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Título : Braid Groups Tipo de documento: documento electrónico Autores: Kassel, Christian ; SpringerLink (Online service) ; Turaev, Vladimir Editorial: New York, NY : Springer New York Fecha de publicación: 2008 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 247 Número de páginas: X, 338 p. 60 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-68548-9 Idioma : Inglés (eng) Palabras clave: Mathematics Group theory Algebra Ordered algebraic structures Algebraic topology Manifolds (Mathematics) Complex manifolds Theory and Generalizations Cell Complexes (incl. Diff.Topology) Order, Lattices, Structures Topology Clasificación: 51 Matemáticas Resumen: Braids and braid groups have been at the heart of mathematical development over the last two decades. Braids play an important role in diverse areas of mathematics and theoretical physics. The special beauty of the theory of braids stems from their attractive geometric nature and their close relations to other fundamental geometric objects, such as knots, links, mapping class groups of surfaces, and configuration spaces. In this presentation the authors thoroughly examine various aspects of the theory of braids, starting from basic definitions and then moving to more recent results. The advanced topics cover the Burau and the Lawrence--Krammer--Bigelow representations of the braid groups, the Alexander--Conway and Jones link polynomials, connections with the representation theory of the Iwahori--Hecke algebras, and the Garside structure and orderability of the braid groups. This book will serve graduate students, mathematicians, and theoretical physicists interested in low-dimensional topology and its connections with representation theory Nota de contenido: Braids and Braid Groups -- Braids, Knots, and Links -- Homological Representations of the Braid Groups -- Symmetric Groups and Iwahori#x2013;Hecke Algebras -- Representations of the Iwahori#x2013;Hecke Algebras -- Garside Monoids and Braid Monoids -- An Order on the Braid Groups -- Presentations of SL(Z) and PSL(Z) -- Fibrations and Homotopy Sequences -- The Birman#x2013;Murakami#x2013;Wenzl Algebras -- Left Self-Distributive Sets En línea: http://dx.doi.org/10.1007/978-0-387-68548-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34153 Braid Groups [documento electrónico] / Kassel, Christian ; SpringerLink (Online service) ; Turaev, Vladimir . - New York, NY : Springer New York, 2008 . - X, 338 p. 60 illus : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 247) .
ISBN : 978-0-387-68548-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Group theory Algebra Ordered algebraic structures Algebraic topology Manifolds (Mathematics) Complex manifolds Theory and Generalizations Cell Complexes (incl. Diff.Topology) Order, Lattices, Structures Topology Clasificación: 51 Matemáticas Resumen: Braids and braid groups have been at the heart of mathematical development over the last two decades. Braids play an important role in diverse areas of mathematics and theoretical physics. The special beauty of the theory of braids stems from their attractive geometric nature and their close relations to other fundamental geometric objects, such as knots, links, mapping class groups of surfaces, and configuration spaces. In this presentation the authors thoroughly examine various aspects of the theory of braids, starting from basic definitions and then moving to more recent results. The advanced topics cover the Burau and the Lawrence--Krammer--Bigelow representations of the braid groups, the Alexander--Conway and Jones link polynomials, connections with the representation theory of the Iwahori--Hecke algebras, and the Garside structure and orderability of the braid groups. This book will serve graduate students, mathematicians, and theoretical physicists interested in low-dimensional topology and its connections with representation theory Nota de contenido: Braids and Braid Groups -- Braids, Knots, and Links -- Homological Representations of the Braid Groups -- Symmetric Groups and Iwahori#x2013;Hecke Algebras -- Representations of the Iwahori#x2013;Hecke Algebras -- Garside Monoids and Braid Monoids -- An Order on the Braid Groups -- Presentations of SL(Z) and PSL(Z) -- Fibrations and Homotopy Sequences -- The Birman#x2013;Murakami#x2013;Wenzl Algebras -- Left Self-Distributive Sets En línea: http://dx.doi.org/10.1007/978-0-387-68548-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34153 Ejemplares
