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Título : Geometric Optics : Theory and Design of Astronomical Optical Systems Using Mathematica® Tipo de documento: documento electrónico Autores: Antonio Romano ; SpringerLink (Online service) Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2010 Colección: Modeling and Simulation in Science, Engineering and Technology Número de páginas: XII, 224 p. 130 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4872-5 Idioma : Inglés (eng) Palabras clave: Physics Mathematical models Geometry Astronomy Astrophysics Cosmology Optics Optoelectronics Plasmons (Physics) Microwaves Optical engineering Optics, Optoelectronics, Plasmonics and Devices Astronomy, Physics, general Modeling Industrial Mathematics Microwaves, RF Engineering Clasificación: 51 Matemáticas Resumen: This book—unique in the literature—provides readers with the mathematical background needed to design many of the optical combinations that are used in astronomical telescopes and cameras. The results presented in the work were obtained by using a different approach to third-order aberration theory as well as the extensive use of the software package Mathematica®. The newly presented approach to third-order aberration theory adopted is based on Fermat’s principle and the use of particular optical paths—not rays—termed stigmatic paths, allowing for easy derivation of third-order formulae. This approach enables readers to understand and handle the formulae required to design optical combinations without resorting to the much more complex Hamiltonian formalism and Seidel's relations. Additional features and topics: * Presentation of the third-order design of cameras and telescopes with the aid of Mathematica eliminates the need for tedious computer calculations * Mathematica notebooks accompanying each optical combination analyzed in the book are available for download at http://extra.springer.com/978-0-8176-4871-8 * Discussion and analysis of specific optical devices: Newtonian and Cassegrain telescopes; Schmidt, Wright, Houghton, and Maksutov cameras; and other optical combinations, such as the Klevtsov telescope and the Baker–Schmidt flat-field camera * Additional supplementary material available at the publisher's website * Many worked-out examples and exercises Geometric Optics is an excellent reference for advanced graduate students, researchers, and practitioners in applied mathematics, engineering, astronomy, and astronomical optics. The work may be used as a supplementary textbook for graduate-level courses in astronomical optics, optical design, optical engineering, programming with Mathematica, or geometric optics Nota de contenido: Fermat#x2019;s Principle and General Considerations Regarding Centered Optical Systems -- Gaussian Optics -- Fermat#x2019;s Principle and Third-Order Aberrations -- Newtonian and Cassegrain Telescopes -- Cameras for Astronomy -- Compound Cassegrain Telescopes -- Doublets and Triplets -- Other Optical Combinations -- Fermat#x2019;s Principle and Wavefronts -- Hamiltonian Optics -- Monochromatic Third-Order Aberrations En línea: http://dx.doi.org/10.1007/978-0-8176-4872-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33545 Geometric Optics : Theory and Design of Astronomical Optical Systems Using Mathematica® [documento electrónico] / Antonio Romano ; SpringerLink (Online service) . - Boston : Birkhäuser Boston, 2010 . - XII, 224 p. 130 illus : online resource. - (Modeling and Simulation in Science, Engineering and Technology) .
