Applications of continuous mathematics to computer science
The book under review was devised as a text for senior undergraduate/junior graduate students. The emphasis was put by the authors on showing the interplay between ``continuous'' mathematics and computer science. This goal was realized by a judicious selection of 15 interesting problems in computer science and showing how continuous mathematics could be applied towards their analysis and solution. In accordance with their purpose, the authors avoided an in-depth and highly technical analysis of selected problems striving instead at presenting a wide panoramic view on these problems and related mathematical tools; the potential reader will certainly appreciate this aspect of the book as providing a well-justified motivation for respective problems as well as for the tools chosen. The result is a very interesting book which may well serve as a text for a one-semester course on mathematics in computer science or vice versa. Among the mathematical topics covered we may mention e.g. solving linear functional equations motivated by studies of algorithm complexity, optimization problems arising in algorithm design area, discrete optimization realized via simulated annealing or genetic algorithms, systems of differential equations or partial differential equations applied to problems of RISC architecture, Internet growth, network congestion as well as neural networks and continuous (many-valued) logic applied to fuzzy control problems. In a number of appendices the reader will find more information on topics discussed in the main body of the book. Technical aspects of the above topics are presented in an easy-going style, free of unnecessary technical details, which makes reading this book a pleasure. A very detailed exposition of basic principles and ideas focusing on motivations and intuitions and a collection of exercises will make this book a good companion for the student who will gain from it a good deal of general mathematical culture.
scientific article; zbMATH DE number 1199690