Ornaments and icons, symbols of complexity or evil, aesthetically
appealing and endlessly useful in everyday ways, knots are also the
object of mathematical theory, used to unravel ideas about the
topological nature of space. In recent years knot theory has been
brought to bear on the study of equations describing weather
systems, mathematical models used in physics, and even, with the
realization that DNA sometimes is knotted, molecular biology.
This book, written by a mathematician known for his own work on
knot theory, is a clear, concise, and engaging introduction to this
complicated subject. A guide to the basic ideas and applications of
knot theory, "Knots" takes us from Lord Kelvin's early--and
mistaken--idea of using the knot to model the atom, almost a
century and a half ago, to the central problem confronting knot
theorists today: distinguishing among various knots, classifying
them, and finding a straightforward and general way of determining
whether two knots--treated as mathematical objects--are equal.
Communicating the excitement of recent ferment in the field, as
well as the joys and frustrations of his own work, Alexei Sossinsky
reveals how analogy, speculation, coincidence, mistakes, hard work,
aesthetics, and intuition figure far more than plain logic or
magical inspiration in the process of discovery. His spirited,
timely, and lavishly illustrated work shows us the pleasure of
mathematics for its own sake as well as the surprising usefulness
of its connections to real-world problems in the sciences. It will
instruct and delight the expert, the amateur, and the curious
alike.
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