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OverviewNumber 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. Full Product DetailsAuthor: Marc HindryPublisher: Springer London Ltd Imprint: Springer London Ltd Edition: 2011 ed. Dimensions: Width: 15.50cm , Height: 1.80cm , Length: 23.50cm Weight: 0.522kg ISBN: 9781447121305ISBN 10: 1447121309 Pages: 322 Publication Date: 05 August 2011 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsFinite 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 TheoryReviewsFrom the reviews: This is a detailed presentation of modern number theory, complete with overviews of current research problems. ... Hindry (Univ. Paris 7, France) includes the standard topics in undergraduate number theory courses ... . Summing Up: Recommended. Upper-division undergraduates through researchers/faculty. (J. Johnson, Choice, Vol. 49 (6), February, 2012) From the reviews: This is a detailed presentation of modern number theory, complete with overviews of current research problems. ! Hindry (Univ. Paris 7, France) includes the standard topics in undergraduate number theory courses ! . Summing Up: Recommended. Upper-division undergraduates through researchers/faculty. (J. Johnson, Choice, Vol. 49 (6), February, 2012) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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