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Título : Functions, Spaces, and Expansions : Mathematical Tools in Physics and Engineering Tipo de documento: documento electrónico Autores: Ole Christensen ; SpringerLink (Online service) Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2010 Colección: Applied and Numerical Harmonic Analysis Número de páginas: XIX, 266 p. 9 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4980-7 Idioma : Inglés (eng) Palabras clave: Mathematics Fourier analysis Functional Special functions Mathematical models Physics Applied mathematics Engineering Modeling and Industrial Analysis Appl.Mathematics/Computational Methods of in Functions Clasificación: 51 Matemáticas Resumen: This graduate-level textbook is a detailed exposition of key mathematical tools in analysis aimed at students, researchers, and practitioners across science and engineering. Every topic covered has been specifically chosen because it plays a key role outside the field of pure mathematics. Although the treatment of each topic is mathematical in nature, and concrete applications are not delineated, the principles and tools presented are fundamental to exploring the computational aspects of physics and engineering. A central theme of the book is the structure of various vector spaces—most importantly, Hilbert spaces—and expansions of elements in these spaces in terms of bases. Key topics and features include: * More than 150 exercises * Abstract and normed vector spaces * Approximation in normed vector spaces * Hilbert and Banach spaces * General bases and orthonormal bases * Linear operators on various normed spaces * The Fourier transform, including the discrete Fourier transform * Wavelets and multiresolution analysis * B-splines * Sturm–Liouville problems As a textbook that provides a deep understanding of central issues in mathematical analysis, Functions, Spaces, and Expansions is intended for graduate students, researchers, and practitioners in applied mathematics, physics, and engineering. Readers are expected to have a solid understanding of linear algebra, in Rn and in general vector spaces. Familiarity with the basic concepts of calculus and real analysis, including Riemann integrals and infinite series of real or complex numbers, is also required. Functions, Spaces, and Expansions is the main textbook for the e-course Mathematics 4: Real Analysis currently being taught at the Technical University of Denmark. Please click the "Course Materials" link on the right to access videos of the lectures, problem sheets, and solutions to selected exercises Nota de contenido: Mathematical Background -- Normed Vector Spaces -- Banach Spaces -- Hilbert Spaces -- The Lp-spaces -- The Hilbert Space L2 -- The Fourier Transform -- An Introduction to Wavelet Analysis -- A Closer Look at Multiresolution Analysis -- B-splines -- Special Functions -- Appendix A -- Appendix B En línea: http://dx.doi.org/10.1007/978-0-8176-4980-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33564 Functions, Spaces, and Expansions : Mathematical Tools in Physics and Engineering [documento electrónico] / Ole Christensen ; SpringerLink (Online service) . - Boston : Birkhäuser Boston, 2010 . - XIX, 266 p. 9 illus : online resource. - (Applied and Numerical Harmonic Analysis) .
