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Título : Affine Maps, Euclidean Motions and Quadrics Tipo de documento: documento electrónico Autores: Agustí Reventós Tarrida ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2011 Colección: Springer Undergraduate Mathematics Series, ISSN 1615-2085 Número de páginas: XVIII, 458p. 49 illus Il.: online resource ISBN/ISSN/DL: 978-0-85729-710-5 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Mathematics, general Clasificación: 51 Matemáticas Resumen: Affine geometry and quadrics are fascinating subjects alone, but they are also important applications of linear algebra. They give a first glimpse into the world of algebraic geometry yet they are equally relevant to a wide range of disciplines such as engineering. This text discusses and classifies affinities and Euclidean motions culminating in classification results for quadrics. A high level of detail and generality is a key feature unmatched by other books available. Such intricacy makes this a particularly accessible teaching resource as it requires no extra time in deconstructing the author’s reasoning. The provision of a large number of exercises with hints will help students to develop their problem solving skills and will also be a useful resource for lecturers when setting work for independent study. Affinities, Euclidean Motions and Quadrics takes rudimentary, and often taken-for-granted, knowledge and presents it in a new, comprehensive form. Standard and non-standard examples are demonstrated throughout and an appendix provides the reader with a summary of advanced linear algebra facts for quick reference to the text. All factors combined, this is a self-contained book ideal for self-study that is not only foundational but unique in its approach.’ This text will be of use to lecturers in linear algebra and its applications to geometry as well as advanced undergraduate and beginning graduate students Nota de contenido: Affine Spaces -- Affinities -- Classification of Affinities -- Classification of Affinities in Arbitrary Dimension -- Euclidean Affine Spaces -- Euclidean motions -- Euclidean Motions of the Line, the Plane and of Space -- Affine Classification of Real Quadrics -- Orthogonal Classification of Quadrics -- Appendices En línea: http://dx.doi.org/10.1007/978-0-85729-710-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33132 Affine Maps, Euclidean Motions and Quadrics [documento electrónico] / Agustí Reventós Tarrida ; SpringerLink (Online service) . - London : Springer London, 2011 . - XVIII, 458p. 49 illus : online resource. - (Springer Undergraduate Mathematics Series, ISSN 1615-2085) .
ISBN : 978-0-85729-710-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Mathematics, general Clasificación: 51 Matemáticas Resumen: Affine geometry and quadrics are fascinating subjects alone, but they are also important applications of linear algebra. They give a first glimpse into the world of algebraic geometry yet they are equally relevant to a wide range of disciplines such as engineering. This text discusses and classifies affinities and Euclidean motions culminating in classification results for quadrics. A high level of detail and generality is a key feature unmatched by other books available. Such intricacy makes this a particularly accessible teaching resource as it requires no extra time in deconstructing the author’s reasoning. The provision of a large number of exercises with hints will help students to develop their problem solving skills and will also be a useful resource for lecturers when setting work for independent study. Affinities, Euclidean Motions and Quadrics takes rudimentary, and often taken-for-granted, knowledge and presents it in a new, comprehensive form. Standard and non-standard examples are demonstrated throughout and an appendix provides the reader with a summary of advanced linear algebra facts for quick reference to the text. All factors combined, this is a self-contained book ideal for self-study that is not only foundational but unique in its approach.’ This text will be of use to lecturers in linear algebra and its applications to geometry as well as advanced undergraduate and beginning graduate students Nota de contenido: Affine Spaces -- Affinities -- Classification of Affinities -- Classification of Affinities in Arbitrary Dimension -- Euclidean Affine Spaces -- Euclidean motions -- Euclidean Motions of the Line, the Plane and of Space -- Affine Classification of Real Quadrics -- Orthogonal Classification of Quadrics -- Appendices En línea: http://dx.doi.org/10.1007/978-0-85729-710-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33132 Ejemplares
