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Computers have stretched the limits of what is possible in
mathematics. More: they have given rise to new fields of
mathematical study; the analysis of new and traditional algorithms,
the creation of new paradigms for implementing computational
methods, the viewing of old techniques from a concrete algorithmic
vantage point, to name but a few. Computational Algebra and Number
Theory lies at the lively intersection of computer science and
mathematics. It highlights the surprising width and depth of the
field through examples drawn from current activity, ranging from
category theory, graph theory and combinatorics, to more classical
computational areas, such as group theory and number theory. Many
of the papers in the book provide a survey of their topic, as well
as a description of present research. Throughout the variety of
mathematical and computational fields represented, the emphasis is
placed on the common principles and the methods employed. Audience:
Students, experts, and those performing current research in any of
the topics mentioned above.
Computers have stretched the limits of what is possible in
mathematics. More: they have given rise to new fields of
mathematical study; the analysis of new and traditional algorithms,
the creation of new paradigms for implementing computational
methods, the viewing of old techniques from a concrete algorithmic
vantage point, to name but a few. Computational Algebra and Number
Theory lies at the lively intersection of computer science and
mathematics. It highlights the surprising width and depth of the
field through examples drawn from current activity, ranging from
category theory, graph theory and combinatorics, to more classical
computational areas, such as group theory and number theory. Many
of the papers in the book provide a survey of their topic, as well
as a description of present research. Throughout the variety of
mathematical and computational fields represented, the emphasis is
placed on the common principles and the methods employed. Audience:
Students, experts, and those performing current research in any of
the topics mentioned above.
Despite their classical nature, continued fractions are a
neverending research area, with a body of results accessible enough
to suit a wide audience, from researchers to students and even
amateur enthusiasts. Neverending Fractions brings these results
together, offering fresh perspectives on a mature subject.
Beginning with a standard introduction to continued fractions, the
book covers a diverse range of topics, from elementary and metric
properties, to quadratic irrationals, to more exotic topics such as
folded continued fractions and Somos sequences. Along the way, the
authors reveal some amazing applications of the theory to seemingly
unrelated problems in number theory. Previously scattered
throughout the literature, these applications are brought together
in this volume for the first time. A wide variety of exercises
guide readers through the material, which will be especially
helpful to readers using the book for self-study, and the authors
also provide many pointers to the literature.
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