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## Autor Knapp, Anthony W |

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Título : Advanced Algebra : Along with a companion volume Basic Algebra Tipo de documento: documento electrónico Autores: Knapp, Anthony W ; SpringerLink (Online service) Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2008 Otro editor: Imprint: Birkhäuser Colección: Cornerstones Número de páginas: XXV, 730 p. 46 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4613-4 Idioma : Inglés ( eng)Palabras clave: Mathematics Algebra Algebraic geometry Category theory (Mathematics) Homological algebra Field (Physics) Nonassociative rings Rings (Algebra) Number Non-associative and Algebras Theory Polynomials Geometry Theory, Clasificación: 51 Matemáticas Resumen: Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. Key topics and features of Advanced Algebra: *Topics build upon the linear algebra, group theory, factorization of ideals, structure of fields, Galois theory, and elementary theory of modules as developed in Basic Algebra *Chapters treat various topics in commutative and noncommutative algebra, providing introductions to the theory of associative algebras, homological algebra, algebraic number theory, and algebraic geometry *Sections in two chapters relate the theory to the subject of Gröbner bases, the foundation for handling systems of polynomial equations in computer applications *Text emphasizes connections between algebra and other branches of mathematics, particularly topology and complex analysis *Book carries on two prominent themes recurring in Basic Algebra: the analogy between integers and polynomials in one variable over a field, and the relationship between number theory and geometry *Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems *The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them; it includes blocks of problems that illuminate aspects of the text and introduce additional topics Advanced Algebra presents its subject matter in a forward-looking way that takes into account the historical development of the subject. It is suitable as a text for the more advanced parts of a two-semester first-year graduate sequence in algebra. It requires of the reader only a familiarity with the topics developed in Basic Algebra Nota de contenido: Transition to Modern Number Theory -- Wedderburn–Artin Ring Theory -- Brauer Group -- Homological Algebra -- Three Theorems in Algebraic Number Theory -- Reinterpretation with Adeles and Ideles -- Infinite Field Extensions -- Background for Algebraic Geometry -- The Number Theory of Algebraic Curves -- Methods of Algebraic Geometry En línea: http://dx.doi.org/10.1007/978-0-8176-4613-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34266 Advanced Algebra : Along with a companion volume Basic Algebra [documento electrónico] / Knapp, Anthony W ; SpringerLink (Online service) . - Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2008 . - XXV, 730 p. 46 illus : online resource. - (Cornerstones) .ISBN: 978-0-8176-4613-4

Idioma : Inglés (eng)

Palabras clave: Mathematics Algebra Algebraic geometry Category theory (Mathematics) Homological algebra Field (Physics) Nonassociative rings Rings (Algebra) Number Non-associative and Algebras Theory Polynomials Geometry Theory, Clasificación: 51 Matemáticas Resumen: Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. Key topics and features of Advanced Algebra: *Topics build upon the linear algebra, group theory, factorization of ideals, structure of fields, Galois theory, and elementary theory of modules as developed in Basic Algebra *Chapters treat various topics in commutative and noncommutative algebra, providing introductions to the theory of associative algebras, homological algebra, algebraic number theory, and algebraic geometry *Sections in two chapters relate the theory to the subject of Gröbner bases, the foundation for handling systems of polynomial equations in computer applications *Text emphasizes connections between algebra and other branches of mathematics, particularly topology and complex analysis *Book carries on two prominent themes recurring in Basic Algebra: the analogy between integers and polynomials in one variable over a field, and the relationship between number theory and geometry *Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems *The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them; it includes blocks of problems that illuminate aspects of the text and introduce additional topics Advanced Algebra presents its subject matter in a forward-looking way that takes into account the historical development of the subject. It is suitable as a text for the more advanced parts of a two-semester first-year graduate sequence in algebra. It requires of the reader only a familiarity with the topics developed in Basic Algebra Nota de contenido: Transition to Modern Number Theory -- Wedderburn–Artin Ring Theory -- Brauer Group -- Homological Algebra -- Three Theorems in Algebraic Number Theory -- Reinterpretation with Adeles and Ideles -- Infinite Field Extensions -- Background for Algebraic Geometry -- The Number Theory of Algebraic Curves -- Methods of Algebraic Geometry En línea: http://dx.doi.org/10.1007/978-0-8176-4613-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34266 ## Ejemplares

