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Título : Algorithmic Topology and Classification of 3-Manifolds Tipo de documento: documento electrónico Autores: Matveev, Sergei ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2007 Colección: Algorithms and Computation in Mathematics, ISSN 1431-1550 num. 9 Número de páginas: XIV, 492 p Il.: online resource ISBN/ISSN/DL: 978-3-540-45899-9 Idioma : Inglés (eng) Palabras clave: Mathematics Computer programming science Algorithms Differential geometry Topology Programming Techniques Geometry Symbolic and Algebraic Manipulation Clasificación: 51 Matemáticas Resumen: From the reviews of the 1st edition: "This book provides a comprehensive and detailed account of different topics in algorithmic 3-dimensional topology, culminating with the recognition procedure for Haken manifolds and including the up-to-date results in computer enumeration of 3-manifolds. Originating from lecture notes of various courses given by the author over a decade, the book is intended to combine the pedagogical approach of a graduate textbook (without exercises) with the completeness and reliability of a research monograph… All the material, with few exceptions, is presented from the peculiar point of view of special polyhedra and special spines of 3-manifolds. This choice contributes to keep the level of the exposition really elementary. In conclusion, the reviewer subscribes to the quotation from the back cover: "the book fills a gap in the existing literature and will become a standard reference for algorithmic 3-dimensional topology both for graduate students and researchers". R. Piergallini, Zentralblatt für Mathematik 1048 (2004) For this 2nd edition, new results, new proofs, and commentaries for a better orientation of the reader have been added Nota de contenido: Simple and Special Polyhedra -- Complexity Theory of 3-Manifolds -- Haken Theory of Normal Surfaces -- Applications of the Theory of Normal Surfaces -- Algorithmic Recognition of S3 -- Classification of Haken 3-Manifolds -- 3-Manifold Recognizer -- The Turaev–Viro Invariants En línea: http://dx.doi.org/10.1007/978-3-540-45899-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34635 Algorithmic Topology and Classification of 3-Manifolds [documento electrónico] / Matveev, Sergei ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2007 . - XIV, 492 p : online resource. - (Algorithms and Computation in Mathematics, ISSN 1431-1550; 9) .
ISBN : 978-3-540-45899-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Computer programming science Algorithms Differential geometry Topology Programming Techniques Geometry Symbolic and Algebraic Manipulation Clasificación: 51 Matemáticas Resumen: From the reviews of the 1st edition: "This book provides a comprehensive and detailed account of different topics in algorithmic 3-dimensional topology, culminating with the recognition procedure for Haken manifolds and including the up-to-date results in computer enumeration of 3-manifolds. Originating from lecture notes of various courses given by the author over a decade, the book is intended to combine the pedagogical approach of a graduate textbook (without exercises) with the completeness and reliability of a research monograph… All the material, with few exceptions, is presented from the peculiar point of view of special polyhedra and special spines of 3-manifolds. This choice contributes to keep the level of the exposition really elementary. In conclusion, the reviewer subscribes to the quotation from the back cover: "the book fills a gap in the existing literature and will become a standard reference for algorithmic 3-dimensional topology both for graduate students and researchers". R. Piergallini, Zentralblatt für Mathematik 1048 (2004) For this 2nd edition, new results, new proofs, and commentaries for a better orientation of the reader have been added Nota de contenido: Simple and Special Polyhedra -- Complexity Theory of 3-Manifolds -- Haken Theory of Normal Surfaces -- Applications of the Theory of Normal Surfaces -- Algorithmic Recognition of S3 -- Classification of Haken 3-Manifolds -- 3-Manifold Recognizer -- The Turaev–Viro Invariants En línea: http://dx.doi.org/10.1007/978-3-540-45899-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34635 Ejemplares
