الصفحة 1
الصفحة 1
Modules and Comodules
The 23 articles in this volume encompass the proceedings of the International Conference on Modules and Comodules held in Porto (Portugal) in 2006 and dedicated to Robert Wisbauer on the occasion of his 65th birthday. These articles reflect Professor Wisbauer's wide interests and give an overview of different fields related to module theory, some of which have a long tradition whereas others have emerged in recent years. They include topics in the formal theory of modules bordering on category theory, in ring theory, in Hopf algebras and quantum groups, and in corings and comodules.
Fundamentals of Algebraic Graph Transformation
Graphs are widely used to represent structural information in the form of objects and connections between them. Graph transformation is the rule-based manipulation of graphs, an increasingly important concept in computer science and related fields. This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory.
Foundations of Quantum Theory : From Classical Concepts to Operator Algebras
This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory.
Datatype-Generic Programming ; International Spring School, SSDGP 2006, Nottingham, UK, April 24-27, 2006, Revised Lectures
A leitmotif in the evolution of programming paradigms has been the level and extent of parametrisation that is facilitated — the so-called genericity of the paradigm. The sorts of parameters that can be envisaged in a programming language range from simple values, like integers and fioating-point numbers, through structured values, types and classes, to kinds (the type of types and/or classes).Datatype-generic programming is about parametrising programsby the structure of the data that they manipulate. To appreciate the importance of data type genericity,one need look no further than the internet. The internet is a massive repository of structured data, but the structure is rarely exploited. For example, compression of data can be much more efiective if its structure is known, but most compression algorithms regard the input data as simply a string of bits, and take no account of its internal organisation. Datatype-generic programming is about exploiting the structure of data when it is relevant and ignoring it when it is not. Programming languages most c- monly used at the present time do not provide efiective mechanisms for do- menting and implementing datatype genericity.
Loop Spaces, Characteristic Classes and Geometric Quantization
This book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Various developments in mathematical physics (e.g., in knot theory, gauge theory, and topological quantum field theory) have led mathematicians and physicists to search for new geometric structures on manifolds and to seek a synthesis of ideas from geometry, topology and category theory. In this spirit, this book develops the differential geometry associated to the topology and obstruction theory of certain fiber bundles (more precisely, associated to grebes). The theory is a 3-dimensional analog of the familiar Kostant--Weil theory of line bundles. In particular the curvature now becomes a 3-form.
Lattices and Ordered Sets
This book is intended to be a thorough introduction to the subject of ordered sets and lattices, with an emphasis on the latter. It can be used for a course at the graduate or advanced undergraduate level or for independent study. Prerequisites are kept to a minimum, but an introductory course in abstract algebra is highly recommended, since many of the examples are drawn from this area. The book has an excellent choice of topics, including a chapter on well ordering and ordinal numbers, which is not usually found in other texts. The approach is user-friendly and the presentation is lucid. There are more than 240 carefully chosen exercises.
Categories for software engineering
This book provides a gentle, software engineering oriented introduction to category theory. Assuming only a minimum of mathematical preparation, this book explores the use of categorical constructions from the point of view of the methods and techniques that have been proposed for the engineering of complex software systems: object-oriented development, software architectures, logical and algebraic specification techniques, models of concurrency, inter alia. After two parts in which basic and more advanced categorical concepts and techniques are introduced, the book illustrates their application to the semantics of CommUnity – a language for the architectural design of interactive systems. "For computer scientists, this unique book presents Category Theory in a manner tailored to their interests and with examples to which they can relate." Ira Forman, IBM "This book applies little-known yet quite powerful formal tools from category theory to software structures: designs, architectures, patterns, and styles. Rather than focus on issues at the level of computational models and semantics, it instead applies these tools to some of the problems facing the sophisticated software architect.
