Vol. 4 No 9 - Pi Mu Epsilon

393BOOK REVIEWSEdited byRoy B. Deal, Oklahoma University Medical CenterTheoretical and Mathematical Biology By Talbot H. Waterman andHarold J. Morowitz, Blaisdell Publishing Company, New York, 1965,xvii + 426 pp.A series of seventeen chapters, written by well-known biologists,which gives an excellent survey of a variety of the importantareas in biology where rather extensive and interesting mathematicalmodels promise to play a big role.An Introduction to Probability Theory and Its Applications Vol I,3rd Edition, By W. Feller, John Wiley & Sons, Inc., New York, 1968,xviii + 509 pp., $10.95.A third and revised edition of the now famous classic in modernmathematical writings. Many proofs and developments have beenmodernized. In particular the chapter on fluctuations in cointossing and random walks has been extensively rewritten andexpanded to incorporate modern probabalistic arguments. Sectionshave been added on branching processes, on Markov chains, and onthe De Moivre-Laplace theorem. These changes, along with otherclarifications and rearrangements, and the established importanceof the earlier editions make this also a valuable book.An Introduction to Probability Theory and Its Applications ByWilliam Feller, John Wiley and Sons, Inc., New York, 1966,xviii + 626 pp.Whereas the first volume was basically a study of discreteprobabilities and was a pioneer in its mathematical treatment ofapplied problems, the second volume covers a larger spectrum,utilizes Lebesgue measure, has many theorems and applications onmore general multidimensional distributions, on more generalMarkov processes, random walks, renewal theory and other aspectsof stochastic processes, and many interesting uses of such thinrsas semi-groups, Tauberian theorems, Laplace transforms, and harmonicanalysis. This volume may not have as much of the pioneeringaspect but it reflects the same organizational talent of a masterwho can bring difficult subjects to within the grasp of one witha minimal background, say elementary real analysis and volume one.Integration By A. C. Zaanen, John Wiley and Sons, Inc., New York,1967, xiii + 604 pp., $16.75.Although this is an advanced and extensive book on integration, andperhaps beyond the level of many Pi Mu Epsilon readers, it is suchan excellent book that it should be brought to the attention of mostmembers. It is a completely revised and enlarged edition of hiswell-written earlier book "An Introduction to the Theory of Integration."