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Título : H8-Optimal Control and Related Minimax Design Problems : A Dynamic Game Approach Tipo de documento: documento electrónico Autores: Tamer Basar ; SpringerLink (Online service) ; Pierre Bernhard Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2008 Otro editor: Imprint: Birkhäuser Colección: Modern Birkhäuser Classics, ISSN 2197-1803 Número de páginas: I, 412 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-4757-5 Idioma : Inglés (eng) Palabras clave: Mathematics Game theory System Calculus of variations Systems Theory, Control Economics, Social and Behav. Sciences Variations Optimal Control; Optimization Clasificación: 51 Matemáticas Resumen: "I believe that the authors have written a first-class book which can be used for a second or third year graduate level course in the subject... Researchers working in the area will certainly use the book as a standard reference... Given how well the book is written and organized, it is sure to become one of the major texts in the subject in the years to come, and it is highly recommended to both researchers working in the field, and those who want to learn about the subject." —SIAM Review (Review of the First Edition) "This book is devoted to one of the fastest developing fields in modern control theory---the so-called 'H-infinity optimal control theory'... In the authors' opinion 'the theory is now at a stage where it can easily be incorporated into a second-level graduate course in a control curriculum'. It seems that this book justifies this claim." —Mathematical Reviews (Review of the First Edition) "This work is a perfect and extensive research reference covering the state-space techniques for solving linear as well as nonlinear H-infinity control problems." —IEEE Transactions on Automatic Control (Review of the Second Edition) "The book, based mostly on recent work of the authors, is written on a good mathematical level. Many results in it are original, interesting, and inspirational...The book can be recommended to specialists and graduate students working in the development of control theory or using modern methods for controller design." —Mathematica Bohemica (Review of the Second Edition) "This book is a second edition of this very well-known text on H-infinity theory...This topic is central to modern control and hence this definitive book is highly recommended to anyone who wishes to catch up with this important theoretical development in applied mathematics and control." —Short Book Reviews (Review of the Second Edition) "The book can be recommended to mathematicians specializing in control theory and dynamic (differential) games. It can be also incorporated into a second-level graduate course in a control curriculum as no background in game theory is required." —Zentralblatt MATH (Review of the Second Edition) Nota de contenido: A General Introduction to Minimax (H?-Optimal) Designs -- Basic Elements of Static and Dynamic Games -- The Discrete-Time Minimax Design Problem with Perfect-State Measurements -- Continuous-Time Systems with Perfect-State Measurements -- The Continuous-Time Problem with Imperfect-State Measurements -- The Discrete-Time Problem with Imperfect-State Measurements -- Minimax Estimators and Performance Levels -- Robustness to Regular and Singular Perturbations -- Appendix A: Conjugate Points and Existence of Value -- Appendix B: Danskin’s Theorem En línea: http://dx.doi.org/10.1007/978-0-8176-4757-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34284 H8-Optimal Control and Related Minimax Design Problems : A Dynamic Game Approach [documento electrónico] / Tamer Basar ; SpringerLink (Online service) ; Pierre Bernhard . - Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2008 . - I, 412 p : online resource. - (Modern Birkhäuser Classics, ISSN 2197-1803) .
