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Autor Shafarevich, Igor R |
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Título : Basic Algebraic Geometry 1 : Varieties in Projective Space Tipo de documento: documento electrónico Autores: Shafarevich, Igor R ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2013 Otro editor: Imprint: Springer Número de páginas: XVIII, 310 p Il.: online resource ISBN/ISSN/DL: 978-3-642-37956-7 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic geometry Physics Geometry Theoretical, Mathematical and Computational Clasificación: 51 Matemáticas Resumen: Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich’s book is a must.'' The third edition, in addition to some minor corrections, now offers a new treatment of the Riemann--Roch theorem for curves, including a proof from first principles. Shafarevich's book is an attractive and accessible introduction to algebraic geometry, suitable for beginning students and nonspecialists, and the new edition is set to remain a popular introduction to the field Nota de contenido: Preface -- Book 1. Varieties in Projective Space: Chapter 1. Basic Notions -- Chapter II. Local Properties -- Chapter III. Divisors and Differential Forms -- Chapter IV. Intersection Numbers -- Algebraic Appendix -- References -- Index En línea: http://dx.doi.org/10.1007/978-3-642-37956-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32581 Basic Algebraic Geometry 1 : Varieties in Projective Space [documento electrónico] / Shafarevich, Igor R ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013 . - XVIII, 310 p : online resource.
ISBN : 978-3-642-37956-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic geometry Physics Geometry Theoretical, Mathematical and Computational Clasificación: 51 Matemáticas Resumen: Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich’s book is a must.'' The third edition, in addition to some minor corrections, now offers a new treatment of the Riemann--Roch theorem for curves, including a proof from first principles. Shafarevich's book is an attractive and accessible introduction to algebraic geometry, suitable for beginning students and nonspecialists, and the new edition is set to remain a popular introduction to the field Nota de contenido: Preface -- Book 1. Varieties in Projective Space: Chapter 1. Basic Notions -- Chapter II. Local Properties -- Chapter III. Divisors and Differential Forms -- Chapter IV. Intersection Numbers -- Algebraic Appendix -- References -- Index En línea: http://dx.doi.org/10.1007/978-3-642-37956-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32581 Ejemplares
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Título : Basic Algebraic Geometry 2 : Schemes and Complex Manifolds Tipo de documento: documento electrónico Autores: Shafarevich, Igor R ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2013 Otro editor: Imprint: Springer Número de páginas: XIV, 262 p. 12 illus Il.: online resource ISBN/ISSN/DL: 978-3-642-38010-5 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic geometry Physics Geometry Theoretical, Mathematical and Computational Clasificación: 51 Matemáticas Resumen: Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich’s book is a must.'' The second volume is in two parts: Book II is a gentle cultural introduction to scheme theory, with the first aim of putting abstract algebraic varieties on a firm foundation; a second aim is to introduce Hilbert schemes and moduli spaces, that serve as parameter spaces for other geometric constructions. Book III discusses complex manifolds and their relation with algebraic varieties, Kähler geometry and Hodge theory. The final section raises an important problem in uniformising higher dimensional varieties that has been widely studied as the ``Shafarevich conjecture''. The style of Basic Algebraic Geometry 2 and its minimal prerequisites make it to a large extent independent of Basic Algebraic Geometry 1, and accessible to beginning graduate students in mathematics and in theoretical physics Nota de contenido: Preface -- Book 1. Varieties in Projective Space: Chapter I. Basic Notions -- Chapter II. Local Properties -- Chapter III. Divisors and Differential Forms -- Chapter IV. Intersection Numbers -- Algebraic Appendix -- References -- Index En línea: http://dx.doi.org/10.1007/978-3-642-38010-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32582 Basic Algebraic Geometry 2 : Schemes and Complex Manifolds [documento electrónico] / Shafarevich, Igor R ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013 . - XIV, 262 p. 12 illus : online resource.
