Now revised and updated, this brisk introduction to functional analysis is intended for advanced undergraduate students, typically final year, who have had some background in real analysis. The author's aim is not just to cover the standard material in a standard way, but to present results of application in contemporary mathematics and to show the relevance of functional analysis to other areas. Unusual topics covered include the geometry of finite-dimensional spaces, invariant subspaces, fixed-point theorems, and the Bishop-Phelps theorem. An outstanding feature is the large number of...

Can a Christian escape from a lion? How quickly can a rumor spread? Can you fool an airline into accepting oversize baggage? Recreational mathematics is full of frivolous questions where the mathematician's art can be brought to bear. But play often has a purpose. In mathematics, it can sharpen skills, provide amusement, or simply surprise, and books of problems have been the stock-in-trade of mathematicians for centuries. This collection is designed to be sipped from, rather than consumed in one sitting. The questions range in difficulty: the most challenging offer a glimpse of deep results...

This is a new edition of the now classic text. The already extensive treatment given in the first edition has been heavily revised by the author. The addition of two new sections, numerous new results and 150 references means that this represents an up-to-date and comprehensive account of random graph theory. The theory estimates the number of graphs of a given degree that exhibit certain properties. It not only has numerous combinatorial applications, but also serves as a model for the probabilistic treatment of more complicated random structures. This book, written by an acknowledged expert...

This is a new edition of the now classic text. The already extensive treatment given in the first edition has been heavily revised by the author. The addition of two new sections, numerous new results and 150 references means that this represents an up-to-date and comprehensive account of random graph theory. The theory estimates the number of graphs of a given degree that exhibit certain properties. It not only has numerous combinatorial applications, but also serves as a model for the probabilistic treatment of more complicated random structures. This book, written by an acknowledged expert...

At the crossroads of representation theory, algebraic geometry and finite group theory, this book brings together many of the main concerns of modern algebra, synthesizing the past twenty-five years of research, by including some of the most remarkable achievements in the field. The text is illustrated throughout by many examples, and background material is provided by several introductory chapters on basic results as well as appendices on algebraic geometry and derived categories. The result is an essential introduction for graduate students and a reference for all algebraists.

The theory of Levy processes in Lie groups is not merely an extension of the theory of Levy processes in Euclidean spaces. Because of the unique structures possessed by non-commutative Lie groups, these processes exhibit certain interesting limiting properties which are not present for their counterparts in Euclidean spaces. This work provides an introduction to Levy processes in general Lie groups, the limiting properties of Levy processes in semi-simple Lie groups of non-compact type and the dynamical behavior of such processes as stochastic flows on certain homogeneous spaces.

The representation theory of symmetric groups is one of the most beautiful, popular, and important parts of algebra with many deep relations to other areas of mathematics, such as combinatorics, Lie theory, and algebraic geometry. Kleshchev describes a new approach to the subject, based on the recent work of Lascoux, Leclerc, Thibon, Ariki, Grojnowski, Brundan, and the author. Much of this work has only appeared in the research literature before. However, to make it accessible to graduate students, the theory is developed from scratch, the only prerequisite being a standard course in abstract...

Percolation theory was initiated some fifty years ago as a mathematical framework for the study of random physical processes such as flow through a disordered porous medium. It has proved to be a remarkably rich theory, with applications beyond natural phenomena to topics such as network modelling. The aims of this book, first published in 2006, are twofold. First to present classical results in a way that is accessible to non-specialists. Second, to describe results of Smirnov in conformal invariance, and outline the proof that the critical probability for random Voronoi percolation in the...

All those researching into any aspect of Combinatorics and its applications will find much in these articles of use and interest.

With the advent of digital computers more than half a century ago, - searchers working in a wide range of scienti?c disciplines have obtained an extremely powerful tool to pursue deep understanding of natural processes in physical, chemical, and biological systems. Computers pose a great ch- lenge to mathematical sciences, as the range of phenomena available for rigorous mathematical analysis has been enormously expanded, demanding the development of a new generation of mathematical tools. There is an explosive growth of new mathematical disciplines to satisfy this demand, in particular...