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Título : Introduction to Boolean Algebras Tipo de documento: documento electrónico Autores: Halmos, Paul ; SpringerLink (Online service) ; Givant, Steven Editorial: New York, NY : Springer New York Fecha de publicación: 2009 Colección: Undergraduate Texts in Mathematics, ISSN 0172-6056 Número de páginas: XIV, 574 p. 10 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-68436-9 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Ordered algebraic structures Mathematical logic Logic and Foundations Order, Lattices, Algebraic Structures Clasificación: 51 Matemáticas Resumen: In a bold and refreshingly informal style, this exciting text steers a middle course between elementary texts emphasizing connections with philosophy, logic, and electronic circuit design, and profound treatises aimed at advanced graduate students and professional mathematicians. It is written for readers who have studied at least two years of college-level mathematics. With carefully crafted prose, lucid explanations, and illuminating insights, it guides students to some of the deeper results of Boolean algebra --- and in particular to the important interconnections with topology --- without assuming a background in algebra, topology, and set theory. The parts of those subjects that are needed to understand the material are developed within the text itself. Highlights of the book include the normal form theorem; the homomorphism extension theorem; the isomorphism theorem for countable atomless Boolean algebras; the maximal ideal theorem; the celebrated Stone representation theorem; the existence and uniqueness theorems for canonical extensions and completions; Tarski’s isomorphism of factors theorem for countably complete Boolean algebras, and Hanf’s related counterexamples; and an extensive treatment of the algebraic-topological duality, including the duality between ideals and open sets, homomorphisms and continuous functions, subalgebras and quotient spaces, and direct products and Stone-Cech compactifications. A special feature of the book is the large number of exercises of varying levels of difficulty, from routine problems that help readers understand the basic definitions and theorems, to intermediate problems that extend or enrich material developed in the text, to harder problems that explore important ideas either not treated in the text, or that go substantially beyond its treatment. Hints for the solutions to the harder problems are given in an appendix. A detailed solutions manual for all exercises is available for instructors who adopt the text for a course Nota de contenido: Boolean Rings -- Boolean Algebras -- Boolean Algebras Versus Rings -- The Principle of Duality -- Fields of Sets -- Elementary Relations -- Order -- Infinite Operations -- Topology -- Regular Open Sets -- Subalgebras -- Homomorphisms -- Extensions of Homomorphisms -- Atoms -- Finite Boolean Algebras -- Atomless Boolean Algebras -- Congruences and Quotients -- Ideals and Filters -- Lattices of Ideals -- Maximal Ideals -- Homomorphism and Isomorphism Theorems -- The Representation Theorem -- Canonical Extensions -- Complete Homomorphisms and Complete Ideals -- Completions -- Products of Algebras -- Isomorphisms of Factors -- Free Algebras -- Boolean s-algebras -- The Countable Chain Condition -- Measure Algebras -- Boolean Spaces -- Continuous Functions -- Boolean Algebras and Boolean Spaces -- Duality for Ideals -- Duality for Homomorphisms -- Duality for Subalgebras -- Duality for Completeness -- Boolean s-spaces -- The Representation of s-algebras -- Boolean Measure Spaces -- Incomplete Algebras -- Duality for Products -- Sums of Algebras -- Isomorphisms of Countable Factors En línea: http://dx.doi.org/10.1007/978-0-387-68436-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33839 Introduction to Boolean Algebras [documento electrónico] / Halmos, Paul ; SpringerLink (Online service) ; Givant, Steven . - New York, NY : Springer New York, 2009 . - XIV, 574 p. 10 illus : online resource. - (Undergraduate Texts in Mathematics, ISSN 0172-6056) .
ISBN : 978-0-387-68436-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Ordered algebraic structures Mathematical logic Logic and Foundations Order, Lattices, Algebraic Structures Clasificación: 51 Matemáticas Resumen: In a bold and refreshingly informal style, this exciting text steers a middle course between elementary texts emphasizing connections with philosophy, logic, and electronic circuit design, and profound treatises aimed at advanced graduate students and professional mathematicians. It is written for readers who have studied at least two years of college-level mathematics. With carefully crafted prose, lucid explanations, and illuminating insights, it guides students to some of the deeper results of Boolean algebra --- and in particular to the important interconnections with topology --- without assuming a background in algebra, topology, and set theory. The parts of those subjects that are needed to understand the material are developed within the text itself. Highlights of the book include the normal form theorem; the homomorphism extension theorem; the isomorphism theorem for countable atomless Boolean algebras; the maximal ideal theorem; the celebrated Stone representation theorem; the existence and uniqueness theorems for canonical extensions and completions; Tarski’s isomorphism of factors theorem for countably complete Boolean algebras, and Hanf’s related counterexamples; and an extensive treatment of the algebraic-topological