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Título : An Introduction to Enumeration Tipo de documento: documento electrónico Autores: Alan Camina ; SpringerLink (Online service) ; Barry Lewis Editorial: London : Springer London Fecha de publicación: 2011 Colección: Springer Undergraduate Mathematics Series, ISSN 1615-2085 Número de páginas: XII, 232p. 62 illus Il.: online resource ISBN/ISSN/DL: 978-0-85729-600-9 Idioma : Inglés (eng) Palabras clave: Mathematics Group theory Combinatorics Theory and Generalizations Clasificación: 51 Matemáticas Resumen: Written for students taking a second or third year undergraduate course in mathematics or computer science, this book is the ideal companion to a course in enumeration. Enumeration is a branch of combinatorics where the fundamental subject matter is numerous methods of pattern formation and counting. An Introduction to Enumeration provides a comprehensive and practical introduction to this subject giving a clear account of fundamental results and a thorough grounding in the use of powerful techniques and tools. Two major themes run in parallel through the book, generating functions and group theory. The former theme takes enumerative sequences and then uses analytic tools to discover how they are made up. Group theory provides a concise introduction to groups and illustrates how the theory can be used to count the number of symmetries a particular object has. These enrich and extend basic group ideas and techniques. The authors present their material through examples that are carefully chosen to establish key results in a natural setting. The aim is to progressively build fundamental theorems and techniques. This development is interspersed with exercises that consolidate ideas and build confidence. Some exercises are linked to particular sections while others range across a complete chapter. Throughout, there is an attempt to present key enumerative ideas in a graphic way, using diagrams to make them immediately accessible. The development assumes some basic group theory, a familiarity with analytic functions and their power series expansion along with some basic linear algebra Nota de contenido: What Is Enumeration? -- Generating Functions Count -- Working with Generating Functions -- Permutation Groups -- Matrices, Sequences and Sums -- Group Actions and Counting -- Exponential Generating Functions -- Graphs -- partitions and Paths En línea: http://dx.doi.org/10.1007/978-0-85729-600-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33130 An Introduction to Enumeration [documento electrónico] / Alan Camina ; SpringerLink (Online service) ; Barry Lewis . - London : Springer London, 2011 . - XII, 232p. 62 illus : online resource. - (Springer Undergraduate Mathematics Series, ISSN 1615-2085) .
ISBN : 978-0-85729-600-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Group theory Combinatorics Theory and Generalizations Clasificación: 51 Matemáticas Resumen: Written for students taking a second or third year undergraduate course in mathematics or computer science, this book is the ideal companion to a course in enumeration. Enumeration is a branch of combinatorics where the fundamental subject matter is numerous methods of pattern formation and counting. An Introduction to Enumeration provides a comprehensive and practical introduction to this subject giving a clear account of fundamental results and a thorough grounding in the use of powerful techniques and tools. Two major themes run in parallel through the book, generating functions and group theory. The former theme takes enumerative sequences and then uses analytic tools to discover how they are made up. Group theory provides a concise introduction to groups and illustrates how the theory can be used to count the number of symmetries a particular object has. These enrich and extend basic group ideas and techniques. The authors present their material through examples that are carefully chosen to establish key results in a natural setting. The aim is to progressively build fundamental theorems and techniques. This development is interspersed with exercises that consolidate ideas and build confidence. Some exercises are linked to particular sections while others range across a complete chapter. Throughout, there is an attempt to present key enumerative ideas in a graphic way, using diagrams to make them immediately accessible. The development assumes some basic group theory, a familiarity with analytic functions and their power series expansion along with some basic linear algebra Nota de contenido: What Is Enumeration? -- Generating Functions Count -- Working with Generating Functions -- Permutation Groups -- Matrices, Sequences and Sums -- Group Actions and Counting -- Exponential Generating Functions -- Graphs -- partitions and Paths En línea: http://dx.doi.org/10.1007/978-0-85729-600-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33130 Ejemplares