ISBN : 978-0-8176-4872-5
Idioma : Inglés (eng)
Palabras clave: Physics Mathematical models Geometry Astronomy Astrophysics Cosmology Optics Optoelectronics Plasmons (Physics) Microwaves Optical engineering Optics, Optoelectronics, Plasmonics and Devices Astronomy, Physics, general Modeling Industrial Mathematics Microwaves, RF Engineering Clasificación: 51 Matemáticas Resumen: This book—unique in the literature—provides readers with the mathematical background needed to design many of the optical combinations that are used in astronomical telescopes and cameras. The results presented in the work were obtained by using a different approach to third-order aberration theory as well as the extensive use of the software package Mathematica®. The newly presented approach to third-order aberration theory adopted is based on Fermat’s principle and the use of particular optical paths—not rays—termed stigmatic paths, allowing for easy derivation of third-order formulae. This approach enables readers to understand and handle the formulae required to design optical combinations without resorting to the much more complex Hamiltonian formalism and Seidel's relations. Additional features and topics: * Presentation of the third-order design of cameras and telescopes with the aid of Mathematica eliminates the need for tedious computer calculations * Mathematica notebooks accompanying each optical combination analyzed in the book are available for download at http://extra.springer.com/978-0-8176-4871-8 * Discussion and analysis of specific optical devices: Newtonian and Cassegrain telescopes; Schmidt, Wright, Houghton, and Maksutov cameras; and other optical combinations, such as the Klevtsov telescope and the Baker–Schmidt flat-field camera * Additional supplementary material available at the publisher's website * Many worked-out examples and exercises Geometric Optics is an excellent reference for advanced graduate students, researchers, and practitioners in applied mathematics, engineering, astronomy, and astronomical optics. The work may be used as a supplementary textbook for graduate-level courses in astronomical optics, optical design, optical engineering, programming with Mathematica, or geometric optics Nota de contenido: Fermat#x2019;s Principle and General Considerations Regarding Centered Optical Systems -- Gaussian Optics -- Fermat#x2019;s Principle and Third-Order Aberrations -- Newtonian and Cassegrain Telescopes -- Cameras for Astronomy -- Compound Cassegrain Telescopes -- Doublets and Triplets -- Other Optical Combinations -- Fermat#x2019;s Principle and Wavefronts -- Hamiltonian Optics -- Monochromatic Third-Order Aberrations En línea: http://dx.doi.org/10.1007/978-0-8176-4872-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33545 Ejemplares
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Título : Algorithmic Randomness and Complexity Tipo de documento: documento electrónico Autores: Rodney G. Downey ; SpringerLink (Online service) ; Denis R. Hirschfeldt Editorial: New York, NY : Springer New York Fecha de publicación: 2010 Colección: Theory and Applications of Computability, In cooperation with the association Computability in Europe, ISSN 2190-619X Número de páginas: XXVIII, 855 p. 8 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-68441-3 Idioma : Inglés (eng) Palabras clave: Mathematics Computers Algorithms Algorithm Analysis and Problem Complexity Theory of Computation by Abstract Devices Clasificación: 51 Matemáticas Resumen: Intuitively, a sequence such as 101010101010101010… does not seem random, whereas 101101011101010100…, obtained using coin tosses, does. How can we reconcile this intuition with the fact that both are statistically equally likely? What does it mean to say that an individual mathematical object such as a real number is random, or to say that one real is more random than another? And what is the relationship between randomness and computational power. The theory of algorithmic randomness uses tools from computability theory and algorithmic information theory to address questions such as these. Much of this theory can be seen as exploring the relationships between three fundamental concepts: relative computability, as measured by notions such as Turing reducibility; information content, as measured by notions such as Kolmogorov complexity; and randomness of individual objects, as first successfully defined by Martin-Löf. Although algorithmic randomness has been studied for several decades, a dramatic upsurge of interest in the area, starting in the late 1990s, has led to significant advances. This is the first comprehensive treatment of this important field, designed to be both a reference tool for experts and a guide for newcomers. It surveys a broad section of work in the area, and presents most of its major results and techniques in depth. Its organization is designed to guide the reader through this large body of work, providing context for its many concepts and theorems, discussing their significance, and highlighting their interactions. It includes a discussion of effective dimension, which allows us to assign concepts like Hausdorff dimension to individual reals, and a focused but detailed introduction to computability theory. It will be of interest to researchers and students in computability theory, algorithmic information theory, and theoretical computer science Nota de contenido: Background -- Preliminaries -- Computability Theory -- Kolmogorov Complexity of Finite Strings -- Relating Complexities -- Effective Reals -- Notions of Randomness -- Martin-Löf Randomness -- Other Notions of Algorithmic Randomness -- Algorithmic Randomness and Turing Reducibility -- Relative Randomness -- Measures of Relative Randomness -- Complexity and Relative Randomness for 1-Random Sets -- Randomness-Theoretic Weakness -- Lowness and Triviality for Other Randomness Notions -- Algorithmic Dimension -- Further Topics -- Strong Jump Traceability -- ? as an Operator -- Complexity of Computably Enumerable Sets En línea: http://dx.doi.org/10.1007/978-0-387-68441-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33497 Algorithmic Randomness and Complexity [documento electrónico] / Rodney G. Downey ; SpringerLink (Online service) ; Denis R. Hirschfeldt . - New York, NY : Springer New York, 2010 . - XXVIII, 855 p. 8 illus : online resource. - (Theory and Applications of Computability, In cooperation with the association Computability in Europe, ISSN 2190-619X) .