ISBN : 978-0-8176-4980-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Fourier analysis Functional Special functions Mathematical models Physics Applied mathematics Engineering Modeling and Industrial Analysis Appl.Mathematics/Computational Methods of in Functions Clasificación: 51 Matemáticas Resumen: This graduate-level textbook is a detailed exposition of key mathematical tools in analysis aimed at students, researchers, and practitioners across science and engineering. Every topic covered has been specifically chosen because it plays a key role outside the field of pure mathematics. Although the treatment of each topic is mathematical in nature, and concrete applications are not delineated, the principles and tools presented are fundamental to exploring the computational aspects of physics and engineering. A central theme of the book is the structure of various vector spaces—most importantly, Hilbert spaces—and expansions of elements in these spaces in terms of bases. Key topics and features include: * More than 150 exercises * Abstract and normed vector spaces * Approximation in normed vector spaces * Hilbert and Banach spaces * General bases and orthonormal bases * Linear operators on various normed spaces * The Fourier transform, including the discrete Fourier transform * Wavelets and multiresolution analysis * B-splines * Sturm–Liouville problems As a textbook that provides a deep understanding of central issues in mathematical analysis, Functions, Spaces, and Expansions is intended for graduate students, researchers, and practitioners in applied mathematics, physics, and engineering. Readers are expected to have a solid understanding of linear algebra, in Rn and in general vector spaces. Familiarity with the basic concepts of calculus and real analysis, including Riemann integrals and infinite series of real or complex numbers, is also required. Functions, Spaces, and Expansions is the main textbook for the e-course Mathematics 4: Real Analysis currently being taught at the Technical University of Denmark. Please click the "Course Materials" link on the right to access videos of the lectures, problem sheets, and solutions to selected exercises Nota de contenido: Mathematical Background -- Normed Vector Spaces -- Banach Spaces -- Hilbert Spaces -- The Lp-spaces -- The Hilbert Space L2 -- The Fourier Transform -- An Introduction to Wavelet Analysis -- A Closer Look at Multiresolution Analysis -- B-splines -- Special Functions -- Appendix A -- Appendix B En línea: http://dx.doi.org/10.1007/978-0-8176-4980-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33564 Ejemplares
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Título : Mathematical Systems Theory I : Modelling, State Space Analysis, Stability and Robustness Tipo de documento: documento electrónico Autores: Diederich Hinrichsen ; SpringerLink (Online service) ; Anthony J. Pritchard Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2005 Colección: Texts in Applied Mathematics, ISSN 0939-2475 num. 48 Número de páginas: XVI, 804 p. 180 illus Il.: online resource ISBN/ISSN/DL: 978-3-540-26410-1 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Dynamics Ergodic theory System Calculus of variations Complexity, Computational Systems Theory, Control Dynamical and Theory Variations Optimal Control; Optimization Complexity Clasificación: 51 Matemáticas Resumen: This book presents the mathematical foundations of systems theory in a self-contained, comprehensive, detailed and mathematically rigorous way. This first volume is devoted to the analysis of dynamical systems with emphasis on problems of uncertainty, whereas the second volume will be devoted to control. It combines features of a detailed introductory textbook with that of a reference source. The book contains many examples and figures illustrating the text which help to bring out the intuitive ideas behind the mathematical constructions. It is accessible to mathematics students after two years of mathematics and graduate engineering students specializing in mathematical systems theory. The reader is gradually brought to the frontiers of research in stability and robustness analysis. As such the book will be useful for established researchers in systems theory as well as mathematicians and engineers interested in the mathematical foundations of systems and control. From the reviews: "This textbook on finite-dimensional time-invariant linear systems theory ... links up with the extensive research contributions of the authors, geared towards developing a spectral theory for uncertain systems. ... is bound to become a standard textbook and reference in its area." M. Kawski, Mathematical Reviews, 2005 "... the content ranges from rigorous proofs of basic results in linear systems theory to new results on the research frontier. In that sense, the book also serves as a valuable research reference." W.J. Satzer, MathDL, May, 2005 "I heartily recommend this book as a remarkably complete reference for researchers doing theoretical work involving linear systems. The book is a unique compilation of the mathematics underlying the field, and I look forward to seeing the authors' treatment of synthesis problems in the second volume." Brian Ingalls, IEEE Control Systems Magazine, April 2006 "MST-1 can be properly deemed an essential addition to the personal library of any researcher in systems theory. ...the authors indicate that MST-I was developed over a twenty-year period and the enormous effort that they have invested in writing the book is readily apoparent. MST-I is a superb exposition of advanced aspects of linear systems theory and is highly recommended for graduate students and researchers who have some prior background in control-systems and who have specific interests in problems of stability, robustness, and uncertainty. If the authors are able to maintain their high standards of exposition through the promised second volume, then MST-I and -II are destined to be placed among the pre-eminent authoritative references for the area of controlled dynamical systems." K.A. Grasse, IEEE Trans. Automatic Control 51, April 2006 "... This book is one of the best books on the subject." A.O. Ignatyev, Zentralblatt MATH 1074 :l Nota de contenido: Mathematical Models -- Introduction to State Space Theory -- Stability Theory -- Perturbation Theory -- Uncertain Spaces -- Appendix: Linear Algebra -- Complex Analysis -- Convolutions and Transforms -- Linear Operators En línea: http://dx.doi.org/10.1007/b137541 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35236 Mathematical Systems Theory I : Modelling, State Space Analysis, Stability and Robustness [documento electrónico] / Diederich Hinrichsen ; SpringerLink (Online service) ; Anthony J. Pritchard . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2005 . - XVI, 804 p. 180 illus : online resource. - (Texts in Applied Mathematics, ISSN 0939-2475; 48) .