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Título : Applied Geometry for Computer Graphics and CAD Tipo de documento: documento electrónico Autores: Marsh Duncan ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2005 Colección: Springer Undergraduate Mathematics Series, ISSN 1615-2085 Número de páginas: XV, 350 p Il.: online resource ISBN/ISSN/DL: 978-1-84628-109-9 Idioma : Inglés (eng) Palabras clave: Computer science graphics Application software Applied mathematics Engineering Geometry Science Applications of Mathematics Graphics Engineering, general Clasificación: 51 Matemáticas Resumen: Focusing on the manipulation and representation of geometrical objects, this book explores the application of geometry to computer graphics and computer-aided design (CAD). An introduction to transformations of the plane and three-dimensional space describes how objects can be constructed from geometric primitives and manipulated. This leads into a treatment of projections and the method of rendering objects on a computer screen by application of the complete viewing operation. Subsequently, the emphasis is on the two principal curve and surface representations, namely, Bézier and B-spline (including NURBS). As in the first edition, applications of the geometric theory are exemplified throughout the book, but new features in this revised and updated edition include: the application of quaternions to computer graphics animation and orientation; discussions of the main geometric CAD surface operations and constructions: extruded, rotated and swept surfaces; offset surfaces; thickening and shelling; and skin and loft surfaces; an introduction to rendering methods in computer graphics and CAD: colour, illumination models, shading algorithms, silhouettes and shadows. Over 300 exercises are included, some new to this edition, and many of which encourage the reader to implement the techniques and algorithms discussed through the use of a computer package with graphing and computer algebra capabilities. A dedicated website also offers further resources and links to other useful websites. Designed for students of computer science and engineering as well as of mathematics, the book provides a foundation in the extensive applications of geometry in real world situations Nota de contenido: Transformations of the Plane -- Homogeneous Coordinates and Transformations of the Plane -- Homogeneous Coordinates and Transformations of Space -- Projections and the Viewing Pipeline -- Curves -- Bézier Curves I -- Bézier Curves II -- B-splines -- Surfaces -- Curve and Surface Curvatures -- Rendering En línea: http://dx.doi.org/10.1007/b138823 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35219 Applied Geometry for Computer Graphics and CAD [documento electrónico] / Marsh Duncan ; SpringerLink (Online service) . - London : Springer London, 2005 . - XV, 350 p : online resource. - (Springer Undergraduate Mathematics Series, ISSN 1615-2085) .
ISBN : 978-1-84628-109-9
Idioma : Inglés (eng)
Palabras clave: Computer science graphics Application software Applied mathematics Engineering Geometry Science Applications of Mathematics Graphics Engineering, general Clasificación: 51 Matemáticas Resumen: Focusing on the manipulation and representation of geometrical objects, this book explores the application of geometry to computer graphics and computer-aided design (CAD). An introduction to transformations of the plane and three-dimensional space describes how objects can be constructed from geometric primitives and manipulated. This leads into a treatment of projections and the method of rendering objects on a computer screen by application of the complete viewing operation. Subsequently, the emphasis is on the two principal curve and surface representations, namely, Bézier and B-spline (including NURBS). As in the first edition, applications of the geometric theory are exemplified throughout the book, but new features in this revised and updated edition include: the application of quaternions to computer graphics animation and orientation; discussions of the main geometric CAD surface operations and constructions: extruded, rotated and swept surfaces; offset surfaces; thickening and shelling; and skin and loft surfaces; an introduction to rendering methods in computer graphics and CAD: colour, illumination models, shading algorithms, silhouettes and shadows. Over 300 exercises are included, some new to this edition, and many of which encourage the reader to implement the techniques and algorithms discussed through the use of a computer package with graphing and computer algebra capabilities. A dedicated website also offers further resources and links to other useful websites. Designed for students of computer science and engineering as well as of mathematics, the book provides a foundation in the extensive applications of geometry in real world situations Nota de contenido: Transformations of the Plane -- Homogeneous Coordinates and Transformations of the Plane -- Homogeneous Coordinates and Transformations of Space -- Projections and the Viewing Pipeline -- Curves -- Bézier Curves I -- Bézier Curves II -- B-splines -- Surfaces -- Curve and Surface Curvatures -- Rendering En línea: http://dx.doi.org/10.1007/b138823 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35219 Ejemplares
