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Differential algebraic groups were introduced by P. Cassidy and E.
Kolchin and are, roughly speaking, groups defined by algebraic
differential equations in the same way as algebraic groups are
groups defined by algebraic equations. The aim of the book is
two-fold: 1) the provide an algebraic geometer's introduction to
differential algebraic groups and 2) to provide a structure and
classification theory for the finite dimensional ones. The main
idea of... more...

The Geometry and Topology of Coxeter Groups is a
comprehensive and authoritative treatment of Coxeter groups from
the viewpoint of geometric group theory. Groups generated by
reflections are ubiquitous in mathematics, and there are
classical examples of reflection groups in spherical, Euclidean,
and hyperbolic geometry. Any Coxeter group can be realized as a
group generated by reflection on a certain contractible cell
complex, and this... more...

Originally published in 1985, this classic textbook is an English
translation of Einführung in die kommutative Algebra und
algebraische Geometrie. As part of the Modern Birkhäuser
Classics series, the publisher is proud to make Introduction
to Commutative Algebra and Algebraic Geometry available to a
wider audience.
Aimed at students who have taken a basic course in algebra, the
goal of the text is to present important... more...

This is an extended second edition of "The Topology of Torus
Actions on Symplectic Manifolds" published in this series in
1991. The material and references have been updated. Symplectic
manifolds and torus actions are investigated, with numerous
examples of torus actions, for instance on some moduli spaces.
Although the book is still centered on convexity theorems, it
contains much more results, proofs and examples.
Chapter I deals... more...

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...

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