This open access textbook presents a comprehensive treatment of the arithmetic theory of
quaternion algebras and orders, a subject with applications in diverse areas of mathematics …

This book studies when a prime p can be written in the form x2+ ny2. It begins at an
elementary level with results of Fermat and Euler and then discusses the work of Lagrange …

The present book gives an exposition of the classical basic algebraic and analytic number
theory and supersedes my Algebraic Numbers, including much more material, eg the class …

Homological Algebra has grown in the nearly three decades since the rst e-tion of this book
appeared in 1979. Two books discussing more recent results are Weibel, An Introduction to …

Our objective in this chapter is to show off a few examples of algebras that occur naturally.
After a brief orientation toward concepts and notation, the reader is introduced to group …

To those precious colleagues who can appreciate the goals of and connections to other
areas. To those who acknowledge the depth of what we already know from the absorbed …

For the past 25 years, the Geometrization Program of Thurston has been a driving force for
research in 3-manifold topology. This has inspired a surge of activity investigating hyperbolic …

The unifying theme of this book is the interplay among noncommutative geometry, physics,
and number theory. The two main objects of investigation are spaces where both the …

In a recent paper, we introduced the concept of quasicrystals [Phys. Rev. Lett. 53, 2477
(1984)], a new class of ordered atomic structures. Quasicrystals have long-range …

This comprehensive book covers both long-standing results in the theory of polynomials and
recent developments which have until now only been available in the research literature …