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As many readers will know, the 20th century was a time when the
fields of mathematics and the sciences were seen as two separate
entities. Caused by the rapid growth of the physical sciences and
an increasing abstraction in mathematical research, each party,
physicists and mathematicians alike, suffered a misconception; not
only of the opposition's theoretical underpinning, but of how the
two subjects could be intertwined and effectively utilized. One
sub-discipline that played a part in the union of the two subjects
is Theoretical Physics. Breaking it down further came the
fundamental theories, Relativity and Quantum theory, and later on
Yang-Mills theory. Other areas to emerge in this area are those
derived from the works of Donaldson, Chern-Simons, Floer-Fukaya,
and Seiberg-Witten. Aimed at a wide audience, Physical Topics in
Mathematics demonstrates how various physical theories have played
a crucial role in the developments of Mathematics and in
particular, Geometric Topology. Issues are studied in great detail,
and the book steadfastly covers the background of both Mathematics
and Theoretical Physics in an effort to bring the reader to a
deeper understanding of their interaction. Whilst the world of
Theoretical Physics and Mathematics is boundless; it is not the
intention of this book to cover its enormity. Instead, it seeks to
lead the reader through the world of Physical Mathematics; leaving
them with a choice of which realm they wish to visit next.
As many readers will know, the 20th century was a time when the
fields of mathematics and the sciences were seen as two separate
entities. Caused by the rapid growth of the physical sciences and
an increasing abstraction in mathematical research, each party,
physicists and mathematicians alike, suffered a misconception; not
only of the opposition's theoretical underpinning, but of how the
two subjects could be intertwined and effectively utilized. One
sub-discipline that played a part in the union of the two subjects
is Theoretical Physics. Breaking it down further came the
fundamental theories, Relativity and Quantum theory, and later on
Yang-Mills theory. Other areas to emerge in this area are those
derived from the works of Donaldson, Chern-Simons, Floer-Fukaya,
and Seiberg-Witten. Aimed at a wide audience, Physical Topics in
Mathematics demonstrates how various physical theories have played
a crucial role in the developments of Mathematics and in
particular, Geometric Topology. Issues are studied in great detail,
and the book steadfastly covers the background of both Mathematics
and Theoretical Physics in an effort to bring the reader to a
deeper understanding of their interaction. Whilst the world of
Theoretical Physics and Mathematics is boundless; it is not the
intention of this book to cover its enormity. Instead, it seeks to
lead the reader through the world of Physical Mathematics; leaving
them with a choice of which realm they wish to visit next.
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