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Título : Algorithms in Real Algebraic Geometry Tipo de documento: documento electrónico Autores: Saugata Basu ; SpringerLink (Online service) ; Pollack, Richard ; Roy, Marie-Françoise Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2006 Colección: Algorithms and Computation in Mathematics, ISSN 1431-1550 num. 10 Número de páginas: X, 662 p Il.: online resource ISBN/ISSN/DL: 978-3-540-33099-8 Idioma : Inglés (eng) Palabras clave: Mathematics Computer science Algebraic geometry Algorithms Geometry Symbolic and Manipulation Clasificación: 51 Matemáticas Resumen: The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, finding global maxima or deciding whether two points belong in the same connected component of a semi-algebraic set appear frequently in many areas of science and engineering. In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects, and researchers in computer science and engineering will find the required mathematical background. Being self-contained the book is accessible to graduate students and even, for invaluable parts of it, to undergraduate students. This revised second edition contains several recent results, notably on discriminants of symmetric matrices, real root isolation, global optimization, quantitative results on semi-algebraic sets and the first single exponential algorithm computing their first Betti number. An index of notation has also been added Nota de contenido: Algebraically Closed Fields -- Real Closed Fields -- Semi-Algebraic Sets -- Algebra -- Decomposition of Semi-Algebraic Sets -- Elements of Topology -- Quantitative Semi-algebraic Geometry -- Complexity of Basic Algorithms -- Cauchy Index and Applications -- Real Roots -- Cylindrical Decomposition Algorithm -- Polynomial System Solving -- Existential Theory of the Reals -- Quantifier Elimination -- Computing Roadmaps and Connected Components of Algebraic Sets -- Computing Roadmaps and Connected Components of Semi-algebraic Sets En línea: http://dx.doi.org/10.1007/3-540-33099-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34952 Algorithms in Real Algebraic Geometry [documento electrónico] / Saugata Basu ; SpringerLink (Online service) ; Pollack, Richard ; Roy, Marie-Françoise . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2006 . - X, 662 p : online resource. - (Algorithms and Computation in Mathematics, ISSN 1431-1550; 10) .
ISBN : 978-3-540-33099-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Computer science Algebraic geometry Algorithms Geometry Symbolic and Manipulation Clasificación: 51 Matemáticas Resumen: The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, finding global maxima or deciding whether two points belong in the same connected component of a semi-algebraic set appear frequently in many areas of science and engineering. In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects, and researchers in computer science and engineering will find the required mathematical background. Being self-contained the book is accessible to graduate students and even, for invaluable parts of it, to undergraduate students. This revised second edition contains several recent results, notably on discriminants of symmetric matrices, real root isolation, global optimization, quantitative results on semi-algebraic sets and the first single exponential algorithm computing their first Betti number. An index of notation has also been added Nota de contenido: Algebraically Closed Fields -- Real Closed Fields -- Semi-Algebraic Sets -- Algebra -- Decomposition of Semi-Algebraic Sets -- Elements of Topology -- Quantitative Semi-algebraic Geometry -- Complexity of Basic Algorithms -- Cauchy Index and Applications -- Real Roots -- Cylindrical Decomposition Algorithm -- Polynomial System Solving -- Existential Theory of the Reals -- Quantifier Elimination -- Computing Roadmaps and Connected Components of Algebraic Sets -- Computing Roadmaps and Connected Components of Semi-algebraic Sets En línea: http://dx.doi.org/10.1007/3-540-33099-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34952 Ejemplares
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Título : Binary Quadratic Forms : An Algorithmic Approach Tipo de documento: documento electrónico Autores: Johannes Buchmann ; SpringerLink (Online service) ; Vollmer, Ulrich Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2007 Colección: Algorithms and Computation in Mathematics, ISSN 1431-1550 num. 20 Número de páginas: XIV, 318 p Il.: online resource ISBN/ISSN/DL: 978-3-540-46368-9 Idioma : Inglés (eng) Palabras clave: Mathematics Data encryption (Computer science) Computer science Algebra Number theory Theory of Computing Encryption Clasificación: 51 Matemáticas Resumen: This book deals with algorithmic problems concerning binary quadratic