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Autor Jean Gallier |
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Título : Discrete Mathematics Tipo de documento: documento electrónico Autores: Jean Gallier ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Colección: Universitext, ISSN 0172-5939 Número de páginas: XIV, 466 p. 220 illus., 20 illus. in color Il.: online resource ISBN/ISSN/DL: 978-1-4419-8047-2 Idioma : Inglés (eng) Palabras clave: Mathematics Computer graphics Applied mathematics Engineering Number theory design Theory Imaging, Vision, Pattern Recognition and Graphics Design Applications of Clasificación: 51 Matemáticas Resumen: This book gives an introduction to discrete mathematics for beginning undergraduates and starts with a chapter on the rules of mathematical reasoning. This book begins with a presentation of the rules of logic as used in mathematics where many examples of formal and informal proofs are given. With this logical framework firmly in place, the book describes the major axioms of set theory and introduces the natural numbers. The rest of the book deals with functions and relations, directed and undirected graphs and an introduction to combinatorics, partial orders and complete induction. There is a section on public key cryptography and RSA, with complete proofs of Fermat's little theorem and the correctness of the RSA scheme, as well as explicit algorithms to perform modular arithmetic. The last chapter provides more graph theory where Eulerian and Hamiltonian cycles are discussed. This book also includes network flows, matchings, covering, bipartite graphs, planar graphs and state the graph minor theorem of Seymour and Robertson. The book is highly illustrated and each chapter ends with a list of problems of varying difficulty. Undergraduates in mathematics and computer science will find this book useful. Nota de contenido: Mathematical Reasoning, Proof Principles and Logic -- Relations, Functions, Partial Functions -- Graphs, Part I: Basic Notions -- Some Counting Problems; Multinomial Coefficients -- Partial Orders, GCD's, RSA, Lattices -- Graphs, Part II: More Advanced Notions -- Answers to Selected Problems En línea: http://dx.doi.org/10.1007/978-1-4419-8047-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33179 Discrete Mathematics [documento electrónico] / Jean Gallier ; SpringerLink (Online service) . - New York, NY : Springer New York, 2011 . - XIV, 466 p. 220 illus., 20 illus. in color : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-1-4419-8047-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Computer graphics Applied mathematics Engineering Number theory design Theory Imaging, Vision, Pattern Recognition and Graphics Design Applications of Clasificación: 51 Matemáticas Resumen: This book gives an introduction to discrete mathematics for beginning undergraduates and starts with a chapter on the rules of mathematical reasoning. This book begins with a presentation of the rules of logic as used in mathematics where many examples of formal and informal proofs are given. With this logical framework firmly in place, the book describes the major axioms of set theory and introduces the natural numbers. The rest of the book deals with functions and relations, directed and undirected graphs and an introduction to combinatorics, partial orders and complete induction. There is a section on public key cryptography and RSA, with complete proofs of Fermat's little theorem and the correctness of the RSA scheme, as well as explicit algorithms to perform modular arithmetic. The last chapter provides more graph theory where Eulerian and Hamiltonian cycles are discussed. This book also includes network flows, matchings, covering, bipartite graphs, planar graphs and state the graph minor theorem of Seymour and Robertson. The book is highly illustrated and each chapter ends with a list of problems of varying difficulty. Undergraduates in mathematics and computer science will find this book useful. Nota de contenido: Mathematical Reasoning, Proof Principles and Logic -- Relations, Functions, Partial Functions -- Graphs, Part I: Basic Notions -- Some Counting Problems; Multinomial Coefficients -- Partial Orders, GCD's, RSA, Lattices -- Graphs, Part II: More Advanced Notions -- Answers to Selected Problems En línea: http://dx.doi.org/10.1007/978-1-4419-8047-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33179 Ejemplares
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Título : Geometric Methods and Applications : For Computer Science and Engineering Tipo de documento: documento electrónico Autores: Jean Gallier ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Colección: Texts in Applied Mathematics, ISSN 0939-2475 num. 38 Número de páginas: XXVIII, 680 p Il.: online resource ISBN/ISSN/DL: 978-1-4419-9961-0 Idioma : Inglés (eng) Palabras clave: Mathematics Computer graphics Geometry Mathematical optimization Control engineering Robotics Mechatronics Imaging, Vision, Pattern Recognition and Graphics Control, Robotics, Optimization Clasificación: 51 Matemáticas Resumen: This book is an introduction to the fundamental concepts and tools needed for solving problems of a geometric nature using a