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Título : Abstract Algebra Tipo de documento: documento electrónico Autores: Pierre Antoine Grillet ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2007 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 242 Número de páginas: XII, 674 p Il.: online resource ISBN/ISSN/DL: 978-0-387-71568-1 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Associative rings Rings (Algebra) Group theory and Algebras Theory Generalizations Clasificación: 51 Matemáticas Resumen: "Abstract Algebra" is a clearly written, self-contained basic algebra text for graduate students, with a generous amount of additional material that suggests the scope of contemporary algebra. The first chapters blend standard contents with a careful introduction to proofs with arrows. The last chapters, on universal algebras and categories, including tripleability, give valuable general views of algebra. There are over 1400 exercises, at varying degrees of difficulty. For the new edition, the author has completely rewritten the entire text, streamlining the first chapters for rapid access to Galois theory, removing some material, and adding introductions to Groebner bases, Ext and Tor, and other topics. From a review of the First Edition: ...combines an exceptionally accessible discussion of the basic material with a just as thorough and well-organized treatment of the many additional (advanced) topics included.... represents an outstanding introduction to modern abstract algebra as a whole, with many unique features. It captivates the reader by its remarkable diversity, comprehensiveness, elegant succinctness, and coherence. - Werner Kleinert, Zentralblatt Nota de contenido: Groups -- Structure of Groups -- Rings -- Field Extensions -- Galois Theory -- Fields with Orders or Valuations -- Commutative Rings -- Modules -- Semisimple Rings and Modules -- Projectives and Injectives -- Constructions -- Ext and Tor -- Algebras -- Lattices -- Universal Algebra -- Categories En línea: http://dx.doi.org/10.1007/978-0-387-71568-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34527 Abstract Algebra [documento electrónico] / Pierre Antoine Grillet ; SpringerLink (Online service) . - New York, NY : Springer New York, 2007 . - XII, 674 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 242) .
ISBN : 978-0-387-71568-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Associative rings Rings (Algebra) Group theory and Algebras Theory Generalizations Clasificación: 51 Matemáticas Resumen: "Abstract Algebra" is a clearly written, self-contained basic algebra text for graduate students, with a generous amount of additional material that suggests the scope of contemporary algebra. The first chapters blend standard contents with a careful introduction to proofs with arrows. The last chapters, on universal algebras and categories, including tripleability, give valuable general views of algebra. There are over 1400 exercises, at varying degrees of difficulty. For the new edition, the author has completely rewritten the entire text, streamlining the first chapters for rapid access to Galois theory, removing some material, and adding introductions to Groebner bases, Ext and Tor, and other topics. From a review of the First Edition: ...combines an exceptionally accessible discussion of the basic material with a just as thorough and well-organized treatment of the many additional (advanced) topics included.... represents an outstanding introduction to modern abstract algebra as a whole, with many unique features. It captivates the reader by its remarkable diversity, comprehensiveness, elegant succinctness, and coherence. - Werner Kleinert, Zentralblatt Nota de contenido: Groups -- Structure of Groups -- Rings -- Field Extensions -- Galois Theory -- Fields with Orders or Valuations -- Commutative Rings -- Modules -- Semisimple Rings and Modules -- Projectives and Injectives -- Constructions -- Ext and Tor -- Algebras -- Lattices -- Universal Algebra -- Categories En línea: http://dx.doi.org/10.1007/978-0-387-71568-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34527 Ejemplares
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Título : Advanced Linear Algebra Tipo de documento: documento electrónico Autores: Steven Roman ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2005 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 135 Número de páginas: XVI, 486 p. 18 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-27474-4 Idioma : Inglés (eng) Palabras clave: Mathematics Matrix theory Algebra Linear and Multilinear Algebras, Theory Clasificación: 51 Matemáticas Resumen: This is a graduate textbook covering an especially broad range of topics. The first part of the book contains a careful but rapid discussion of the basics of linear algebra, including vector spaces, linear transformations, quotient spaces, and isomorphism theorems. The author then proceeds to modules, emphasizing a comparison with vector spaces. A thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory