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Título : Algebraic Function Fields and Codes Tipo de documento: documento electrónico Autores: Henning Stichtenoth ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2009 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 254 Número de páginas: XIV, 360 p Il.: online resource ISBN/ISSN/DL: 978-3-540-76878-4 Idioma : Inglés (eng) Palabras clave: Mathematics Data structures (Computer science) Algebra Algebraic geometry Information theory Applied mathematics Engineering Geometry Structures, Cryptology and Theory Communication, Circuits Appl.Mathematics/Computational Methods of Clasificación: 51 Matemáticas Resumen: The theory of algebraic function fields has its origins in number theory, complex analysis (compact Riemann surfaces), and algebraic geometry. Since about 1980, function fields have found surprising applications in other branches of mathematics such as coding theory, cryptography, sphere packings and others. The main objective of this book is to provide a purely algebraic, self-contained and in-depth exposition of the theory of function fields. This new edition, published in the series Graduate Texts in Mathematics, has been considerably expanded. Moreover, the present edition contains numerous exercises. Some of them are fairly easy and help the reader to understand the basic material. Other exercises are more advanced and cover additional material which could not be included in the text. This volume is mainly addressed to graduate students in mathematics and theoretical computer science, cryptography, coding theory and electrical engineering Nota de contenido: Foundations of the Theory of Algebraic Function Fields -- Algebraic Geometry Codes -- Extensions of Algebraic Function Fields -- Differentials of Algebraic Function Fields -- Algebraic Function Fields over Finite Constant Fields -- Examples of Algebraic Function Fields -- Asymptotic Bounds for the Number of Rational Places -- More about Algebraic Geometry Codes -- Subfield Subcodes and Trace Codes En línea: http://dx.doi.org/10.1007/978-3-540-76878-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34025 Algebraic Function Fields and Codes [documento electrónico] / Henning Stichtenoth ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2009 . - XIV, 360 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 254) .
ISBN : 978-3-540-76878-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Data structures (Computer science) Algebra Algebraic geometry Information theory Applied mathematics Engineering Geometry Structures, Cryptology and Theory Communication, Circuits Appl.Mathematics/Computational Methods of Clasificación: 51 Matemáticas Resumen: The theory of algebraic function fields has its origins in number theory, complex analysis (compact Riemann surfaces), and algebraic geometry. Since about 1980, function fields have found surprising applications in other branches of mathematics such as coding theory, cryptography, sphere packings and others. The main objective of this book is to provide a purely algebraic, self-contained and in-depth exposition of the theory of function fields. This new edition, published in the series Graduate Texts in Mathematics, has been considerably expanded. Moreover, the present edition contains numerous exercises. Some of them are fairly easy and help the reader to understand the basic material. Other exercises are more advanced and cover additional material which could not be included in the text. This volume is mainly addressed to graduate students in mathematics and theoretical computer science, cryptography, coding theory and electrical engineering Nota de contenido: Foundations of the Theory of Algebraic Function Fields -- Algebraic Geometry Codes -- Extensions of Algebraic Function Fields -- Differentials of Algebraic Function Fields -- Algebraic Function Fields over Finite Constant Fields -- Examples of Algebraic Function Fields -- Asymptotic Bounds for the Number of Rational Places -- More about Algebraic Geometry Codes -- Subfield Subcodes and Trace Codes En línea: http://dx.doi.org/10.1007/978-3-540-76878-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34025 Ejemplares
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Título : An Introduction to Markov Processes Tipo de documento: documento electrónico Autores: Daniel W. Stroock ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2005 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 230 Número de páginas: XIV, 178 p Il.: online resource ISBN/ISSN/DL: 978-3-540-26990-8 Idioma : Inglés (eng) Palabras clave: Mathematics Probabilities Probability Theory and Stochastic Processes Clasificación: 51 Matemáticas Resumen: To some extent, it would be accurate to summarize the contents of this book as an intolerably protracted description of what happens when either one raises a transition probability matrix P (i. e. , all entries (P)»j are n- negative and each row of P sums to 1) to higher and higher powers or one exponentiates R(P — I), where R is a diagonal matrix with non-negative entries. Indeed, when it comes right down to it, that is all that is done in this book. However, I, and others of my ilk, would take offense at such a dismissive characterization of the theory of Markov chains and processes with values in a countable state space, and a primary goal