duality, including the duality between ideals and open sets, homomorphisms and continuous functions, subalgebras and quotient spaces, and direct products and Stone-Cech compactifications. A special feature of the book is the large number of exercises of varying levels of difficulty, from routine problems that help readers understand the basic definitions and theorems, to intermediate problems that extend or enrich material developed in the text, to harder problems that explore important ideas either not treated in the text, or that go substantially beyond its treatment. Hints for the solutions to the harder problems are given in an appendix. A detailed solutions manual for all exercises is available for instructors who adopt the text for a course Nota de contenido: Boolean Rings -- Boolean Algebras -- Boolean Algebras Versus Rings -- The Principle of Duality -- Fields of Sets -- Elementary Relations -- Order -- Infinite Operations -- Topology -- Regular Open Sets -- Subalgebras -- Homomorphisms -- Extensions of Homomorphisms -- Atoms -- Finite Boolean Algebras -- Atomless Boolean Algebras -- Congruences and Quotients -- Ideals and Filters -- Lattices of Ideals -- Maximal Ideals -- Homomorphism and Isomorphism Theorems -- The Representation Theorem -- Canonical Extensions -- Complete Homomorphisms and Complete Ideals -- Completions -- Products of Algebras -- Isomorphisms of Factors -- Free Algebras -- Boolean s-algebras -- The Countable Chain Condition -- Measure Algebras -- Boolean Spaces -- Continuous Functions -- Boolean Algebras and Boolean Spaces -- Duality for Ideals -- Duality for Homomorphisms -- Duality for Subalgebras -- Duality for Completeness -- Boolean s-spaces -- The Representation of s-algebras -- Boolean Measure Spaces -- Incomplete Algebras -- Duality for Products -- Sums of Algebras -- Isomorphisms of Countable Factors En línea: http://dx.doi.org/10.1007/978-0-387-68436-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33839 Ejemplares
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Título : Novelty, Information and Surprise Tipo de documento: documento electrónico Autores: Palm, Günther ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2012 Otro editor: Imprint: Springer Número de páginas: XXIV, 248 p Il.: online resource ISBN/ISSN/DL: 978-3-642-29075-6 Idioma : Inglés (eng) Palabras clave: Mathematics Artificial intelligence Pattern recognition Neurobiology Algebra Ordered algebraic structures Information theory Biomathematics and Communication, Circuits Intelligence (incl. Robotics) Order, Lattices, Algebraic Structures Recognition Mathematical Computational Biology Clasificación: 51 Matemáticas Resumen: The book offers a new approach to information theory that is more general then the classical approach by Shannon. The classical definition of information is given for an alphabet of symbols or for a set of mutually exclusive propositions (a partition of the probability space O) with corresponding probabilities adding up to 1. The new definition is given for an arbitrary cover of O, i.e. for a set of possibly overlapping propositions. The generalized information concept is called novelty and it is accompanied by two new concepts derived from it, designated as information and surprise, which describe "opposite" versions of novelty, information being related more to classical information theory and surprise being related more to the classical concept of statistical significance. In the discussion of these three concepts and their interrelations several properties or classes of covers are defined, which turn out to be lattices. The book also presents applications of these new concepts, mostly in statistics and in neuroscience Nota de contenido: Part I Surprise and Information of Descriptions: Prerequisites -- Improbability and Novelty of Descriptions -- Conditional Novelty and Information -- Part II Coding and Information Transmission: On Guessing and Coding -- Information Transmission -- Part III Information Rate and Channel Capacity: Stationary Processes and Information Rate -- Channel Capacity -- Shannon's Theorem -- Part IV Repertoires and Covers: Repertoires and Descriptions -- Novelty, Information and Surprise of Repertoires -- Conditioning, Mutual Information and Information Gain -- Part V Information, Novelty and Surprise in Science: Information, Novelty and Surprise in Brain Theory -- Surprise from Repetitions and Combination of Surprises -- Entropy in Physics -- Part VI Generalized Information Theory: Order- and Lattice-Structures -- Three Orderings on Repertoires -- Information Theory on Lattices of Covers -- Appendices: A. Fuzzy Repertoires and Descriptions -- A.1 Basic Definitions -- A.2 Definition and Properties of Fuzzy Repertoires -- Glossary -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-3-642-29075-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32977 Novelty, Information and Surprise [documento electrónico] / Palm, Günther ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012 . - XXIV, 248 p : online resource.