ISBN : 978-3-540-26410-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Dynamics Ergodic theory System Calculus of variations Complexity, Computational Systems Theory, Control Dynamical and Theory Variations Optimal Control; Optimization Complexity Clasificación: 51 Matemáticas Resumen: This book presents the mathematical foundations of systems theory in a self-contained, comprehensive, detailed and mathematically rigorous way. This first volume is devoted to the analysis of dynamical systems with emphasis on problems of uncertainty, whereas the second volume will be devoted to control. It combines features of a detailed introductory textbook with that of a reference source. The book contains many examples and figures illustrating the text which help to bring out the intuitive ideas behind the mathematical constructions. It is accessible to mathematics students after two years of mathematics and graduate engineering students specializing in mathematical systems theory. The reader is gradually brought to the frontiers of research in stability and robustness analysis. As such the book will be useful for established researchers in systems theory as well as mathematicians and engineers interested in the mathematical foundations of systems and control. From the reviews: "This textbook on finite-dimensional time-invariant linear systems theory ... links up with the extensive research contributions of the authors, geared towards developing a spectral theory for uncertain systems. ... is bound to become a standard textbook and reference in its area." M. Kawski, Mathematical Reviews, 2005 "... the content ranges from rigorous proofs of basic results in linear systems theory to new results on the research frontier. In that sense, the book also serves as a valuable research reference." W.J. Satzer, MathDL, May, 2005 "I heartily recommend this book as a remarkably complete reference for researchers doing theoretical work involving linear systems. The book is a unique compilation of the mathematics underlying the field, and I look forward to seeing the authors' treatment of synthesis problems in the second volume." Brian Ingalls, IEEE Control Systems Magazine, April 2006 "MST-1 can be properly deemed an essential addition to the personal library of any researcher in systems theory. ...the authors indicate that MST-I was developed over a twenty-year period and the enormous effort that they have invested in writing the book is readily apoparent. MST-I is a superb exposition of advanced aspects of linear systems theory and is highly recommended for graduate students and researchers who have some prior background in control-systems and who have specific interests in problems of stability, robustness, and uncertainty. If the authors are able to maintain their high standards of exposition through the promised second volume, then MST-I and -II are destined to be placed among the pre-eminent authoritative references for the area of controlled dynamical systems." K.A. Grasse, IEEE Trans. Automatic Control 51, April 2006 "... This book is one of the best books on the subject." A.O. Ignatyev, Zentralblatt MATH 1074 :l Nota de contenido: Mathematical Models -- Introduction to State Space Theory -- Stability Theory -- Perturbation Theory -- Uncertain Spaces -- Appendix: Linear Algebra -- Complex Analysis -- Convolutions and Transforms -- Linear Operators En línea: http://dx.doi.org/10.1007/b137541 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35236 Ejemplares
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Título : Mathematical Analysis : Foundations and Advanced Techniques for Functions of Several Variables Tipo de documento: documento electrónico Autores: Mariano Giaquinta ; SpringerLink (Online service) ; Giuseppe Modica Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2012 Número de páginas: XIII, 405 p. 66 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-8310-8 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Clasificación: 51 Matemáticas Resumen: Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables builds upon the basic ideas and techniques of differential and integral calculus for functions of several variables, as outlined in an earlier introductory volume. The presentation is largely focused on the foundations of measure and integration theory. The book begins with a discussion of the geometry of Hilbert spaces, convex functions and domains, and differential forms, particularly k-forms. The exposition continues with an introduction to the calculus of variations with applications to geometric optics and mechanics. The authors conclude with the study of measure and integration theory – Borel, Radon, and Hausdorff measures and the derivation of measures. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis. This work may be used as a supplementary text in the classroom or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering. One of the key strengths of this presentation, along with the other four books on analysis published by the authors, is the motivation for understanding the subject through examples, observations, exercises, and illustrations. Other books published by the authors – all of which provide the reader with a strong foundation in modern-day analysis – include: * Mathematical Analysis: Functions of One Variable * Mathematical Analysis: Approximation and Discrete Processes * Mathematical Analysis: Linear and Metric Structures and Continuity * Mathematical Analysis: An Introduction to Functions of Several Variables Reviews of previous volumes of Mathematical Analysis: The presentation of the theory is clearly arranged, all theorems have rigorous proofs, and every chapter closes with a summing up of the results and exercises with different requirements. . . . This book is excellently suitable for students in mathematics, physics, engineering, computer science and all students of technological and scientific faculties. —Journal of Analysis and its Applications The exposition requires only a sound knowledge of calculus and the functions of one variable. A key feature of this lively yet rigorous and systematic treatment is the historical accounts of ideas and methods of the subject. Ideas in mathematics develop in cultural, historical and economical contexts, thus the authors made brief accounts of those aspects and used a large number of beautiful illustrations. —Zentralblatt MATH Nota de contenido: Preface -- Spaces of Summable Functions and Partial Differential Equations -- Convex Sets and Convex Functions -- The Formalism of the Calculus of Variations -- Differential Forms -- Measures and Integrations -- Hausdorff and Radon Measures -- Mathematicians and Other Scientists -- Bibliographical Notes -- Index En línea: http://dx.doi.org/10.1007/978-0-8176-8310-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32692 Mathematical Analysis : Foundations and Advanced Techniques for Functions of Several Variables [documento electrónico] / Mariano Giaquinta ; SpringerLink (Online service) ; Giuseppe Modica . - Boston : Birkhäuser Boston, 2012 . - XIII, 405 p. 66 illus : online resource.
ISBN : 978-0-8176-8310-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Clasificación: 51 Matemáticas Resumen: Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables builds upon the basic ideas and techniques of differential and integral calculus for functions of several variables, as outlined in an earlier introductory volume. The presentation is largely focused on the foundations of measure and integration theory. The book begins with a discussion of the geometry of Hilbert spaces, convex functions and domains, and differential forms, particularly k-forms. The exposition continues with an introduction to the calculus of variations with applications to geometric optics and mechanics. The authors conclude with the study of measure and integration theory – Borel, Radon, and Hausdorff measures and the derivation of measures. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis. This work may be used as a supplementary text in the classroom or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering. One of the key strengths of this presentation, along with the other four books on analysis published by the authors, is the motivation for understanding the subject through examples, observations, exercises, and illustrations. Other books published by the authors – all of which provide the reader with a strong foundation in modern-day analysis – include: * Mathematical Analysis: Functions of One Variable * Mathematical Analysis: Approximation and Discrete Processes * Mathematical Analysis: Linear and Metric Structures and Continuity * Mathematical Analysis: An Introduction to Functions of Several Variables Reviews of previous volumes of Mathematical Analysis: The presentation of the theory is clearly arranged, all theorems have rigorous proofs, and every chapter closes with a summing up of the results and exercises with different requirements. . . . This book is excellently suitable for students in mathematics, physics, engineering, computer science and all students of technological and scientific faculties. —Journal of Analysis and its Applications The exposition requires only a sound knowledge of calculus and the functions of one variable. A key feature of this lively yet rigorous and systematic treatment is the historical accounts of ideas and methods of the subject. Ideas in mathematics develop in cultural, historical and economical contexts, thus the authors made brief accounts of those aspects and used a large number of beautiful illustrations. —Zentralblatt MATH Nota de contenido: Preface -- Spaces of Summable Functions and Partial Differential Equations -- Convex Sets and Convex Functions -- The Formalism of the Calculus of Variations -- Differential Forms -- Measures and Integrations -- Hausdorff and Radon Measures -- Mathematicians and Other Scientists -- Bibliographical Notes -- Index En línea: http://dx.doi.org/10.1007/978-0-8176-8310-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32692 Ejemplares
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Título : Mathematical Aspects of Network Routing Optimization Tipo de documento: documento electrónico Autores: Carlos A. S. Oliveira ; SpringerLink (Online service) ; Pardalos, Panos M Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Otro editor: Imprint: Springer Colección: Springer Optimization and Its Applications, ISSN 1931-6828 num. 53 Número de páginas: XXIV, 208 p Il.: online resource ISBN/ISSN/DL: 978-1-4614-0311-1 Idioma : Inglés (eng) Palabras clave: Mathematics Computer communication systems Algorithms Mathematical optimization Optimization Communication Networks Information Systems Applications (incl. Internet) Algorithm Analysis and Problem Complexity Clasificación: 51 Matemáticas Resumen: Mathematical Aspects of Network Routing Optimization provides a thorough introduction to the subject of algorithms for network routing and focuses on multicast and wireless ad hoc systems. The modern world is connected through large-scale, computational networked systems such as the Internet and because of the ever-advancing technology of networking, efficient algorithms have become increasingly necessary to solve some of the problems developing in this area. This work focuses on computational issues arising from the process of optimizing network routes, such as the quality of resulting links and their reliability. Algorithms are key to understanding the protocols underlying multicast routing. The main objective in the text is to derive efficient algorithms, with or without the guarantee of approximation, that can be applied to address these problems. Notes have been provided for basic topics such as graph theory and linear programming to assist those who are not fully acquainted with the mathematical topics presented throughout the book. This book is designed for graduate students, researchers, and professionals interested in understanding the algorithmic and mathematical ideas behind routing in computer networks and network algorithms Nota de contenido: Preface -- 1. Unicast Routing Algorithms -- 2. Multicast Routing -- 3. Steiner Trees and Multicast -- 4. Online Multicast Routing -- 5. Distributed Algorithms for Multicast Routing -- 6. Center-Based Trees and Multicast Packing -- 7. Metaheuristics for Multicast Routing -- 8. The Point-to-Point Connection Problem -- 9. Streaming Cache Placement -- 10. Algorithms for Cache Placement -- 11. Distributed Routing on Ad Hoc Networks -- 12. Power-Aware Routing in MANETs -- Appendix -- References -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-0311-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33218 Mathematical Aspects of Network Routing Optimization [documento electrónico] / Carlos A. S. Oliveira ; SpringerLink (Online service) ; Pardalos, Panos M . - New York, NY : Springer New York : Imprint: Springer, 2011 . - XXIV, 208 p : online resource. - (Springer Optimization and Its Applications, ISSN 1931-6828; 53) .