computer. It attempts to fill the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, robotics, or machine learning. This book covers the following topics: affine geometry, projective geometry, Euclidean geometry, convex sets, SVD and principal component analysis, manifolds and Lie groups, quadratic optimization, basics of differential geometry, and a glimpse of computational geometry (Voronoi diagrams and Delaunay triangulations). Some practical applications of the concepts presented in this book include computer vision, more specifically contour grouping, motion interpolation, and robot kinematics. In this extensively updated second edition, more material on convex sets, Farkas’s lemma, quadratic optimization and the Schur complement have been added. The chapter on SVD has been greatly expanded and now includes a presentation of PCA. The book is well illustrated and has chapter summaries and a large number of exercises throughout. It will be of interest to a wide audience including computer scientists, mathematicians, and engineers. Reviews of first edition: "Gallier's book will be a useful source for anyone interested in applications of geometrical methods to solve problems that arise in various branches of engineering. It may help to develop the sophisticated concepts from the more advanced parts of geometry into useful tools for applications." (Mathematical Reviews, 2001) "...it will be useful as a reference book for postgraduates wishing to find the connection between their current problem and the underlying geometry." (The Australian Mathematical Society, 2001) Nota de contenido: Introduction -- Basics of Affine Geometry -- Basic Properties of Convex Sets -- Embedding an Affine Space in a Vector Space -- Basics of Projective Geometry -- Basics of Euclidean Geometry -- Separating and Supporting Hyperplanes; Polar Duality -- Polytopes and Polyhedra -- The Cartan–Dieudonn´e Theorem -- The Quaternions and the Spaces S3, SU(2), SO(3), and RP3 -- Dirichlet–Voronoi Diagrams -- Basics of Hermitian Geometry -- Spectral Theorems -- Singular Value Decomposition (SVD) and Polar Form -- Applications of SVD and Pseudo-Inverses -- Quadratic Optimization Problems -- Schur Complements and Applications -- Quadratic Optimization and Contour Grouping -- Basics of Manifolds and Classical Lie Groups -- Basics of the Differential Geometry of Curves -- Basics of the Differential Geometry of Surfaces -- Appendix -- References -- Symbol Index -- IndexAppendix -- References -- Symbol Index -- Index En línea: http://dx.doi.org/10.1007/978-1-4419-9961-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33210 Geometric Methods and Applications : For Computer Science and Engineering [documento electrónico] / Jean Gallier ; SpringerLink (Online service) . - New York, NY : Springer New York, 2011 . - XXVIII, 680 p : online resource. - (Texts in Applied Mathematics, ISSN 0939-2475; 38) .
ISBN : 978-1-4419-9961-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Computer graphics Geometry Mathematical optimization Control engineering Robotics Mechatronics Imaging, Vision, Pattern Recognition and Graphics Control, Robotics, Optimization Clasificación: 51 Matemáticas Resumen: This book is an introduction to the fundamental concepts and tools needed for solving problems of a geometric nature using a computer. It attempts to fill the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, robotics, or machine learning. This book covers the following topics: affine geometry, projective geometry, Euclidean geometry, convex sets, SVD and principal component analysis, manifolds and Lie groups, quadratic optimization, basics of differential geometry, and a glimpse of computational geometry (Voronoi diagrams and Delaunay triangulations). Some practical applications of the concepts presented in this book include computer vision, more specifically contour grouping, motion interpolation, and robot kinematics. In this extensively updated second edition, more material on convex sets, Farkas’s lemma, quadratic optimization and the Schur complement have been added. The chapter on SVD has been greatly expanded and now includes a presentation of PCA. The book is well illustrated and has chapter summaries and a large number of exercises throughout. It will be of interest to a wide audience including computer scientists, mathematicians, and engineers. Reviews of first edition: "Gallier's book will be a useful source for anyone interested in applications of geometrical methods to solve problems that arise in various branches of engineering. It may help to develop the sophisticated concepts from the more advanced parts of geometry into useful tools for applications." (Mathematical Reviews, 2001) "...it will be useful as a reference book for postgraduates wishing to find the connection between their current problem and the underlying geometry." (The Australian Mathematical Society, 2001) Nota de contenido: Introduction -- Basics of Affine Geometry -- Basic Properties of Convex Sets -- Embedding an Affine Space in a Vector Space -- Basics of Projective Geometry -- Basics of Euclidean Geometry -- Separating and Supporting Hyperplanes; Polar Duality -- Polytopes and Polyhedra -- The Cartan–Dieudonn´e Theorem -- The Quaternions and the Spaces S3, SU(2), SO(3), and RP3 -- Dirichlet–Voronoi Diagrams -- Basics of Hermitian Geometry -- Spectral Theorems -- Singular Value Decomposition (SVD) and Polar Form -- Applications of SVD and Pseudo-Inverses -- Quadratic Optimization Problems -- Schur Complements and Applications -- Quadratic Optimization and Contour Grouping -- Basics of Manifolds and Classical Lie Groups -- Basics of the Differential Geometry of Curves -- Basics of the Differential Geometry of Surfaces -- Appendix -- References -- Symbol Index -- IndexAppendix -- References -- Symbol Index -- Index En línea: http://dx.doi.org/10.1007/978-1-4419-9961-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33210 Ejemplares
