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Link de la búsquedaAssociahedra, Tamari Lattices and Related Structures / SpringerLink (Online service) ; Folkert Müller Hoissen ; Jean Marcel Pallo ; Stasheff, Jim (2012)
Título : Associahedra, Tamari Lattices and Related Structures : Tamari Memorial Festschrift Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Folkert Müller Hoissen ; Jean Marcel Pallo ; Stasheff, Jim Editorial: Basel : Springer Basel Fecha de publicación: 2012 Otro editor: Imprint: Birkhäuser Colección: Progress in Mathematics, ISSN 0743-1643 num. 299 Número de páginas: XX, 436 p Il.: online resource ISBN/ISSN/DL: 978-3-0348-0405-9 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Ordered algebraic structures Convex geometry Discrete Number theory Algebraic topology and Geometry Theory Order, Lattices, Structures Topology Clasificación: 51 Matemáticas Resumen: Tamari lattices originated from weakenings or reinterpretations of the familar associativity law. This was the subject of Dov Tamari's thesis at the Sorbonne in Paris in 1951 and the central theme of his subsequent mathematical work. Tamari lattices can be realized in terms of polytopes called associahedra, which in fact also appeared first in Tamari's thesis. By now these beautiful structures have made their appearance in many different areas of pure and applied mathematics, such as algebra, combinatorics, computer science, category theory, geometry, topology, and also in physics. Their interdisciplinary nature provides much fascination and value. On the occasion of Dov Tamari's centennial birthday, this book provides an introduction to topical research related to Tamari's work and ideas. Most of the articles collected in it are written in a way accessible to a wide audience of students and researchers in mathematics and mathematical physics and are accompanied by high quality illustrations En línea: http://dx.doi.org/10.1007/978-3-0348-0405-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32887 Associahedra, Tamari Lattices and Related Structures : Tamari Memorial Festschrift [documento electrónico] / SpringerLink (Online service) ; Folkert Müller Hoissen ; Jean Marcel Pallo ; Stasheff, Jim . - Basel : Springer Basel : Imprint: Birkhäuser, 2012 . - XX, 436 p : online resource. - (Progress in Mathematics, ISSN 0743-1643; 299) .
ISBN : 978-3-0348-0405-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Ordered algebraic structures Convex geometry Discrete Number theory Algebraic topology and Geometry Theory Order, Lattices, Structures Topology Clasificación: 51 Matemáticas Resumen: Tamari lattices originated from weakenings or reinterpretations of the familar associativity law. This was the subject of Dov Tamari's thesis at the Sorbonne in Paris in 1951 and the central theme of his subsequent mathematical work. Tamari lattices can be realized in terms of polytopes called associahedra, which in fact also appeared first in Tamari's thesis. By now these beautiful structures have made their appearance in many different areas of pure and applied mathematics, such as algebra, combinatorics, computer science, category theory, geometry, topology, and also in physics. Their interdisciplinary nature provides much fascination and value. On the occasion of Dov Tamari's centennial birthday, this book provides an introduction to topical research related to Tamari's work and ideas. Most of the articles collected in it are written in a way accessible to a wide audience of students and researchers in mathematics and mathematical physics and are accompanied by high quality illustrations En línea: http://dx.doi.org/10.1007/978-3-0348-0405-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32887 Ejemplares
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Título : Lattices and Ordered Algebraic Structures Tipo de documento: documento electrónico Autores: T.S. Blyth ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2005 Colección: Universitext, ISSN 0172-5939 Número de páginas: X, 304 p Il.: online resource ISBN/ISSN/DL: 978-1-84628-127-3 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Ordered algebraic structures Order, Lattices, Algebraic Structures Clasificación: 51 Matemáticas Resumen: Lattices and Ordered Algebraic Structures provides a lucid and concise introduction to the basic results concerning the notion of an order. Although as a whole it is mainly intended for beginning postgraduates, the prerequisities are minimal and selected parts can profitably be used to broaden the horizon of the advanced undergraduate. The treatment is modern, with a slant towards recent developments in the theory of residuated lattices and ordered regular semigroups. Topics covered include: [bulleted list] residuated mappings Galois connections modular, distributive, and complemented lattices Boolean algebras pseudocomplemented lattices Stone algebras Heyting algebras ordered groups lattice-ordered groups representable groups Archimedean ordered structures ordered semigroups naturally ordered regular and inverse Dubreil-Jacotin semigroups [end od bulleted list] Featuring material that has been hitherto available only in research articles, and an account of the range of applications of the theory, there are also many illustrative examples and numerous exercises throughout, making it