Fundamentals of the average case analysis of particular algorithms.

R.M. Johnson: Theory and Applications of Linear Differential and Difference Equations. Ellis Horwood, Chichester, United Kingdom, 1984, 183 pages, g18.50, ISBN o-85312-670-4. This textbook provides a compact treatment of linear differential and linear difference equations using transform techniques. It is written as a textbook for second year students who are such as scientists and engineers. The relation between the not specialists in mathematics, transform variables and frequency is established and system stability is considered. A chapter on the analysis and filtering of discrete signals is a change from books emphasizing only continuous systems. Examples are chosen from Electrical, Mechanical, Civil, and Control Engineering. Contents: 1. Laplace Transform; 2. Solution of Linear Differential Equations; 3. Steady State Oscillations; 4. Piecewise Continuous Functions; 5. The Ideal Sampler and the z-Transforms; 6. Solution of Linear Difference Equations; 7. Analysis of Simple Sampled-Data Systems: 8. Digital Filters; Tables; References; Index. (WFA) R. Kemp: Fundamentals of the Average Case Analvsis of Particular Algorithms. Wiley. Chichester. United Kingdom, 233 pages, 218.50, ISBN 0-471-90322-l. This is a textbook on the analysis of particular algorithms. The contents is as follows: Introduction; A simple class of algorithms: Permutations and their applications: Random walks. trees, lists; Exact and asymptotical enumeration results; Applications to the reduction of binary trees, to the recognition of Dycklanguages and to Batcher’s algorithm. (CB) J. Loeckx, K. Sieber and R. Stansifer: The Foundations of Program Verification. Wiley, Chichester, United Kingdom, 1985, 230 pages, E18.50, ISBN O-519-02101-3. This is a textbook on program verification. Part A presents the mathematical background required. Part B is devoted to the description of the semantics of programming languages. Part C deals with verification methods. Part D presents a short overview of other approaches and further development. Each chapter ends with exercises and bibliographic notes. (CB) D.H. Meadows and J.M. Robinson: The Electronic Oracle. Wiley, New York, 1985. 445 pages, f24.95, ISBN o-471-90558-5. A model is any set of generalizations or assumptions about reality. This book is about models, specifically mental models. Mental models can be, partially, approximately expressed in mathematical symbols. Such symbols are, of course, more precise and unambiguous than words. They lend themselves to the great symbol processer, the computer, which permits their storage and manipulation in quantities and speeds of high order. The use of computer (mathematical) models has spread from the physical sciences and engineering to the biological and social sciences as well. But these complex models of social systems are more often made than used. An applications gap, familiar to many mathematicians, exists. This book was developed to help close the gap. The authors have carried out a comparison study of nine models, each of which met a set of five predetermined criteria and they conclude with recommendations for the models of other social systems. The book is divided into five parts, The Electronic Oracle, Modeling Paradigms and Nine Models, the State of the Art and Prescriptions. The contents are listed below. Contents: Prologue; 1. The Electronic Oracle; 2. Models of Modeling; 3. How to Describe a Model; 4. The Tragedy of the Commons; 5. Adding a Combine to a Tractor; 6. The Perfectly Adjusting Society; 7. Educating the Third World; 8. The Race Between Production and