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Título : Algebraic Geometry : An Introduction Tipo de documento: documento electrónico Autores: Daniel Perrin ; 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] / Daniel Perrin ; 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: Siegfried Bosch ; 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] / Siegfried Bosch ; 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 : Arithmetic Tales Tipo de documento: documento electrónico Autores: Olivier Bordellès ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2012 Otro editor: Imprint: Springer Colección: Universitext, ISSN 0172-5939 Número de páginas: XXI, 556 p. 5 illus Il.: online resource ISBN/ISSN/DL: 978-1-4471-4096-2 Idioma : Inglés (eng) Palabras clave: Mathematics Number theory Theory Mathematics, general Clasificación: 51 Matemáticas Resumen: Number theory was once famously labeled the queen of mathematics by Gauss. The multiplicative structure of the integers in particular deals with many fascinating problems some of which are easy to understand but very difficult to solve. In the past, a variety of very different techniques has been applied to further its understanding. Classical methods in analytic theory such as Mertens’ theorem and Chebyshev’s inequalities and the celebrated Prime Number Theorem give estimates for the distribution of prime numbers. Later on, multiplicative structure of integers leads to multiplicative arithmetical functions for which there are many important examples in number theory. Their theory involves the Dirichlet convolution product which arises with the inclusion of several summation techniques and a survey of classical results such as Hall and Tenenbaum’s theorem and the Möbius Inversion Formula. Another topic is the counting integer points close to smooth curves and its relation to the distribution of squarefree numbers, which is rarely covered in existing texts. Final chapters focus on exponential sums and algebraic number fields. A number of exercises at varying levels are also included. Topics in Multiplicative Number Theory introduces offers a comprehensive introduction into these topics with an emphasis on analytic number theory. Since it requires very little technical expertise it will appeal to a wide target group including upper level undergraduates, doctoral and masters level students Nota de contenido: Basic Tools -- Bézout and Gauss -- Prime Numbers -- Arithmetic Functions -- Integer Points Close to Smooth Curves -- Exponential Sums -- Algebraic Number Fields En línea: http://dx.doi.org/10.1007/978-1-4471-4096-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32728 Arithmetic Tales [documento electrónico] / Olivier Bordellès ; SpringerLink (Online service) . - London : Springer London : Imprint: Springer, 2012 . - XXI, 556 p. 5 illus : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-1-4471-4096-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Number theory Theory Mathematics, general Clasificación: 51 Matemáticas Resumen: Number theory was once famously labeled the queen of mathematics by Gauss. The multiplicative structure of the integers in particular deals with many fascinating problems some of which are easy to understand but very difficult to solve. In the past, a variety of very different techniques has been applied to further its understanding. Classical methods in analytic theory such as Mertens’ theorem and Chebyshev’s inequalities and the celebrated Prime Number Theorem give estimates for the distribution of prime numbers. Later on, multiplicative structure of integers leads to multiplicative arithmetical functions for which there are many important examples in number theory. Their theory involves the Dirichlet convolution product which arises with the inclusion of several summation techniques and a survey of classical results such as Hall and Tenenbaum’s theorem and the Möbius Inversion Formula. Another topic is the counting integer points close to smooth curves and its relation to the distribution of squarefree numbers, which is rarely covered in existing texts. Final chapters focus on exponential sums and algebraic number fields. A number of exercises at varying levels are also included. Topics in Multiplicative Number Theory introduces offers a comprehensive introduction into these topics with an emphasis on analytic number theory. Since it requires very little technical expertise it will appeal to a wide target group including upper level undergraduates, doctoral and masters level students Nota de contenido: Basic Tools -- Bézout and Gauss -- Prime Numbers -- Arithmetic Functions -- Integer Points Close to Smooth Curves -- Exponential Sums -- Algebraic Number Fields En línea: http://dx.doi.org/10.1007/978-1-4471-4096-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32728 Ejemplares
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Título : Arithmetics Tipo de documento: documento electrónico Autores: Marc Hindry ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2011 Colección: Universitext, ISSN 0172-5939 Número de páginas: XVIII, 322 p. 5 illus Il.: online resource ISBN/ISSN/DL: 978-1-4471-2131-2 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Algebraic geometry Field theory (Physics) Algorithms Number Theory Geometry and Polynomials Clasificación: 51 Matemáticas Resumen: Number theory is a branch of mathematics which draws its vitality from a rich historical background. It is also traditionally nourished through interactions with other areas of research, such as algebra, algebraic geometry, topology, complex analysis and harmonic analysis. More recently, it has made a spectacular appearance in the field of theoretical computer science and in questions of communication, cryptography and error-correcting codes. Providing an elementary introduction to the central topics in number theory, this book spans multiple areas of research. The first part corresponds to an advanced undergraduate course. All of the statements given in this part are of course accompanied by their proofs, with perhaps the exception of some results appearing at the end of the chapters. A copious list of exercises, of varying difficulty, are also included here. The second part is of a higher level and is relevant for the first year of graduate school. It contains an introduction to elliptic curves and a chapter entitled “Developments and Open Problems”, which introduces and brings together various themes