Theory of Association Schemes

Publisher: Springer
Language: English
ISBN: 3540261362
Paperback: 283 pages
Data: Dec 2005
Format: PDF
Description: Theory of Association Schemes is the first concept-oriented treatment of the structure theory of association schemes. It contains several recent results which appear for the first time in book form. The generalization of Sylow’s group theoretic theorems to scheme theory arises as a consequence of arithmetical considerations about quotient schemes. The theory of Coxeter schemes (equivalent to the theory of buildings) emerges naturally and yields a purely algebraic proof of Tits’ main theorem on buildings of spherical type. Also a scheme-theoretic characterization of Glauberman’s Z*-involutions is included. The text is self-contained and accessible for advanced undergraduate students.

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A Course in Credibility Theory and its Applications

Publisher: Springer
Language: English
ISBN: 3540257535
Paperback: 336 pages
Data: Sep 2005
Format: PDF
Description: The book is aimed at teachers and students as well as practising experts in the financial area, in particular at actuaries in the field of property-casualty insurance, life insurance, reinsurance and insurance supervision. Persons working in the wider world of finance will also find many relevant ideas and examples even though credibility methods have not yet been widely applied here. The book covers the subject of Credibility Theory extensively and includes most aspects of this topic from the simplest case to the most general dynamic model. Credibility is a lifeless topic if it is not linked closely to practical applications. The book therefore treats explicitly the tasks which the actuary encounters in his daily work such as estimation of loss ratios, claim frequencies and claim sizes. This book deserves a place on the bookshelf of every actuary and mathematician who works, teaches or does research in the area of insurance and finance.

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Lattices and Ordered Algebraic Structures

Publisher: Springer
Language: English
ISBN: 1852339055
Paperback: 310 pages
Data: May 2005
Format: PDF
Description: Lattices and Ordered Algebraic Structures provides a lucid and concise introduction to the basic results concerning the notion of an order. Although as a whole it is mainly intended for beginning postgraduates, the prerequisities are minimal and selected parts can profitably be used to broaden the horizon of the advanced undergraduate. The treatment is modern, with a slant towards recent developments in the theory of residuated lattices and ordered regular semigroups. Topics covered include: residuated mappings; Galois connections; modular, distributive, and complemented lattices; Boolean algebras; seudocomplemented lattices; Stone algebras; Heyting algebras; ordered groups; lattice-ordered groups; representable groups; Archimedean ordered structures; ordered semigroups; naturally ordered regular and inverse Dubreil-Jacotin semigroups. Featuring material that has been hitherto available only in research articles, and an account of the range of applications of the theory, there are also many illustrative examples and numerous exercises throughout, making it ideal for use as a course text, or as a basic introduction to the field for researchers in mathematics, logic and computer science.

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Digraphs: Theory, Algorithms and Applications

Publisher: Springer
Language: English
ISBN: 1852332689
Paperback: 754 pages
Data: Aug 2002
Format: PDF
Description: The study of directed graphs has developed enormously over recent decades, yet no book covers more than a tiny fraction of the results from more than 3000 research articles on the topic. Digraphs is the first book to present a unified and comprehensive survey of the subject. In addition to covering the theoretical aspects, including detailed proofs of many important results, the authors present a number of algorithms and applications. The applications of digraphs and their generalizations include among other things recent developments in the Travelling Salesman Problem, genetics and network connectivity. More than 700 exercises and 180 figures will help readers to study the topic while open problems and conjectures will inspire further research.

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Foundations of Classical Electrodynamics

Publisher: Birkh?user Boston
Language: English
ISBN: 0817642226
Paperback: 320 pages
Data: Aug 2003
Format: PDF
Description: This book presents a fresh, original exposition of the foundations of classical electrodynamics in the tradition of the so-called metric-free approach. The fundamental structure of classical electrodynamics is described in the form of six axioms: (1) electric charge conservation, (2) existence of the Lorentz force, (3) magnetic flux conservation, (4) localization of electromagnetic energy-momentum, (5) existence of an electromagnetic spacetime relation, and (6) splitting of the electric current into material and external pieces. The first four axioms require an arbitrary 4-dimensional differentiable manifold. The fifth axiom characterizes spacetime as the environment in which the electromagnetic field propagates — a research topic of considerable interest — and in which the metric tensor of spacetime makes its appearance, thus coupling electromagnetism and gravitation. Repeated emphasis is placed on interweaving the mathematical definitions of physical notions and the actual physical measurement procedures. The tool for formulating the theory is the calculus of exterior differential forms, which is explained in sufficient detail, along with the corresponding computer algebra programs. Prerequisites for the reader include a knowledge of elementary electrodynamics (with Maxwell’s equations), linear algebra and elementary vector analysis; some knowledge of differential geometry would help. Foundations of Classical Electrodynamics unfolds systematically at a level suitable for graduate students and researchers in mathematics, physics, and electrical engineering.

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An Invitation to Morse Theory

Publisher: Springer
Language: English
ISBN: 0387495096
Paperback: 241 pages
Data: Feb 2007
Format: PDF
Description: This self-contained treatment of Morse Theory focuses on applications and is intended for a graduate course on differential or algebraic topology. The book is divided into three conceptually distinct parts. The first part contains the foundations of Morse theory (over the reals). The second part consists of applications of Morse theory over the reals, while the last part describes the basics and some applications of complex Morse theory, a.k.a. Picard-Lefschetz theory. This is the first textbook to include topics such as Morse-Smale flows, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. The exposition is enhanced with examples, problems, and illustrations, and will be of interest to graduate students as well as researchers. The reader is expected to have some familiarity with cohomology theory and with the differential and integral calculus on smooth manifolds. Liviu Nicolaescu is Associate Professor of Mathematics at University of Notre Dame.

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Most Honourable Remembrance: The Life and Work of Thomas Bayes

Publisher: Springer
Language: English
ISBN: 0387004998
Paperback: 667 pages
Data: Sep 2003
Format: PDF
Description: Thomas Bayes (1702 - 1761) was an English clergyman and mathematician. Until around 1950, he was considered a minor contributor to the history of mathematics, and if he was known at all it was because his name was attached to a simple theorem in the calculus of probabilities. Since then, however, that theorem and the problem Bayes was able to solve with it have become the basis for an important branch of statistical methodology, the problem of inverse probability. Little is known of Bayes’ life and few records mentioning him remain. Dale has meticulously researched the material and here gives a picture of Bayes and his time, as well as the intellectual and social climate in which Bayes worked. The writing is both instructive and entertaining, representing superb historical scholarship and excellent mathematics. (these are comments from our reviewers)

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