ISBN : 978-3-642-38010-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic geometry Physics Geometry Theoretical, Mathematical and Computational Clasificación: 51 Matemáticas Resumen: Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich’s book is a must.'' The second volume is in two parts: Book II is a gentle cultural introduction to scheme theory, with the first aim of putting abstract algebraic varieties on a firm foundation; a second aim is to introduce Hilbert schemes and moduli spaces, that serve as parameter spaces for other geometric constructions. Book III discusses complex manifolds and their relation with algebraic varieties, Kähler geometry and Hodge theory. The final section raises an important problem in uniformising higher dimensional varieties that has been widely studied as the ``Shafarevich conjecture''. The style of Basic Algebraic Geometry 2 and its minimal prerequisites make it to a large extent independent of Basic Algebraic Geometry 1, and accessible to beginning graduate students in mathematics and in theoretical physics Nota de contenido: Preface -- Book 1. Varieties in Projective Space: Chapter I. Basic Notions -- Chapter II. Local Properties -- Chapter III. Divisors and Differential Forms -- Chapter IV. Intersection Numbers -- Algebraic Appendix -- References -- Index En línea: http://dx.doi.org/10.1007/978-3-642-38010-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32582 Ejemplares
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Título : Basic Notions of Algebra Tipo de documento: documento electrónico Autores: Shafarevich, Igor R ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2005 Otro editor: Imprint: Springer Colección: Encyclopaedia of Mathematical Sciences, ISSN 0938-0396 num. 11 Número de páginas: IV, 260 p Il.: online resource ISBN/ISSN/DL: 978-3-540-26474-3 Idioma : Inglés (eng) Palabras clave: Mathematics K-theory Topological groups Lie Groups, Groups K-Theory Clasificación: 51 Matemáticas Resumen: From the reviews: "This is one of the few mathematical books, the reviewer has read from cover to cover ... The main merit is that nearly on every page you will find some unexpected insights..." Zentralblatt für Mathematik und Ihre Grenzgebiete, 1991 "...which I read like a novel and undoubtedly will become a classic. ... A merit of the book under review is that it contains several important articles from journals which are not all so easily accessible. ... Furthermore, at the end of the book, there are some Notes by the author which are indispensible for the necessary historical background information. ... This valuable book should be on the shelf of every algebraist and algebraic geometer." Nieuw Archief voor Wiskunde, 1992 "... There are few proofs in full, but there is an exhilarating combination of sureness of foot and lightness of touch in the exposition ... which transports the reader effortlessly across the whole spectrum of algebra.... The challenge to Ezekiel, "Can these bones live?" is, all too often, the reaction of students when introduced to the bare bones of the concepts and constructs of modern algebra. Shafarevich's book - which reads as comfortably as an extended essay - breathes life into the skeleton and will be of interest to many classes of readers..." The Mathematical Gazette, 1991 "... According to the preface, the book is addressed to "students of mathematics in the first years of an undergraduate course, or theoretical physicists or mathematicians from outside algebra wanting to get an impression of the spirit of algebra and its place in mathematics." I think that this promise is fully justified. The beginner, the experts and also the interested scientist who had contact with algebraic notions - all will read this exceptional book with great pleasure and benefit." Zeitschrift für Kristallographie, 1991 Nota de contenido: What is Algebra? -- Fields -- Commutative Rings -- Homomorphisms and Ideals -- Modules -- Algebraic Aspects of Dimension -- The Algebraic View of Infinitesimal Notions -- Noncommutative Rings -- Modules over Noncommutative Rings -- Semisimple Modules and Rings -- Division Algebras of Finite Rank -- The Notion of a Group -- Examples of Groups: Finite Groups -- Examples of Groups: Infinite Discrete Groups -- Examples of Groups: Lie Groups and Algebraic Groups -- General Results of Group Theory -- Group Representations -- Some Applications of Groups -- Lie Algebras and Nonassociative Algebra -- Categories -- Homological Algebra -- K-theory En línea: http://dx.doi.org/10.1007/b137643 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35240 Basic Notions of Algebra [documento electrónico] / Shafarevich, Igor R ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2005 . - IV, 260 p : online resource. - (Encyclopaedia of Mathematical Sciences, ISSN 0938-0396; 11) .