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Título : Calculus of One Variable Tipo de documento: documento electrónico Autores: Keith E. Hirst ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2006 Colección: Springer Undergraduate Mathematics Series, ISSN 1615-2085 Número de páginas: XII, 268 p. 72 illus Il.: online resource ISBN/ISSN/DL: 978-1-84628-222-5 Idioma : Inglés (eng) Palabras clave: Mathematics Functions of real variables Real Clasificación: 51 Matemáticas Resumen: Understanding the techniques and applications of calculus is at the heart of mathematics, science and engineering. This book presents the key topics of introductory calculus through an extensive, well-chosen collection of worked examples, covering; algebraic techniques functions and graphs an informal discussion of limits techniques of differentiation and integration Maclaurin and Taylor expansions geometrical applications Aimed at first-year undergraduates in mathematics and the physical sciences, the only prerequisites are basic algebra, coordinate geometry and the beginnings of differentiation as covered in school. The transition from school to university mathematics is addressed by means of a systematic development of important classes of techniques, and through careful discussion of the basic definitions and some of the theorems of calculus, with proofs where appropriate, but stopping short of the rigour involved in Real Analysis. The influence of technology on the learning and teaching of mathematics is recognised through the use of the computer algebra and graphical package MAPLE to illustrate many of the ideas. Readers are also encouraged to practice the essential techniques through numerous exercises which are an important component of the book. Supplementary material, including detailed solutions to exercises and MAPLE worksheets, is available via the web. Nota de contenido: Functions and Graphs -- Limits of Functions -- Differentiation -- Techniques of Differentiation -- Applications of Differentiation -- Maclaurin and Taylor Expansions -- Integration -- Integration by Parts -- Integration by Substitution -- Integration of Rational Functions -- Geometrical Applications of Integration En línea: http://dx.doi.org/10.1007/1-84628-222-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34902 Calculus of One Variable [documento electrónico] / Keith E. Hirst ; SpringerLink (Online service) . - London : Springer London, 2006 . - XII, 268 p. 72 illus : online resource. - (Springer Undergraduate Mathematics Series, ISSN 1615-2085) .
ISBN : 978-1-84628-222-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Functions of real variables Real Clasificación: 51 Matemáticas Resumen: Understanding the techniques and applications of calculus is at the heart of mathematics, science and engineering. This book presents the key topics of introductory calculus through an extensive, well-chosen collection of worked examples, covering; algebraic techniques functions and graphs an informal discussion of limits techniques of differentiation and integration Maclaurin and Taylor expansions geometrical applications Aimed at first-year undergraduates in mathematics and the physical sciences, the only prerequisites are basic algebra, coordinate geometry and the beginnings of differentiation as covered in school. The transition from school to university mathematics is addressed by means of a systematic development of important classes of techniques, and through careful discussion of the basic definitions and some of the theorems of calculus, with proofs where appropriate, but stopping short of the rigour involved in Real Analysis. The influence of technology on the learning and teaching of mathematics is recognised through the use of the computer algebra and graphical package MAPLE to illustrate many of the ideas. Readers are also encouraged to practice the essential techniques through numerous exercises which are an important component of the book. Supplementary material, including detailed solutions to exercises and MAPLE worksheets, is available via the web. Nota de contenido: Functions and Graphs -- Limits of Functions -- Differentiation -- Techniques of Differentiation -- Applications of Differentiation -- Maclaurin and Taylor Expansions -- Integration -- Integration by Parts -- Integration by Substitution -- Integration of Rational Functions -- Geometrical Applications of Integration En línea: http://dx.doi.org/10.1007/1-84628-222-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34902 Ejemplares
