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32 produkter

Abstract Algebra
An Integrated Approach
AvJoseph H. Silverman
Häftad, Engelska, 2022
582 kr
Skickas inom 5-8 vardagar
This abstract algebra textbook takes an integrated approach that highlights the similarities of fundamental algebraic structures among a number of topics. The book begins by introducing groups, rings, vector spaces, and fields, emphasizing examples, definitions, homomorphisms, and proofs. The goal is to explain how all of the constructions fit into an axiomatic framework and to emphasize the importance of studying those maps that preserve the underlying algebraic structure. This fast-paced introduction is followed by chapters in which each of the four main topics is revisited and deeper results are proven. The second half of the book contains material of a more advanced nature. It includes a thorough development of Galois theory, a chapter on modules, and short surveys of additional algebraic topics designed to whet the reader's appetite for further study. This book is intended for a first introduction to abstract algebra and requires only a course in linear algebra as a prerequisite. The more advanced material could be used in an introductory graduate-level course.
Rational Points on Elliptic Curves
AvJoseph H. Silverman,John T. Tate
Inbunden, Engelska, 2015
551 kr
Skickas inom 10-15 vardagar
The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This volume stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergraduate curriculum. This accessibility, the informal writing style, and a wealth of exercises make Rational Points on Elliptic Curves an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry.Most concretely, an elliptic curve is the set of zeroes of a cubic polynomial in two variables. If the polynomial has rational coefficients, then one can ask for a description of those zeroes whose coordinates are either integers or rational numbers. It is this number theoretic question that is the main subject of Rational Points on Elliptic Curves. Topics covered include the geometry and group structure of elliptic curves, the Nagell–Lutz theorem describing points of finite order, the Mordell–Weil theorem on the finite generation of the group of rational points, the Thue–Siegel theorem on the finiteness of the set of integer points, theorems on counting points with coordinates in finite fields, Lenstra's elliptic curve factorization algorithm, and a discussion of complex multiplication and the Galois representations associated to torsion points. Additional topics new to the second edition include an introduction to elliptic curve cryptography and a brief discussion of the stunning proof of Fermat's Last Theorem by Wiles et al. via the use of elliptic curves.
Del 106 - Graduate Texts in Mathematics
Arithmetic of Elliptic Curves
AvJoseph H. Silverman
Inbunden, Engelska, 2009
558 kr
Skickas inom 10-15 vardagar
The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. The book begins with a brief discussion of the necessary algebro-geometric results, and proceeds with an exposition of the geometry of elliptic curves, the formal group of an elliptic curve, elliptic curves over finite fields, the complex numbers, local fields, and global fields. The last two chapters deal with integral and rational points, including Siegel’s theorem and explicit computations for the curve Y^2 = X^3 + DX.
Arithmetic of Elliptic Curves
AvJoseph H. Silverman
E-bok
PDF, Engelska, 2009
712 kr
Läs direkt efter köp
The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. The book begins with a brief discussion of the necessary algebro-geometric results, and proceeds with an exposition of the geometry of elliptic curves, the formal group of an elliptic curve, elliptic curves over finite fields, the complex numbers, local fields, and global fields. The last two chapters deal with integral and rational points, including Siegel's theorem and explicit computations for the curve Y^2 = X^3 + DX.
Del 151 - Graduate Texts in Mathematics
Advanced Topics in the Arithmetic of Elliptic Curves
AvJoseph H. Silverman
Inbunden, Engelska, 1994
1 000 kr
Skickas inom 10-15 vardagar
In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.
Del 151 - Graduate Texts in Mathematics
Advanced Topics in the Arithmetic of Elliptic Curves
AvJoseph H. Silverman
Häftad, Engelska, 1994
724 kr
Skickas inom 10-15 vardagar
In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.
Modular Forms and Fermat's Last Theorem
AvGary Cornell,Glenn Stevensm. fl.
Inbunden, Engelska, 2000
1 111 kr
Skickas inom 10-15 vardagar
This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 through 18, 1995 at Boston University. The purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi- stable) elliptic curve over Q is modular, and to explain how Wiles' result can be combined with Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat's Last Theorem is true. Contributors to this volume include: B. Conrad, H. Darmon, E. de Shalit, B. de Smit, F. Diamond, S.J. Edixhoven, G. Frey, S. Gelbart, K. Kramer, H.W. Lenstra, Jr., B. Mazur, K. Ribet, D.E. Rohrlich, M. Rosen, K. Rubin, R. Schoof, A. Silverberg, J.H. Silverman, P. Stevenhagen, G. Stevens, J. Tate, J. Tilouine, and L. Washington. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes.Representation theory, which lies at the core of Wiles' proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serre's conjectures, Galois deformations, universal deformation rings, Hecke algebras, complete intersections and more, as the reader is led step-by-step through Wiles' proof. In recognition of the historical significance of Fermat's Last Theorem, the volume concludes by looking both forward and backward in time, reflecting on the history of the problem, while placing Wiles' theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this volume to be an indispensable
Rational Points on Elliptic Curves
AvJoseph H. Silverman,John Tate
Inbunden, Engelska, 1992
551 kr
Skickas inom 5-8 vardagar
The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. "Rational Points on Elliptic Curves" streses this interplay as it develops the basic theory, thereby providing an opportunity for advance undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergraduate curriculum. This accessibility, the informal writing style, and a wealth of exercises make "Rational Points on Elliptic Curves" an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry.
Del 201 - Graduate Texts in Mathematics
Diophantine Geometry
An Introduction
AvMarc Hindry,Joseph H. Silverman
Inbunden, Engelska, 2000
1 111 kr
Skickas inom 10-15 vardagar
This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.