ISBN : 978-0-8176-4757-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Game theory System Calculus of variations Systems Theory, Control Economics, Social and Behav. Sciences Variations Optimal Control; Optimization Clasificación: 51 Matemáticas Resumen: "I believe that the authors have written a first-class book which can be used for a second or third year graduate level course in the subject... Researchers working in the area will certainly use the book as a standard reference... Given how well the book is written and organized, it is sure to become one of the major texts in the subject in the years to come, and it is highly recommended to both researchers working in the field, and those who want to learn about the subject." —SIAM Review (Review of the First Edition) "This book is devoted to one of the fastest developing fields in modern control theory---the so-called 'H-infinity optimal control theory'... In the authors' opinion 'the theory is now at a stage where it can easily be incorporated into a second-level graduate course in a control curriculum'. It seems that this book justifies this claim." —Mathematical Reviews (Review of the First Edition) "This work is a perfect and extensive research reference covering the state-space techniques for solving linear as well as nonlinear H-infinity control problems." —IEEE Transactions on Automatic Control (Review of the Second Edition) "The book, based mostly on recent work of the authors, is written on a good mathematical level. Many results in it are original, interesting, and inspirational...The book can be recommended to specialists and graduate students working in the development of control theory or using modern methods for controller design." —Mathematica Bohemica (Review of the Second Edition) "This book is a second edition of this very well-known text on H-infinity theory...This topic is central to modern control and hence this definitive book is highly recommended to anyone who wishes to catch up with this important theoretical development in applied mathematics and control." —Short Book Reviews (Review of the Second Edition) "The book can be recommended to mathematicians specializing in control theory and dynamic (differential) games. It can be also incorporated into a second-level graduate course in a control curriculum as no background in game theory is required." —Zentralblatt MATH (Review of the Second Edition) Nota de contenido: A General Introduction to Minimax (H?-Optimal) Designs -- Basic Elements of Static and Dynamic Games -- The Discrete-Time Minimax Design Problem with Perfect-State Measurements -- Continuous-Time Systems with Perfect-State Measurements -- The Continuous-Time Problem with Imperfect-State Measurements -- The Discrete-Time Problem with Imperfect-State Measurements -- Minimax Estimators and Performance Levels -- Robustness to Regular and Singular Perturbations -- Appendix A: Conjugate Points and Existence of Value -- Appendix B: Danskin’s Theorem En línea: http://dx.doi.org/10.1007/978-0-8176-4757-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34284 Ejemplares
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Título : Linear Differential Equations and Group Theory from Riemann to Poincaré Tipo de documento: documento electrónico Autores: Gray, Jeremy J. ; SpringerLink (Online service) Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2008 Colección: Modern Birkhäuser Classics, ISSN 2197-1803 Número de páginas: XX, 338 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-4773-5 Idioma : Inglés (eng) Palabras clave: Mathematics Group theory Functional analysis Functions of complex variables Differential equations Geometry History Analysis Mathematical Sciences Theory and Generalizations Ordinary Equations a Complex Variable Clasificación: 51 Matemáticas Resumen: This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and on-Euclidean geometry. The text for this second edition has been greatly expanded and revised, and the existing appendices enriched with historical accounts of the Riemann–Hilbert problem, the uniformization theorem, Picard–Vessiot theory, and the hypergeometric equation in higher dimensions. The exercises have been retained, making it possible to use the book as a companion to mathematics courses at the graduate level. "If you want to know what mathematicians like Gauss, Euler and Dirichlet were doing...this book could be for you. It fills in many historical gaps, in a story which is largely unknown...This book is the result of work done by a serious historian of mathematics...If you are intrigued by such topics studied years ago but now largely forgotten...then read this book."--The Mathematical Gazette (on the second edition) "One among the most interesting books on the history of mathematics... Very stimulating reading for both historians of modern mathematics and mathematicians as well."--Mathematical Reviews (on the first edition) "The book contains an amazing wealth of material relating to the algebra, geometry, and analysis of the nineteenth century.... Written with accurate historical perspective and clear exposition, this book is truly hard to put down."--Zentralblatt fur Mathematik (review of 1st edition) Nota de contenido: Hypergeometric Equations -- Lazarus Fuchs -- Algebraic Solutions to a Differential Equation -- Modular Equations -- Some Algebraic Curves -- Automorphic Functions En línea: http://dx.doi.org/10.1007/978-0-8176-4773-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34286 Linear Differential Equations and Group Theory from Riemann to Poincaré [documento electrónico] / Gray, Jeremy J. ; SpringerLink (Online service) . - Boston, MA : Birkhäuser Boston, 2008 . - XX, 338 p : online resource. - (Modern Birkhäuser Classics, ISSN 2197-1803) .