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Título : Codes: An Introduction to Information Communication and Cryptography Tipo de documento: documento electrónico Autores: Norman L. Biggs ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2008 Colección: Springer Undergraduate Mathematics Series, ISSN 1615-2085 Número de páginas: X, 274 p. 36 illus Il.: online resource ISBN/ISSN/DL: 978-1-84800-273-9 Idioma : Inglés (eng) Palabras clave: Computer science Data structures (Computer science) Coding theory Information Number Combinatorics Electrical engineering Science and Theory Communications Engineering, Networks Communication, Circuits Structures, Cryptology Clasificación: 51 Matemáticas Resumen: Information is an important feature of the modern world. Mathematical techniques underlie the devices that we use to handle it, for example, mobile phones, digital cameras, and personal computers. This book is an integrated introduction to the mathematics of coding, that is, replacing information expressed in symbols, such as a natural language or a sequence of bits, by another message using (possibly) different symbols. There are three main reasons for doing this: economy, reliability, and security, and each is covered in detail. Only a modest mathematical background is assumed, the mathematical theory being introduced at a level that enables the basic problems to be stated carefully, but without unnecessary abstraction. Other features include: clear and careful exposition of fundamental concepts, including optimal coding, data compression, and public-key cryptography; concise but complete proofs of results; coverage of recent advances of practical interest, for example in encryption standards, authentication schemes, and elliptic curve cryptography; numerous examples and exercises, and a full solutions manual available to lecturers from www.springer.com This modern introduction to all aspects of coding is suitable for advanced undergraduate or postgraduate courses in mathematics, computer science, electrical engineering, or informatics. It is also useful for researchers and practitioners in related areas of science, engineering and economics Nota de contenido: Coding and its uses -- Prefix free codes -- Economical coding -- Data compression -- Noisy channels -- The problem of reliable communication -- The noisy coding theorems -- Linear codes -- Algebraic coding theory -- Coding natural languages -- The development of cryptography -- Cryptography in theory and practice -- The RSA cryptosystem -- Cryptography and calculation -- Elliptic curve cryptography En línea: http://dx.doi.org/10.1007/978-1-84800-273-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34306 Codes: An Introduction to Information Communication and Cryptography [documento electrónico] / Norman L. Biggs ; SpringerLink (Online service) . - London : Springer London, 2008 . - X, 274 p. 36 illus : online resource. - (Springer Undergraduate Mathematics Series, ISSN 1615-2085) .
ISBN : 978-1-84800-273-9
Idioma : Inglés (eng)
Palabras clave: Computer science Data structures (Computer science) Coding theory Information Number Combinatorics Electrical engineering Science and Theory Communications Engineering, Networks Communication, Circuits Structures, Cryptology Clasificación: 51 Matemáticas Resumen: Information is an important feature of the modern world. Mathematical techniques underlie the devices that we use to handle it, for example, mobile phones, digital cameras, and personal computers. This book is an integrated introduction to the mathematics of coding, that is, replacing information expressed in symbols, such as a natural language or a sequence of bits, by another message using (possibly) different symbols. There are three main reasons for doing this: economy, reliability, and security, and each is covered in detail. Only a modest mathematical background is assumed, the mathematical theory being introduced at a level that enables the basic problems to be stated carefully, but without unnecessary abstraction. Other features include: clear and careful exposition of fundamental concepts, including optimal coding, data compression, and public-key cryptography; concise but complete proofs of results; coverage of recent advances of practical interest, for example in encryption standards, authentication schemes, and elliptic curve cryptography; numerous examples and exercises, and a full solutions manual available to lecturers from www.springer.com This modern introduction to all aspects of coding is suitable for advanced undergraduate or postgraduate courses in mathematics, computer science, electrical engineering, or informatics. It is also useful for researchers and practitioners in related areas of science, engineering and economics Nota de contenido: Coding and its uses -- Prefix free codes -- Economical coding -- Data compression -- Noisy channels -- The problem of reliable communication -- The noisy coding theorems -- Linear codes -- Algebraic coding theory -- Coding natural languages -- The development of cryptography -- Cryptography in theory and practice -- The RSA cryptosystem -- Cryptography and calculation -- Elliptic curve cryptography En línea: http://dx.doi.org/10.1007/978-1-84800-273-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34306 Ejemplares
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