Bøger i University Series in Mathematics serien

His friends in China have also established a Zhong Jia-Qing Memorial Fund, which has since twice awarded the Zhong Jia-Qing prizes for Chinese mathematics graduate students. In addition to putting Zhong's mathematical contributions in perspective, these articles should be useful also to a large segment of the mathematical community;

Elliptic cohomology is an extremely beautiful theory with both geometric and arithmetic aspects. The former is explained by the fact that the theory is a quotient of oriented cobordism localised away from 2, the latter by the fact that the coefficients coincide with a ring of modular forms. The aim of the book is to construct this cohomology theory, and evaluate it on classifying spaces BG of finite groups G. This class of spaces is important, since (using ideas borrowed from `Monstrous Moonshine') it is possible to give a bundle-theoretic definition of EU-(BG). Concluding chapters also discuss variants, generalisations and potential applications.

In the few years since their appearance in the mid-sixties, variational inequalities have developed to such an extent and so thoroughly that they may now be considered an "e;institutional"e; development of the theory of differential equations (with appreciable feedback as will be shown). This book was written in the light of these considerations both in regard to the choice of topics and to their treatment. In short, roughly speaking my intention was to write a book on second-order elliptic operators, with the first half of the book, as might be expected, dedicated to function spaces and to linear theory whereas the second, nonlinear half would deal with variational inequalities and non variational obstacle problems, rather than, for example, with quasilinear or fully nonlinear equations (with a few exceptions to which I shall return later). This approach has led me to omit any mention of "e;physical"e; motivations in the wide sense of the term, in spite of their historical and continuing importance in the development of variational inequalities. I here addressed myself to a potential reader more or less aware of the significant role of variational inequalities in numerous fields of applied mathematics who could use an analytic presentation of the fundamental theory, which would be as general and self-contained as possible.

His friends in China have also established a Zhong Jia-Qing Memorial Fund, which has since twice awarded the Zhong Jia-Qing prizes for Chinese mathematics graduate students. In addition to putting Zhong's mathematical contributions in perspective, these articles should be useful also to a large segment of the mathematical community;

This is a book of "impressions" of a journey through the theory of com plex algebraic curves. Looking back at the end of the journey, one can see that a common theme in fact does emerge, as is so often the case; More than once, in fact, we tear ourselves away from interesting topics leading elsewhere and return to our main route.

This book is a translation of my book Suron Josetsu (An Introduction to Number Theory), Second Edition, published by Shokabo, Tokyo, in 1988.

Intuitionistic logic is presented here as part of familiar classical logic which allows mechanical extraction of programs from proofs.

That is, each return time set is a so-called syndetic subset ofT= the positive reals (continuous time system) or T = the positive integers (discrete time system). In particular, frequency is measured by membership in a family of subsets of the space modeling time, in this case the family of syndetic subsets of T.

There are also articles concerned with the computability of aspects of familiar mathematical structures, and - a return to the sort of basic underlying questions considered by Alan Turing in the early days of the subject - an article giving a new perspective on computability in the real world.

Anyone seeking a gentle introduction to the methods of modern control theory and engineering, written at the level of a first-year graduate course, should consider this book seriously.

There are also articles concerned with the computability of aspects of familiar mathematical structures, and - a return to the sort of basic underlying questions considered by Alan Turing in the early days of the subject - an article giving a new perspective on computability in the real world.

Anyone seeking a gentle introduction to the methods of modern control theory and engineering, written at the level of a first-year graduate course, should consider this book seriously.

In the few years since their appearance in the mid-sixties, variational inequalities have developed to such an extent and so thoroughly that they may now be considered an "institutional" development of the theory of differential equations (with appreciable feedback as will be shown).

Problems in Set Theory, Mathematical Logic and the Theory of Algorithms by I. It covers major classical topics in proof theory and the semantics of propositional and predicate logic as well as set theory and computation theory.

Intuitionistic logic is presented here as part of familiar classical logic which allows mechanical extraction of programs from proofs.

Linear algebra and matrix theory are essentially synonymous terms for an area of mathematics that has become one of the most useful and pervasive tools in a wide range of disciplines.

This book reproduces, with minor changes, the notes prepared for a course given at Brigham Young University during the academic year 1984-1985. However, because the discussion was, generally, carried far enough to introduce the audience to some areas of current research, the book should also be useful to graduate students.