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Cubierta del libro
Autor Hindry, Marc. author.

Título Arithmetics [electronic resource] / by Marc Hindry.

Publicación London : Springer London, 2011.
Descripción física XVIII, 322 p. 5 illus. online resource.
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
text file PDF rda
Colección Universitext, 0172-5939
Universitext, 0172-5939
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Springer eBooks. Mathematics and Statistics
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Contiene: Finite Structures -- Applications: Algorithms, Primality and Factorization, Codes -- Algebra and Diophantine Equations -- Analytic Number Theory -- Elliptic Curves -- Developments and Open Problems -- Factorization -- Elementary Projective Geometry -- Galois Theory.
Resumen: 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 ́섥velopments and Open Problemśwhich 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.
Materia Mathematics.
Algebraic geometry.
Field theory (Physics).
Number theory.
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Number Theory.
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Algebraic Geometry.
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Field Theory and Polynomials.
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Autor secundario SpringerLink (Online service)
En Springer eBooks
OTRO SOPORTE Printed edition: 9781447121305
ISBN 9781447121312 978-1-4471-2131-2
ISBN/ISSN 10.1007/978-1-4471-2131-2 doi