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Título : Advanced Real Analysis : Along with a companion volume Basic Real Analysis Tipo de documento: documento electrónico Autores: Knapp, Anthony W ; SpringerLink (Online service) Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2005 Colección: Cornerstones Número de páginas: XXIV, 466 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-4442-0 Idioma : Inglés ( eng)Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Fourier Functional Global Manifolds Partial differential equations Probabilities Differential Equations and on Probability Theory Stochastic Processes Clasificación: 51 Matemáticas Resumen: Basic Real Analysis and Advanced Real Analysis (available separately or together as a Set) systematically develop those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. These works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics. Key topics and features of Advanced Real Analysis: * Develops Fourier analysis and functional analysis with an eye toward partial differential equations * Includes chapters on Sturm–Liouville theory, compact self-adjoint operators, Euclidean Fourier analysis, topological vector spaces and distributions, compact and locally compact groups, and aspects of partial differential equations * Contains chapters about analysis on manifolds and foundations of probability * Proceeds from the particular to the general, often introducing examples well before a theory that incorporates them * Includes many examples and nearly two hundred problems, and a separate 45-page section gives hints or complete solutions for most of the problems * Incorporates, in the text and especially in the problems, material in which real analysis is used in algebra, in topology, in complex analysis, in probability, in differential geometry, and in applied mathematics of various kinds Advanced Real Analysis requires of the reader a first course in measure theory, including an introduction to the Fourier transform and to Hilbert and Banach spaces. Some familiarity with complex analysis is helpful for certain chapters. The book is suitable as a text in graduate courses such as Fourier and functional analysis, modern analysis, and partial differential equations. Because it focuses on what every young mathematician needs to know about real analysis, the book is ideal both as a course text and for self-study, especially for graduate students preparing for qualifying examinations. Its scope and approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, mathematical physics, and differential equations. Indeed, the clarity and breadth of Advanced Real Analysis make it a welcome addition to the personal library of every mathematician Nota de contenido: to Boundary-Value Problems -- Compact Self-Adjoint Operators -- Topics in Euclidean Fourier Analysis -- Topics in Functional Analysis -- Distributions -- Compact and Locally Compact Groups -- Aspects of Partial Differential Equations -- Analysis on Manifolds -- Foundations of Probability En línea: http://dx.doi.org/10.1007/0-8176-4442-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35192 Advanced Real Analysis : Along with a companion volume Basic Real Analysis [documento electrónico] / Knapp, Anthony W ; SpringerLink (Online service) . - Boston, MA : Birkhäuser Boston, 2005 . - XXIV, 466 p : online resource. - (Cornerstones) .ISBN: 978-0-8176-4442-0

Idioma : Inglés (eng)

Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Fourier Functional Global Manifolds Partial differential equations Probabilities Differential Equations and on Probability Theory Stochastic Processes Clasificación: 51 Matemáticas Resumen: Basic Real Analysis and Advanced Real Analysis (available separately or together as a Set) systematically develop those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. These works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics. Key topics and features of Advanced Real Analysis: * Develops Fourier analysis and functional analysis with an eye toward partial differential equations * Includes chapters on Sturm–Liouville theory, compact self-adjoint operators, Euclidean Fourier analysis, topological vector spaces and distributions, compact and locally compact groups, and aspects of partial differential equations * Contains chapters about analysis on manifolds and foundations of probability * Proceeds from the particular to the general, often introducing examples well before a theory that incorporates them * Includes many examples and nearly two hundred problems, and a separate 45-page section gives hints or complete solutions for most of the problems * Incorporates, in the text and especially in the problems, material in which real analysis is used in algebra, in topology, in complex analysis, in probability, in differential geometry, and in applied mathematics of various kinds Advanced Real Analysis requires of the reader a first course in measure theory, including an introduction to the Fourier transform and to Hilbert and Banach spaces. Some familiarity with complex analysis is helpful for certain chapters. The book is suitable as a text in graduate courses such as Fourier and functional analysis, modern analysis, and partial differential equations. Because it focuses on what every young mathematician needs to know about real analysis, the book is ideal both as a course text and for self-study, especially for graduate students preparing for qualifying examinations. Its scope and approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, mathematical physics, and differential equations. Indeed, the clarity and breadth of Advanced Real Analysis make it a welcome addition to the personal library of every mathematician Nota de contenido: to Boundary-Value Problems -- Compact Self-Adjoint Operators -- Topics in Euclidean Fourier Analysis -- Topics in Functional Analysis -- Distributions -- Compact and Locally Compact Groups -- Aspects of Partial Differential Equations -- Analysis on Manifolds -- Foundations of Probability En línea: http://dx.doi.org/10.1007/0-8176-4442-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35192 ## Ejemplares

