Silvester,J.

Geometry: Ancient and Modern.

0-19-850758-5 Hard cover
0-19-850825-5 Paper cover
Feb. 2001 352 pp.

This book is a guided tour of geometry, from Euclid through to algebraic geometry. It shows how mathematicians use a variety of techniques to tackle problems, and it links geometry to other branches of mathematics it is a teaching text, with a large number of exercises woven into the exposition. Topics covered: ruler and compass constructions, transformations, triangle and circle theorems, classification of isometries and groups of isometries in dimensions 2 and 3, Platonic solids, conics, similarities, affine, projective and Mobius transformation, non-Euclidean geometry, projective geometry, the beginnings of algebraic geometry.

Semmes,S.

Some Novel Types of Fractal Geometry.
(Oxford Mathematical Monographs, Series)

0-19-850806-9
Mar. 2001 176 pp.
The present book deals with fractal geometries which have features similar to ones of ordinary Euclidean spaces while at the same time being quite different from Euclidean spaces in other ways. A basic type of feature being considered is the presence of Sobolev or Poincare inequalities, concerning the relationship between the average behaviour of a function and the average behaviour of its small-scale oscillations. Remarkable results in the last few years of Bourdon-Pajot and Laakso have shown that there is much more in the way of geometries like this than has been realized. Examples related to nilpotent Lie groups and Carnot metrics were known previously. On the other hand, 'typical' fractals that might be seen in pictures do not have these same kinds of features.

Rossmann,W.

Lie Groups: an Introduction Through Linear Groups.
(Oxford Graduate Texts in Mathematics, Vol. 20)

0-19-859683-9
Mar. 2001 288 pp.

This book is intended as an introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. It covers the essentials of the subject starting from basic undergraduate mathematics. The correspondence between linear Lie groups and Lie algebras is developed in its local and global aspects. The classical groups are analysed in detail, first with elementary matrix methods, then with the help of the structural tools typical of the theory of semisimple groups, such as Cartan subgroups, roots, weights, and reflections. The fundamental groups of the classical groups are worked out as an application of these methods. Manifolds are introduced when needed, in connection with homogeneous spaces, and the elements of differential and integral calculus on manifolds are presented, with special emphasis on integration on groups and homogeneous spaces. Representation theory starts from first principles, such as Schur's lemma and its consequences, and proceeds from there to the Peter-Weyl theorem, Weyl's character formula, and the Borel-Weil theorem, all in the context of linear groups.

Budd,C./Sangwin,C.

Mathematical Galore!:
Masterclasses, Workshops and Team Projects in Mathematics and its Applications.

0-19-850769-0 Hard cover
0-19-850770-4 Paper cover
Apr. 2001 288 pp.

This book is a series of self-contained workshops in mathematics which aim to enthuse and inspire young people, their parents and teachers. Each chapter describes how novel mathematical ideas relate to real life, and includes problem sheets, their solutions, ideas for further work, projects and field trips. The book, written in an informal style, is accessible to young people from age thirteen upwards and contains material which should stretch the brightest students.

Kemp,K.

The Efficient Use of Quality Control Data.
(Institute of Mathematics & its Applications Monograph Series, Vol. 25)

0-19-853674-7
Apr. 2001 320 pp.

Accurate measurements in clinical and industrial testing are often not possible. Each measurement contains what can be regarded as containing an uncontrollable component of error. Their use to control quality therefore inevitably leads to right and wrong conclusions. This book describes methods which can be used to control the frequency with which these occur. It describes recent developments which can be employed when very few control measurements can be taken due to limitations of cost or technical difficulty.

Bossaerts,P./Odegaard,B.

Lectures on Corporate Finance.

981-02-4425-8 Hard cover
981-02-4426-6 Paper cover
Nov. 2000 200 pp.

This course of lectures --- developed and taught at the Yale School of Management and the California Institute of Technology --- introduces students to elementary concepts of corporate finance using a more systematic approach than is generally found in other textbooks. Within a simple logical framework, axioms are first highlighted and the implications of these important concepts are studied. These implications are used to answer questions about corporate finance, including issues related to derivatives pricing, state price probabilities, dynamic hedging, dividends, capital structure decisions, and risk and incentive management. Numerical examples are provided, and the mathematics is kept simple throughout.

Kamchatnov,A.

Nonlinear Periodic Waves and Their Modulations.

981-02-4407-X
Nov. 2000 350 pp.

Although the mathematical theory of nonlinear waves and solitons has made great progress, its applications to concrete physical problems are rather poor, especially when compared with the classical theory of linear dispersive waves and nonlinear fluid motion. The Whitham method, which describes the combining action of the dispersive and nonlinear effects as modulations of periodic waves, is not widely used by applied mathematicians and physicists, though it provides a direct and natural way to treat various problems in nonlinear wave theory. Therefore it is topical to describe recent developments of the Whitham theory in a clear and simple form suitable for applications in various branches of physics.

Leung,T./Qin,H.(ed.)

Advanced Topics in Nonlinear Control Systems.
(World Scientific Series on Nonlinear Science, Series A)

981-02-4442-8
Dec. 2000 250 pp.

Over the last 50 years or so, a number of textbooks, monographs and even popular books have been published on nonlinear control theory and design methods. In the area of classical control, for example, there exist books concerned with phase-plane analysis, describing the function approach, absolute stability and so on. In the area of modern control there are those related to optimal control, using differential geometry and the differential algebra method, variable structural control, H-infinite control and so on. These books have been useful in promoting the development of automatic control science and technology. Since 1990 there have been many new results and contributions in the area of nonlinear control. This book introduces those topics to interested leaders. It will also benefit automation engineers and researchers.

Okamoto Hisashi /Shoji Mayumi

A Mathematical Introduction to the Bifurcation of Periodic Progressive Water Waves.

981-02-4449-5 Hard cover
981-02-4450-9 Paper cover
Dec. 2000 250 pp.

This book is a self-contained introduction to the theory of periodic, progressive, permanent water waves on the surface of incompressible inviscid fluid. The problem of permanent water waves has attracted a large number of physicists and mathematicians since Stokes' pioneering papers appeared in 1847 and 1880. Among many aspects of the problem, the authors consider only periodic progressive waves, by which they mean waves traveling at a constant speed with no change of shape. As a consequence, they exclude everything about solitary waves and standing waves. Even for this restricted problem, quite a number of papers and books, in physics and mathematics, have appeared and more will continue to appear. Nevertheless there remain many open questions to be answered.