ISBN : 978-0-387-68441-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Computers Algorithms Algorithm Analysis and Problem Complexity Theory of Computation by Abstract Devices Clasificación: 51 Matemáticas Resumen: Intuitively, a sequence such as 101010101010101010… does not seem random, whereas 101101011101010100…, obtained using coin tosses, does. How can we reconcile this intuition with the fact that both are statistically equally likely? What does it mean to say that an individual mathematical object such as a real number is random, or to say that one real is more random than another? And what is the relationship between randomness and computational power. The theory of algorithmic randomness uses tools from computability theory and algorithmic information theory to address questions such as these. Much of this theory can be seen as exploring the relationships between three fundamental concepts: relative computability, as measured by notions such as Turing reducibility; information content, as measured by notions such as Kolmogorov complexity; and randomness of individual objects, as first successfully defined by Martin-Löf. Although algorithmic randomness has been studied for several decades, a dramatic upsurge of interest in the area, starting in the late 1990s, has led to significant advances. This is the first comprehensive treatment of this important field, designed to be both a reference tool for experts and a guide for newcomers. It surveys a broad section of work in the area, and presents most of its major results and techniques in depth. Its organization is designed to guide the reader through this large body of work, providing context for its many concepts and theorems, discussing their significance, and highlighting their interactions. It includes a discussion of effective dimension, which allows us to assign concepts like Hausdorff dimension to individual reals, and a focused but detailed introduction to computability theory. It will be of interest to researchers and students in computability theory, algorithmic information theory, and theoretical computer science Nota de contenido: Background -- Preliminaries -- Computability Theory -- Kolmogorov Complexity of Finite Strings -- Relating Complexities -- Effective Reals -- Notions of Randomness -- Martin-Löf Randomness -- Other Notions of Algorithmic Randomness -- Algorithmic Randomness and Turing Reducibility -- Relative Randomness -- Measures of Relative Randomness -- Complexity and Relative Randomness for 1-Random Sets -- Randomness-Theoretic Weakness -- Lowness and Triviality for Other Randomness Notions -- Algorithmic Dimension -- Further Topics -- Strong Jump Traceability -- ? as an Operator -- Complexity of Computably Enumerable Sets En línea: http://dx.doi.org/10.1007/978-0-387-68441-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33497 Ejemplares
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Título : Instruction Sequences for Computer Science Tipo de documento: documento electrónico Autores: Jan A. Bergstra ; SpringerLink (Online service) ; Cornelis A. Middelburg Editorial: Paris : Atlantis Press Fecha de publicación: 2012 Colección: Atlantis Studies in Computing, ISSN 2212-8557 num. 2 Número de páginas: XVI, 232 p Il.: online resource ISBN/ISSN/DL: 978-94-91216-65-7 Idioma : Inglés (eng) Palabras clave: Computer science organization Programming languages (Electronic computers) Computers logic Mathematical Science Computation by Abstract Devices Logics and Meanings of Programs Logic Formal Languages Languages, Compilers, Interpreters Systems Organization Communication Networks Clasificación: 51 Matemáticas Resumen: This book demonstrates that the concept of an instruction sequence offers a novel and useful viewpoint on issues relating to diverse subjects in computer science. Selected issues relating to well-known subjects from the theory of computation and the area of computer architecture are rigorously investigated in this book thinking in terms of instruction sequences. The subjects from the theory of computation, to wit the halting problem and non-uniform computational complexity, are usually investigated thinking in terms of a common model of computation such as Turing machines and Boolean circuits. The subjects from the area of computer architecture, to wit instruction sequence performance, instruction set architectures and remote instruction processing, are usually not investigated in a rigorous way at all Nota de contenido: Introduction -- Instruction Sequences -- Instruction Processing -- Expressiveness of Instruction Sequences -- Computation-Theoretic Issues -- Computer-Architectural Issues -- Instruction Sequences and Process Algebra -- Variations on a Theme -- Appendix A: Five Challenges for Projectionism -- Appendix B: Natural Number Functional Units -- Appendix C: Dynamically Instantiated Instructions -- Appendix D: Analytic Execution Architectures En línea: http://dx.doi.org/10.2991/978-94-91216-65-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33067 Instruction Sequences for Computer Science [documento electrónico] / Jan A. Bergstra ; SpringerLink (Online service) ; Cornelis A. Middelburg . - Paris : Atlantis Press, 2012 . - XVI, 232 p : online resource. - (Atlantis Studies in Computing, ISSN 2212-8557; 2) .
