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The central problem considered in this introduction for graduate
students is the determination of rational parametrizability of an
algebraic curve and, in the positive case, the computation of a
good rational parametrization. This amounts to determining the
genus of a curve: its complete singularity structure, computing
regular points of the curve in small coordinate fields, and
constructing linear systems of curves with prescribed... more...

This book presents a detailed and mostly elementary exposition of
the generalized Riemann-Stieltjes integrals discovered by Henstock,
Kurzweil, and McShane. Along with the classical results, it
contains some recent developments connected with lipeomorphic
change of variables and the divergence theorem for discontinuously
differentiable vector fields.

Shipped from UK, please allow 10 to 21 business days for arrival.
xvi, 245pp. Bibliography: p. 235-245. Progress in Mathematics Vol.
44. ex. lib. Good Copy.

What is order that is not based on simple repetition, that is,
periodicity? How must atoms be arranged in a material so that it
diffracts like a quasicrystal? How can we describe aperiodically
ordered systems mathematically?
Originally triggered by the – later Nobel prize-winning –
discovery of quasicrystals, the investigation of aperiodic order
has since become a well-established and rapidly evolving field of
mathematical... more...

The aim of this book is to make accessible the two important but
rare works of Brook Taylor and to describe his role in the history
of linear perspective. Taylor's works, Linear Perspective and New
Principles on Linear Perspective, are among the most important
sources in the history of the theory of perspective. This text
focuses on two aspects of this history. The first is the
development, starting in the beginning of the 17th century, of a... more...

Ricci Flow for Shape Analysis and Surface Registration introduces
the beautiful and profound Ricci flow theory in a discrete setting.
By using basic tools in linear algebra and multivariate calculus,
readers can deduce all the major theorems in surface' Ricci flow by
themselves. The authors adapt the Ricci flow theory to practical
computational algorithms, apply Ricci flow for shape analysis and
surface registration, and demonstrate the power of Ricci... more...

In his "Géométrie" of 1637 Descartes achieved a monumental
innovation of mathematical techniques by introducing what is now
called analytic geometry. Yet the key question of the book was
foundational rather than technical: When are geometrical objects
known with such clarity and distinctness as befits the exact
science of geometry? Classically, the answer was sought in
procedures of geometrical construction, in particular by ruler and
compass, but... more...

This volume covers in a comprehensive way and at an elementary
level essentially all the theorems and techniques which are
commonly used and needed in any branches of mathematics,
particularly in complex and in real analytic geometry, in
commutative algebra, in algebraic geometry and in real algebraic
geometry. In particular it presents Rueckert's complex
nullstellensatz, Risler's real nullstellensatz, Tougeron's implicit
function theorem and Artin's... more...

Start with a single shape. Repeat it in some way—translation,
reflection over a line, rotation around a point—and you have
created symmetry.
Symmetry is a fundamental phenomenon in art, science, and nature
that has been captured, described, and analyzed using
mathematical concepts for a long time. Inspired by the geometric
intuition of Bill Thurston and empowered by his own analytical
skills, John Conway, with his coauthors, has... more...