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This book is a thorough introduction to the Cantor (Ternary) Set
and its applications and brings together many of the topics
(advanced calculus, probability, topology, and algebra) that
mathematics students are required to study, but unfortunately are
treated as separate ideas. This book successfully bridges the gap
between how several mathematical fields interact using Cantor
Sets as the common theme. While the book is... more...

"This book is a major treatise in mathematics and is essential in
the working library of the modern analyst." (Bulletin of the London
Mathematical Society)

Integrable Hamiltonian systems have been of growing interest over
the past 30 years and represent one of the most intriguing and
mysterious classes of dynamical systems. This book explores the
topology of integrable systems and the general theory underlying
their qualitative properties, singularites, and topological
invariants.
The authors, both of whom have contributed significantly to the
field, develop the classification theory for integrable... more...

Stochastic geometry deals with models for random geometric
structures. Its early beginnings are found in playful
geometric probability questions, and it has vigorously developed
during recent decades, when an increasing number of real-world
applications in various sciences required solid mathematical
foundations. Integral geometry studies geometric mean values with
respect to invariant measures and is, therefore, the appropriate... more...

An easily accessible introduction to over three
centuries of innovations in geometry
Praise for the First Edition
“. . . a welcome alternative to compartmentalized treatments
bound to the old thinking. This clearly written, well-illustrated
book supplies sufficient background to be self-contained.”
—CHOICE
This fully revised new edition offers the most comprehensive
coverage of modern geometry currently available at an... more...

Presents an in-depth analysis of geometry of part surfaces and
provides the tools for solving complex engineering problems
Geometry of Surfaces: A Practical Guide for Mechanical
Engineers is a comprehensive guide to applied geometry of
surfaces with focus on practical applications in various areas of
mechanical engineering. The book is divided into three parts on
Part Surfaces, Geometry of Contact of Part Surfaces and Mapping
of the... more...

Essentials of the integral geometry in a homogenous space are
presented and the focus is on the basic results and applications.
This book provides the readers with new findings, some being
published for the first time.

Describing a striking connection between topology and algebra,
rather than only proving the theorem, this study demonstrates how
the result fits into a more general pattern. Throughout the text
emphasis is on the interplay between algebra and topology, with
graphical interpretation of algebraic operations, and topological
structures described algebraically in terms of generators and
relations. Includes numerous exercises and examples.

This book investigates the geometry of the quaternion and octonion
algebras. Following a comprehensive historical introduction, the
special properties of 3- and 4-dimensional Euclidean spaces are
illuminated using quaternions, leading to enumerations of the
corresponding finite groups of symmetries. The second half of the
book discusses the less familiar octonion algebra, concentrating on
its remarkable "triality symmetry" after an appropriate study... more...

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