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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Functional Analysis, Calculus of Variations and Optimal Control / Clarke, Francis (2013)  

Público ISBD Título : Functional Analysis, Calculus of Variations and Optimal Control Tipo de documento: documento electrónico Autores: Clarke, Francis ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 264 Número de páginas: XIV, 591 p. 24 illus., 8 illus. in color Il.: online resource ISBN/ISSN/DL: 978-1-4471-4820-3 Idioma : Inglés (eng) Palabras clave: Mathematics  Functional  analysis  System  theory  Calculus  of  variations  Mathematical  optimization  Analysis  Variations  and  Optimal  Control;  Optimization  Continuous  Systems  Theory,  Control Clasificación: 51 Matemáticas Resumen: Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields Nota de contenido: Normed Spaces -- Convex sets and functions -- Weak topologies -- Convex analysis -- Banach spaces -- Lebesgue spaces -- Hilbert spaces -- Additional exercises for Part I -- Optimization and multipliers -- Generalized gradients -- Proximal analysis -- Invariance and monotonicity -- Additional exercises for Part II -- The classical theory -- Nonsmooth extremals -- Absolutely continuous solutions -- The multiplier rule -- Nonsmooth Lagrangians -- Hamilton-Jacobi methods -- Additional exercises for Part III -- Multiple integrals -- Necessary conditions -- Existence and regularity -- Inductive methods -- Differential inclusions -- Additional exercises for Part IV En línea: http://dx.doi.org/10.1007/978-1-4471-4820-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32194 Functional Analysis, Calculus of Variations and Optimal Control [documento electrónico] / Clarke, Francis ; SpringerLink (Online service) . - London : Springer London : Imprint: Springer, 2013 . - XIV, 591 p. 24 illus., 8 illus. in color : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 264) . ISBN : 978-1-4471-4820-3 Idioma : Inglés (eng) Palabras clave: Mathematics  Functional  analysis  System  theory  Calculus  of  variations  Mathematical  optimization  Analysis  Variations  and  Optimal  Control;  Optimization  Continuous  Systems  Theory,  Control Clasificación: 51 Matemáticas Resumen: Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields Nota de contenido: Normed Spaces -- Convex sets and functions -- Weak topologies -- Convex analysis -- Banach spaces -- Lebesgue spaces -- Hilbert spaces -- Additional exercises for Part I -- Optimization and multipliers -- Generalized gradients -- Proximal analysis -- Invariance and monotonicity -- Additional exercises for Part II -- The classical theory -- Nonsmooth extremals -- Absolutely continuous solutions -- The multiplier rule -- Nonsmooth Lagrangians -- Hamilton-Jacobi methods -- Additional exercises for Part III -- Multiple integrals -- Necessary conditions -- Existence and regularity -- Inductive methods -- Differential inclusions -- Additional exercises for Part IV En línea: http://dx.doi.org/10.1007/978-1-4471-4820-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32194

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The Finite Simple Groups / Wilson, Robert A (2009)  

Público ISBD Título : The Finite Simple Groups Tipo de documento: documento electrónico Autores: Wilson, Robert A ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2009 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 251 Número de páginas: XV, 298 p Il.: online resource ISBN/ISSN/DL: 978-1-84800-988-2 Idioma : Inglés (eng) Palabras clave: Mathematics  Algebra  Group  theory  Topological  groups  Lie  Theory  and  Generalizations  Groups,  Groups Clasificación: 51 Matemáticas Resumen: The finite simple groups are the building blocks from which all the finite groups are made and as such they are objects of fundamental importance throughout mathematics. The classification of the finite simple groups was one of the great mathematical achievements of the twentieth century, yet these groups remain difficult to study which hinders applications of the classification. This textbook brings the finite simple groups to life by giving concrete constructions of most of them, sufficient to illuminate their structure and permit real calculations both in the groups themselves and in the underlying geometrical or algebraic structures. This is the first time that all the finite simple groups have been treated together in this way and the book points out their connections, for example between exceptional behaviour of generic groups and the existence of sporadic groups, and discusses a number of new approaches to some of the groups. Many exercises of varying difficulty are provided. The Finite Simple Groups is aimed at advanced undergraduate and graduate students in algebra as well as professional mathematicians and scientists who use groups and want to apply the knowledge which the classification has given us. The main prerequisite is an undergraduate course in group theory up to the level of Sylow’s theorems Nota de contenido: The alternating groups -- The classical groups -- The exceptional groups -- The sporadic groups En línea: http://dx.doi.org/10.1007/978-1-84800-988-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33982 The Finite Simple Groups [documento electrónico] / Wilson, Robert A ; SpringerLink (Online service) . - London : Springer London, 2009 . - XV, 298 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 251) . ISBN : 978-1-84800-988-2 Idioma : Inglés (eng) Palabras clave: Mathematics  Algebra  Group  theory  Topological  groups  Lie  Theory  and  Generalizations  Groups,  Groups Clasificación: 51 Matemáticas Resumen: The finite simple groups are the building blocks from which all the finite groups are made and as such they are objects of fundamental importance throughout mathematics. The classification of the finite simple groups was one of the great mathematical achievements of the twentieth century, yet these groups remain difficult to study which hinders applications of the classification. This textbook brings the finite simple groups to life by giving concrete constructions of most of them, sufficient to illuminate their structure and permit real calculations both in the groups themselves and in the underlying geometrical or algebraic structures. This is the first time that all the finite simple groups have been treated together in this way and the book points out their connections, for example between exceptional behaviour of generic groups and the existence of sporadic groups, and discusses a number of new approaches to some of the groups. Many exercises of varying difficulty are provided. The Finite Simple Groups is aimed at advanced undergraduate and graduate students in algebra as well as professional mathematicians and scientists who use groups and want to apply the knowledge which the classification has given us. The main prerequisite is an undergraduate course in group theory up to the level of Sylow’s theorems Nota de contenido: The alternating groups -- The classical groups -- The exceptional groups -- The sporadic groups En línea: http://dx.doi.org/10.1007/978-1-84800-988-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33982

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