ISBN : 978-0-8176-4773-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Group theory Functional analysis Functions of complex variables Differential equations Geometry History Analysis Mathematical Sciences Theory and Generalizations Ordinary Equations a Complex Variable Clasificación: 51 Matemáticas Resumen: This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and on-Euclidean geometry. The text for this second edition has been greatly expanded and revised, and the existing appendices enriched with historical accounts of the Riemann–Hilbert problem, the uniformization theorem, Picard–Vessiot theory, and the hypergeometric equation in higher dimensions. The exercises have been retained, making it possible to use the book as a companion to mathematics courses at the graduate level. "If you want to know what mathematicians like Gauss, Euler and Dirichlet were doing...this book could be for you. It fills in many historical gaps, in a story which is largely unknown...This book is the result of work done by a serious historian of mathematics...If you are intrigued by such topics studied years ago but now largely forgotten...then read this book."--The Mathematical Gazette (on the second edition) "One among the most interesting books on the history of mathematics... Very stimulating reading for both historians of modern mathematics and mathematicians as well."--Mathematical Reviews (on the first edition) "The book contains an amazing wealth of material relating to the algebra, geometry, and analysis of the nineteenth century.... Written with accurate historical perspective and clear exposition, this book is truly hard to put down."--Zentralblatt fur Mathematik (review of 1st edition) Nota de contenido: Hypergeometric Equations -- Lazarus Fuchs -- Algebraic Solutions to a Differential Equation -- Modular Equations -- Some Algebraic Curves -- Automorphic Functions En línea: http://dx.doi.org/10.1007/978-0-8176-4773-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34286 Ejemplares
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Título : Mathematical Control Theory : An Introduction Tipo de documento: documento electrónico Autores: Jerzy Zabczyk ; SpringerLink (Online service) Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2008 Colección: Modern Birkhäuser Classics, ISSN 2197-1803 Número de páginas: X, 260 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-4733-9 Idioma : Inglés (eng) Palabras clave: Mathematics Applied mathematics Engineering System theory Calculus of variations Control engineering Robotics Mechatronics Systems Theory, Applications Variations and Optimal Control; Optimization Control, Robotics, Clasificación: 51 Matemáticas Resumen: Mathematical Control Theory: An Introduction presents, in a mathematically precise manner, a unified introduction to deterministic control theory. With the exception of a few more advanced concepts required for the final part of the book, the presentation requires only a knowledge of basic facts from linear algebra, differential equations, and calculus. In addition to classical concepts and ideas, the author covers the stabilization of nonlinear systems using topological methods, realization theory for nonlinear systems, impulsive control and positive systems, the control of rigid bodies, the stabilization of infinite dimensional systems, and the solution of minimum energy problems. The book will be ideal for a beginning graduate course in mathematical control theory, or for self study by professionals needing a complete picture of the mathematical theory that underlies the applications of control theory. "This book is designed as a graduate text on the mathematical theory of deterministic control. It covers a remarkable number of topics...The exposition is excellent, and the book is a joy to read. A novel one-semester course covering both linear and nonlinear systems could be given...The book is an excellent one for introducing a mathematician to control theory." — Bulletin of the AMS "The book is very well written from a mathematical point of view of control theory. The author deserves much credit for bringing out such a book which is a useful and welcome addition to books on the mathematics of control theory." — Control Theory and Advance Technology "At last! We did need an introductory textbook on control which can be read, understood, and enjoyed by anyone." — Gian-Carlo Rota, The Bulletin of Mathematics Books Nota de contenido: Elements of classical control theory -- Controllability and observability -- Stability and stabilizability -- Realization theory -- Systems with constraints -- Nonlinear control systems -- Controllability and observability of nonlinear systems -- Stability and stabilizability -- Realization theory -- Optimal control -- Dynamic programming -- Dynamic programming for impulse control -- The maximum principle -- The existence of optimal strategies -- Infinite dimensional linear systems -- Linear control systems -- Controllability -- Stability and stabilizability -- Linear regulators in Hilbert spaces En línea: http://dx.doi.org/10.1007/978-0-8176-4733-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34283 Mathematical Control Theory : An Introduction [documento electrónico] / Jerzy Zabczyk ; SpringerLink (Online service) . - Boston, MA : Birkhäuser Boston, 2008 . - X, 260 p : online resource. - (Modern Birkhäuser Classics, ISSN 2197-1803) .