ISBN : 978-3-540-26474-3
Idioma : Inglés (eng)
Palabras clave: Mathematics K-theory Topological groups Lie Groups, Groups K-Theory Clasificación: 51 Matemáticas Resumen: From the reviews: "This is one of the few mathematical books, the reviewer has read from cover to cover ... The main merit is that nearly on every page you will find some unexpected insights..." Zentralblatt für Mathematik und Ihre Grenzgebiete, 1991 "...which I read like a novel and undoubtedly will become a classic. ... A merit of the book under review is that it contains several important articles from journals which are not all so easily accessible. ... Furthermore, at the end of the book, there are some Notes by the author which are indispensible for the necessary historical background information. ... This valuable book should be on the shelf of every algebraist and algebraic geometer." Nieuw Archief voor Wiskunde, 1992 "... There are few proofs in full, but there is an exhilarating combination of sureness of foot and lightness of touch in the exposition ... which transports the reader effortlessly across the whole spectrum of algebra.... The challenge to Ezekiel, "Can these bones live?" is, all too often, the reaction of students when introduced to the bare bones of the concepts and constructs of modern algebra. Shafarevich's book - which reads as comfortably as an extended essay - breathes life into the skeleton and will be of interest to many classes of readers..." The Mathematical Gazette, 1991 "... According to the preface, the book is addressed to "students of mathematics in the first years of an undergraduate course, or theoretical physicists or mathematicians from outside algebra wanting to get an impression of the spirit of algebra and its place in mathematics." I think that this promise is fully justified. The beginner, the experts and also the interested scientist who had contact with algebraic notions - all will read this exceptional book with great pleasure and benefit." Zeitschrift für Kristallographie, 1991 Nota de contenido: What is Algebra? -- Fields -- Commutative Rings -- Homomorphisms and Ideals -- Modules -- Algebraic Aspects of Dimension -- The Algebraic View of Infinitesimal Notions -- Noncommutative Rings -- Modules over Noncommutative Rings -- Semisimple Modules and Rings -- Division Algebras of Finite Rank -- The Notion of a Group -- Examples of Groups: Finite Groups -- Examples of Groups: Infinite Discrete Groups -- Examples of Groups: Lie Groups and Algebraic Groups -- General Results of Group Theory -- Group Representations -- Some Applications of Groups -- Lie Algebras and Nonassociative Algebra -- Categories -- Homological Algebra -- K-theory En línea: http://dx.doi.org/10.1007/b137643 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35240 Ejemplares
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Título : Linear Algebra and Geometry Tipo de documento: documento electrónico Autores: Shafarevich, Igor R ; SpringerLink (Online service) ; Alexey O. Remizov Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2013 Otro editor: Imprint: Springer Número de páginas: XXII, 526 p Il.: online resource ISBN/ISSN/DL: 978-3-642-30994-6 Idioma : Inglés (eng) Materias: Álgebra lineal Palabras clave: Mathematics Algebra Associative rings Rings (Algebra) Matrix theory Geometry Linear and Multilinear Algebras, Theory Algebras Clasificación: 512.64 Álgebra lineal y multilineal Resumen: This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements of matrix theory and continues with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but are usually not covered in such courses: exterior algebras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitely generated periodic modules (similar to Jordan normal forms of linear operators). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equations and differential geometry, as well as from mechanics and physics Nota de contenido: Preface -- Preliminaries -- 1. Linear Equations -- 2. Matrices and Determinants -- 3. Vector Spaces -- 4. Linear Transformations of a Vector Space to Itself -- 5. Jordan Normal Form -- 6. Quadratic and Bilinear Forms -- 7. Euclidean Spaces -- 8. Affine Spaces -- 9. Projective Spaces -- 10. The Exterior Product and Exterior Algebras -- 11. Quadrics -- 12. Hyperbolic Geometry -- 13. Groups, Rings, and Modules -- 14. Elements of Representation Theory -- Historical Note -- References -- Index En línea: http://dx.doi.org/10.1007/978-3-642-30994-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32508 Linear Algebra and Geometry [documento electrónico] / Shafarevich, Igor R ; SpringerLink (Online service) ; Alexey O. Remizov . - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013 . - XXII, 526 p : online resource.
ISBN : 978-3-642-30994-6
Idioma : Inglés (eng)
Materias: Álgebra lineal Palabras clave: Mathematics Algebra Associative rings Rings (Algebra) Matrix theory Geometry Linear and Multilinear Algebras, Theory Algebras Clasificación: 512.64 Álgebra lineal y multilineal Resumen: This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements of matrix theory and continues with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but are usually not covered in such courses: exterior algebras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitely generated periodic modules (similar to Jordan normal forms of linear operators). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equations and differential geometry, as well as from mechanics and physics Nota de contenido: Preface -- Preliminaries -- 1. Linear Equations -- 2. Matrices and Determinants -- 3. Vector Spaces -- 4. Linear Transformations of a Vector Space to Itself -- 5. Jordan Normal Form -- 6. Quadratic and Bilinear Forms -- 7. Euclidean Spaces -- 8. Affine Spaces -- 9. Projective Spaces -- 10. The Exterior Product and Exterior Algebras -- 11. Quadrics -- 12. Hyperbolic Geometry -- 13. Groups, Rings, and Modules -- 14. Elements of Representation Theory -- Historical Note -- References -- Index En línea: http://dx.doi.org/10.1007/978-3-642-30994-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32508 Ejemplares
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