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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...

Now more that a quarter of a century old, intersection homology
theory has proven to be a powerful tool in the study of the
topology of singular spaces, with deep links to many other areas of
mathematics, including combinatorics, differential equations, group
representations, and number theory.
Like its predecessor, An Introduction to Intersection Homology
Theory, Second Edition introduces the power and beauty of
intersection homology, explaining the... 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.

Presenting a classical approach to the foundations and development
of the geometry of vector fields, this volume space, three
orthogonal systems, and applications in mechanics. Other topics,
including vector fields, Pfaff forms and systems in n-dimensional
space, foliations and Godbillon-Vey invariant, are also considered.
There is much interest in the study of geometrical objects in
n-dimensional Euclidean space, and this volume provides a useful
and... more...

This is an introduction to diophantine geometry at the advanced
graduate level. The book contains a proof of the Mordell
conjecture which will make it quite attractive to graduate
students and professional mathematicians. In each part of the
book, the reader will find numerous exercises.

This book provides a comprehensive introduction to modern global
variational theory on fibred spaces. It is based on differentiation
and integration theory of differential forms on smooth manifolds,
and on the concepts of global analysis and geometry such as jet
prolongations of manifolds, mappings, and Lie groups.
The book will be invaluable for researchers and PhD students in
differential geometry, global analysis, differential equations on... more...

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