ISBN : 978-1-4614-0311-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Computer communication systems Algorithms Mathematical optimization Optimization Communication Networks Information Systems Applications (incl. Internet) Algorithm Analysis and Problem Complexity Clasificación: 51 Matemáticas Resumen: Mathematical Aspects of Network Routing Optimization provides a thorough introduction to the subject of algorithms for network routing and focuses on multicast and wireless ad hoc systems. The modern world is connected through large-scale, computational networked systems such as the Internet and because of the ever-advancing technology of networking, efficient algorithms have become increasingly necessary to solve some of the problems developing in this area. This work focuses on computational issues arising from the process of optimizing network routes, such as the quality of resulting links and their reliability. Algorithms are key to understanding the protocols underlying multicast routing. The main objective in the text is to derive efficient algorithms, with or without the guarantee of approximation, that can be applied to address these problems. Notes have been provided for basic topics such as graph theory and linear programming to assist those who are not fully acquainted with the mathematical topics presented throughout the book. This book is designed for graduate students, researchers, and professionals interested in understanding the algorithmic and mathematical ideas behind routing in computer networks and network algorithms Nota de contenido: Preface -- 1. Unicast Routing Algorithms -- 2. Multicast Routing -- 3. Steiner Trees and Multicast -- 4. Online Multicast Routing -- 5. Distributed Algorithms for Multicast Routing -- 6. Center-Based Trees and Multicast Packing -- 7. Metaheuristics for Multicast Routing -- 8. The Point-to-Point Connection Problem -- 9. Streaming Cache Placement -- 10. Algorithms for Cache Placement -- 11. Distributed Routing on Ad Hoc Networks -- 12. Power-Aware Routing in MANETs -- Appendix -- References -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-0311-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33218 Ejemplares
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Título : Mathematical Logic and Model Theory : A Brief Introduction Tipo de documento: documento electrónico Autores: Prestel, Alexander ; SpringerLink (Online service) ; Charles N. Delzell Editorial: London : Springer London Fecha de publicación: 2011 Colección: Universitext, ISSN 0172-5939 Número de páginas: X, 194 p Il.: online resource ISBN/ISSN/DL: 978-1-4471-2176-3 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical logic Mathematics, general Logic and Formal Languages Clasificación: 51 Matemáticas Resumen: Mathematical Logic and Model Theory: A Brief Introduction offers a streamlined yet easy-to-read introduction to mathematical logic and basic model theory. It presents, in a self-contained manner, the essential aspects of model theory needed to understand model theoretic algebra. As a profound application of model theory in algebra, the last part of this book develops a complete proof of Ax and Kochen's work on Artin's conjecture about Diophantine properties of p-adic number fields. The character of model theoretic constructions and results differs significantly from that commonly found in algebra, by the treatment of formulae as mathematical objects. It is therefore indispensable to first become familiar with the problems and methods of mathematical logic. Therefore, the text is divided into three parts: an introduction into mathematical logic (Chapter 1), model theory (Chapters 2 and 3), and the model theoretic treatment of several algebraic theories (Chapter 4). This book will be of interest to both advanced undergraduate and graduate students studying model theory and its applications to algebra. It may also be used for self-study Nota de contenido: First-Order Logic -- Model Constructions -- Properties of Model Classes -- Model Theory of Several Algebraic Theories En línea: http://dx.doi.org/10.1007/978-1-4471-2176-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33213 Mathematical Logic and Model Theory : A Brief Introduction [documento electrónico] / Prestel, Alexander ; SpringerLink (Online service) ; Charles N. Delzell . - London : Springer London, 2011 . - X, 194 p : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-1-4471-2176-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical logic Mathematics, general Logic and Formal Languages Clasificación: 51 Matemáticas Resumen: Mathematical Logic and Model Theory: A Brief Introduction offers a streamlined yet easy-to-read introduction to mathematical logic and basic model theory. It presents, in a self-contained manner, the essential aspects of model theory needed to understand model theoretic algebra. As a profound application of model theory in algebra, the last part of this book develops a complete proof of Ax and Kochen's work on Artin's conjecture about Diophantine properties of p-adic number fields. The character of model theoretic constructions and results differs significantly from that commonly found in algebra, by the treatment of formulae as mathematical objects. It is therefore indispensable to first become familiar with the problems and methods of mathematical logic. Therefore, the text is divided into three parts: an introduction into mathematical logic (Chapter 1), model theory (Chapters 2 and 3), and the model theoretic treatment of several algebraic theories (Chapter 4). This book will be of interest to both advanced undergraduate and graduate students studying model theory and its applications to algebra. It may also be used for self-study Nota de contenido: First-Order Logic -- Model Constructions -- Properties of Model Classes -- Model Theory of Several Algebraic Theories En línea: http://dx.doi.org/10.1007/978-1-4471-2176-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33213 Ejemplares
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