ISBN : 978-0-8176-4733-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Applied mathematics Engineering System theory Calculus of variations Control engineering Robotics Mechatronics Systems Theory, Applications Variations and Optimal Control; Optimization Control, Robotics, Clasificación: 51 Matemáticas Resumen: Mathematical Control Theory: An Introduction presents, in a mathematically precise manner, a unified introduction to deterministic control theory. With the exception of a few more advanced concepts required for the final part of the book, the presentation requires only a knowledge of basic facts from linear algebra, differential equations, and calculus. In addition to classical concepts and ideas, the author covers the stabilization of nonlinear systems using topological methods, realization theory for nonlinear systems, impulsive control and positive systems, the control of rigid bodies, the stabilization of infinite dimensional systems, and the solution of minimum energy problems. The book will be ideal for a beginning graduate course in mathematical control theory, or for self study by professionals needing a complete picture of the mathematical theory that underlies the applications of control theory. "This book is designed as a graduate text on the mathematical theory of deterministic control. It covers a remarkable number of topics...The exposition is excellent, and the book is a joy to read. A novel one-semester course covering both linear and nonlinear systems could be given...The book is an excellent one for introducing a mathematician to control theory." — Bulletin of the AMS "The book is very well written from a mathematical point of view of control theory. The author deserves much credit for bringing out such a book which is a useful and welcome addition to books on the mathematics of control theory." — Control Theory and Advance Technology "At last! We did need an introductory textbook on control which can be read, understood, and enjoyed by anyone." — Gian-Carlo Rota, The Bulletin of Mathematics Books Nota de contenido: Elements of classical control theory -- Controllability and observability -- Stability and stabilizability -- Realization theory -- Systems with constraints -- Nonlinear control systems -- Controllability and observability of nonlinear systems -- Stability and stabilizability -- Realization theory -- Optimal control -- Dynamic programming -- Dynamic programming for impulse control -- The maximum principle -- The existence of optimal strategies -- Infinite dimensional linear systems -- Linear control systems -- Controllability -- Stability and stabilizability -- Linear regulators in Hilbert spaces En línea: http://dx.doi.org/10.1007/978-0-8176-4733-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34283 Ejemplares
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Título : Metric Structures for Riemannian and Non-Riemannian Spaces Tipo de documento: documento electrónico Autores: Mikhail (Misha) Gromov ; SpringerLink (Online service) Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2007 Colección: Modern Birkhäuser Classics, ISSN 2197-1803 Número de páginas: XX, 586 p. 100 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4583-0 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Measure theory Differential geometry Algebraic topology Manifolds Complex manifolds Geometry and Cell Complexes (incl. Diff.Topology) Topology Integration Clasificación: 51 Matemáticas Resumen: Metric theory has undergone a dramatic phase transition in the last decades when its focus moved from the foundations of real analysis to Riemannian geometry and algebraic topology, to the theory of infinite groups and probability theory. The new wave began with seminal papers by Svarc and Milnor on the growth of groups and the spectacular proof of the rigidity of lattices by Mostow. This progress was followed by the creation of the asymptotic metric theory of infinite groups by Gromov. The structural metric approach to the Riemannian category, tracing back to Cheeger's thesis, pivots around the notion of the Gromov–Hausdorff distance between Riemannian manifolds. This distance organizes Riemannian manifolds of all possible topological types into a single connected moduli space, where convergence allows the collapse of dimension with unexpectedly rich geometry, as revealed in the work of Cheeger, Fukaya, Gromov and Perelman. Also, Gromov found metric structure within homotopy theory and thus introduced new invariants controlling combinatorial complexity of maps and spaces, such as the simplicial volume, which is responsible for degrees of maps between manifolds. During the same period, Banach spaces and probability theory underwent a geometric metamorphosis, stimulated by the Levy–Milman concentration phenomenon, encompassing the law of large numbers for metric spaces with measures and dimensions going to infinity. The first stages of the new developments were presented in Gromov's course in Paris, which turned into the famous "Green Book" by Lafontaine and Pansu (1979). The present English translation of that work has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices—by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures—as well as an extensive bibliography and index round out this unique and beautiful book Nota de contenido: Preface to the French Edition -- Preface to the English Edition -- Introduction: Metrics Everywhere -- Length Structures: Path Metric Spaces -- Degree and Dilatation -- Metric Structures on Families of Metric Spaces -- Convergence and Concentration of Metrics and Measures -- Loewner Rediscovered -- Manifolds with Bounded Ricci Curvature -- Isoperimetric Inequalities and Amenability -- Morse Theory and Minimal Models -- Pinching and Collapse -- Appendix A: 'Quasiconvex' Domains in Rn -- Appendix B: Metric Spaces and Mappings Seen at Many Scales -- Appendix C: Paul Levy's Isoperimetric Inequality -- Appendix D: Systolically Free Manifolds -- Bibliography -- Glossary of Notation -- Index En línea: http://dx.doi.org/10.1007/978-0-8176-4583-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34561 Metric Structures for Riemannian and Non-Riemannian Spaces [documento electrónico] / Mikhail (Misha) Gromov ; SpringerLink (Online service) . - Boston, MA : Birkhäuser Boston, 2007 . - XX, 586 p. 100 illus : online resource. - (Modern Birkhäuser Classics, ISSN 2197-1803) .