of mine in writing this book was to convince its readers that our offense would be warranted. The reason why I, and others of my persuasion, refuse to consider the theory here as no more than a subset of matrix theory is that to do so is to ignore the pervasive role that probability plays throughout. Namely, probability theory provides a model which both motivates and provides a context for what we are doing with these matrices. To wit, even the term "transition probability matrix" lends meaning to an otherwise rather peculiar set of hypotheses to make about a matrix Nota de contenido: Random Walks A Good Place to Begin -- Doeblin's Theory for Markov Chains -- More about the Ergodic Theory of Markov Chains -- Markov Processes in Continuous Time -- Reversible Markov Processes -- Some Mild Measure Theory En línea: http://dx.doi.org/10.1007/b138428 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35265 An Introduction to Markov Processes [documento electrónico] / Daniel W. Stroock ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2005 . - XIV, 178 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 230) .
ISBN : 978-3-540-26990-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Probabilities Probability Theory and Stochastic Processes Clasificación: 51 Matemáticas Resumen: To some extent, it would be accurate to summarize the contents of this book as an intolerably protracted description of what happens when either one raises a transition probability matrix P (i. e. , all entries (P)»j are n- negative and each row of P sums to 1) to higher and higher powers or one exponentiates R(P — I), where R is a diagonal matrix with non-negative entries. Indeed, when it comes right down to it, that is all that is done in this book. However, I, and others of my ilk, would take offense at such a dismissive characterization of the theory of Markov chains and processes with values in a countable state space, and a primary goal of mine in writing this book was to convince its readers that our offense would be warranted. The reason why I, and others of my persuasion, refuse to consider the theory here as no more than a subset of matrix theory is that to do so is to ignore the pervasive role that probability plays throughout. Namely, probability theory provides a model which both motivates and provides a context for what we are doing with these matrices. To wit, even the term "transition probability matrix" lends meaning to an otherwise rather peculiar set of hypotheses to make about a matrix Nota de contenido: Random Walks A Good Place to Begin -- Doeblin's Theory for Markov Chains -- More about the Ergodic Theory of Markov Chains -- Markov Processes in Continuous Time -- Reversible Markov Processes -- Some Mild Measure Theory En línea: http://dx.doi.org/10.1007/b138428 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35265 Ejemplares
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Título : Combinatorics of Coxeter Groups Tipo de documento: documento electrónico Autores: Anders Bjorner ; SpringerLink (Online service) ; Francesco Brenti Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2005 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 231 Número de páginas: XIV, 366 p Il.: online resource ISBN/ISSN/DL: 978-3-540-27596-1 Idioma : Inglés (eng) Palabras clave: Mathematics Group theory Topological groups Lie Combinatorics Groups, Groups Theory and Generalizations Clasificación: 51 Matemáticas Resumen: Coxeter groups are of central importance in several areas of algebra, geometry, and combinatorics. This clear and rigorous exposition focuses on the combinatorial aspects of Coxeter groups, such as reduced expressions, partial order of group elements, enumeration, associated graphs and combinatorial cell complexes, and connections with combinatorial representation theory. While Coxeter groups have already been exposited from algebraic and geometric perspectives, this text is the first one to focus mainly on the combinatorial aspects of Coxeter groups. The first part of the book provides a self-contained introduction to combinatorial Coxeter group theory. The emphasis here is on the combinatorics of reduced decompositions, Bruhat order, weak order, and some aspects of root systems. The second part deals with more advanced topics, such as Kazhdan-Lusztig polynomials and representations, enumeration, and combinatorial descriptions of the classical finite and affine Weyl groups. A wide variety of exercises, ranging from easy to quite difficult are also included. The book will serve graduate students as well as researchers. Anders Björner is Professor of Mathematics at the Royal Institute of Technology in Stockholm, Sweden. Francesco Brenti is Professor of Mathematics at the University of Rome Nota de contenido: I -- The basics -- Bruhat order -- Weak order and reduced words -- Roots, games, and automata -- II -- Kazhdan-Lusztig and R-polynomials -- Kazhdan-Lusztig representations -- Enumeration -- Combinatorial Descriptions En línea: http://dx.doi.org/10.1007/3-540-27596-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35283 Combinatorics of Coxeter Groups [documento electrónico] / Anders Bjorner ; SpringerLink (Online service) ; Francesco Brenti . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2005 . - XIV, 366 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 231) .
