Bücher der Reihe London Mathematical Society Lecture Note Series

The aim of this book, which was originally published in 1985, is to cover from first principles the theory of Syzygies, building up from a discussion of the basic commutative algebra to such results as the authors' proof of the Syzygy Theorem. In the last three chapters applications of the theory to commutative algebra and algebraic geometry are given.

The British Combinatorial Conference is an established biennial international gathering. This volume contains the invited papers presented, by several distinguished mathematicians, at the 1985 conference. The papers cover a broad range of combinatorial topics, including cryptography, greedy algorithms, graph minors, irregularities of point distributions and reconstruction of infinite graphs.

This book, which was originally published in 1985 and has been translated and revised by the author from notes of a course, is an introduction to certain central ideas in group theory and geometry. Professor Lyndon emphasises and exploits the well-known connections between the two subjects and, whilst keeping the presentation at a level that assumes only a basic background in mathematics, leads the reader to the frontiers of current research at the time of publication. The treatment is concrete and combinatorial with a minimal use of analytic geometry. In the interest of the reader's intuition, most of the geometry considered is two-dimensional and there is an emphasis on examples, both in the text and in the problems at the end of each chapter.

This 1987 volume presents a collection of papers given at the 1985 Durham Symposium on homotopy theory. They survey recent developments in the subject including localisation and periodicity, computational complexity, and the algebraic K-theory of spaces.

In this volume, originally published in 1990, are included papers presented at two meetings; one a workshop on Number Theory and Cryptography, and the other, the annual meeting of the Australian Mathematical Society. Questions in number theory are of military and commercial importance for the security of communication, as they are related to codes and code-breaking. Papers in the volume range from problems in pure mathematics whose study has been intensified by this connection, through interesting theoretical and combinatorial problems which arise in the implementation, to practical questions that come from banking and telecommunications. The contributors are prominent within their field. The whole volume will be an attractive purchase for all number theorists, 'pure' or 'applied'.

A collection of reviews and more traditional research articles emerging from a workshop at the University of Warwick in May 2007. This volume provides an accessible overview for graduate students just entering the field and also serves as a useful resource for more established researchers.

This ground-breaking volume assembles experts in different areas of active research into highly oscillatory problems, with a particular emphasis on computation. The publication of these articles came about after the huge wave of interest that followed the very successful six-month programme held at the Newton Institute of Mathematical Sciences.

Poisson geometry lies at the cusp of noncommutative algebra and differential geometry, with natural and important links to classical physics and quantum mechanics. This book presents an accessible introduction to the subject suitable for graduate students.

Leading figures in modern computational mathematics present here latest research and provide surveys of contemporary topics. This is a valuable resource for all working in numerical analysis, optimization, computer algebra and scientific computing.

These selected contributions reflect different approaches to the integration of differential equations, originating from Differential Galois Theory, Symmetry, Integrability and Soliton Theory. The ideas of several mathematical communities are here brought together and connections between them sought.

Geometric group theory is a vibrant subject at the heart of modern mathematics. Major survey articles form the backbone of this book, providing an extended tour through a selection of the most important trends in modern geometric group theory, supported by shorter research articles on diverse topics.

The theory of transformation groups is a key mathematical concept, and studies symmetries of various mathematical objects such as topological spaces, manifolds, polyhedra and function spaces. This volume contains 25 of the papers submitted at the conference on transformation groups held at the University of Newcastle upon Tyne in August 1976.

In these notes, first published in 1980, Professor Northcott provides a self-contained introduction to the theory of affine algebraic groups for mathematicians with a basic knowledge of communicative algebra and field theory. The book divides into two parts. The first four chapters contain all the geometry needed for the second half of the book which deals with affine groups. Alternatively the first part provides a sure introduction to the foundations of algebraic geometry. Any affine group has an associated Lie algebra. In the last two chapters, the author studies these algebras and shows how, in certain important cases, their properties can be transferred back to the groups from which they arose. These notes provide a clear and carefully written introduction to algebraic geometry and algebraic groups.