forms 2 2 f(X,Y)= aX +bXY +cY with integer coe?cients a, b, c, the mathem- ical theories that permit the solution of these problems, and applications to cryptography. A considerable part of the theory is developed for forms with real coe?cients and it is shown that forms with integer coe?cients appear in a natural way. Much of the progress of number theory has been stimulated by the study of concrete computational problems. Deep theories were developed from the classic time of Euler and Gauss onwards to this day that made the solutions ofmanyof theseproblemspossible.Algorithmicsolutionsandtheirproperties became an object of study in their own right. Thisbookintertwinestheexpositionofoneveryclassicalstrandofnumber theory with the presentation and analysis of algorithms both classical and modern which solve its motivating problems. This algorithmic approach will lead the reader, we hope, not only to an understanding of theory and solution methods, but also to an appreciation of the e?ciency with which solutions can be reached. The computer age has led to a marked advancement of algorithmic - search. On the one hand, computers make it feasible to solve very hard pr- lems such as the solution of Pell equations with large coe?cients. On the other, the application of number theory in public-key cryptography increased the urgency for establishing the complexity of several computational pr- lems: many a computer system stays only secure as long as these problems remain intractable Nota de contenido: Binary Quadratic Forms -- Equivalence of Forms -- Constructing Forms -- Forms, Bases, Points, and Lattices -- Reduction of Positive Definite Forms -- Reduction of Indefinite Forms -- Multiplicative Lattices -- Quadratic Number Fields -- Class Groups -- Infrastructure -- Subexponential Algorithms -- Cryptographic Applications En línea: http://dx.doi.org/10.1007/978-3-540-46368-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34637 Binary Quadratic Forms : An Algorithmic Approach [documento electrónico] / Johannes Buchmann ; SpringerLink (Online service) ; Vollmer, Ulrich . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2007 . - XIV, 318 p : online resource. - (Algorithms and Computation in Mathematics, ISSN 1431-1550; 20) .
ISBN : 978-3-540-46368-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Data encryption (Computer science) Computer science Algebra Number theory Theory of Computing Encryption Clasificación: 51 Matemáticas Resumen: This book deals with algorithmic problems concerning binary quadratic forms 2 2 f(X,Y)= aX +bXY +cY with integer coe?cients a, b, c, the mathem- ical theories that permit the solution of these problems, and applications to cryptography. A considerable part of the theory is developed for forms with real coe?cients and it is shown that forms with integer coe?cients appear in a natural way. Much of the progress of number theory has been stimulated by the study of concrete computational problems. Deep theories were developed from the classic time of Euler and Gauss onwards to this day that made the solutions ofmanyof theseproblemspossible.Algorithmicsolutionsandtheirproperties became an object of study in their own right. Thisbookintertwinestheexpositionofoneveryclassicalstrandofnumber theory with the presentation and analysis of algorithms both classical and modern which solve its motivating problems. This algorithmic approach will lead the reader, we hope, not only to an understanding of theory and solution methods, but also to an appreciation of the e?ciency with which solutions can be reached. The computer age has led to a marked advancement of algorithmic - search. On the one hand, computers make it feasible to solve very hard pr- lems such as the solution of Pell equations with large coe?cients. On the other, the application of number theory in public-key cryptography increased the urgency for establishing the complexity of several computational pr- lems: many a computer system stays only secure as long as these problems remain intractable Nota de contenido: Binary Quadratic Forms -- Equivalence of Forms -- Constructing Forms -- Forms, Bases, Points, and Lattices -- Reduction of Positive Definite Forms -- Reduction of Indefinite Forms -- Multiplicative Lattices -- Quadratic Number Fields -- Class Groups -- Infrastructure -- Subexponential Algorithms -- Cryptographic Applications En línea: http://dx.doi.org/10.1007/978-3-540-46368-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34637 Ejemplares