follows, culminating in the finite dimensional spectral theorem for normal operators. The second part of the book is a collection of topics, including metric vector spaces, metric spaces, Hilbert spaces, tensor products, and affine geometry. The last chapter discusses the umbral calculus, an area of modern algebra with many important applications. The new edition has been thoroughly rewritten, both in the text and exercise sets, and contains new chapters on convexity and separation, positive solutions to linear systems, singular values and QR decompostion. Treatments of tensor products and the umbral calculus have been greatly expanded and discussions of determinants, complexification of a real vector space, Schur's lemma and Gersgorin disks have been added. The author is Emeritus Professor of Mathematics, having taught at a number of universities, including MIT, UC Santa Barabara, the University of South Florida, the California State University at Fullerton and UC Irvine. He has written 27 books in mathematics at various levels and 9 books on computing. His interests lie mostly in the areas of algebra, set theory and logic, probability and finance Nota de contenido: Preliminaries -- Preliminaries -- Basic Linear Algebra -- Vector Spaces -- Linear Transformations -- The Isomorphism Theorems -- Modules I: Basic Properties -- Modules II: Free and Noetherian Modules -- Modules over a Principal Ideal Domain -- The Structure of a Linear Operator -- Eigenvalues and Eigenvectors -- Real and Complex Inner Product Spaces -- Structure Theory for Normal Operators -- Topics -- Metric Vector Spaces: The Theory of Bilinear Forms -- Metric Spaces -- Hilbert Spaces -- Tensor Products -- Positive Solutions to Linear Systems: Convexity and Separation -- Affine Geometry -- Operator Factorizations: QR and Singular Value -- The Umbral Calculus En línea: http://dx.doi.org/10.1007/0-387-27474-X Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35120 Advanced Linear Algebra [documento electrónico] / Steven Roman ; SpringerLink (Online service) . - New York, NY : Springer New York, 2005 . - XVI, 486 p. 18 illus : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 135) .
ISBN : 978-0-387-27474-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Matrix theory Algebra Linear and Multilinear Algebras, Theory Clasificación: 51 Matemáticas Resumen: This is a graduate textbook covering an especially broad range of topics. The first part of the book contains a careful but rapid discussion of the basics of linear algebra, including vector spaces, linear transformations, quotient spaces, and isomorphism theorems. The author then proceeds to modules, emphasizing a comparison with vector spaces. A thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory follows, culminating in the finite dimensional spectral theorem for normal operators. The second part of the book is a collection of topics, including metric vector spaces, metric spaces, Hilbert spaces, tensor products, and affine geometry. The last chapter discusses the umbral calculus, an area of modern algebra with many important applications. The new edition has been thoroughly rewritten, both in the text and exercise sets, and contains new chapters on convexity and separation, positive solutions to linear systems, singular values and QR decompostion. Treatments of tensor products and the umbral calculus have been greatly expanded and discussions of determinants, complexification of a real vector space, Schur's lemma and Gersgorin disks have been added. The author is Emeritus Professor of Mathematics, having taught at a number of universities, including MIT, UC Santa Barabara, the University of South Florida, the California State University at Fullerton and UC Irvine. He has written 27 books in mathematics at various levels and 9 books on computing. His interests lie mostly in the areas of algebra, set theory and logic, probability and finance Nota de contenido: Preliminaries -- Preliminaries -- Basic Linear Algebra -- Vector Spaces -- Linear Transformations -- The Isomorphism Theorems -- Modules I: Basic Properties -- Modules II: Free and Noetherian Modules -- Modules over a Principal Ideal Domain -- The Structure of a Linear Operator -- Eigenvalues and Eigenvectors -- Real and Complex Inner Product Spaces -- Structure Theory for Normal Operators -- Topics -- Metric Vector Spaces: The Theory of Bilinear Forms -- Metric Spaces -- Hilbert Spaces -- Tensor Products -- Positive Solutions to Linear Systems: Convexity and Separation -- Affine Geometry -- Operator Factorizations: QR and Singular Value -- The Umbral Calculus En línea: http://dx.doi.org/10.1007/0-387-27474-X Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35120 Ejemplares