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Título : Basic Algebra : Along with a companion volume Advanced Algebra Tipo de documento: documento electrónico Autores: Knapp, Anthony W ; SpringerLink (Online service) Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2006 Otro editor: Imprint: Birkhäuser Colección: Cornerstones Número de páginas: XXV, 735 p. 46 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4529-8 Idioma : Inglés ( eng)Palabras clave: Mathematics Algebra Associative rings Rings (Algebra) Commutative algebra Field theory (Physics) Group Matrix Linear and Multilinear Algebras, Theory Algebras Generalizations Polynomials Clasificación: 51 Matemáticas Resumen: Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. Key topics and features of Basic Algebra: *Linear algebra and group theory build on each other continually *Chapters on modern algebra treat groups, rings, fields, modules, and Galois groups, with emphasis on methods of computation throughout *Three prominent themes recur and blend together at times: the analogy between integers and polynomials in one variable over a field, the interplay between linear algebra and group theory, and the relationship between number theory and geometry *Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems *The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them; includes blocks of problems that introduce additional topics and applications for further study *Applications to science and engineering (e.g., the fast Fourier transform, the theory of error-correcting codes, the use of the Jordan canonical form in solving linear systems of ordinary differential equations, and constructions of interest in mathematical physics) appear in sequences of problems Basic Algebra presents the subject matter in a forward-looking way that takes into account its historical development. It is suitable as a text in a two-semester advanced undergraduate or first-year graduate sequence in algebra, possibly supplemented by some material from Advanced Algebra at the graduate level. It requires of the reader only familiarity with matrix algebra, an understanding of the geometry and reduction of linear equations, and an acquaintance with proofs Nota de contenido: Preliminaries about the Integers, Polynomials, and Matrices -- Vector Spaces over ?, ?, and ? -- Inner-Product Spaces -- Groups and Group Actions -- Theory of a Single Linear Transformation -- Multilinear Algebra -- Advanced Group Theory -- Commutative Rings and Their Modules -- Fields and Galois Theory -- Modules over Noncommutative Rings En línea: http://dx.doi.org/10.1007/978-0-8176-4529-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34882 Basic Algebra : Along with a companion volume Advanced Algebra [documento electrónico] / Knapp, Anthony W ; SpringerLink (Online service) . - Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2006 . - XXV, 735 p. 46 illus : online resource. - (Cornerstones) .ISBN: 978-0-8176-4529-8

Idioma : Inglés (eng)

Palabras clave: Mathematics Algebra Associative rings Rings (Algebra) Commutative algebra Field theory (Physics) Group Matrix Linear and Multilinear Algebras, Theory Algebras Generalizations Polynomials Clasificación: 51 Matemáticas Resumen: Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. Key topics and features of Basic Algebra: *Linear algebra and group theory build on each other continually *Chapters on modern algebra treat groups, rings, fields, modules, and Galois groups, with emphasis on methods of computation throughout *Three prominent themes recur and blend together at times: the analogy between integers and polynomials in one variable over a field, the interplay between linear algebra and group theory, and the relationship between number theory and geometry *Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems *The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them; includes blocks of problems that introduce additional topics and applications for further study *Applications to science and engineering (e.g., the fast Fourier transform, the theory of error-correcting codes, the use of the Jordan canonical form in solving linear systems of ordinary differential equations, and constructions of interest in mathematical physics) appear in sequences of problems Basic Algebra presents the subject matter in a forward-looking way that takes into account its historical development. It is suitable as a text in a two-semester advanced undergraduate or first-year graduate sequence in algebra, possibly supplemented by some material from Advanced Algebra at the graduate level. It requires of the reader only familiarity with matrix algebra, an understanding of the geometry and reduction of linear equations, and an acquaintance with proofs Nota de contenido: Preliminaries about the Integers, Polynomials, and Matrices -- Vector Spaces over ?, ?, and ? -- Inner-Product Spaces -- Groups and Group Actions -- Theory of a Single Linear Transformation -- Multilinear Algebra -- Advanced Group Theory -- Commutative Rings and Their Modules -- Fields and Galois Theory -- Modules over Noncommutative Rings En línea: http://dx.doi.org/10.1007/978-0-8176-4529-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34882 ## Ejemplares

