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Books > Science & Mathematics > Mathematics > Algebra
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Arithmetics (Paperback, 2011 ed.)
Loot Price: R2,272
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Arithmetics (Paperback, 2011 ed.)
Series: Universitext
Expected to ship within 10 - 15 working days
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Number theory is a branch of mathematics which draws its vitality
from a rich historical background. It is also traditionally
nourished through interactions with other areas of research, such
as algebra, algebraic geometry, topology, complex analysis and
harmonic analysis. More recently, it has made a spectacular
appearance in the field of theoretical computer science and in
questions of communication, cryptography and error-correcting
codes. Providing an elementary introduction to the central topics
in number theory, this book spans multiple areas of research. The
first part corresponds to an advanced undergraduate course. All of
the statements given in this part are of course accompanied by
their proofs, with perhaps the exception of some results appearing
at the end of the chapters. A copious list of exercises, of varying
difficulty, are also included here. The second part is of a higher
level and is relevant for the first year of graduate school. It
contains an introduction to elliptic curves and a chapter entitled
"Developments and Open Problems", which introduces and brings
together various themes oriented toward ongoing mathematical
research. Given the multifaceted nature of number theory, the
primary aims of this book are to: - provide an overview of the
various forms of mathematics useful for studying numbers -
demonstrate the necessity of deep and classical themes such as
Gauss sums - highlight the role that arithmetic plays in modern
applied mathematics - include recent proofs such as the polynomial
primality algorithm - approach subjects of contemporary research
such as elliptic curves - illustrate the beauty of arithmetic The
prerequisites for this text are undergraduate level algebra and a
little topology of Rn. It will be of use to undergraduates,
graduates and phd students, and may also appeal to professional
mathematicians as a reference text.
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