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Título : Classification Algorithms for Codes and Designs Tipo de documento: documento electrónico Autores: Kaski, Petteri ; SpringerLink (Online service) ; Östergård, Patric R.J Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2006 Colección: Algorithms and Computation in Mathematics, ISSN 1431-1550 num. 15 Número de páginas: XI, 412 p Il.: online resource ISBN/ISSN/DL: 978-3-540-28991-3 Idioma : Inglés (eng) Palabras clave: Mathematics Coding theory Computer mathematics Combinatorics Electrical engineering Computational and Numerical Analysis Information Theory Communications Engineering, Networks Signal, Image Speech Processing Clasificación: 51 Matemáticas Resumen: A new starting-point and a new method are requisite, to insure a complete [classi?cation of the Steiner triple systems of order 15]. This method was furnished, and its tedious and di?cult execution und- taken, by Mr. Cole. F. N. Cole, L. D. Cummings, and H. S. White (1917) [129] The history of classifying combinatorial objects is as old as the history of the objects themselves. In the mid-19th century, Kirkman, Steiner, and others became the fathers of modern combinatorics, and their work – on various objects, including (what became later known as) Steiner triple systems – led to several classi?cation results. Almost a century earlier, in 1782, Euler [180] published some results on classifying small Latin squares, but for the ?rst few steps in this direction one should actually go at least as far back as ancient Greece and the proof that there are exactly ?ve Platonic solids. One of the most remarkable achievements in the early, pre-computer era is the classi?cation of the Steiner triple systems of order 15, quoted above. An onerous task that, today, no sensible person would attempt by hand calcu- tion. Because, with the exception of occasional parameters for which com- natorial arguments are e?ective (often to prove nonexistence or uniqueness), classi?cation in general is about algorithms and computation Nota de contenido: Graphs, Designs, and Codes -- Representations and Isomorphism -- Isomorph-Free Exhaustive Generation -- Auxiliary Algorithms -- Classification of Designs -- Classification of Codes -- Classification of Related Structures -- Prescribing Automorphism Groups -- Validity of Computational Results -- Computational Complexity -- Nonexistence of Projective Planes of Order 10 En línea: http://dx.doi.org/10.1007/3-540-28991-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34917 Classification Algorithms for Codes and Designs [documento electrónico] / Kaski, Petteri ; SpringerLink (Online service) ; Östergård, Patric R.J . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2006 . - XI, 412 p : online resource. - (Algorithms and Computation in Mathematics, ISSN 1431-1550; 15) .
ISBN : 978-3-540-28991-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Coding theory Computer mathematics Combinatorics Electrical engineering Computational and Numerical Analysis Information Theory Communications Engineering, Networks Signal, Image Speech Processing Clasificación: 51 Matemáticas Resumen: A new starting-point and a new method are requisite, to insure a complete [classi?cation of the Steiner triple systems of order 15]. This method was furnished, and its tedious and di?cult execution und- taken, by Mr. Cole. F. N. Cole, L. D. Cummings, and H. S. White (1917) [129] The history of classifying combinatorial objects is as old as the history of the objects themselves. In the mid-19th century, Kirkman, Steiner, and others became the fathers of modern combinatorics, and their work – on various objects, including (what became later known as) Steiner triple systems – led to several classi?cation results. Almost a century earlier, in 1782, Euler [180] published some results on classifying small Latin squares, but for the ?rst few steps in this direction one should actually go at least as far back as ancient Greece and the proof that there are exactly ?ve Platonic solids. One of the most remarkable achievements in the early, pre-computer era is the classi?cation of the Steiner triple systems of order 15, quoted above. An onerous task that, today, no sensible person would attempt by hand calcu- tion. Because, with the exception of occasional parameters for which com- natorial arguments are e?ective (often to prove nonexistence or uniqueness), classi?cation in general is about algorithms and computation Nota de contenido: Graphs, Designs, and Codes -- Representations and Isomorphism -- Isomorph-Free Exhaustive Generation -- Auxiliary Algorithms -- Classification of Designs -- Classification of Codes -- Classification of Related Structures -- Prescribing Automorphism Groups -- Validity of Computational Results -- Computational Complexity -- Nonexistence of Projective Planes of Order 10 En línea: http://dx.doi.org/10.1007/3-540-28991-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34917 Ejemplares
