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Stochastic geometry, based on current developments in geometry,
probability and measure theory, makes possible modeling of two- and
three-dimensional random objects with interactions as they appear
in the microstructure of materials, biological tissues,
macroscopically in soil, geological sediments etc. In combination
with spatial statistics it is used for the solution of practical
problems such as the description of spatial arrangements and the... more...

Traditionally a subject of number theory, continued fractions
appear in dynamical systems, algebraic geometry, topology, and
even celestial mechanics. The rise of computational geometry has
resulted in renewed interest in multidimensional generalizations
of continued fractions. Numerous classical theorems have been
extended to the multidimensional case, casting light on phenomena
in diverse areas of mathematics. This book introduces a... more...

Many books in linear algebra focus purely on getting students
through exams, but this text explains both the how and the why of
linear algebra and enables students to begin thinking like
mathematicians. The author demonstrates how different topics
(geometry, abstract algebra, numerical analysis, physics) make use
of vectors in different ways and how these ways are connected,
preparing students for further work in these areas. The book is
packed with... more...

Classical algebraic geometry, inseparably connected with the names
of Abel, Riemann, Weierstrass, Poincaré, Clebsch, Jacobi and other
outstanding mathematicians of the last century, was mainly an
analytical theory. In our century the methods and ideas of
topology, commutative algebra and Grothendieck's schemes enriched
it and seemed to have replaced once and forever the somewhat naive
language of classical algebraic geometry. This classic book,... more...

This book gives a systematic account of the structure and
representation theory of finite-dimensional complex Lie
superalgebras of classical type and serves as a good introduction
to representation theory of Lie superalgebras. Several folklore
results are rigorously proved (and occasionally corrected in
detail), sometimes with new proofs. Three important dualities are
presented in the book, with the unifying theme of determining
irreducible characters... more...

This volume is the third of three in a series surveying the
theory of theta functions. Based on lectures given by the author
at the Tata Institute of Fundamental Research in Bombay, these
volumes constitute a systematic exposition of theta functions,
beginning with their historical roots as analytic functions in
one variable (Volume I), touching on some of the beautiful ways
they can be used to describe moduli spaces (Volume II), and... more...

Topics include: ways modern statistical procedures can yield
estimates of pi more precisely than the original Buffon procedure
traditionally used; the question of density and measure for random
geometric elements that leave probability and expectation
statements invariant under translation and rotation; and much more.

A central problem in differential geometry is to relate algebraic
properties of the Riemann curvature tensor to the underlying
geometry of the manifold. The full curvature tensor is in general
quite difficult to deal with. This book presents results about the
geometric consequences that follow if various natural operators
defined in terms of the Riemann curvature tensor (the Jacobi
operator, the skew-symmetric curvature operator, the Szabo
operator,... more...

Geometry is central to many branches of mathematics and physics,
and offers a complete range of views on the universe. This
introduction includes many simple explanations and examples. With
minimal prerequisites, the book provides a first glimpse of many
research topics in modern algebra, geometry and theoretical
physics. The book is based on many years' teaching experience, and
is thoroughly class-tested. There are copious illustrations, and
each... more...

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