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Título : Advanced Linear Algebra Tipo de documento: documento electrónico Autores: Steven Roman ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2008 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 135 Número de páginas: XVIII, 526 p Il.: online resource ISBN/ISSN/DL: 978-0-387-72831-5 Idioma : Inglés (eng) Palabras clave: Mathematics Matrix theory Algebra Linear and Multilinear Algebras, Theory Clasificación: 51 Matemáticas Resumen: For the third edition, the author has added a new chapter on associative algebras that includes the well known characterizations of the finite-dimensional division algebras over the real field (a theorem of Frobenius) and over a finite field (Wedderburn's theorem); polished and refined some arguments (such as the discussion of reflexivity, the rational canonical form, best approximations and the definitions of tensor products); upgraded some proofs that were originally done only for finite-dimensional/rank cases; added new theorems, including the spectral mapping theorem; considerably expanded the reference section with over a hundred references to books on linear algebra. From the reviews of the second edition: "In this 2nd edition, the author has rewritten the entire book and has added more than 100 pages of new materials....As in the previous edition, the text is well written and gives a thorough discussion of many topics of linear algebra and related fields...the exercises are rewritten and expanded....Overall, I found the book a very useful one....It is a suitable choice as a graduate text or as a reference book." Ali-Akbar Jafarian, ZentralblattMATH "This is a formidable volume, a compendium of linear algebra theory, classical and modern... The development of the subject is elegant...The proofs are neat...The exercise sets are good, with occasional hints given for the solution of trickier problems...It represents linear algebra and does so comprehensively." Henry Ricardo, MAA Online Nota de contenido: Basic Linear Algebra -- Vector Spaces -- Linear Transformations -- The Isomorphism Theorems -- Modules I: Basic Properties -- Modules II: Free and Noetherian Modules -- Modules over a Principal Ideal Domain -- The Structure of a Linear Operator -- Eigenvalues and Eigenvectors -- Real and Complex Inner Product Spaces -- Structure Theory for Normal Operators -- Topics -- Metric Vector Spaces: The Theory of Bilinear Forms -- Metric Spaces -- Hilbert Spaces -- Tensor Products -- Positive Solutions to Linear Systems: Convexity and Separation -- Affine Geometry -- Singular Values and the Moore–Penrose Inverse -- An Introduction to Algebras -- The Umbral Calculus En línea: http://dx.doi.org/10.1007/978-0-387-72831-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34171 Advanced Linear Algebra [documento electrónico] / Steven Roman ; SpringerLink (Online service) . - New York, NY : Springer New York, 2008 . - XVIII, 526 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 135) .
ISBN : 978-0-387-72831-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Matrix theory Algebra Linear and Multilinear Algebras, Theory Clasificación: 51 Matemáticas Resumen: For the third edition, the author has added a new chapter on associative algebras that includes the well known characterizations of the finite-dimensional division algebras over the real field (a theorem of Frobenius) and over a finite field (Wedderburn's theorem); polished and refined some arguments (such as the discussion of reflexivity, the rational canonical form, best approximations and the definitions of tensor products); upgraded some proofs that were originally done only for finite-dimensional/rank cases; added new theorems, including the spectral mapping theorem; considerably expanded the reference section with over a hundred references to books on linear algebra. From the reviews of the second edition: "In this 2nd edition, the author has rewritten the entire book and has added more than 100 pages of new materials....As in the previous edition, the text is well written and gives a thorough discussion of many topics of linear algebra and related fields...the exercises are rewritten and expanded....Overall, I found the book a very useful one....It is a suitable choice as a graduate text or as a reference book." Ali-Akbar Jafarian, ZentralblattMATH "This is a formidable volume, a compendium of linear algebra theory, classical and modern... The development of the subject is elegant...The proofs are neat...The exercise sets are good, with occasional hints given for the solution of trickier problems...It represents linear algebra and does so comprehensively." Henry Ricardo, MAA Online Nota de contenido: Basic Linear Algebra -- Vector Spaces -- Linear Transformations -- The Isomorphism Theorems -- Modules I: Basic Properties -- Modules II: Free and Noetherian Modules -- Modules over a Principal Ideal Domain -- The Structure of a Linear Operator -- Eigenvalues and Eigenvectors -- Real and Complex Inner Product Spaces -- Structure Theory for Normal Operators -- Topics -- Metric Vector Spaces: The Theory of Bilinear Forms -- Metric Spaces -- Hilbert Spaces -- Tensor Products -- Positive Solutions to Linear Systems: Convexity and Separation -- Affine Geometry -- Singular Values and the Moore–Penrose Inverse -- An Introduction to Algebras -- The Umbral Calculus En línea: http://dx.doi.org/10.1007/978-0-387-72831-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34171 Ejemplares
