Fuzzy Logic and Soft Computing

Sample

Jonathan S. Golan

This volume presents a course in linear algebra for undergraduate mathematics students. It is considerably wider in its scope than most of the available methods and prepares the students for advanced work in algebra, differential equations, and functional analysis. Therefore, for example, it is transformation-oriented rather than matrix oriented, and whenever possible results are proved for arbitrary vector spaces and not merely for finite-dimensional vector spaces. Also, by proving results for vector spaces over arbitrary fields, rather than only the field of real or complex numbers, it prepares the way for the study of algebraic coding theory, automata theory, and other subjects in theoretical computer science. Topics are dealt with thoroughly, including ones that normally do not feature in undergraduate textbooks, and many novel and challenging exercises are given. The fact that most students are computer-literate is taken into account, not so much by emphasizing computational aspects of linear algebra which are best left to the computer, but by concentrating on the theory behind it. Audience: Recommended for a one-year undergraduate course in linear algebra.

Sample

Susanne C. Brenner, L. Ridgway Scott

This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. It formalizes basic tools that are commonly used by researchers in the field but not previously published. The book will be useful to mathematicians as well as engineers and physical scientists. It can be used for a course that provides an introduction to basic functional analysis, approximation theory, and numerical analysis, while building upon and applying basic techniques of real variable theory. The initial chapter provides an introduction to the entire subject, developed in the one-dimensional case. Four subsequent chapters develop the basic theory in the multidimensional case, and a fifth chapter presents basic applications of this theory. Subsequent chapters provide an introduction to multigrid methods and other iterative solution techniques, mixed methods with applications to elasticity and fluid flow models, variational "crimes" including nonconforming and isoparametric methods and numerical integration, error estimates in the maximum norm with applications to nonlinear problems, and Banach-space operator-interpolation techniques. Different course paths can be chosen, allowing the book to be used for courses designed for students with different interests. For example, courses can emphasize physical applications, or algorithmic efficiency and code development issues, or the more difficult convergence theorems of the subject.

Sample

José Júlio Alferes, João Leite (eds

Logics have, for many years, laid claim to providing a formal basis for the study and development of applications and systems in arti?cial intelligence. With the depth and maturity of formalisms, methodologies and logic-based systems - day, this claim is stronger than ever. The European Conference on Logics in Arti?cial Intelligence (or Journ´ ees Europ´ eennes sur la Logique en Intelligence Arti?cielle, JELIA) began back in 1988, as a workshop, in response to the need for a European forum for the discussion of emerging work in this ?eld. Since then, JELIA has been organized biennially, with English as its o?cial language, previous meetings taking place in Rosco?, France (1988), Amsterdam, Nether- ´ lands (1990), Berlin, Germany (1992), York, UK (1994), Evora, Portugal (1996), Dagstuhl,Germany(1998),M´ alaga,Spain(2000)andCosenza,Italy(2002). The increasinginterestinthisforum,itsinternationallevelwithgrowingparticipation from researchers outside Europe, and the overall technical quality have turned JELIA into a major biennial forum for the discussion of logic-based approaches to arti?cial intelligence. The 9th European Conference on Logics in AI, JELIA 2004, took place in Lisbon, Portugal, between the 27th and the 30th of September 2004, and was hosted by the Universidade Nova de Lisboa. Its technical program comprised 3 invited talks, by Francesca Rossi, Franz Baader, and Bernhard Nebel, and the presentationof52refereedtechnicalarticlesselectedbytheProgramCommittee among the 144 that were submitted, a number which in our opinion clearly indicates that the research area of logics in AI is one with a great and increasing interest.

Sample

Christian Kassel

This book provides an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and on Drinfeld's recent fundamental contributions. The first part presents in detail the quantum groups attached to SL2 as well as the basic concepts of the theory of Hopf algebras. Part Two focuses on Hopf algebras that produce solutions of the Yang-Baxter equation, and on Drinfeld's quantum double construction. In the following part we construct isotopy invariants of knots and links in the three-dimensional Euclidean space, using the language of tensor categories. The last part is an account of Drinfeld's elegant treatment of the monodromy of the Knizhnik-Zamolodchikov equations, culminating in the construction of Kontsevich's universal knot invariant.