ISBN : 978-94-91216-65-7
Idioma : Inglés (eng)
Palabras clave: Computer science organization Programming languages (Electronic computers) Computers logic Mathematical Science Computation by Abstract Devices Logics and Meanings of Programs Logic Formal Languages Languages, Compilers, Interpreters Systems Organization Communication Networks Clasificación: 51 Matemáticas Resumen: This book demonstrates that the concept of an instruction sequence offers a novel and useful viewpoint on issues relating to diverse subjects in computer science. Selected issues relating to well-known subjects from the theory of computation and the area of computer architecture are rigorously investigated in this book thinking in terms of instruction sequences. The subjects from the theory of computation, to wit the halting problem and non-uniform computational complexity, are usually investigated thinking in terms of a common model of computation such as Turing machines and Boolean circuits. The subjects from the area of computer architecture, to wit instruction sequence performance, instruction set architectures and remote instruction processing, are usually not investigated in a rigorous way at all Nota de contenido: Introduction -- Instruction Sequences -- Instruction Processing -- Expressiveness of Instruction Sequences -- Computation-Theoretic Issues -- Computer-Architectural Issues -- Instruction Sequences and Process Algebra -- Variations on a Theme -- Appendix A: Five Challenges for Projectionism -- Appendix B: Natural Number Functional Units -- Appendix C: Dynamically Instantiated Instructions -- Appendix D: Analytic Execution Architectures En línea: http://dx.doi.org/10.2991/978-94-91216-65-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33067 Ejemplares
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Título : Mathematical Problems in Image Processing : Partial Differential Equations and the Calculus of Variations Tipo de documento: documento electrónico Autores: Gilles Aubert ; SpringerLink (Online service) ; Pierre Kornprobst Editorial: New York, NY : Springer New York Fecha de publicación: 2006 Colección: Applied Mathematical Sciences, ISSN 0066-5452 num. 147 Número de páginas: XXXI, 379 p Il.: online resource ISBN/ISSN/DL: 978-0-387-44588-5 Idioma : Inglés (eng) Palabras clave: Mathematics Image processing Mathematical analysis Analysis (Mathematics) Partial differential equations Optics Optoelectronics Plasmons (Physics) Applied mathematics Engineering Optics, Optoelectronics, Plasmonics and Optical Devices Appl.Mathematics/Computational Methods of Differential Equations Processing Computer Vision Signal, Speech Clasificación: 51 Matemáticas Resumen: Partial differential equations (PDEs) and variational methods were introduced into image processing about fifteen years ago. Since then, intensive research has been carried out. The goals of this book are to present a variety of image analysis applications, the precise mathematics involved and how to discretize them. Thus, this book is intended for two audiences. The first is the mathematical community by showing the contribution of mathematics to this domain. It is also the occasion to highlight some unsolved theoretical questions. The second is the computer vision community by presenting a clear, self-contained and global overview of the mathematics involved in image processing problems. This work will serve as a useful source of reference and inspiration for fellow researchers in Applied Mathematics and Computer Vision, as well as being a basis for advanced courses within these fields. During the four years since the publication of the first edition, there has been substantial progress in the range of image processing applications covered by the PDE framework. The main goals of the second edition are to update the first edition by giving a coherent account of some of the recent challenging applications, and to update the existing material. In addition, this book provides the reader with the opportunity to make his own simulations with a minimal effort. To this end, programming tools are made available, which will allow the reader to implement and test easily some classical approaches. Reviews of the earlier edition: "Mathematical Problems in Image Processing is a major, elegant, and unique contribution to the applied mathematics literature, oriented toward applications in image processing and computer vision.... Researchers and practitioners working in the field will benefit by adding this book to their personal collection. Students and instructors will benefit by using this book as a graduate course textbook." -- SIAM Review "The Mathematician -- and he doesn't need to be a 'die-hard' applied mathematician -- will love it because there are all these spectacular applications of nontrivial mathematical techniques and he can even find some open theoretical questions. The numerical analyst will discover many challenging problems and implementations. The image processor will be an eager reader because the book provides all the mathematical elements, including most of the proofs.... Both content and typography are a delight. I can recommend the book warmly for theoretical and applied researchers." -- Bulletin of the Belgian Mathematics Nota de contenido: Foreword -- Preface to the Second Edition -- Preface -- Guide to the Main Mathematical Concepts and their Application -- Notation and Symbols -- Introduction -- Mathematical Preliminaries -- Image Restoration -- The Segmentation Problem -- Other Challenging Applications -- A Introduction to Finite Difference Methods -- B Experiment Yourself!- References -- Index En línea: http://dx.doi.org/10.1007/978-0-387-44588-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34844 Mathematical Problems in Image Processing : Partial Differential Equations and the Calculus of Variations [documento electrónico] / Gilles Aubert ; SpringerLink (Online service) ; Pierre Kornprobst . - New York, NY : Springer New York, 2006 . - XXXI, 379 p : online resource. - (Applied Mathematical Sciences, ISSN 0066-5452; 147) .