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Título : An Introduction to Operators on the Hardy-Hilbert Space Tipo de documento: documento electrónico Autores: Rubén A. Martínez-Avendaño ; SpringerLink (Online service) ; Peter Rosenthal Editorial: New York, NY : Springer New York Fecha de publicación: 2007 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 237 Número de páginas: XII, 220 p Il.: online resource ISBN/ISSN/DL: 978-0-387-48578-2 Idioma : Inglés (eng) Palabras clave: Mathematics Functional analysis Functions of complex variables Operator theory Theory Analysis a Complex Variable Clasificación: 51 Matemáticas Resumen: The subject of this book is operator theory on the Hardy space H2, also called the Hardy-Hilbert space. This is a popular area, partially because the Hardy-Hilbert space is the most natural setting for operator theory. A reader who masters the material covered in this book will have acquired a firm foundation for the study of all spaces of analytic functions and of operators on them. The goal is to provide an elementary and engaging introduction to this subject that will be readable by everyone who has understood introductory courses in complex analysis and in functional analysis. The exposition, blending techniques from "soft" and "hard" analysis, is intended to be as clear and instructive as possible. Many of the proofs are very elegant. This book evolved from a graduate course that was taught at the University of Toronto. It should prove suitable as a textbook for beginning graduate students, or even for well-prepared advanced undergraduates, as well as for independent study. There are numerous exercises at the end of each chapter, along with a brief guide for further study which includes references to applications to topics in engineering Nota de contenido: The Unilateral Shift and Factorization of Functions -- Toeplitz Operators -- Hankel Operators -- Composition Operators -- Further Reading En línea: http://dx.doi.org/10.1007/978-0-387-48578-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34477 An Introduction to Operators on the Hardy-Hilbert Space [documento electrónico] / Rubén A. Martínez-Avendaño ; SpringerLink (Online service) ; Peter Rosenthal . - New York, NY : Springer New York, 2007 . - XII, 220 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 237) .
ISBN : 978-0-387-48578-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Functional analysis Functions of complex variables Operator theory Theory Analysis a Complex Variable Clasificación: 51 Matemáticas Resumen: The subject of this book is operator theory on the Hardy space H2, also called the Hardy-Hilbert space. This is a popular area, partially because the Hardy-Hilbert space is the most natural setting for operator theory. A reader who masters the material covered in this book will have acquired a firm foundation for the study of all spaces of analytic functions and of operators on them. The goal is to provide an elementary and engaging introduction to this subject that will be readable by everyone who has understood introductory courses in complex analysis and in functional analysis. The exposition, blending techniques from "soft" and "hard" analysis, is intended to be as clear and instructive as possible. Many of the proofs are very elegant. This book evolved from a graduate course that was taught at the University of Toronto. It should prove suitable as a textbook for beginning graduate students, or even for well-prepared advanced undergraduates, as well as for independent study. There are numerous exercises at the end of each chapter, along with a brief guide for further study which includes references to applications to topics in engineering Nota de contenido: The Unilateral Shift and Factorization of Functions -- Toeplitz Operators -- Hankel Operators -- Composition Operators -- Further Reading En línea: http://dx.doi.org/10.1007/978-0-387-48578-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34477 Ejemplares
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Título : Analysis and Probability Wavelets, Signals, Fractals Tipo de documento: documento electrónico Autores: Palle E.T. Jorgensen ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2006 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 234 Número de páginas: XLVIII, 280 p Il.: online resource ISBN/ISSN/DL: 978-0-387-33082-2 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Applied mathematics Engineering Information theory Probabilities Probability Theory and Stochastic Processes Applications of Appl.Mathematics/Computational Methods Signal, Image Speech Processing Communication, Circuits Clasificación: 51 Matemáticas Resumen: This book, combining analysis and tools from mathematical probability, focuses on a systematic and novel presentation of recent trends in pure and applied mathematics: the emergence of three fields, wavelets, signals and fractals. The unity of basis constructions and their expansions