I've read over 40 books on this area of mathematics cover to cover, and Tignol's stands out as best for several important reasons – - most comprehensive, covering quadratic equations in ancient times contrasted to middle ages, Renaissance, 17th century symbolic algebra all the way through Galois Theory, with appendices on modern ways of seeing Galois' work. - Cleanest, most focused path through the topic - Clearest exposition, easies...

In the fifteen years since the discovery that Artin's braid groups enjoy a left-invariant linear ordering, several quite different approaches have been used to understand this phenomenon. This book is an account of those approaches, which involve such varied objects and domains as combinatorial group theory, self-distributive algebra, finite combinatorics, automata, low-dimensional topology, mapping class groups, and hyperbolic geome...

The direct sum behaviour of its projective modules is a fundamental property of any ring. Hereditary Noetherian prime rings are perhaps the only noncommutative Noetherian rings for which this direct sum behaviour (for both finitely and infinitely generated projective modules) is well-understood, yet highly nontrivial. This book surveys material previously available only in the research literature. It provides a re-worked and simplifi...

This volume consists of a collection of tutorial papers, by leading experts, on statistical and probabilistic aspects of chaos and networks, in particular neural networks. While written for the non-expert, they are intended to bring the reader up to the forefront of knowledge and research in the subject areas concerned. The papers, which contain extensive references to the literature, can separately or in various combinations serve a...

Let f be a periodic measurable function and x (nk) an increasing sequence of positive integers. The authors study conditions under which the series k=1 Ckf(nkx)_ converges in mean and for almost every x. There is a wide classical literature on this problem going back to the 30's, but the results for general f are much less complete than in the trigonometric case f(x) = sin x. As it turns out, the convergence properties of k=1 ckf(nkx...

A very valuable source for many techniques in the representation theory of general Lie groups. These techniques are beautiful combinations of methods in abstract harmonic analysis and others which are more specific to Lie theory and related to coadjoint orbits. I can recommend the book to everyone interested in general and abstract aspects of the representation theory of Lie groups.

After Karl Jöreskog's first presentation in 1970, Structural Equation Modelling or Sem has become a main statistical tool in many fields of science. It is the standard approach of factor analytic and causal modelling in such diverse fields as sociology, education, psychology, economics, management and medical sciences. In addition to an extension of its application area, Structural Equation Modelling also features a continual renewal...

This monograph, authored by a leading expert and main contributor in the field, is very painstakingly written ... The book offers an ideal road of entry into the subject, for everybody with an interest in local Galois module theory or in the theory of Hopf algebras. This book studies Hopf algebras over valuation rings of local fields and their application to the theory of wildly ramified extensions of local fields. The results...

Modern model theory began with Morley's categoricity theorem: A countable first-order theory that has a unique (up to isomorphism) model in one uncountable cardinal (i.e., is categorical in cardinality) if and only if the same holds in all uncountable cardinals. Over the last 35 years Shelah made great strides in extending this result to infinitary logic, where the basic tool of compactness fails. He invented the notion of an Abstrac...

The results of this book are given with complete proofs and also an emphasis on the intuitive understanding of the results. This extends the audience beyond mathematicians to include engineers, physicists and biologists with a good background in Analysis and PDEs. --Mathematical Reviews