ISBN : 978-3-540-27596-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Group theory Topological groups Lie Combinatorics Groups, Groups Theory and Generalizations Clasificación: 51 Matemáticas Resumen: Coxeter groups are of central importance in several areas of algebra, geometry, and combinatorics. This clear and rigorous exposition focuses on the combinatorial aspects of Coxeter groups, such as reduced expressions, partial order of group elements, enumeration, associated graphs and combinatorial cell complexes, and connections with combinatorial representation theory. While Coxeter groups have already been exposited from algebraic and geometric perspectives, this text is the first one to focus mainly on the combinatorial aspects of Coxeter groups. The first part of the book provides a self-contained introduction to combinatorial Coxeter group theory. The emphasis here is on the combinatorics of reduced decompositions, Bruhat order, weak order, and some aspects of root systems. The second part deals with more advanced topics, such as Kazhdan-Lusztig polynomials and representations, enumeration, and combinatorial descriptions of the classical finite and affine Weyl groups. A wide variety of exercises, ranging from easy to quite difficult are also included. The book will serve graduate students as well as researchers. Anders Björner is Professor of Mathematics at the Royal Institute of Technology in Stockholm, Sweden. Francesco Brenti is Professor of Mathematics at the University of Rome Nota de contenido: I -- The basics -- Bruhat order -- Weak order and reduced words -- Roots, games, and automata -- II -- Kazhdan-Lusztig and R-polynomials -- Kazhdan-Lusztig representations -- Enumeration -- Combinatorial Descriptions En línea: http://dx.doi.org/10.1007/3-540-27596-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35283 Ejemplares
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Título : A Course in Commutative Algebra Tipo de documento: documento electrónico Autores: Gregor Kemper ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2011 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 256 Número de páginas: XII, 248 p Il.: online resource ISBN/ISSN/DL: 978-3-642-03545-6 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic geometry Commutative algebra rings Computer mathematics Geometry Rings and Algebras Computational Numerical Analysis Clasificación: 51 Matemáticas Resumen: This textbook offers a thorough, modern introduction into commutative algebra. It is intented mainly to serve as a guide for a course of one or two semesters, or for self-study. The carefully selected subject matter concentrates on the concepts and results at the center of the field. The book maintains a constant view on the natural geometric context, enabling the reader to gain a deeper understanding of the material. Although it emphasizes theory, three chapters are devoted to computational aspects. Many illustrative examples and exercises enrich the text Nota de contenido: Introduction -- Part I The Algebra Geometry Lexicon: 1 Hilbert's Nullstellensatz; 2 Noetherian and Artinian Rings; 3 The Zariski Topology; 4 A Summary of the Lexicon -- Part II Dimension: 5 Krull Dimension and Transcendence Degree; 6 Localization; 7 The Principal Ideal Theorem; 8 Integral Extensions -- Part III Computational Methods: 9 Gröbner Bases; 10 Fibers and Images of Morphisms Revisited; 11 Hilbert Series and Dimension -- Part IV Local Rings: 12 Dimension Theory; 13 Regular Local Rings; 14 Rings of Dimension One -- References -- Notation -- Index En línea: http://dx.doi.org/10.1007/978-3-642-03545-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33278 A Course in Commutative Algebra [documento electrónico] / Gregor Kemper ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2011 . - XII, 248 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 256) .