ideal for use as a course text, or as a basic introduction to the field for researchers in mathematics, logic and computer science. T. S. Blyth is Professor Emeritus at St. Andrews University, UK Nota de contenido: Ordered sets; residuated mappings -- Lattices; lattice morphisms -- Regular equivalences -- Modular lattices -- Distributive lattices -- Complementation; boolean algebras -- Pseudocomplementation; Stone and Heyting algebras -- Congruences; subdirectly irreducible algebras -- Ordered groups -- Archimedean ordered structures -- Ordered semigroups; residuated semigroups -- Epimorphic group images; Dubreil-Jacotin semigroups -- Ordered regular semigroups -- Structure theorems En línea: http://dx.doi.org/10.1007/b139095 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35223 Lattices and Ordered Algebraic Structures [documento electrónico] / T.S. Blyth ; SpringerLink (Online service) . - London : Springer London, 2005 . - X, 304 p : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-1-84628-127-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Ordered algebraic structures Order, Lattices, Algebraic Structures Clasificación: 51 Matemáticas Resumen: Lattices and Ordered Algebraic Structures provides a lucid and concise introduction to the basic results concerning the notion of an order. Although as a whole it is mainly intended for beginning postgraduates, the prerequisities are minimal and selected parts can profitably be used to broaden the horizon of the advanced undergraduate. The treatment is modern, with a slant towards recent developments in the theory of residuated lattices and ordered regular semigroups. Topics covered include: [bulleted list] residuated mappings Galois connections modular, distributive, and complemented lattices Boolean algebras pseudocomplemented lattices Stone algebras Heyting algebras ordered groups lattice-ordered groups representable groups Archimedean ordered structures ordered semigroups naturally ordered regular and inverse Dubreil-Jacotin semigroups [end od bulleted list] Featuring material that has been hitherto available only in research articles, and an account of the range of applications of the theory, there are also many illustrative examples and numerous exercises throughout, making it ideal for use as a course text, or as a basic introduction to the field for researchers in mathematics, logic and computer science. T. S. Blyth is Professor Emeritus at St. Andrews University, UK Nota de contenido: Ordered sets; residuated mappings -- Lattices; lattice morphisms -- Regular equivalences -- Modular lattices -- Distributive lattices -- Complementation; boolean algebras -- Pseudocomplementation; Stone and Heyting algebras -- Congruences; subdirectly irreducible algebras -- Ordered groups -- Archimedean ordered structures -- Ordered semigroups; residuated semigroups -- Epimorphic group images; Dubreil-Jacotin semigroups -- Ordered regular semigroups -- Structure theorems En línea: http://dx.doi.org/10.1007/b139095 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35223 Ejemplares
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Título : Lattices and Ordered Sets Tipo de documento: documento electrónico Autores: Roman, Steven ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2008 Número de páginas: XV, 305 p Il.: online resource ISBN/ISSN/DL: 978-0-387-78901-9 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Ordered algebraic structures Order, Lattices, Algebraic Structures Clasificación: 51 Matemáticas Resumen: This book is intended to be a thorough introduction to the subject of ordered sets and lattices, with an emphasis on the latter. It can be used for a course at the graduate or advanced undergraduate level or for independent study. Prerequisites are kept to a minimum, but an introductory course in abstract algebra is highly recommended, since many of the examples are drawn from this area. The book has an excellent choice of topics, including a chapter on well ordering and ordinal numbers, which is not usually found in other texts. The approach is user-friendly and the presentation is lucid. There are more than 240 carefully chosen exercises. Topic coverage includes: modular, semimodular and distributive lattices, boolean algebras, representation of distributive lattices, algebraic lattices, congruence relations on lattices, free lattices, fixed-point theorems, duality theory and more. Steven Roman is the author of many successful textbooks, including Advanced Linear Algebra, 3rd Edition (Springer 2007), Field Theory, 2nd Edition (Springer 2005), and Introduction to the Mathematics of Finance (2004) Nota de contenido: Basic Theory -- Partially Ordered Sets -- Well-Ordered Sets -- Lattices -- Modular and Distributive Lattices -- Boolean Algebras -- The Representation of Distributive Lattices -- Algebraic Lattices -- Prime and Maximal Ideals; Separation Theorems -- Congruence Relations on Lattices -- Topics -- Duality for Distributive Lattices: The Priestley Topology -- Free Lattices -- Fixed-Point Theorems En línea: http://dx.doi.org/10.1007/978-0-387-78901-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34254 Lattices and Ordered Sets [documento electrónico] / Roman, Steven ; SpringerLink (Online service) . - New York, NY : Springer New York, 2008 . - XV, 305 p : online resource.