is emphasized as the starting point for the development of bases that are computationally efficient for use in several areas from wavelets to fractals. The book brings together tools from engineering and math, especially from signal- and image processing, and from harmonic analysis and operator theory. The presentation is aimed at graduate students, as well as users from a diverse spectrum of applications. Key features: • A hands-on approach for students, including tutorials and numerous exercises; • Excellent motivation throughout; • New pedagogical features: glossary of terms, their use in mathematics and in engineering, help for cross-audiences, image processing, visual presentation of key algorithms, structure and geometry of big matrix computations, explanation of uses of the theory in applications outside of mathematics; • Includes more than 50 figures with captions, illustrating the main ideas, plus engineering diagrams, graphic renditions of algorithms, and separate illustrations; • Separate sections in the book explain engineering terms to mathematicians, and operator theory to engineers; • Each chapter concludes with a helpful guide to the literature allowing students to follow up on the topics in the book. Palle E.T. Jorgensen is a Professor of Mathematics at the University of Iowa. This book is based in part on interdisciplinary courses that he has taught over the last several years, and on his work with his current and former students. His most recent book was written jointly with Ola Bratteli and is entitled Wavelets through a Looking Glass, ©2002 Birkhäuser Boston Nota de contenido: Introduction: Measures on path space -- Transition probabilities: Random walk -- ?o vs. ? -- A case study: Duality for Cantor sets -- Infinite products -- The minimal eigenfunction -- Generalizations and applications -- Pyramids and operators -- Pairs of representations of the Cuntz algebras , and their application to multiresolutions En línea: http://dx.doi.org/10.1007/978-0-387-33082-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34802 Analysis and Probability Wavelets, Signals, Fractals [documento electrónico] / Palle E.T. Jorgensen ; SpringerLink (Online service) . - New York, NY : Springer New York, 2006 . - XLVIII, 280 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 234) .
ISBN : 978-0-387-33082-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Applied mathematics Engineering Information theory Probabilities Probability Theory and Stochastic Processes Applications of Appl.Mathematics/Computational Methods Signal, Image Speech Processing Communication, Circuits Clasificación: 51 Matemáticas Resumen: This book, combining analysis and tools from mathematical probability, focuses on a systematic and novel presentation of recent trends in pure and applied mathematics: the emergence of three fields, wavelets, signals and fractals. The unity of basis constructions and their expansions is emphasized as the starting point for the development of bases that are computationally efficient for use in several areas from wavelets to fractals. The book brings together tools from engineering and math, especially from signal- and image processing, and from harmonic analysis and operator theory. The presentation is aimed at graduate students, as well as users from a diverse spectrum of applications. Key features: • A hands-on approach for students, including tutorials and numerous exercises; • Excellent motivation throughout; • New pedagogical features: glossary of terms, their use in mathematics and in engineering, help for cross-audiences, image processing, visual presentation of key algorithms, structure and geometry of big matrix computations, explanation of uses of the theory in applications outside of mathematics; • Includes more than 50 figures with captions, illustrating the main ideas, plus engineering diagrams, graphic renditions of algorithms, and separate illustrations; • Separate sections in the book explain engineering terms to mathematicians, and operator theory to engineers; • Each chapter concludes with a helpful guide to the literature allowing students to follow up on the topics in the book. Palle E.T. Jorgensen is a Professor of Mathematics at the University of Iowa. This book is based in part on interdisciplinary courses that he has taught over the last several years, and on his work with his current and former students. His most recent book was written jointly with Ola Bratteli and is entitled Wavelets through a Looking Glass, ©2002 Birkhäuser Boston Nota de contenido: Introduction: Measures on path space -- Transition probabilities: Random walk -- ?o vs. ? -- A case study: Duality for Cantor sets -- Infinite products -- The minimal eigenfunction -- Generalizations and applications -- Pyramids and operators -- Pairs of representations of the Cuntz algebras , and their application to multiresolutions En línea: http://dx.doi.org/10.1007/978-0-387-33082-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34802 Ejemplares
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