ISBN : 978-0-8176-4583-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Measure theory Differential geometry Algebraic topology Manifolds Complex manifolds Geometry and Cell Complexes (incl. Diff.Topology) Topology Integration Clasificación: 51 Matemáticas Resumen: Metric theory has undergone a dramatic phase transition in the last decades when its focus moved from the foundations of real analysis to Riemannian geometry and algebraic topology, to the theory of infinite groups and probability theory. The new wave began with seminal papers by Svarc and Milnor on the growth of groups and the spectacular proof of the rigidity of lattices by Mostow. This progress was followed by the creation of the asymptotic metric theory of infinite groups by Gromov. The structural metric approach to the Riemannian category, tracing back to Cheeger's thesis, pivots around the notion of the Gromov–Hausdorff distance between Riemannian manifolds. This distance organizes Riemannian manifolds of all possible topological types into a single connected moduli space, where convergence allows the collapse of dimension with unexpectedly rich geometry, as revealed in the work of Cheeger, Fukaya, Gromov and Perelman. Also, Gromov found metric structure within homotopy theory and thus introduced new invariants controlling combinatorial complexity of maps and spaces, such as the simplicial volume, which is responsible for degrees of maps between manifolds. During the same period, Banach spaces and probability theory underwent a geometric metamorphosis, stimulated by the Levy–Milman concentration phenomenon, encompassing the law of large numbers for metric spaces with measures and dimensions going to infinity. The first stages of the new developments were presented in Gromov's course in Paris, which turned into the famous "Green Book" by Lafontaine and Pansu (1979). The present English translation of that work has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices—by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures—as well as an extensive bibliography and index round out this unique and beautiful book Nota de contenido: Preface to the French Edition -- Preface to the English Edition -- Introduction: Metrics Everywhere -- Length Structures: Path Metric Spaces -- Degree and Dilatation -- Metric Structures on Families of Metric Spaces -- Convergence and Concentration of Metrics and Measures -- Loewner Rediscovered -- Manifolds with Bounded Ricci Curvature -- Isoperimetric Inequalities and Amenability -- Morse Theory and Minimal Models -- Pinching and Collapse -- Appendix A: 'Quasiconvex' Domains in Rn -- Appendix B: Metric Spaces and Mappings Seen at Many Scales -- Appendix C: Paul Levy's Isoperimetric Inequality -- Appendix D: Systolically Free Manifolds -- Bibliography -- Glossary of Notation -- Index En línea: http://dx.doi.org/10.1007/978-0-8176-4583-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34561 Ejemplares
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Título : Prime Numbers and Computer Methods for Factorization Tipo de documento: documento electrónico Autores: Hans Riesel ; SpringerLink (Online service) Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2012 Otro editor: Imprint: Birkhäuser Colección: Modern Birkhäuser Classics, ISSN 2197-1803 Número de páginas: XVIII, 464 p. 20 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-8298-9 Idioma : Inglés (eng) Palabras clave: Mathematics Data encryption (Computer science) Applied mathematics Engineering Algorithms Number theory Theory Encryption Applications of Mathematics, general Clasificación: 51 Matemáticas Resumen: Published in the mid 1980s, the highly successful first edition of this title investigated the mathematical underpinnings of computer encryption, a discipline drawing heavily on the factorization of large numbers into primes. The book served a broad audience of researchers, students, practitioners of cryptography, and non-scientific readers with a mathematical inclination, treating four fundamental problems: the number of primes below a given limit, the approximate number of primes, the recognition of primes, and the factorization of large numbers. The second edition of the work, released in the mid 1990s, expanded significantly upon the original book, including important advances in computational prime number theory and factorization, as well as revised and updated tables. With explicit algorithms and computer programs, the author illustrated applications while attempting to discuss many classically important results along with more modern discoveries. Although it has been over a decade since the publication of this second edition, the theory it contained remains still highly relevant, and the particular cryptosystem it addressed (RSA public-key) is ubiquitous. Therefore, in addition to providing a historical perspective on many of the issues in modern prime number theory and data encryption, this soft cover version—which reproduces the second edition exactly as it originally appeared—offers affordable access to a great deal of valuable information. Highly readable for a wide variety of mathematicians, students of applied number theory, and others, this modern classic will be of interest to anyone involved in the study of number theory and cryptography. Reviews: