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This book introduces the concepts of linear algebra through the
careful study of two and three-dimensional Euclidean geometry.
This approach makes it possible to start with vectors, linear
transformations, and matrices in the context of familiar plane
geometry and to move directly to topics such as dot products,
determinants, eigenvalues, and quadratic forms. The later
chapters deal with n-dimensional Euclidean space and other... more...

The recent revolution in differential topology related to the
discovery of non-standard ("exotic") smoothness structures on
topologically trivial manifolds such as R4 suggests many exciting
opportunities for applications of potentially deep importance for
the spacetime models of theoretical physics, especially general
relativity. This rich panoply of new differentiable structures lies
in the previously unexplored region between topology and geometry.... more...

In The Arithmetic of Elliptic Curves, the author presented
the basic theory culminating in two fundamental global results, the
Mordell-Weil theorem on the finite generation of the group of
rational points and Siegel's theorem on the finiteness of the set
of integral points. This book continues the study of elliptic
curves by presenting six important, but somewhat more specialized
topics: I. Elliptic and modular functions for the full modular
group. II.... more...

Leonardo da Pisa, perhaps better known as Fibonacci (ca. 1170 –
ca. 1240), selected the most useful parts of Greco-Arabic
geometry for the book known as De Practica Geometrie. This
translation offers a reconstruction of De Practica Geometrie as
the author judges Fibonacci wrote it, thereby correcting
inaccuracies found in numerous modern histories. It is a high
quality translation with supplemental text to explain text that
has been... more...

This monograph presents the basic theorems of differential
geometry in three-dimensional space, including a thorough
coverage of surface theory. By means of a series of carefully
selected and representative mathematical models this monograph
also explains at length how these theorems are used in
three-dimensional elasticity and in shell theory. The
presentation is essentially selfcontained, with a great emphasis
on pedagogy. In... more...

Mathematicians and non-mathematicians alike have long been
fascinated by geometrical problems, particularly those that are
intuitive in the sense of being easy to state, perhaps with the aid
of a simple diagram. Each section in the book describes a problem
or a group of related problems. Usually the problems are capable of
generalization of variation in many directions. The book can be
appreciated at many levels and is intended for everyone from... more...

The aim of this volume is to provide a synthetic account of past
research, to give an up-to-date guide to current intertwined
developments of control theory and nonsmooth analysis, and also to
point to future research directions.
Contents: Multiscale Singular Perturbations and
Homogenization of Optimal Control Problems (M Bardi et al.);
Patchy Feedbacks for Stabilization and Optimal Control: General
Theory and Robustness Properties (F Ancona... more...

The theory of connections is central not only in pure mathematics
(differential and algebraic geometry), but also in mathematical and
theoretical physics (general relativity, gauge fields, mechanics of
continuum media). The now-standard approach to this subject was
proposed by Ch. Ehresmann 60 years ago, attracting first
mathematicians and later physicists by its transparent geometrical
simplicity. Unfortunately, it does not extend well to a number of... more...

This text covers Riemann surface theory from elementary aspects to
the fontiers of current research. Open and closed surfaces are
treated with emphasis on the compact case, while basic tools are
developed to describe the analytic, geometric, and algebraic
properties of Riemann surfaces and the associated Abelian varities.
Topics covered include existence of meromorphic functions, the
Riemann-Roch theorem, Abel's theorem, the Jacobi inversion problem,... more...