ISBN : 978-0-387-78901-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Ordered algebraic structures Order, Lattices, Algebraic Structures Clasificación: 51 Matemáticas Resumen: This book is intended to be a thorough introduction to the subject of ordered sets and lattices, with an emphasis on the latter. It can be used for a course at the graduate or advanced undergraduate level or for independent study. Prerequisites are kept to a minimum, but an introductory course in abstract algebra is highly recommended, since many of the examples are drawn from this area. The book has an excellent choice of topics, including a chapter on well ordering and ordinal numbers, which is not usually found in other texts. The approach is user-friendly and the presentation is lucid. There are more than 240 carefully chosen exercises. Topic coverage includes: modular, semimodular and distributive lattices, boolean algebras, representation of distributive lattices, algebraic lattices, congruence relations on lattices, free lattices, fixed-point theorems, duality theory and more. Steven Roman is the author of many successful textbooks, including Advanced Linear Algebra, 3rd Edition (Springer 2007), Field Theory, 2nd Edition (Springer 2005), and Introduction to the Mathematics of Finance (2004) Nota de contenido: Basic Theory -- Partially Ordered Sets -- Well-Ordered Sets -- Lattices -- Modular and Distributive Lattices -- Boolean Algebras -- The Representation of Distributive Lattices -- Algebraic Lattices -- Prime and Maximal Ideals; Separation Theorems -- Congruence Relations on Lattices -- Topics -- Duality for Distributive Lattices: The Priestley Topology -- Free Lattices -- Fixed-Point Theorems En línea: http://dx.doi.org/10.1007/978-0-387-78901-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34254 Ejemplares
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Título : An Introduction to Mathematical Cryptography Tipo de documento: documento electrónico Autores: Joseph H. Silverman ; SpringerLink (Online service) ; Pipher, Jill ; Jeffrey Hoffstein Editorial: New York, NY : Springer New York Fecha de publicación: 2008 Colección: Undergraduate Texts in Mathematics, ISSN 0172-6056 Número de páginas: XVI, 524 p. 29 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-77994-2 Idioma : Inglés (eng) Palabras clave: Mathematics Data structures (Computer science) encryption Coding theory Algebra Ordered algebraic Information Number Theory and Structures, Cryptology Encryption Communication, Circuits Order, Lattices, Algebraic Structures Clasificación: 51 Matemáticas Resumen: This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: * classical cryptographic constructions, such as Diffie-Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures; * fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms; * an in-depth treatment of important recent cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem. This book is an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online Nota de contenido: An Introduction to Cryptography -- Discrete Logarithms and Diffie Hellman -- Integer Factorization and RSA -- Combinatorics, Probability and Information Theory -- Elliptic Curves and Cryptography -- Lattices and Cryptography -- Digital Signatures -- Additional Topics in Cryptography En línea: http://dx.doi.org/10.1007/978-0-387-77993-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34241 An Introduction to Mathematical Cryptography [documento electrónico] / Joseph H. Silverman ; SpringerLink (Online service) ; Pipher, Jill ; Jeffrey Hoffstein . - New York, NY : Springer New York, 2008 . - XVI, 524 p. 29 illus : online resource. - (Undergraduate Texts in Mathematics, ISSN 0172-6056) .
ISBN : 978-0-387-77994-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Data structures (Computer science) encryption Coding theory Algebra Ordered algebraic Information Number Theory and Structures, Cryptology Encryption Communication, Circuits Order, Lattices, Algebraic Structures Clasificación: 51 Matemáticas Resumen: This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: * classical cryptographic constructions, such as Diffie-Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures; * fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms; * an in-depth treatment of important recent cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem. This book is an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online Nota de contenido: An Introduction to Cryptography -- Discrete Logarithms and Diffie Hellman -- Integer Factorization and RSA -- Combinatorics, Probability and Information Theory -- Elliptic Curves and Cryptography -- Lattices and Cryptography -- Digital Signatures -- Additional Topics in Cryptography En línea: http://dx.doi.org/10.1007/978-0-387-77993-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34241 Ejemplares
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Título : Introduction to Boolean Algebras Tipo de documento: documento electrónico Autores: Paul Halmos ; SpringerLink (Online service) ; Steven Givant 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] / Paul Halmos ; SpringerLink (Online service) ; Steven Givant . - 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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