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Título : Basic Real Analysis : Along with a companion volume Advanced Real Analysis Tipo de documento: documento electrónico Autores: Knapp, Anthony W ; SpringerLink (Online service) Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2005 Colección: Cornerstones Número de páginas: XXIV, 656 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-4441-3 Idioma : Inglés ( eng)Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Fourier Measure theory Differential equations Functions of real variables Topology and Integration Real Ordinary Equations Clasificación: 51 Matemáticas Resumen: Basic Real Analysis and Advanced Real Analysis (available separately or together as a Set) systematically develop those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. These works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics. Key topics and features of Basic Real Analysis: * Early chapters treat the fundamentals of real variables, sequences and series of functions, the theory of Fourier series for the Riemann integral, metric spaces, and the theoretical underpinnings of multivariable calculus and differential equations * Subsequent chapters develop the Lebesgue theory in Euclidean and abstract spaces, Fourier series and the Fourier transform for the Lebesgue integral, point-set topology, measure theory in locally compact Hausdorff spaces, and the basics of Hilbert and Banach spaces * The subjects of Fourier series and harmonic functions are used as recurring motivation for a number of theoretical developments * The development proceeds from the particular to the general, often introducing examples well before a theory that incorporates them * The text includes many examples and hundreds of problems, and a separate 55-page section gives hints or complete solutions for most of the problems Basic Real Analysis requires of the reader only familiarity with some linear algebra and real variable theory, the very beginning of group theory, and an acquaintance with proofs. It is suitable as a text in an advanced undergraduate course in real variable theory and in most basic graduate courses in Lebesgue integration and related topics. Because it focuses on what every young mathematician needs to know about real analysis, the book is ideal both as a course text and for self-study, especially for graduate students preparing for qualifying examinations. Its scope and approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, mathematical physics, and differential equations. Indeed, the clarity and breadth of Basic Real Analysis make it a welcome addition to the personal library of every mathematician Nota de contenido: Theory of Calculus in One Real Variable -- Metric Spaces -- Theory of Calculus in Several Real Variables -- Theory of Ordinary Differential Equations and Systems -- Lebesgue Measure and Abstract Measure Theory -- Measure Theory for Euclidean Space -- Differentiation of Lebesgue Integrals on the Line -- Fourier Transform in Euclidean Space -- Lp Spaces -- Topological Spaces -- Integration on Locally Compact Spaces -- Hilbert and Banach Spaces En línea: http://dx.doi.org/10.1007/0-8176-4441-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35191 Basic Real Analysis : Along with a companion volume Advanced Real Analysis [documento electrónico] / Knapp, Anthony W ; SpringerLink (Online service) . - Boston, MA : Birkhäuser Boston, 2005 . - XXIV, 656 p : online resource. - (Cornerstones) .ISBN: 978-0-8176-4441-3

Idioma : Inglés (eng)

Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Fourier Measure theory Differential equations Functions of real variables Topology and Integration Real Ordinary Equations Clasificación: 51 Matemáticas Resumen: Basic Real Analysis and Advanced Real Analysis (available separately or together as a Set) systematically develop those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. These works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics. Key topics and features of Basic Real Analysis: * Early chapters treat the fundamentals of real variables, sequences and series of functions, the theory of Fourier series for the Riemann integral, metric spaces, and the theoretical underpinnings of multivariable calculus and differential equations * Subsequent chapters develop the Lebesgue theory in Euclidean and abstract spaces, Fourier series and the Fourier transform for the Lebesgue integral, point-set topology, measure theory in locally compact Hausdorff spaces, and the basics of Hilbert and Banach spaces * The subjects of Fourier series and harmonic functions are used as recurring motivation for a number of theoretical developments * The development proceeds from the particular to the general, often introducing examples well before a theory that incorporates them * The text includes many examples and hundreds of problems, and a separate 55-page section gives hints or complete solutions for most of the problems Basic Real Analysis requires of the reader only familiarity with some linear algebra and real variable theory, the very beginning of group theory, and an acquaintance with proofs. It is suitable as a text in an advanced undergraduate course in real variable theory and in most basic graduate courses in Lebesgue integration and related topics. Because it focuses on what every young mathematician needs to know about real analysis, the book is ideal both as a course text and for self-study, especially for graduate students preparing for qualifying examinations. Its scope and approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, mathematical physics, and differential equations. Indeed, the clarity and breadth of Basic Real Analysis make it a welcome addition to the personal library of every mathematician Nota de contenido: Theory of Calculus in One Real Variable -- Metric Spaces -- Theory of Calculus in Several Real Variables -- Theory of Ordinary Differential Equations and Systems -- Lebesgue Measure and Abstract Measure Theory -- Measure Theory for Euclidean Space -- Differentiation of Lebesgue Integrals on the Line -- Fourier Transform in Euclidean Space -- Lp Spaces -- Topological Spaces -- Integration on Locally Compact Spaces -- Hilbert and Banach Spaces En línea: http://dx.doi.org/10.1007/0-8176-4441-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35191 ## Ejemplares

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