oriented toward ongoing mathematical research. Given the multifaceted nature of number theory, the primary aims of this book are to: - provide an overview of the various forms of mathematics useful for studying numbers - demonstrate the necessity of deep and classical themes such as Gauss sums - highlight the role that arithmetic plays in modern applied mathematics - include recent proofs such as the polynomial primality algorithm - approach subjects of contemporary research such as elliptic curves - illustrate the beauty of arithmetic The prerequisites for this text are undergraduate level algebra and a little topology of Rn. It will be of use to undergraduates, graduates and phd students, and may also appeal to professional mathematicians as a reference text Nota de contenido: Finite Structures -- Applications: Algorithms, Primality and Factorization, Codes -- Algebra and Diophantine Equations -- Analytic Number Theory -- Elliptic Curves -- Developments and Open Problems -- Factorization -- Elementary Projective Geometry -- Galois Theory En línea: http://dx.doi.org/10.1007/978-1-4471-2131-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33211 Arithmetics [documento electrónico] / Marc Hindry ; SpringerLink (Online service) . - London : Springer London, 2011 . - XVIII, 322 p. 5 illus : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-1-4471-2131-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Algebraic geometry Field theory (Physics) Algorithms Number Theory Geometry and Polynomials Clasificación: 51 Matemáticas Resumen: Number theory is a branch of mathematics which draws its vitality from a rich historical background. It is also traditionally nourished through interactions with other areas of research, such as algebra, algebraic geometry, topology, complex analysis and harmonic analysis. More recently, it has made a spectacular appearance in the field of theoretical computer science and in questions of communication, cryptography and error-correcting codes. Providing an elementary introduction to the central topics in number theory, this book spans multiple areas of research. The first part corresponds to an advanced undergraduate course. All of the statements given in this part are of course accompanied by their proofs, with perhaps the exception of some results appearing at the end of the chapters. A copious list of exercises, of varying difficulty, are also included here. The second part is of a higher level and is relevant for the first year of graduate school. It contains an introduction to elliptic curves and a chapter entitled “Developments and Open Problems”, which introduces and brings together various themes oriented toward ongoing mathematical research. Given the multifaceted nature of number theory, the primary aims of this book are to: - provide an overview of the various forms of mathematics useful for studying numbers - demonstrate the necessity of deep and classical themes such as Gauss sums - highlight the role that arithmetic plays in modern applied mathematics - include recent proofs such as the polynomial primality algorithm - approach subjects of contemporary research such as elliptic curves - illustrate the beauty of arithmetic The prerequisites for this text are undergraduate level algebra and a little topology of Rn. It will be of use to undergraduates, graduates and phd students, and may also appeal to professional mathematicians as a reference text Nota de contenido: Finite Structures -- Applications: Algorithms, Primality and Factorization, Codes -- Algebra and Diophantine Equations -- Analytic Number Theory -- Elliptic Curves -- Developments and Open Problems -- Factorization -- Elementary Projective Geometry -- Galois Theory En línea: http://dx.doi.org/10.1007/978-1-4471-2131-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33211 Ejemplares
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Título : Automorphic Forms Tipo de documento: documento electrónico Autores: Anton Deitmar ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2012 Otro editor: Imprint: Springer Colección: Universitext, ISSN 0172-5939 Número de páginas: IX, 252 p. 2 illus Il.: online resource ISBN/ISSN/DL: 978-1-4471-4435-9 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Group theory Number Mathematics, general Theory and Generalizations Clasificación: 51 Matemáticas Resumen: Automorphic forms are an important complex analytic tool in number theory and modern arithmetic geometry. They played for example a vital role in Andrew Wiles's proof of Fermat's Last Theorem. This text provides a concise introduction to the world of automorphic forms using two approaches: the classic elementary theory and the modern point of view of adeles and representation theory. The reader will learn the important aims and results of the theory by focussing on its essential aspects and restricting it to the 'base field' of rational numbers. Students interested for example in arithmetic geometry or number theory will find that this book provides an optimal and easily accessible introduction into this topic En línea: http://dx.doi.org/10.1007/978-1-4471-4435-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32730 Automorphic Forms [documento electrónico] / Anton Deitmar ; SpringerLink (Online service) . - London : Springer London : Imprint: Springer, 2012 . - IX, 252 p. 2 illus : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-1-4471-4435-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Group theory Number Mathematics, general Theory and Generalizations Clasificación: 51 Matemáticas Resumen: Automorphic forms are an important complex analytic tool in number theory and modern arithmetic geometry. They played for example a vital role in Andrew Wiles's proof of Fermat's Last Theorem. This text provides a concise introduction to the world of automorphic forms using two approaches: the classic elementary theory and the modern point of view of adeles and representation theory. The reader will learn the important aims and results of the theory by focussing on its essential aspects and restricting it to the 'base field' of rational numbers. Students interested for example in arithmetic geometry or number theory will find that this book provides an optimal and easily accessible introduction into this topic En línea: http://dx.doi.org/10.1007/978-1-4471-4435-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32730 Ejemplares
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