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Título : Affine Maps, Euclidean Motions and Quadrics Tipo de documento: documento electrónico Autores: Reventós Tarrida, Agustí ; 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] / Reventós Tarrida, Agustí ; 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 : Algebraic Geometry : An Introduction Tipo de documento: documento electrónico Autores: Perrin, Daniel ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2008 Colección: Universitext, ISSN 0172-5939 Número de páginas: XI, 263 p Il.: online resource ISBN/ISSN/DL: 978-1-84800-056-8 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic geometry Algebra Geometry General Systems Mathematics, general Clasificación: 51 Matemáticas Resumen: Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject and assumes only the standard background of undergraduate algebra. It is developed from a masters course given at the Université Paris-Sud, Orsay, and focusses on projective algebraic geometry over an algebraically closed base field. The book starts with easily-formulated problems with non-trivial solutions – for example, Bézout’s theorem and the problem of rational curves – and uses these problems to introduce the fundamental tools of modern algebraic geometry: dimension; singularities; sheaves; varieties; and cohomology. The treatment uses as little commutative algebra as possible by quoting without proof (or proving only in special cases) theorems whose proof is not necessary in practice, the priority being to develop an understanding of the phenomena rather than a mastery of the technique. A range of exercises is provided for each topic discussed, and a selection of problems and exam papers are collected in an appendix to provide material for further study Nota de contenido: Affine algebraic sets -- Projective algebraic sets -- Sheaves and varieties -- Dimension -- Tangent spaces and singular points -- Bézout's theorem -- Sheaf cohomology -- Arithmetic genus of curves and the weak Riemann-Roch theorem -- Rational maps, geometric genus and rational curves -- Liaison of space curves En línea: http://dx.doi.org/10.1007/978-1-84800-056-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34304 Algebraic Geometry : An Introduction [documento electrónico] / Perrin, Daniel ; SpringerLink (Online service) . - London : Springer London, 2008 . - XI, 263 p : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-1-84800-056-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic geometry Algebra Geometry General Systems Mathematics, general Clasificación: 51 Matemáticas Resumen: Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject and assumes only the standard background of undergraduate algebra. It is developed from a masters course given at the Université Paris-Sud, Orsay, and focusses on projective algebraic geometry over an algebraically closed base field. The book starts with easily-formulated problems with non-trivial solutions – for example, Bézout’s theorem and the problem of rational curves – and uses these problems to introduce the fundamental tools of modern algebraic geometry: dimension; singularities; sheaves; varieties; and cohomology. The treatment uses as little commutative algebra as possible by quoting without proof (or proving only in special cases) theorems whose proof is not necessary in practice, the priority being to develop an understanding of the phenomena rather than a mastery of the technique. A range of exercises is provided for each topic discussed, and a selection of problems and exam papers are collected in an appendix to provide material for further study Nota de contenido: Affine algebraic sets -- Projective algebraic sets -- Sheaves and varieties -- Dimension -- Tangent spaces and singular points -- Bézout's theorem -- Sheaf cohomology -- Arithmetic genus of curves and the weak Riemann-Roch theorem -- Rational maps, geometric genus and rational curves -- Liaison of space curves En línea: http://dx.doi.org/10.1007/978-1-84800-056-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34304 Ejemplares
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Título : Algebraic Geometry and Commutative Algebra Tipo de documento: documento electrónico Autores: Bosch, Siegfried ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Universitext, ISSN 0172-5939 Número de páginas: X, 504 p Il.: online resource ISBN/ISSN/DL: 978-1-4471-4829-6 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic geometry Commutative algebra rings Geometry Rings and Algebras Clasificación: 51 Matemáticas Resumen: Algebraic geometry is a fascinating branch of mathematics that combines methods from both algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover, Grothendieck’s schemes invented in the late 1950s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from geometry (algebraic number theory, for example). The new techniques paved the way to spectacular progress such as the proof of Fermat’s Last Theorem by Wiles and Taylor. The scheme-theoretic approach to algebraic geometry is explained for non-experts whilst more advanced readers can use the book to broaden their view on the subject. A separate part studies the necessary prerequisites from commutative algebra. The book provides an accessible and self-contained introduction to algebraic geometry, up to an advanced level. Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents. Typical examples and an abundance of exercises illustrate each section. Therefore the book is an excellent solution for learning by yourself or for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature Nota de contenido: Rings and Modules -- The Theory of Noetherian Rings -- Integral Extensions -- Extension of Coefficients and Descent -- Homological Methods: Ext and Tor -- Affine Schemes and Basic Constructions -- Techniques of Global Schemes -- Etale and Smooth Morphisms -- Projective Schemes and Proper Morphisms En línea: http://dx.doi.org/10.1007/978-1-4471-4829-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32195 Algebraic Geometry and Commutative Algebra [documento electrónico] / Bosch, Siegfried ; SpringerLink (Online service) . - London : Springer London : Imprint: Springer, 2013 . - X, 504 p : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-1-4471-4829-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic geometry Commutative algebra rings Geometry Rings and Algebras Clasificación: 51 Matemáticas Resumen: Algebraic geometry is a fascinating branch of mathematics that combines methods from both algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover, Grothendieck’s schemes invented in the late 1950s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from geometry (algebraic number theory, for example). The new techniques paved the way to spectacular progress such as the proof of Fermat’s Last Theorem by Wiles and Taylor. The scheme-theoretic approach to algebraic geometry is explained for non-experts whilst more advanced readers can use the book to broaden their view on the subject. A separate part studies the necessary prerequisites from commutative algebra. The book provides an accessible and self-contained introduction to algebraic geometry, up to an advanced level. Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents. Typical examples and an abundance of exercises illustrate each section. Therefore the book is an excellent solution for learning by yourself or for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature Nota de contenido: Rings and Modules -- The Theory of Noetherian Rings -- Integral Extensions -- Extension of Coefficients and Descent -- Homological Methods: Ext and Tor -- Affine Schemes and Basic Constructions -- Techniques of Global Schemes -- Etale and Smooth Morphisms -- Projective Schemes and Proper Morphisms En línea: http://dx.doi.org/10.1007/978-1-4471-4829-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32195 Ejemplares
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Título : An Introduction to Echo Analysis : Scattering Theory and Wave Propagation Tipo de documento: documento electrónico Autores: Roach, G. F ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2008 Colección: Springer Monographs in Mathematics, ISSN 1439-7382 Número de páginas: X, 320 p Il.: online resource ISBN/ISSN/DL: 978-1-84628-852-4 Idioma : Inglés (eng) Palabras clave: Physics Functional analysis Operator theory Partial differential equations Optics Electrodynamics and Analysis Theory Differential Equations Clasificación: 51 Matemáticas Resumen: The use of various types of wave energy is an increasingly promising, non-destructive means of detecting objects and of diagnosing the properties of quite complicated materials. An analysis of this technique requires an understanding of how waves evolve in the medium of interest and how they are scattered by inhomogeneities in the medium. These scattering phenomena can be thought of as arising from some perturbation of a given, known system and they are analysed by developing a scattering theory. This monograph provides an introductory account of scattering phenomena and a guide to the technical requirements for investigating wave scattering problems. It gathers together the principal mathematical topics which are required when dealing with wave propagation and scattering problems, and indicates how to use the material to develop the required solutions. Both potential and target scattering phenomena are investigated and extensions of the theory to the electromagnetic and elastic fields are provided. Throughout, the emphasis is on concepts and results rather than on the fine detail of proof; a bibliography at the end of each chapter points the interested reader to more detailed proofs of the theorems and suggests directions for further reading. Aimed at graduate and postgraduate students and researchers in mathematics and the applied sciences, this book aims to provide the newcomer to the field with a unified, and reasonably self-contained, introduction to an exciting research area and, for the more experienced reader, a source of information and techniques Nota de contenido: and Outline of Contents -- Some One-Dimensional Examples -- Preliminary Mathematical Material -- Hilbert Spaces -- Two Important Techniques -- A Scattering Theory Strategy -- An Approach to Echo Analysis -- Scattering Processes in Stratified Media -- Scattering in Spatially Periodic Media -- Inverse Scattering Problems -- Scattering in Other Wave Systems -- Commentary En línea: http://dx.doi.org/10.1007/978-1-84628-852-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34298 An Introduction to Echo Analysis : Scattering Theory and Wave Propagation [documento electrónico] / Roach, G. F ; SpringerLink (Online service) . - London : Springer London, 2008 . - X, 320 p : online resource. - (Springer Monographs in Mathematics, ISSN 1439-7382) .
ISBN : 978-1-84628-852-4
Idioma : Inglés (eng)
Palabras clave: Physics Functional analysis Operator theory Partial differential equations Optics Electrodynamics and Analysis Theory Differential Equations Clasificación: 51 Matemáticas Resumen: The use of various types of wave energy is an increasingly promising, non-destructive means of detecting objects and of diagnosing the properties of quite complicated materials. An analysis of this technique requires an understanding of how waves evolve in the medium of interest and how they are scattered by inhomogeneities in the medium. These scattering phenomena can be thought of as arising from some perturbation of a given, known system and they are analysed by developing a scattering theory. This monograph provides an introductory account of scattering phenomena and a guide to the technical requirements for investigating wave scattering problems. It gathers together the principal mathematical topics which are required when dealing with wave propagation and scattering problems, and indicates how to use the material to develop the required solutions. Both potential and target scattering phenomena are investigated and extensions of the theory to the electromagnetic and elastic fields are provided. Throughout, the emphasis is on concepts and results rather than on the fine detail of proof; a bibliography at the end of each chapter points the interested reader to more detailed proofs of the theorems and suggests directions for further reading. Aimed at graduate and postgraduate students and researchers in mathematics and the applied sciences, this book aims to provide the newcomer to the field with a unified, and reasonably self-contained, introduction to an exciting research area and, for the more experienced reader, a source of information and techniques Nota de contenido: and Outline of Contents -- Some One-Dimensional Examples -- Preliminary Mathematical Material -- Hilbert Spaces -- Two Important Techniques -- A Scattering Theory Strategy -- An Approach to Echo Analysis -- Scattering Processes in Stratified Media -- Scattering in Spatially Periodic Media -- Inverse Scattering Problems -- Scattering in Other Wave Systems -- Commentary En línea: http://dx.doi.org/10.1007/978-1-84628-852-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34298 Ejemplares
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Título : An Introduction to Enumeration Tipo de documento: documento electrónico Autores: Camina, Alan ; SpringerLink (Online service) ; Lewis, Barry 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] / Camina, Alan ; SpringerLink (Online service) ; Lewis, Barry . - 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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