ISBN : 978-3-642-03545-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic geometry Commutative algebra rings Computer mathematics Geometry Rings and Algebras Computational Numerical Analysis Clasificación: 51 Matemáticas Resumen: This textbook offers a thorough, modern introduction into commutative algebra. It is intented mainly to serve as a guide for a course of one or two semesters, or for self-study. The carefully selected subject matter concentrates on the concepts and results at the center of the field. The book maintains a constant view on the natural geometric context, enabling the reader to gain a deeper understanding of the material. Although it emphasizes theory, three chapters are devoted to computational aspects. Many illustrative examples and exercises enrich the text Nota de contenido: Introduction -- Part I The Algebra Geometry Lexicon: 1 Hilbert's Nullstellensatz; 2 Noetherian and Artinian Rings; 3 The Zariski Topology; 4 A Summary of the Lexicon -- Part II Dimension: 5 Krull Dimension and Transcendence Degree; 6 Localization; 7 The Principal Ideal Theorem; 8 Integral Extensions -- Part III Computational Methods: 9 Gröbner Bases; 10 Fibers and Images of Morphisms Revisited; 11 Hilbert Series and Dimension -- Part IV Local Rings: 12 Dimension Theory; 13 Regular Local Rings; 14 Rings of Dimension One -- References -- Notation -- Index En línea: http://dx.doi.org/10.1007/978-3-642-03545-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33278 Ejemplares
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Título : A Course in Enumeration Tipo de documento: documento electrónico Autores: Martin Aigner ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2007 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 238 Número de páginas: X, 565 p. 55 illus Il.: online resource ISBN/ISSN/DL: 978-3-540-39035-0 Idioma : Inglés (eng) Palabras clave: Mathematics Computer science Algebra Combinatorics Physics Theoretical, Mathematical and Computational Discrete in Science Clasificación: 51 Matemáticas Resumen: Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from the basic notions to a variety of topics, ranging from algebra to statistical physics. Its aim is to introduce the student to a fascinating field, and to be a source of information for the professional mathematician who wants to learn more about the subject. The book is organized in three parts: Basics, Methods, and Topics. There are 666 exercises, and as a special feature every chapter ends with a highlight, discussing a particularly beautiful or famous result Nota de contenido: Basics -- Fundamental Coefficients -- Formal Series and Infinite Matrices -- Methods -- Generating Functions -- Hypergeometric Summation -- Sieve Methods -- Enumeration of Patterns -- Topics -- The Catalan Connection -- Symmetric Functions -- Counting Polynomials -- Models from Statistical Physics En línea: http://dx.doi.org/10.1007/978-3-540-39035-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34632 A Course in Enumeration [documento electrónico] / Martin Aigner ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2007 . - X, 565 p. 55 illus : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 238) .
ISBN : 978-3-540-39035-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Computer science Algebra Combinatorics Physics Theoretical, Mathematical and Computational Discrete in Science Clasificación: 51 Matemáticas Resumen: Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from the basic notions to a variety of topics, ranging from algebra to statistical physics. Its aim is to introduce the student to a fascinating field, and to be a source of information for the professional mathematician who wants to learn more about the subject. The book is organized in three parts: Basics, Methods, and Topics. There are 666 exercises, and as a special feature every chapter ends with a highlight, discussing a particularly beautiful or famous result Nota de contenido: Basics -- Fundamental Coefficients -- Formal Series and Infinite Matrices -- Methods -- Generating Functions -- Hypergeometric Summation -- Sieve Methods -- Enumeration of Patterns -- Topics -- The Catalan Connection -- Symmetric Functions -- Counting Polynomials -- Models from Statistical Physics En línea: http://dx.doi.org/10.1007/978-3-540-39035-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34632 Ejemplares
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