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Título : A Guide to the Classification Theorem for Compact Surfaces Tipo de documento: documento electrónico Autores: Jean Gallier ; SpringerLink (Online service) ; Dianna Xu Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Geometry and Computing, ISSN 1866-6795 num. 9 Número de páginas: XII, 178 p. 78 illus., 20 illus. in color Il.: online resource ISBN/ISSN/DL: 978-3-642-34364-3 Idioma : Inglés (eng) Palabras clave: Mathematics Topology Algebraic topology Manifolds (Mathematics) Complex manifolds and Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: This welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those without detailed background knowledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated, student-centred approach details a near-complete proof of this theorem, widely admired for its efficacy and formal beauty. The authors present the technical tools needed to deploy the method effectively as well as demonstrating their use in a clearly structured, worked example. Ideal for students whose mastery of algebraic topology may be a work-in-progress, the text introduces key notions such as fundamental groups, homology groups, and the Euler-Poincaré characteristic. These prerequisites are the subject of detailed appendices that enable focused, discrete learning where it is required, without interrupting the carefully planned structure of the core exposition. Gently guiding readers through the principles, theory, and applications of the classification theorem, the authors aim to foster genuine confidence in its use and in so doing encourage readers to move on to a deeper exploration of the versatile and valuable techniques available in algebraic topology Nota de contenido: The Classification Theorem: Informal Presentation -- Surfaces -- Simplices, Complexes, and Triangulations -- The Fundamental Group, Orientability -- Homology Groups -- The Classification Theorem for Compact Surfaces -- Viewing the Real Projective Plane in R3 -- Proof of Proposition 5.1 -- Topological Preliminaries -- History of the Classification Theorem -- Every Surface Can be Triangulated -- Notes En línea: http://dx.doi.org/10.1007/978-3-642-34364-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32549 A Guide to the Classification Theorem for Compact Surfaces [documento electrónico] / Jean Gallier ; SpringerLink (Online service) ; Dianna Xu . - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013 . - XII, 178 p. 78 illus., 20 illus. in color : online resource. - (Geometry and Computing, ISSN 1866-6795; 9) .
ISBN : 978-3-642-34364-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Topology Algebraic topology Manifolds (Mathematics) Complex manifolds and Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: This welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those without detailed background knowledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated, student-centred approach details a near-complete proof of this theorem, widely admired for its efficacy and formal beauty. The authors present the technical tools needed to deploy the method effectively as well as demonstrating their use in a clearly structured, worked example. Ideal for students whose mastery of algebraic topology may be a work-in-progress, the text introduces key notions such as fundamental groups, homology groups, and the Euler-Poincaré characteristic. These prerequisites are the subject of detailed appendices that enable focused, discrete learning where it is required, without interrupting the carefully planned structure of the core exposition. Gently guiding readers through the principles, theory, and applications of the classification theorem, the authors aim to foster genuine confidence in its use and in so doing encourage readers to move on to a deeper exploration of the versatile and valuable techniques available in algebraic topology Nota de contenido: The Classification Theorem: Informal Presentation -- Surfaces -- Simplices, Complexes, and Triangulations -- The Fundamental Group, Orientability -- Homology Groups -- The Classification Theorem for Compact Surfaces -- Viewing the Real Projective Plane in R3 -- Proof of Proposition 5.1 -- Topological Preliminaries -- History of the Classification Theorem -- Every Surface Can be Triangulated -- Notes En línea: http://dx.doi.org/10.1007/978-3-642-34364-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32549 Ejemplares
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