Book Reviews 83

Ebbinghaw et al., Ivumbers. Springer, Berlin, 1990. 395 pp., DM98, ISBN 3-540-97202-l.

This book is simultaneously a mathematical and a historical book. Its subject is obviously numbers, all kinds of numbers, integers, p-adics, complex, the numper pi,. . . .

rationals, octoiiions, reals, quaternions. It can be used as a supplement to a mathematical course or as the

main support for lectures on the history of numbers.

(CB)

R. Maeder, Programming in Muthemuticu. Addison-Wesley, Reading, MA, 1990. 267 pp., ISBN 0-201-51002-2.

Mathematics is a language developed for helping mathematicians, scientists and engineers. It allows easy numerical programming, symbolic computations, graphics applications, combina- torics, an9 algebra among other possibilities. This book explains all the features of the language but its most :mportant characteristic is to provide many examples. Mathematics is really a very powerful tool and many pure and applied mathematicians already used it. This book will greatly help them in using all the possibilities and advantages of the language. It can also be used as a starting point for beginners.

(CB)

D.J. Bell, Mathematics of Linear and Nonlinear Systems. Clarendon Press, Oxford, 1990.304 pp., %O.OQ, ISBN O-19-856332-9.

The importance of linear and nonlinear dynamical systems has no longer to be pointed out. The mathematical knowledge necessary for understanding their modern formulation is not normally acquired in courses other than those of mathematics. As for the books, they are usually written by mathematicians and other students have great difficulties in reading such books. Thus the purpose of this book is to make easier to the nonmathematician the understanding of the necessary mathematical background needed. The topics covered include groups, rings, modules, vector spaces and the geometric approach to nonlinear system theory.

(W

M. Metcalf ;ind J. Reid, Fortran 90 Explained. Oxford Univ. Press, Oxford, 1 . 294 pp., E14.95,

ISBN O-19-853772-7.

Fortran is the predominant programming language fo;. scientific and numerical computing. Computer scientists criticize it very much and they are possibly right. However, it is a language which is very close to the mathematical formulation of the problems to be solved. For that reason, and also because so many programs already exist (after so many years), it will not be possible to suppress it or even to convince numerical analysts and applied mathematicians to change for a better language. Moreover Fortran evoluates with the years and new features are regularly incorporated. Its last version is Fortran 90 and it is the purpose of this book to present

84 Book Rcaiews

its last developments. These last possibilities include array operations, pointers, a new form for the loops, dynamic storage allocation, recursivity, among others.

(CB)

Kehe Zhu, Operator Tlieoy in Function Spaces. Marcel Dekker, New York, 1990. 258 pp., ISBN O-8247-8411-1.

Hankel and composition operators on the Bergman and spaces plane. Its main emphasis

these operators: boundedness, compactness,

B.R. Gelbaum and J.M.H. Olmsted, l%eorcms and Counter-examples Berlin, 1990. 345 pp., DM84, ISBN 3-540-97342-7.

(CW

in Mathematics. Springer,

This book presents the most important theorems in algebra, analysis, geometry and topology, probability theory and foundations of mathematics. They are all illustrated by several examples and exercices. It ‘was already a very good idea to gather such material into one single volume. But the book is made still more valuable and useful by the counterexamples it contains. I always found counterexamples even more interestmg ald illuminating than examples and this book provides a collection of them. This book will be very useful to every student in ma&hematics and even to every mathematician.

(CB)

S. Ruscheweyh et al. (eds.), Computational Methods and Function ;Ilieoy, Lecture Notes in Mathematics 1435. Springer, Berlin, 1990. 211 p?,, DM37, ISBN 3-540-52768-o.

This volume contains the papers presented at an international conference held in Valparaiso in March 1989. They are devoted to applied and computational complex analysis including orthogonal polynomials, continued fractions, conformal mapping and various approximation problems. They provide an interesting view of the various questions which are actually under interest in the field.

(CW

E.L. Allgower and I&. Georg, Numerical Continua&m Methods. Springer, Berlin, 1990. 388 pp., DMl28, ISBN 3-540-12760-7.

Numerical continuation methods of predictor-corrector and piecewise-linear types are very important in the numerical solution of nonlinear systems of equations. This book provides an