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Título : Combinatorial Algebraic Topology Tipo de documento: documento electrónico Autores: Kozlov, Dmitry ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2008 Colección: Algorithms and Computation in Mathematics, ISSN 1431-1550 num. 21 Número de páginas: XX, 390 p. 115 illus Il.: online resource ISBN/ISSN/DL: 978-3-540-71962-5 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic topology Combinatorics Topology Clasificación: 51 Matemáticas Resumen: Combinatorial algebraic topology is a fascinating and dynamic field at the crossroads of algebraic topology and discrete mathematics. This volume is the first comprehensive treatment of the subject in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology, including Stiefel-Whitney characteristic classes, which are needed for the later parts. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Our presentation of standard topics is quite different from that of existing texts. In addition, several new themes, such as spectral sequences, are included. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms. The main benefit for the reader will be the prospect of fairly quickly getting to the forefront of modern research in this active field Nota de contenido: Concepts of Algebraic Topology -- Overture -- Cell Complexes -- Homology Groups -- Concepts of Category Theory -- Exact Sequences -- Homotopy -- Cofibrations -- Principal ?-Bundles and Stiefel—Whitney Characteristic Classes -- Methods of Combinatorial Algebraic Topology -- Combinatorial Complexes Melange -- Acyclic Categories -- Discrete Morse Theory -- Lexicographic Shellability -- Evasiveness and Closure Operators -- Colimits and Quotients -- Homotopy Colimits -- Spectral Sequences -- Complexes of Graph Homomorphisms -- Chromatic Numbers and the Kneser Conjecture -- Structural Theory of Morphism Complexes -- Using Characteristic Classes to Design Tests for Chromatic Numbers of Graphs -- Applications of Spectral Sequences to Hom Complexes En línea: http://dx.doi.org/10.1007/978-3-540-71962-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34329 Combinatorial Algebraic Topology [documento electrónico] / Kozlov, Dmitry ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2008 . - XX, 390 p. 115 illus : online resource. - (Algorithms and Computation in Mathematics, ISSN 1431-1550; 21) .
ISBN : 978-3-540-71962-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic topology Combinatorics Topology Clasificación: 51 Matemáticas Resumen: Combinatorial algebraic topology is a fascinating and dynamic field at the crossroads of algebraic topology and discrete mathematics. This volume is the first comprehensive treatment of the subject in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology, including Stiefel-Whitney characteristic classes, which are needed for the later parts. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Our presentation of standard topics is quite different from that of existing texts. In addition, several new themes, such as spectral sequences, are included. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms. The main benefit for the reader will be the prospect of fairly quickly getting to the forefront of modern research in this active field Nota de contenido: Concepts of Algebraic Topology -- Overture -- Cell Complexes -- Homology Groups -- Concepts of Category Theory -- Exact Sequences -- Homotopy -- Cofibrations -- Principal ?-Bundles and Stiefel—Whitney Characteristic Classes -- Methods of Combinatorial Algebraic Topology -- Combinatorial Complexes Melange -- Acyclic Categories -- Discrete Morse Theory -- Lexicographic Shellability -- Evasiveness and Closure Operators -- Colimits and Quotients -- Homotopy Colimits -- Spectral Sequences -- Complexes of Graph Homomorphisms -- Chromatic Numbers and the Kneser Conjecture -- Structural Theory of Morphism Complexes -- Using Characteristic Classes to Design Tests for Chromatic Numbers of Graphs -- Applications of Spectral Sequences to Hom Complexes En línea: http://dx.doi.org/10.1007/978-3-540-71962-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34329 Ejemplares
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