Here is an outstanding technical monograph on recursive number theory and its numerous automated techniques. It successfully passes a critical milestone not allowed to many books, viz., a second edition... All in all, this handy volume continues to be an attractive combination of number-theoretic precision, practicality, and theory with a rich blend of computer science. —Zentralblatt MATH The book...is an enthusiastic introduction to some of the ideas concerned with primes and factorization. It should be of interest to anyone who would like to learn about the use of computers in number theory. —Mathematical Reviews Nota de contenido: Preface -- The Number of Primes Below a Given Limit -- The Primes Viewed at Large -- Subtleties in the Distribution of Primes -- The Recognition of Primes -- Classical Methods of Factorization -- Modern Factorization Methods -- Prime Numbers and Cryptography -- Appendix 1. Basic Concepts in Higher Algebra -- Appendix 2. Basic concepts in Higher Arithmetic -- Appendix 3. Quadratic Residues -- Appendix 4. The Arithmetic of Quadratic Fields -- Appendix 5. Higher Algebraic Number Fields -- Appendix 6. Algebraic Factors -- Appendix 7. Elliptic Curves -- Appendix 8. Continued Fractions -- Appendix 9. Multiple-Precision Arithmetic -- Appendix 10. Fast Multiplication of Large Integers -- Appendix 11. The Stieltjes Integral -- Tables -- List of Textbooks -- Index En línea: http://dx.doi.org/10.1007/978-0-8176-8298-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32688 Prime Numbers and Computer Methods for Factorization [documento electrónico] / Hans Riesel ; SpringerLink (Online service) . - Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2012 . - XVIII, 464 p. 20 illus : online resource. - (Modern Birkhäuser Classics, ISSN 2197-1803) .
ISBN : 978-0-8176-8298-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Data encryption (Computer science) Applied mathematics Engineering Algorithms Number theory Theory Encryption Applications of Mathematics, general Clasificación: 51 Matemáticas Resumen: Published in the mid 1980s, the highly successful first edition of this title investigated the mathematical underpinnings of computer encryption, a discipline drawing heavily on the factorization of large numbers into primes. The book served a broad audience of researchers, students, practitioners of cryptography, and non-scientific readers with a mathematical inclination, treating four fundamental problems: the number of primes below a given limit, the approximate number of primes, the recognition of primes, and the factorization of large numbers. The second edition of the work, released in the mid 1990s, expanded significantly upon the original book, including important advances in computational prime number theory and factorization, as well as revised and updated tables. With explicit algorithms and computer programs, the author illustrated applications while attempting to discuss many classically important results along with more modern discoveries. Although it has been over a decade since the publication of this second edition, the theory it contained remains still highly relevant, and the particular cryptosystem it addressed (RSA public-key) is ubiquitous. Therefore, in addition to providing a historical perspective on many of the issues in modern prime number theory and data encryption, this soft cover version—which reproduces the second edition exactly as it originally appeared—offers affordable access to a great deal of valuable information. Highly readable for a wide variety of mathematicians, students of applied number theory, and others, this modern classic will be of interest to anyone involved in the study of number theory and cryptography. Reviews: Here is an outstanding technical monograph on recursive number theory and its numerous automated techniques. It successfully passes a critical milestone not allowed to many books, viz., a second edition... All in all, this handy volume continues to be an attractive combination of number-theoretic precision, practicality, and theory with a rich blend of computer science. —Zentralblatt MATH The book...is an enthusiastic introduction to some of the ideas concerned with primes and factorization. It should be of interest to anyone who would like to learn about the use of computers in number theory. —Mathematical Reviews Nota de contenido: Preface -- The Number of Primes Below a Given Limit -- The Primes Viewed at Large -- Subtleties in the Distribution of Primes -- The Recognition of Primes -- Classical Methods of Factorization -- Modern Factorization Methods -- Prime Numbers and Cryptography -- Appendix 1. Basic Concepts in Higher Algebra -- Appendix 2. Basic concepts in Higher Arithmetic -- Appendix 3. Quadratic Residues -- Appendix 4. The Arithmetic of Quadratic Fields -- Appendix 5. Higher Algebraic Number Fields -- Appendix 6. Algebraic Factors -- Appendix 7. Elliptic Curves -- Appendix 8. Continued Fractions -- Appendix 9. Multiple-Precision Arithmetic -- Appendix 10. Fast Multiplication of Large Integers -- Appendix 11. The Stieltjes Integral -- Tables -- List of Textbooks -- Index En línea: http://dx.doi.org/10.1007/978-0-8176-8298-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32688 Ejemplares
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