ISBN : 978-0-387-44588-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Image processing Mathematical analysis Analysis (Mathematics) Partial differential equations Optics Optoelectronics Plasmons (Physics) Applied mathematics Engineering Optics, Optoelectronics, Plasmonics and Optical Devices Appl.Mathematics/Computational Methods of Differential Equations Processing Computer Vision Signal, Speech Clasificación: 51 Matemáticas Resumen: Partial differential equations (PDEs) and variational methods were introduced into image processing about fifteen years ago. Since then, intensive research has been carried out. The goals of this book are to present a variety of image analysis applications, the precise mathematics involved and how to discretize them. Thus, this book is intended for two audiences. The first is the mathematical community by showing the contribution of mathematics to this domain. It is also the occasion to highlight some unsolved theoretical questions. The second is the computer vision community by presenting a clear, self-contained and global overview of the mathematics involved in image processing problems. This work will serve as a useful source of reference and inspiration for fellow researchers in Applied Mathematics and Computer Vision, as well as being a basis for advanced courses within these fields. During the four years since the publication of the first edition, there has been substantial progress in the range of image processing applications covered by the PDE framework. The main goals of the second edition are to update the first edition by giving a coherent account of some of the recent challenging applications, and to update the existing material. In addition, this book provides the reader with the opportunity to make his own simulations with a minimal effort. To this end, programming tools are made available, which will allow the reader to implement and test easily some classical approaches. Reviews of the earlier edition: "Mathematical Problems in Image Processing is a major, elegant, and unique contribution to the applied mathematics literature, oriented toward applications in image processing and computer vision.... Researchers and practitioners working in the field will benefit by adding this book to their personal collection. Students and instructors will benefit by using this book as a graduate course textbook." -- SIAM Review "The Mathematician -- and he doesn't need to be a 'die-hard' applied mathematician -- will love it because there are all these spectacular applications of nontrivial mathematical techniques and he can even find some open theoretical questions. The numerical analyst will discover many challenging problems and implementations. The image processor will be an eager reader because the book provides all the mathematical elements, including most of the proofs.... Both content and typography are a delight. I can recommend the book warmly for theoretical and applied researchers." -- Bulletin of the Belgian Mathematics Nota de contenido: Foreword -- Preface to the Second Edition -- Preface -- Guide to the Main Mathematical Concepts and their Application -- Notation and Symbols -- Introduction -- Mathematical Preliminaries -- Image Restoration -- The Segmentation Problem -- Other Challenging Applications -- A Introduction to Finite Difference Methods -- B Experiment Yourself!- References -- Index En línea: http://dx.doi.org/10.1007/978-0-387-44588-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34844 Ejemplares
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Título : The Pillars of Computation Theory : State, Encoding, Nondeterminism Tipo de documento: documento electrónico Autores: Arnold L. Rosenberg ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2010 Colección: Universitext, ISSN 0172-5939 Número de páginas: XVIII, 326 p. 49 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-09639-1 Idioma : Inglés (eng) Palabras clave: Computer science Computers Algorithms Mathematical logic Mathematics Science Theory of Computation Computing Algorithm Analysis and Problem Complexity Logic Foundations by Abstract Devices Formal Languages Clasificación: 51 Matemáticas Resumen: Computation theory is a discipline that strives to use mathematical tools and concepts in order to expose the nature of the activity that we call “computation” and to explain a broad range of observed computational phenomena. Why is it harder to perform some computations than others? Are the differences in difficulty that we observe inherent, or are they artifacts of the way we try to perform the