new book, two eminent authoritiesone Russian, the other English-put forward detailed analyses of these subjects. After a general introduction, they deal exhaustively with Venus, Mars, and Jupiter in turn, incorporating the very latest research. This is not a book for the layman. It is not intended to be, and some prior knowledge is needed if the text is to be followed throughout. But for serious students, and for professionals in this field, the book must surely become a standard work. Certainly

no astronomical without it.

library

will

be complete Patrick Moore

The Dictionary of Human Geography. Edited by R. G. Johnston. Pp. 411. Basil Blackwell, Oxford. 7981. f19.50. Sometimes book reviews just have to descend into cliche: this latest product of the awesome Johnstonian academic industry, really does fill a long-felt want. Other dictionaries are few on the ground, or long out-of-date; but this, master-minded by an impressive team of Derek Gregory, Peter Haggett, David Smith, and D. R. Stoddart, represents the state of the art. Consisting of longish review pieces interspersed with shorter definitional notes, it will prove an invaluable student guide. Striving hard to achieve balance of paradigm and of world view, it puts the quantitative models of the 1960s in their place besides the behavioural and structuralist approaches that now rival them. The principle of horses for courses ensures that each approach and each topic gets expert treatment. No less than 18 leading human geographers, including the editors, have contributed. Inevitably the reviewer will leaf the pages, trying to find flaws. Everyone will doubtless find some key concept that has slipped between the cracks. It is surprising not to find Ullman’s name associated with economic base theory, though he gets generous attention elsewhere. A key Marxist like concept the organic composition of capital does not show in the index, though it does appear in Smith’s excellent review of Marxian economics. More seriously, perhaps, Harvey on Marxist geography does not capture the full flavour of the debates currently raging within that tradition. But these are quibbles: despite the steep price, this is good value for a geographer’s money. P. G. Hall Cell Death in Biology and Pathology. Edited by I. 0. Bowen and R. A. Lockshin. Pp. 493. Chapman & Hall, London. 1981. f30.00. This is the first book to provide a comprehensive compendium of our present knowledge on cell death, by combining within a single volume material from many diverse fields of modern biology. The book comprises thirteen chapters contributed by experts in their particular fields of research. The first chapter presents an overall classification of cell death with the proposal that the mechanism of ‘accidental’ cell death may differ from that of physiological cell death. There then follow chapters dealing with cell death in specific circumstances including embryogenesis, metamorphosis, tissue homeostasis, cell senescence in plants, in vitro cell culture and its role in the immune system, the nervous system, and in certain pathological conditions. Where possible, the