This book is devoted to recent developments in symbolic dynamics, and it comprises eight chapters. The first two are concerned with the study of symbolic sequences of 'low complexity', the following two introduce 'high complexity' systems. The later chapters go on to deal with more specialised topics including ergodic theory, number theory, and one-dimensional dynamics.

Professor Braverman investigates independent random variables in rearrangement invariant (r.i.) spaces.

This book presents the basic methods and applications in semiclassical approximation in the light of developments.

This book summarizes knowledge built up within Hewlett-Packard over a number of years, and explains the mathematics behind practical implementations of elliptic curve systems. Due to the advanced nature of the mathematics there is a high barrier to entry for individuals and companies to this technology. Hence this book will be invaluable not only to mathematicians wanting to see how pure mathematics can be applied but also to engineers and computer scientists wishing (or needing) to actually implement such systems.

This volume contains the invited papers presented at the 14th British Combinatorial Conference, held at the University of Keele in July 1993.

Probabilistic methods have become a vital tool in the arsenal of every combinatorialist. The theory of random graphs is still a prime area for the use of probabilistic methods, and, over the years, these methods have also proved of paramount importance in many associated areas such as the design and analysis of computer algorithms. In recent years, probabilistic combinatorics has undergone revolutionary changes as the result of the appearance of some exciting new techniques such as martingale inequalities, discrete isoperimetric inequalities, Fourier analysis on groups, eigenvalue techniques, branching processes, and rapidly mixing Markov chains. The aim of this volume is to review briefly the classical results in the theory of random graphs and to present several of the important recent developments in probabilistic combinatorics, together with some applications. The first paper contains a brief introduction to the theory of random graphs. The second paper reviews explicit constructions of random-like graphs and discusses graphs having a variety of useful properties. Isoperimetric inequalities, of paramount importance in probabilistic combinatorics, are covered in the third paper. The chromatic number of random graphs is presented in the fourth paper, together with a beautiful inequality due to Janson and the important and powerful Stein-Chen method for Poisson approximation. The aim of the fifth paper is to present a number of powerful new methods for proving that a Markov chain is "rapidly mixing" and to survey various related questions, while the sixth paper looks at the same topic in a very different context. For the random walk on the cube, the convergence to the stable distribution is best analysed through Fourier analysis; the final paper examines this topic and proceeds to several more sophisticated applications. Open problems can be found throughout each paper.

These lecture notes provide a unique introduction to Pesin theory and its applications.

For anyone whose interest lies in the interplay between groups and geometry, these books will be an essential addition to their library.

Introduction to buildings and their geometries with emphasis on model theoretic constructions, covering recent developments.

Conference proceedings based on the 1996 LMS Durham Symposium 'Galois representations in arithmetic algebraic geometry'.