Mathematics : Algebra

This book constitutes the refereed proceedings of the 10th International Workshop on Computer Algebra in Scientific Computing, CASC 2007, held in Bonn, Germany, in September 2007. The volume is dedicated to Professor Vladimir P. Gerdt on the occasion of his 60th birthday. The 35 revised full papers presented were carefully reviewed and selected from numerous submissions for inclusion in the book. The papers cover not only various expanding applications of computer algebra to scientific computing but also the computer algebra systems themselves and the CA algorithms. Topics addressed are studies in polynomial and matrix algebra, quantifier elimination, and Gr??bner bases, as well as stability investigation of both differential equations and difference methods for them. Several papers are devoted to the application of computer algebra methods and algorithms to the derivation of new mathematical models in biology and in mathematical physics. more...

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Since the impressive works of Talagrand, concentration inequalities have been recognized as fundamental tools in several domains such as geometry of Banach spaces or random combinatorics. They also turn out to be essential tools to develop a non-asymptotic theory in statistics, exactly as the central limit theorem and large deviations are known to play a central part in the asymptotic theory. An overview of a non-asymptotic theory for model selection is given here and some selected applications to variable selection, change points detection and statistical learning are discussed. This volume reflects the content of the course given by P. Massart in St. Flour in 2003. It is mostly self-contained and accessible to graduate students. more...

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Information content and programming semantics are just two of the applications of the mathematical concepts of order, continuity and domains. This authoritative and comprehensive account of the subject will be an essential handbook for all those working in the area. more...

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This is the first extensive treatment of the theory of corings and their comodules. In the first part, the module-theoretic aspects of coalgebras over commutative rings are described. Corings are then defined as coalgebras over non-commutative rings. Topics covered include module-theoretic aspects of corings, such as the relation of comodules to special subcategories of the category of modules (sigma-type categories), connections between corings and extensions of rings, properties of new examples of corings associated to entwining structures, generalisations of bialgebras such as bialgebroids and weak bialgebras, and the appearance of corings in non-commutative geometry. more...

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'This is an incredibly interesting and thought provoking book. Intended for anyone interested in developing their own mathematical thinking, or of the students they teach, whether at a primary level or right through to FE. The book is a delightful blend of theory and practice - encouraging the reader to participate, to solve problems and to develop their own thinking' - Peter Hall, Imberhorne School, East Grinstead. Algebra has always been a watershed for pupils learning mathematics. Nevertheless pupils bring to school all the necessary natural powers for thinking algebraically, including organizing, classifying and generalizing. Developing Thinking in Algebra enables teachers and their support staff to experience and to teach algebraic thinking to pupils aged seven to 16 years. By integrating pedagogy and subject knowledge through experiencing a variety of tasks for learners, readers of this book will see how to engage all learners in successfully thinking algebraically. This book is the course reader for The Open University Course ME625 Developing Algebraic Thinking more...

Price: $44.95