Manifolds are everywhere. These generalizations of curves and surfaces
to arbitrarily many dimensions provide the mathematical context for
under standing "space" in all of its manifestations. Today, the
tools of manifold theory are indispensable in most major subfields of
pure mathematics, and outside of pure mathematics they are becoming
increasingly important to scientists in such diverse fields as
genetics, robotics, econometrics, com puter graphics, biomedical
imaging, and, of course, the undisputed leader among consumers (and
inspirers) of mathematics-theoretical physics. No longer a specialized
subject that is studied only by differential geometers, manifold
theory is now one of the basic skills that all mathematics students
should acquire as early as possible. Over the past few centuries,
mathematicians have developed a wondrous collection of conceptual
machines designed to enable us to peer ever more deeply into the
invisible world of geometry in higher dimensions. Once their operation
is mastered, these powerful machines enable us to think geometrically
about the 6-dimensional zero set of a polynomial in four complex
variables, or the lO-dimensional manifold of 5 x 5 orthogonal ma
trices, as easily as we think about the familiar 2-dimensional sphere
in ]R3.
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Produktdetaljer
ISBN
9780387217529
Publisert
2020
Utgiver
Vendor
Springer
Språk
Product language
Engelsk
Format
Product format
Digital bok
Forfatter