ISBN : 978-3-642-29075-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Artificial intelligence Pattern recognition Neurobiology Algebra Ordered algebraic structures Information theory Biomathematics and Communication, Circuits Intelligence (incl. Robotics) Order, Lattices, Algebraic Structures Recognition Mathematical Computational Biology Clasificación: 51 Matemáticas Resumen: The book offers a new approach to information theory that is more general then the classical approach by Shannon. The classical definition of information is given for an alphabet of symbols or for a set of mutually exclusive propositions (a partition of the probability space O) with corresponding probabilities adding up to 1. The new definition is given for an arbitrary cover of O, i.e. for a set of possibly overlapping propositions. The generalized information concept is called novelty and it is accompanied by two new concepts derived from it, designated as information and surprise, which describe "opposite" versions of novelty, information being related more to classical information theory and surprise being related more to the classical concept of statistical significance. In the discussion of these three concepts and their interrelations several properties or classes of covers are defined, which turn out to be lattices. The book also presents applications of these new concepts, mostly in statistics and in neuroscience Nota de contenido: Part I Surprise and Information of Descriptions: Prerequisites -- Improbability and Novelty of Descriptions -- Conditional Novelty and Information -- Part II Coding and Information Transmission: On Guessing and Coding -- Information Transmission -- Part III Information Rate and Channel Capacity: Stationary Processes and Information Rate -- Channel Capacity -- Shannon's Theorem -- Part IV Repertoires and Covers: Repertoires and Descriptions -- Novelty, Information and Surprise of Repertoires -- Conditioning, Mutual Information and Information Gain -- Part V Information, Novelty and Surprise in Science: Information, Novelty and Surprise in Brain Theory -- Surprise from Repetitions and Combination of Surprises -- Entropy in Physics -- Part VI Generalized Information Theory: Order- and Lattice-Structures -- Three Orderings on Repertoires -- Information Theory on Lattices of Covers -- Appendices: A. Fuzzy Repertoires and Descriptions -- A.1 Basic Definitions -- A.2 Definition and Properties of Fuzzy Repertoires -- Glossary -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-3-642-29075-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32977 Ejemplares
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Título : Ordered Sets Tipo de documento: documento electrónico Autores: Harzheim, Egbert ; SpringerLink (Online service) Editorial: Boston, MA : Springer US Fecha de publicación: 2005 Colección: Advances in Mathematics num. 7 Número de páginas: XII, 386 p Il.: online resource ISBN/ISSN/DL: 978-0-387-24222-4 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Ordered algebraic structures Order, Lattices, Algebraic Structures Clasificación: 51 Matemáticas Resumen: The textbook literature on ordered sets is still rather limited. A lot of material is presented in this book that appears now for the first time in a textbook. Order theory works with combinatorial and set-theoretical methods, depending on whether the sets under consideration are finite or infinite. In this book the set-theoretical parts prevail. The book treats in detail lexicographic products and their connections with universally ordered sets, and further it gives thorough investigations on the structure of power sets. Other topics dealt with include dimension theory of ordered sets, well-quasi-ordered sets, trees, combinatorial set theory for ordered sets, comparison of order types, and comparibility graphs. Audience This book is intended for mathematics students and for mathemeticians who are interested in set theory. Only some fundamental parts of naïve set theory are presupposed. Since all proofs are worked out in great detail, the book should be suitable as a text for a course on order theory Nota de contenido: Fundamental notions of set theory -- Fundamental notions -- General relations between posets and their chains and antichains -- Linearly ordered sets -- Products of orders -- Universally ordered sets -- Applications of the splitting method -- The dimension of posets -- Well-founded posets, pwo-sets and trees -- On the order structure of power sets -- Comparison of order types -- Comparability graphs En línea: http://dx.doi.org/10.1007/b104891 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35079 Ordered Sets [documento electrónico] / Harzheim, Egbert ; SpringerLink (Online service) . - Boston, MA : Springer US, 2005 . - XII, 386 p : online resource. - (Advances in Mathematics; 7) .
