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In this Very Short Introduction Peter M. Higgins presents an overview of the number types featured in modern science and mathematics. Providing a non-technical account, he explores the evolution of the modern number system, examines the fascinating role of primes, and explains th...eir role in contemporary cryptography.
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Each chapter provides an exploration section with problems that deal with software evaluation, selection, modificationm and the solution of not entirely open-ended problems.
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Thoroughly revised and updated, the new Second Edition of Neville Robbinsa (TM) Beginning Number Theory includes all of the major topics covered in a classic Number Theory course and blends in numerous applications and specialized treatments of number theory, including Cryptology..., Fibonacci numbers, and Computational Number Theory. The text strikes a balance between traditional and algorithmic approaches to elementary number theory and is supported with numerous exercises, applications, and case studies throughout. Computer exercises for CAS systems are also included.
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This book is an introduction to the algorithmic aspects of number theory and its applications to cryptography, with special emphasis on the RSA cryptosys-tem. It covers many of the familiar topics of elementary number theory, all with an algorithmic twist. The text also includes ...many interesting historical notes.
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This book looks to expand on the relationship between Christoffel words and Markoff theory. Part 1 focuses on the classical theory of Markoff, while part II explores the more advanced and recent results around Christoffel words.
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This book shows how to construct new Abelian model structures on the categories of modules and chain complexes from the notions of the Gorenstein-projective, injective, and flat dimensions. The method used for these new constructions is based on a theorem developed by Mark Hovey ...just a few years ago. The book provides a modern, readable introduction to the theory along with solid examples and nicely drawn diagrams that make proofs much easier to follow.
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Hailed by Science Progress as admirable, this classic presents the best systematic elementary account of the continuum as a type of serial order and requires no knowledge of higher mathematics. 1917 edition.
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This work focuses on the number theory of quadratic irrationalities in various forms, including continued fractions, orders in quadratic number fields, and binary quadratic forms. It presents classical results obtained by the famous number theorists Gauss, Legendre, Lagrange, and... Dirichlet. Collecting information previously scattered in the literature, the book covers the classical theory of continued fractions, quadratic orders, binary quadratic forms, and class groups based on the concept of a quadratic irrational.
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This volume reviews some of the major number theory achievements of this century and charts some of the directions in which the subject will be heading during the new century. It should be a useful reference for researchers in the area and an introduction to interested general re...aders.
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Describes computational number theory and its applications to deriving fast algorithms for digital signal processing. The text demonstrates the importance of computational number theory in the design of processing algorithms and it describes the nature and structure of the algori...thms themselves.
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