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This textbook is intended to serve as a one-semester introductory course in number theory and in this second edition it has been revised throughout and many new exercises have been added. Historical perspective is included and emphasis is given to some of the subject's applied aspects; in particular the field of cryptography is highlighted. At the heart of the book are the major number theoretic accomplishments of Euclid, Fermat, Gauss, Legendre, and Euler, and to fully illustrate the properties of numbers and concepts developed in the text, a wealth of exercises have been included. It is assumed that the reader will have 'pencil in hand' and ready access to a calculator or computer. For students new to number theory, whatever their background, this is a stimulating and entertaining introduction to the subject. In this new edition a wealth of exercises have been included to illustrate the properties of numbers and concepts developed in the text ; The heart of this book contains the major number theoretic accomplishments of Euclid, Fermat, Gauss, Legendre, and Euler ; A historical perspective has been adopted and some of the subject's applied aspects - in particular, the field of cryptography, has been highlighted. Publisher]

Number theory. --- Nombres, Théorie des. --- Number theory --- Number study --- Numbers, Theory of --- Algebra --- Number Theory --- Nombres, Théorie des.

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Ergodic Theory of Numbers is an introduction to the ergodic theory behind common number expansion, like decimal expansions, continued fractions, and many others. However, its aim does not stop there. For undergraduate students with sufficient background knowledge in real analysis and graduate students interested in the area, it is also an introduction to a "dynamical way of thinking." The questions studied here are dynamical as well as number theoretical in nature, and the answers are obtained with the help of ergodic theory. Attention is focused on concepts like measure-preserving, ergodicity, natural extension, induced transformations, and entropy. These concepts are then applied to familiar expansions to obtain old and new results in an elegant and straightforward manner. What it means to be ergodic and the basic ideas behind ergodic theory will be explained along the way. The subjects covered vary from classical to recent, which makes this book appealing to researchers as well as students.

Ergodic theory. --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Number theory. --- Théorie ergodique --- Nombres, Théorie des --- Calculus --- Functions of real variables --- Théorie ergodique --- Nombres, Théorie des

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This collaborative volume presents recent trends arising from the fruitful interaction between the themes of combinatorics on words, automata and formal language theory, and number theory. Presenting several important tools and concepts, the authors also reveal some of the exciting and important relationships that exist between these different fields. Topics include numeration systems, word complexity function, morphic words, Rauzy tilings and substitutive dynamical systems, Bratelli diagrams, frequencies and ergodicity, Diophantine approximation and transcendence, asymptotic properties of digital functions, decidability issues for D0L systems, matrix products and joint spectral radius. Topics are presented in a way that links them to the three main themes, but also extends them to dynamical systems and ergodic theory, fractals, tilings and spectral properties of matrices. Graduate students, research mathematicians and computer scientists working in combinatorics, theory of computation, number theory, symbolic dynamics, fractals, tilings and stringology will find much of interest in this book. [Publisher]

Combinatorial analysis --- Number theory --- Machine theory --- Analyse combinatoire --- Théorie des nombres --- Automates mathématiques, Théorie des --- Number Theory --- Combinatorial analysis. --- Machine theory. --- Number theory. --- Analyse combinatoire. --- Nombres, Théorie des. --- Automates mathématiques, Théorie des. --- Combinatorische analyse --- Computer science --- Dynamics (symbolic) --- Informatica --- Informatique --- Symbolic dynamics --- Théorie des nombres --- Automates mathématiques, Théorie des --- Abstract automata --- Abstract machines --- Automata --- Mathematical machine theory --- Algorithms --- Logic, Symbolic and mathematical --- Recursive functions --- Robotics --- Number study --- Numbers, Theory of --- Algebra --- Combinatorics --- Mathematical analysis --- Théorie des automates mathématiques