This volume gives an overview of linear logic in five parts: category theory; complexity and expressivity; proof theory; proof nets; and the geometry of interaction. The book includes a general introduction to linear logic that will ensure this book's use by the novice as well as the expert. Mathematicians and computer scientists will learn much from this book.

Finite fields are algebraic structures in which there is much research interest. This book gives a state-of-the-art account of finite fields and their applications in communications (coding theory, cryptology), combinatorics, design theory, quasirandom points, algorithms and their complexity. Typically, theory and application are tightly interwoven in the survey articles and original research papers included here. The book also demonstrates interconnections with other branches of pure mathematics such as number theory, group theory and algebraic geometry. This volume is an invaluable resource...

This book contains seven lectures delivered at The Maurice Auslander Memorial Conference at Brandeis University in March 1995. The variety of topics covered at the conference reflects the breadth of Maurice Auslander's contribution to mathematics, including commutative algebra and algebraic geometry, homological algebra and representation theory. He was one of the founding fathers of homological ring theory and representation theory of Artin algebras. Undoubtedly, the most characteristic feature of his mathematics was the profound use of homological and functorial techniques. For any...

This book covers the whole spectrum of number theory and is composed of contributions from well-known, international specialists. These lectures constitute the latest developments in number theory and are expected to form a basis for further discussions. It is an invaluable resource for students and researchers in number theory.

The James space J and the James tree space JT were constructed as counterexamples to several outstanding conjectures in Banach space theory. This book is a compendium of most of the known results about these spaces, frequently taken from the original sources, but presented in a unified and up-to-date fashion. Generalizations of J and JT are also discussed and other pathological Banach spaces are introduced. Specialists will welcome this book for its drawing together of classical material and recent results. Graduate students should also find that this book offers an excellent introduction to...

This volume surveys recent interactions between model theory and other branches of mathematics, notably group theory. Beginning with an introductory chapter describing relevant background material, the book contains contributions from many leading international figures in this area. Topics described include automorphism groups of algebraically closed fields, the model theory of pseudo-finite fields and applications to the subgroup structure of finite Chevalley groups. Model theory of modules, and aspects of model theory of various classes of groups, including free groups are also discussed....

This volume comprises the proceedings of the 1995 Cardiff symposium on sieve methods, exponential sums, and their applications in number theory. Included are contributions from leading international figures in this area, which encompasses the main branches of analytic number theory. In particular, many of the papers reflect the interaction among the different fields of sieve theory, Dirichlet series (including the Riemann Zeta-function), and exponential sums, while displaying the subtle interplay between the additive and multiplicative aspects of the subjects. The fundamental problems...

This is a clear, accessible and up to date exposition of modular representation theory of finite groups from a character-theoretic viewpoint. After a short review of the necessary background material, the early chapters introduce Brauer characters and blocks and develop their basic properties. The next three chapters study and prove Brauer's first, second and third main theorems in turn. The author then applies these results to prove a major application of finite groups, the Glauberman Z*-theorem. Later chapters examine Brauer characters in more detail. Navarro also explores the relationship...

This volume presents up-to-date research on finite geometries and designs, a key area in modern applicable mathematics. An introductory chapter discusses topics presented in each of the main chapters and is followed by articles from leading international figures in this field. These include a discussion of the current state of finite geometry from a group-theoretical viewpoint, and surveys of difference sets and of small embeddings of partial cycle systems into Steiner triple systems. Also presented are successful searches for spreads and packing of designs, rank three geometries with...

The first of two volumes on anabelian algebraic geometry, this book contains the famous manuscript "Esquisse d'un Programme" (Sketch of a Program) by Alexander Grothendieck. This work, written fourteen years after his retirement from public life in mathematics, includes the closely related letter to Gerd Faltings, published for the first time in this volume. Together these documents describe a powerful program of future mathematics, unifying aspects of geometry and arithmetic via the central point of moduli spaces of curves. The book is written in an artistic and informal style. It contains...