This collection of research and survey papers sets out the theory of hidden Markov processes, in particular addressing a central problem of the subject: computation of the Shannon entropy rate of an HMP. Connections are drawn between approaches from various disciplines, whilst recent research results and open problems are described.

This collection of articles brings the researcher up to date with recent applications of logic, specifically model theory, to conjectures associated with those of Manin-Mumford and Andre-Oort. Originating from a short course, it combines original papers with background articles on related topics.

This book consists of nine survey papers by internationally renowned mathematicians. It will be of interest to researchers in combinatorics, from graduate students who want an overview of several areas to advanced researchers who want to have an in-depth analysis of recent developments.

This book comprises a collection of papers from leading researchers in the fields of word problems in algebra and geometric group theory. The papers cover a wide range of topics in algebra, representing a timely record of recent work and providing an indication of the key areas of future development.

This first volume of a two-volume book contains selected papers from the international conference Groups St Andrews 2009. Leading researchers in their respective areas, including Gerhard Hiss and Volodymyr Nekrashevych, survey the latest developments in algebra.

This second volume of a two-volume book contains selected papers from the international conference Groups St Andrews 2009. Leading researchers in their respective areas, including Eammon O'Brien, Mark Sapir and Dan Segal, survey the latest developments in algebra.

The new field of fusion systems and their classifying spaces lies on the frontier of group theory, representation theory and algebraic topology. This book provides a detailed exposition of the foundational material and surveys the current state of the art, including the key theorems and open problems.

This volume contains articles based on the invited lectures given at the 23rd British Combinatorial Conference, held in July 2011 at the University of Exeter. Each article surveys an area of current research in combinatorial mathematics and will be invaluable to anyone wishing to keep abreast of modern developments.

This volume, first published in 2000, is an integrated suite of papers centred around applications of Mori theory to birational geometry. It contains articles by K. Altmann, A. V. Pukhlikov, A. R. Iano-Fletcher, A. Corti, and M. Reid.

This book comprises a collection of papers from a conference on Galois theory, bringing together articles from leading experts in the field. Topics are centred around the Inverse Galois Problem, covering the full range of methods and approaches in this area. Invaluable for all whose research involves Galois theory.

This volume, first published in 2000, contains a collection of survey papers by leading researchers covering a wide variety of recent developments in the interactions between descriptive set theory and various aspects of the theory of dynamical systems. It will be of interest to graduate students and researchers working in either of these areas.

A comprehensive introduction to the subject suitable for graduate students and researchers. This book is also an up-to-date survey of the current state of the art and thus will serve as a valuable reference for specialists in the field.

This book describes the interaction between several key aspects of Galois theory based on Iwasawa theory, fundamental groups and automorphic forms. These ideas encompass a large portion of mainstream number theory and ramifications that are of interest to graduate students and researchers in number theory, algebraic geometry, topology and physics.

Quantum chaos and cosmology are areas of theoretical physics where models involving hyperbolic manifolds and the spectral theory of Maass waveforms have exciting applications. In this book leading experts provide a valuable exposition of hyperbolic geometry and its applications to graduate students and researchers.

This comprehensive book describes modern methods in the analysis of reduced models of Bose-Einstein condensation in periodic lattices. Aimed at researchers and graduate students working in applied mathematics and physical sciences where nonlinear waves arise, its unique focus is on localized nonlinear waves in periodic potentials and lattices.

This volume contains the proceedings of the 18th British Combinatorial Conference, held in 2001. The papers contained here are from the invited speakers and are thus of a quality befitting the event. This book will be a valuable reference both for researchers and graduate students in a variety of branches of combinatorics.

Assembles different theories of motivic integration for the first time, providing all of the necessary background for graduate students and researchers from algebraic geometry, model theory and number theory. In a rapidly-evolving area of research, this volume and Volume 2, which unite the several viewpoints and applications, will prove invaluable.