ISBN : 978-0-387-24222-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Ordered algebraic structures Order, Lattices, Algebraic Structures Clasificación: 51 Matemáticas Resumen: The textbook literature on ordered sets is still rather limited. A lot of material is presented in this book that appears now for the first time in a textbook. Order theory works with combinatorial and set-theoretical methods, depending on whether the sets under consideration are finite or infinite. In this book the set-theoretical parts prevail. The book treats in detail lexicographic products and their connections with universally ordered sets, and further it gives thorough investigations on the structure of power sets. Other topics dealt with include dimension theory of ordered sets, well-quasi-ordered sets, trees, combinatorial set theory for ordered sets, comparison of order types, and comparibility graphs. Audience This book is intended for mathematics students and for mathemeticians who are interested in set theory. Only some fundamental parts of naïve set theory are presupposed. Since all proofs are worked out in great detail, the book should be suitable as a text for a course on order theory Nota de contenido: Fundamental notions of set theory -- Fundamental notions -- General relations between posets and their chains and antichains -- Linearly ordered sets -- Products of orders -- Universally ordered sets -- Applications of the splitting method -- The dimension of posets -- Well-founded posets, pwo-sets and trees -- On the order structure of power sets -- Comparison of order types -- Comparability graphs En línea: http://dx.doi.org/10.1007/b104891 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35079 Ejemplares
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Título : Proof Theory for Fuzzy Logics Tipo de documento: documento electrónico Autores: Metcalfe, George ; SpringerLink (Online service) ; Olivetti, Nicola ; Dov M. Gabbay Editorial: Dordrecht : Springer Netherlands Fecha de publicación: 2009 Colección: Applied Logic Series, ISSN 1386-2790 num. 36 Número de páginas: VIII, 276 p Il.: online resource ISBN/ISSN/DL: 978-1-4020-9409-5 Idioma : Inglés (eng) Palabras clave: Mathematics Logic Artificial intelligence Algebra Ordered algebraic structures Mathematical logic and Foundations Mathematics, general Intelligence (incl. Robotics) Order, Lattices, Algebraic Structures Clasificación: 51 Matemáticas Resumen: Fuzzy logics are many-valued logics that are well suited to reasoning in the context of vagueness. They provide the basis for the wider field of Fuzzy Logic, encompassing diverse areas such as fuzzy control, fuzzy databases, and fuzzy mathematics. This book provides an accessible and up-to-date introduction to this fast-growing and increasingly popular area. It focuses in particular on the development and applications of "proof-theoretic" presentations of fuzzy logics; the result of more than ten years of intensive work by researchers in the area, including the authors. In addition to providing alternative elegant presentations of fuzzy logics, proof-theoretic methods are useful for addressing theoretical problems (including key standard completeness results) and developing efficient deduction and decision algorithms. Proof-theoretic presentations also place fuzzy logics in the broader landscape of non-classical logics, revealing deep relations with other logics studied in Computer Science, Mathematics, and Philosophy. The book builds methodically from the semantic origins of fuzzy logics to proof-theoretic presentations such as Hilbert and Gentzen systems, introducing both theoretical and practical applications of these presentations Nota de contenido: The Semantic Basis -- Hilbert Systems -- Gentzen Systems -- Syntactic Eliminations -- Fundamental Logics -- Uniformity and Efficiency -- First-Order Logics -- Further Topics En línea: http://dx.doi.org/10.1007/978-1-4020-9409-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33960 Proof Theory for Fuzzy Logics [documento electrónico] / Metcalfe, George ; SpringerLink (Online service) ; Olivetti, Nicola ; Dov M. Gabbay . - Dordrecht : Springer Netherlands, 2009 . - VIII, 276 p : online resource. - (Applied Logic Series, ISSN 1386-2790; 36) .
ISBN : 978-1-4020-9409-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Logic Artificial intelligence Algebra Ordered algebraic structures Mathematical logic and Foundations Mathematics, general Intelligence (incl. Robotics) Order, Lattices, Algebraic Structures Clasificación: 51 Matemáticas Resumen: Fuzzy logics are many-valued logics that are well suited to reasoning in the context of vagueness. They provide the basis for the wider field of Fuzzy Logic, encompassing diverse areas such as fuzzy control, fuzzy databases, and fuzzy mathematics. This book provides an accessible and up-to-date introduction to this fast-growing and increasingly popular area. It focuses in particular on the development and applications of "proof-theoretic" presentations of fuzzy logics; the result of more than ten years of intensive work by researchers in the area, including the authors. In addition to providing alternative elegant presentations of fuzzy logics, proof-theoretic methods are useful for addressing theoretical problems (including key standard completeness results) and developing efficient deduction and decision algorithms. Proof-theoretic presentations also place fuzzy logics in the broader landscape of non-classical logics, revealing deep relations with other logics studied in Computer Science, Mathematics, and Philosophy. The book builds methodically from the semantic origins of fuzzy logics to proof-theoretic presentations such as Hilbert and Gentzen systems, introducing both theoretical and practical applications of these presentations Nota de contenido: The Semantic Basis -- Hilbert Systems -- Gentzen Systems -- Syntactic Eliminations -- Fundamental Logics -- Uniformity and Efficiency -- First-Order Logics -- Further Topics En línea: http://dx.doi.org/10.1007/978-1-4020-9409-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33960 Ejemplares
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