computations? Even more basically: how does one reason about such questions? This book strives to endow upper-level undergraduate students and lower-level graduate students with the conceptual and manipulative tools necessary to make Computation theory part of their professional lives. The author tries to achieve this goal via three stratagems that set this book apart from most other texts on the subject. (1) The author develops the necessary mathematical concepts and tools from their simplest instances, so that the student has the opportunity to gain operational control over the necessary mathematics. (2) He organizes the development of the theory around the three “pillars” that give the book its name, so that the student sees computational topics that have the same intellectual origins developed in physical proximity to one another. (3) He strives to illustrate the “big ideas” that computation theory is built upon with applications of these ideas within “practical” domains that the students have seen elsewhere in their courses, in mathematics, in computer science, and in computer engineering Nota de contenido: PROLEGOMENA -- Mathematical Preliminaries -- STATE -- Online Automata: Exemplars of #x201C;State#x201D; -- Finite Automata and Regular Languages -- Applications of the Myhill#x2013;Nerode Theorem -- Enrichment Topics -- ENCODING -- Countability and Uncountability: The Precursors of #x201C;Encoding#x201D; -- Enrichment Topic: #x201C;Efficient#x201D; Pairing Functions, with Applications -- Computability Theory -- NONDETERMINISM -- Nondeterministic Online Automata -- Nondeterministic FAs -- Nondeterminism in Computability Theory -- Complexity Theory En línea: http://dx.doi.org/10.1007/978-0-387-09639-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33493 The Pillars of Computation Theory : State, Encoding, Nondeterminism [documento electrónico] / Arnold L. Rosenberg ; SpringerLink (Online service) . - New York, NY : Springer New York, 2010 . - XVIII, 326 p. 49 illus : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-0-387-09639-1
Idioma : Inglés (eng)
Palabras clave: Computer science Computers Algorithms Mathematical logic Mathematics Science Theory of Computation Computing Algorithm Analysis and Problem Complexity Logic Foundations by Abstract Devices Formal Languages Clasificación: 51 Matemáticas Resumen: Computation theory is a discipline that strives to use mathematical tools and concepts in order to expose the nature of the activity that we call “computation” and to explain a broad range of observed computational phenomena. Why is it harder to perform some computations than others? Are the differences in difficulty that we observe inherent, or are they artifacts of the way we try to perform the computations? Even more basically: how does one reason about such questions? This book strives to endow upper-level undergraduate students and lower-level graduate students with the conceptual and manipulative tools necessary to make Computation theory part of their professional lives. The author tries to achieve this goal via three stratagems that set this book apart from most other texts on the subject. (1) The author develops the necessary mathematical concepts and tools from their simplest instances, so that the student has the opportunity to gain operational control over the necessary mathematics. (2) He organizes the development of the theory around the three “pillars” that give the book its name, so that the student sees computational topics that have the same intellectual origins developed in physical proximity to one another. (3) He strives to illustrate the “big ideas” that computation theory is built upon with applications of these ideas within “practical” domains that the students have seen elsewhere in their courses, in mathematics, in computer science, and in computer engineering Nota de contenido: PROLEGOMENA -- Mathematical Preliminaries -- STATE -- Online Automata: Exemplars of #x201C;State#x201D; -- Finite Automata and Regular Languages -- Applications of the Myhill#x2013;Nerode Theorem -- Enrichment Topics -- ENCODING -- Countability and Uncountability: The Precursors of #x201C;Encoding#x201D; -- Enrichment Topic: #x201C;Efficient#x201D; Pairing Functions, with Applications -- Computability Theory -- NONDETERMINISM -- Nondeterministic Online Automata -- Nondeterministic FAs -- Nondeterminism in Computability Theory -- Complexity Theory En línea: http://dx.doi.org/10.1007/978-0-387-09639-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33493 Ejemplares
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