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Classical valuation theory has applications in number theory and
class field theory as well as in algebraic geometry, e.g. in a
divisor theory for curves. But the noncommutative equivalent
is mainly applied to finite dimensional skewfields. Recently
however, new types of algebras have become popular in modern
algebra; Weyl algebras, deformed and quantized algebras, quantum
groups and Hopf algebras, etc. The advantage of valuation theory in... more...

The Jacobian of a smooth projective curve is undoubtedly one of the
most remarkable and beautiful objects in algebraic geometry. This
work is an attempt to develop an analogous theory for smooth
projective surfaces - a theory of the nonabelian Jacobian of smooth
projective surfaces. Just like its classical counterpart, our
nonabelian Jacobian relates to vector bundles (of rank 2) on a
surface as well as its Hilbert scheme of points. But it also comes... more...

The author defines “Geometric Algebra Computing” as the
geometrically intuitive development of algorithms using geometric
algebra with a focus on their efficient implementation, and the
goal of this book is to lay the foundations for the widespread use
of geometric algebra as a powerful, intuitive mathematical language
for engineering applications in academia and industry. The related
technology is driven by the invention of conformal geometric... more...

The goal of this book is to describe the most powerful methods for
evaluating multiloop Feynman integrals that are currently used in
practice. This book supersedes the author’s previous Springer
book “Evaluating Feynman Integrals” and its textbook version
“Feynman Integral Calculus.” Since the publication of these two
books, powerful new methods have arisen and conventional methods
have been improved on in essential ways. A further... more...

This monograph provides an introduction to the theory of Clifford
algebras, with an emphasis on its connections with the theory of
Lie groups and Lie algebras. The book starts with a detailed
presentation of the main results on symmetric bilinear forms and
Clifford algebras. It develops the spin groups and the spin
representation, culminating in Cartan’s famous triality
automorphism for the group Spin(8). The discussion of enveloping
algebras... more...

The present manuscript is an improved edition of a text that first
appeared under the same title in Bonner Mathematische Schriften,
no.26, and originated from a series of lectures given by the author
in 1965/66 in Wolfgang Krull's seminar in Bonn. Its main goal is to
provide the reader, acquainted with the basics of algebraic number
theory, a quick and immediate access to class field theory. This
script consists of three parts, the first of which... more...

The purpose of coding theory is the design of efficient systems
for the transmission of information. The mathematical
treatment leads to certain finite structures: the error-correcting
codes. Surprisingly problems which are interesting for the
design of codes turn out to be closely related to problems
studied partly earlier and independently in pure mathematics.
In this book, examples of such connections are presented. The... more...

This book consists of eighteen articles in the area of
`Combinatorial Matrix Theory' and `Generalized Inverses of
Matrices'. Original research and expository articles presented in
this publication are written by leading Mathematicians and
Statisticians working in these areas. The articles contained herein
are on the following general topics: `matrices in graph theory',
`generalized inverses of matrices', `matrix methods in statistics'
and `magic... more...

Srinivasa Ramanujan was a mathematician brilliant beyond comparison
who inspired many great mathematicians. There is extensive
literature available on the work of Ramanujan. But what is missing
in the literature is an analysis that would place his mathematics
in context and interpret it in terms of modern developments. The 12
lectures by Hardy, delivered in 1936, served this purpose at the
time they were given. This book presents Ramanujan’s... more...