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One service mathematics has rendered the "Et moi, ...si j'a\'ait su
comment en revenir, human race. It has put common sense back je n'y
scrais point alit: Jules Verne where it belongs, on the topmost
shelf next to the dusty canister labc\led 'discarded non- The
series is divergent; therefore we may be sense'. Eric T. 8c\l able
to do something with it. O. Hcaviside Mathematics is a tool for
thought. A highly necessary tool in a world where both feedback... more...

This volume covers semilinear embeddings of vector spaces over
division rings and the associated mappings of Grassmannians. In
contrast to classical books, we consider a more general class of
semilinear mappings and show that this class is important. A large
portion of the material will be formulated in terms of graph
theory, that is, Grassmann graphs, graph embeddings, and isometric
embeddings. In addition, some relations to linear codes will be... more...

Students and professors of an undergraduate course in
differential geometry will appreciate the clear exposition and
comprehensive exercises in this book that focuses on the
geometric properties of curves and surfaces, one- and
two-dimensional objects in Euclidean space. The problems
generally relate to questions of local properties (the properties
observed at a point on the curve or surface) or global properties
(the properties of the... more...

This book provides quick access to the theory of Lie groups and
isometric actions on smooth manifolds, using a concise geometric
approach. After a gentle introduction to the subject, some of its
recent applications to active research areas are explored, keeping
a constant connection with the basic material. The topics discussed
include polar actions, singular Riemannian foliations,
cohomogeneity one actions, and positively curved manifolds with
many... more...

This book focuses on a large class of geometric objects in moduli
theory and provides explicit computations to investigate their
families. Concrete examples are developed that take advantage of
the intricate interplay between Algebraic Geometry and
Combinatorics. Compactifications of moduli spaces play a crucial
role in Number Theory, String Theory, and Quantum Field Theory – to
mention just a few. In particular, the notion of compactification
of... more...

The Way of Analysis gives a thorough account of real analysis in
one or several variables, from the construction of the real number
system to an introduction of the Lebesgue integral. The text
provides proofs of all main results, as well as motivations,
examples, applications, exercises, and formal chapter summaries.
Additionally, there are three chapters on application of analysis,
ordinary differential equations, Fourier series, and curves and... more...

The present volume provides a fascinating overview of geometrical
ideas and perceptions from the earliest cultures to the
mathematical and artistic concepts of the 20th century. It is the
English translation of the 3rd edition of the well-received
German book “5000 Jahre Geometrie,” in which geometry is
presented as a chain of developments in cultural history and
their interaction with architecture, the visual arts, philosophy,... more...

The second part of a two-volume set concerning the field of
Clifford (geometric) algebra, this work consists of thematically
organized chapters that provide a broad overview of cutting-edge
topics in mathematical physics and the physical applications of
Clifford algebras. This volume is a survey of most aspects of
Clifford analysis. Topics range from applications such as
complex-distance potential theory, supersymmetry, and fluid
dynamics to Fourier... more...

This volume presents the cutting-edge contributions to the Seventh
International Workshop on Complex Structures and Vector Fields,
which was organized as a continuation of the high successful
preceding workshops on similar research. The volume includes works
treating ambitious topics in differential geometry, mathematical
physics and technology such as Bezier curves in space forms,
potential and catastrophy of a soap film, computer-assisted studies
of... more...

This book is a study of how a particular vision of the unity of
mathematics, often called geometric function theory, was created
in the 19th century. The central focus is on the convergence of
three mathematical topics: the hypergeometric and related linear
differential equations, group theory, and on-Euclidean geometry.
The text for this second edition has been greatly expanded and
revised, and the existing appendices enriched. The... more...