Categories and Sheaves
This book covers categories, homological algebra and sheaves in a systematic and exhaustive manner starting from scratch, and continues with full proofs to an exposition of the most recent results in the literature, and sometimes beyond.The authors present the general theory of categories and functors, emphasising inductive and projective limits, tensor categories, representable functors, ind-objects and localization. Then they study homological algebra including additive, abelian, triangulated categories and also unbounded derived categories using transfinite induction and accessible objects. Finally, sheaf theory as well as twisted sheaves and stacks appear in the framework of Grothendieck topologies.
Basic Notions of Algebra
Aims to present a general survey of algebra, of its basic notions and main branches.Those parts of the book devoted to the systematic treatment of notions and results of algebra make very limited demands on the reader: we presuppose only that the reader knows calculus, analytic geometry and linear algebra in the form taught in many high schools and colleges. The extent of the prerequisites required in our treatment of examples is harder to state; an acquaintance with projective space, topological spaces, differentiable and complex analytic manifolds and the basic theory of functions of a complex variable is desirable, but the reader should bear in mind that difficulties arising in the treatment of some specific example are likely to be purely local in nature, and not to affect the understanding of the rest of the book.
Basic bundle theory and K-Cohomology invariants
Based on several recent courses given to mathematical physics students, this volume is an introduction to bundle theory with the aim to provide newcomers to the field with solid foundations in topological K-theory. A fundamental theme, emphasized in the book, centers around the gluing of local bundle data related to bundles into a global object. One renewed motivation for studying this subject, which has developed for almost 50 years in many directions, comes from quantum field theory, especially string theory, where topological invariants play an important role.
Algèbre, Chapitre 9 = Algebra, Chapter 9
Sesquilinear and quadratic forms : The Mathematics Elements of Nicolas BOURBAKI aim to provide a rigorous, systematic presentation without prerequisites of mathematics from their foundations. This ninth chapter of the Book of Algebra, the second Book of the treatise, is devoted to quadratic, symplectic or Hermitian forms and to associated groups.
Algèbre commutative, Chapitre 10 = Commutative Algebra, Chapter 10
Depth, Regularity, Duality The Mathematics Elements of Nicolas BOURBAKI aim to provide a rigorous, systematic presentation without prerequisites of mathematics from their foundations. This volume of the Book of Commutative Algebra, Book 7 of the treatise, is a continuation of the earlier chapters. It introduces in particular the notions of depth and smoothness, fundamental in algebraic geometry. It ends with the introduction of the dualizing modules and the Grothendieck duality.
Algebras, Rings and Modules ; Vol.2
This book provides both the classical aspects of the theory of groups and their representations as well as a general introduction to the modern theory of representations including the representations of quivers and finite partially ordered sets and their applications to finite dimensional algebras.
Algebraic Methodology and Software Technology ; 11th International Conference, AMAST 2006, Kuressaare, Estonia, July 5-8, 2006, Proceedings
This is the proceedings of the 11th edition of the Algebraic Methodology and Software Technology (AMAST) conference series. The rst conference was held in the USA in 1989, and since then AMAST conferences have been held on (or near) fve diferent continents and have been hosted by many of the most prominent people and organizations in the ?eld. The AMAST initiative has always sought to have practical efects by dev- oping the science of software and basing it on a ?rm mathematical foundation. AMAST hasinterpretedsoftwaretechnologybroadly,andhas, for example, held AMAST workshops in areas as diverse as real-time systems and (natural) l- guage processing. Similarly, algebraic methodology is interpreted broadly and includes abstract algebra, category theory, logic, and a range of other ma- ematical subdisciplines.
Algebra 3 : Homological Algebra and Its Applications
Includes algebra, deals with important topics in homological algebra, including abstract theory of derived functors, sheaf co-homology, and an introduction to etale and l-adic co-homology. It contains four chapters which discuss homology theory in an abelian category together with some important and fundamental applications in geometry, topology, algebraic geometry (including basics in abstract algebraic geometry), and group theory.
