An Introduction to Number Theory / Everest, Graham (2005)  

Público ISBD Título : An Introduction to Number Theory Tipo de documento: documento electrónico Autores: Everest, Graham ; SpringerLink (Online service) ; Ward, Thomas Editorial: London : Springer London Fecha de publicación: 2005 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 232 Número de páginas: IX, 297 p Il.: online resource ISBN/ISSN/DL: 978-1-84628-044-3 Idioma : Inglés (eng) Palabras clave: Mathematics  Number  theory  Theory Clasificación: 51 Matemáticas Resumen: An Introduction to Number Theory provides an introduction to the main streams of number theory. Starting with the unique factorization property of the integers, the theme of factorization is revisited several times throughout the book to illustrate how the ideas handed down from Euclid continue to reverberate through the subject. In particular, the book shows how the Fundamental Theorem of Arithmetic, handed down from antiquity, informs much of the teaching of modern number theory. The result is that number theory will be understood, not as a collection of tricks and isolated results, but as a coherent and interconnected theory. A number of different approaches to number theory are presented, and the different streams in the book are brought together in a chapter that describes the class number formula for quadratic fields and the famous conjectures of Birch and Swinnerton-Dyer. The final chapter introduces some of the main ideas behind modern computational number theory and its applications in cryptography. Written for graduate and advanced undergraduate students of mathematics, this text will also appeal to students in cognate subjects who wish to be introduced to some of the main themes in number theory Nota de contenido: A Brief History of Prime -- Diophantine Equations -- Quadratic Diophantine Equations -- Recovering the Fundamental Theorem of Arithmetic -- Elliptic Curves -- Elliptic Functions -- Heights -- The Riemann Zeta Function -- The Functional Equation of the Riemann Zeta Function -- Primes in an Arithmetic Progression -- Converging Streams -- Computational Number Theory En línea: http://dx.doi.org/10.1007/b137432 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35217 An Introduction to Number Theory [documento electrónico] / Everest, Graham ; SpringerLink (Online service) ; Ward, Thomas . - London : Springer London, 2005 . - IX, 297 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 232) . ISBN : 978-1-84628-044-3 Idioma : Inglés (eng) Palabras clave: Mathematics  Number  theory  Theory Clasificación: 51 Matemáticas Resumen: An Introduction to Number Theory provides an introduction to the main streams of number theory. Starting with the unique factorization property of the integers, the theme of factorization is revisited several times throughout the book to illustrate how the ideas handed down from Euclid continue to reverberate through the subject. In particular, the book shows how the Fundamental Theorem of Arithmetic, handed down from antiquity, informs much of the teaching of modern number theory. The result is that number theory will be understood, not as a collection of tricks and isolated results, but as a coherent and interconnected theory. A number of different approaches to number theory are presented, and the different streams in the book are brought together in a chapter that describes the class number formula for quadratic fields and the famous conjectures of Birch and Swinnerton-Dyer. The final chapter introduces some of the main ideas behind modern computational number theory and its applications in cryptography. Written for graduate and advanced undergraduate students of mathematics, this text will also appeal to students in cognate subjects who wish to be introduced to some of the main themes in number theory Nota de contenido: A Brief History of Prime -- Diophantine Equations -- Quadratic Diophantine Equations -- Recovering the Fundamental Theorem of Arithmetic -- Elliptic Curves -- Elliptic Functions -- Heights -- The Riemann Zeta Function -- The Functional Equation of the Riemann Zeta Function -- Primes in an Arithmetic Progression -- Converging Streams -- Computational Number Theory En línea: http://dx.doi.org/10.1007/b137432 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35217

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Ergodic Theory / Einsiedler, Manfred (2011)  

Público ISBD Título : Ergodic Theory : with a view towards Number Theory Tipo de documento: documento electrónico Autores: Einsiedler, Manfred ; SpringerLink (Online service) ; Ward, Thomas Editorial: London : Springer London Fecha de publicación: 2011 Otro editor: Imprint: Springer Número de páginas: XVII, 481 p Il.: online resource ISBN/ISSN/DL: 978-0-85729-021-2 Idioma : Inglés (eng) Palabras clave: Mathematics  Dynamics  Ergodic  theory  Measure  Number  Dynamical  Systems  and  Theory  Integration Clasificación: 51 Matemáticas Resumen: This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits. Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory Nota de contenido: Motivation -- Ergodicity, Recurrence and Mixing -- Continued Fractions -- Invariant Measures for Continuous Maps -- Conditional Measures and Algebras -- Factors and Joinings -- Furstenberg’s Proof of Szemeredi’s Theorem -- Actions of Locally Compact Groups -- Geodesic Flow on Quotients of the Hyperbolic Plane -- Nilrotation -- More Dynamics on Quotients of the Hyperbolic Plane -- Appendix A: Measure Theory -- Appendix B: Functional Analysis -- Appendix C: Topological Groups En línea: http://dx.doi.org/10.1007/978-0-85729-021-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33114 Ergodic Theory : with a view towards Number Theory [documento electrónico] / Einsiedler, Manfred ; SpringerLink (Online service) ; Ward, Thomas . - London : Springer London : Imprint: Springer, 2011 . - XVII, 481 p : online resource. ISBN : 978-0-85729-021-2 Idioma : Inglés (eng) Palabras clave: Mathematics  Dynamics  Ergodic  theory  Measure  Number  Dynamical  Systems  and  Theory  Integration Clasificación: 51 Matemáticas Resumen: This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits. Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory Nota de contenido: Motivation -- Ergodicity, Recurrence and Mixing -- Continued Fractions -- Invariant Measures for Continuous Maps -- Conditional Measures and Algebras -- Factors and Joinings -- Furstenberg’s Proof of Szemeredi’s Theorem -- Actions of Locally Compact Groups -- Geodesic Flow on Quotients of the Hyperbolic Plane -- Nilrotation -- More Dynamics on Quotients of the Hyperbolic Plane -- Appendix A: Measure Theory -- Appendix B: Functional Analysis -- Appendix C: Topological Groups En línea: http://dx.doi.org/10.1007/978-0-85729-021-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33114

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