Elliptic Cohomology

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)..Elliptic Differential Equations and Obstacle Problems This approach has led me to omit any mention of "physical" motivations in the wide sense of the term, in spite of their historical and continuing importance in the development of variational inequalities.

This book reproduces, with minor changes, the notes prepared for a course given at Brigham Young University during the academic year 1984-1985. The only prerequisite to reading the book is an interest in and aptitude for mathe­ matics. Topics in Number Theory The presentation was thus kept as elementary and self-contained as possible.

It is also a subject of great mathematical beauty..Matrix Theory: A Second Course 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. In consequence of both of these facts, linear algebra has increasingly been brought into lower levels of the curriculum, either in conjunction with the calculus or separate from it but at the same level.

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The audience consisted largely of undergraduate students with no more background than high school mathematics. 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.

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The aim of the book is to construct this cohomology theory, and evaluate it on classifying spaces BG of finite groups G. 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.

Readers are assumed to be familiar with basic notions of first order logic.

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The presentation is based on natural deduction. Readers are assumed to be familiar with basic notions of first order logic. A Short Introduction to Intuitionistic Logic.