Modular Forms and Fermat’s Last Theorem
AvGary Cornell,Joseph H. Silvermanm. fl.
Häftad, Engelska, 2000
961 kr
Skickas inom 5-8 vardagar
This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 through 18, 1995 at Boston University. Contributor's includeThe purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi-stable) elliptic curve over Q is modular, and to explain how Wiles' result can be combined with Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat's Last Theorem is true. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of Wiles' proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serre's conjectures, Galois deformations, universal deformation rings, Hecke algebras, complete intersections and more, as the reader is led step-by-step through Wiles' proof. In recognition of the historical significance of Fermat's Last Theorem, the volume concludes by looking both forward and backward in time, reflecting on the history of the problem, while placing Wiles' theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this volume to be an indispensable resource for mastering the epoch-making proof of Fermat's Last Theorem.
Judeo-Spanish Ballads from New York
Collected by Mair Jose Bernardete
AvSamuel G. Armistead,Joseph H. Silverman
Häftad, Engelska, 2021
484 kr
Skickas inom 5-8 vardagar
In New York City during the winter of 1922 and the spring of 1923, Mair Jose Benardete recorded the texts of the thirty-nine traditional ballads published in this volume. His collection, the beginning of Judeo-Spanish ballad research in America, was assembled when the oral tradition was still rich and vigorous among immigrants to New York from the Sephardic settlements of the Eastern Mediterranean and North Africa. Among the ballads are a number of rare text types, some never again recorded in the Sephardic communities of the United States, In addition, many of the texts provide new insights into the origins of the thematic traditions they represent. Samuel G. Armistead and Joseph H. Silverman have edited the ballads collected by Benardete, offering an English abstract and exhaustive bibliography for each ballad. In addition to placing each ballad within the context of its Sephardic variants, the bibliographies refer to the most important collections in the modern Castilian, Portuguese, Catalan, and Hispano-American traditions, to earlier (fifteenth- to seventeenth-century) evidence, and to any known analogs in other European traditions. The volume also includes a general bibliography, a thematic classification of the ballads, several indexes, and a glossary of exotic lexical elements. In an introduction, professors Armistead and Silverman present a documented survey of Judeo-Spanish ballad scholarship with particular attention to fieldwork in teh United States and elsewhere. Benardete himself attributed the decline of ballad singing among the Sephardim to a growing preference for phonographic recordings over traditional family singers. The need for further field-work increases as "Sephardic folkspeech and folklore retreat before the irresistible onslaught of the English language and modern American mass-media culture" (from the Introduction). This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1981.
Folk Literature of the Sephardic Jews, Vol. III
Judeo-Spanish Ballads from Oral Tradition, II Carolingian Ballads, 1: Roncesvalles
AvSamuel G. Armistead,Joseph H. Silverman
Häftad, Engelska, 2022
684 kr
Skickas inom 5-8 vardagar
Folk Literature of the Sephardic Jews: Judeo-Spanish Ballads from Oral Tradition offers a comprehensive exploration of the rich oral traditions within the Sephardic Jewish community, focusing on ballads that trace their roots to medieval epic narratives. Drawing from a collection of ballads recorded between 1957 and 1980 across Eastern and North African Sephardic communities, the book examines five key narrative types, particularly those connected to the French medieval epic Chanson de Roland and the historical event of Roncesvalles. The volume provides a deep dive into the relationship between these modern Sephardic ballads and their epic antecedents, comparing them with sixteenth-century romancero versions, and placing them within the wider context of Pan-European balladry. Through synthetic texts and an analysis of variants, it uncovers the creative evolution of these ballads within the oral tradition, offering a fresh perspective on their narrative structures and thematic elements.The book addresses ongoing debates in scholarship, particularly the contested connection between epic poetry and ballads. While some critics have downplayed or denied this link, the study presents ample evidence to confirm the genetic and oral-traditional relationship between the romancero and its epic origins. It highlights the preservation of medieval poetic forms and narrative motifs across centuries, particularly the survival of specific poetic features in the Sephardic ballads. The volume also emphasizes the importance of these ballads in understanding the continuity of Hispanic epic poetry within the Sephardic diaspora. Through detailed analysis and scholarly commentary, the book sheds light on the dynamic, living tradition of balladry, demonstrating the creative and evolving nature of these oral narratives across generations.This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1994.
Folk Literature of the Sephardic Jews, Vol. III
Judeo-Spanish Ballads from Oral Tradition, II Carolingian Ballads, 1: Roncesvalles
AvJoseph H. Silverman,Samuel G. Armistead
E-bok
Engelska, 2023
487 kr
Läs direkt efter köp
Folk Literature of the Sephardic Jews: Judeo-Spanish Ballads from Oral Tradition offers a comprehensive exploration of the rich oral traditions within the Sephardic Jewish community, focusing on ballads that trace their roots to medieval epic narratives. Drawing from a collection of ballads recorded between 1957 and 1980 across Eastern and North African Sephardic communities, the book examines five key narrative types, particularly those connected to the French medieval epic Chanson de Roland and the historical event of Roncesvalles. The volume provides a deep dive into the relationship between these modern Sephardic ballads and their epic antecedents, comparing them with sixteenth-century romancero versions, and placing them within the wider context of Pan-European balladry. Through synthetic texts and an analysis of variants, it uncovers the creative evolution of these ballads within the oral tradition, offering a fresh perspective on their narrative structures and thematic elements. The book addresses ongoing debates in scholarship, particularly the contested connection between epic poetry and ballads. While some critics have downplayed or denied this link, the study presents ample evidence to confirm the genetic and oral-traditional relationship between the romancero and its epic origins. It highlights the preservation of medieval poetic forms and narrative motifs across centuries, particularly the survival of specific poetic features in the Sephardic ballads. The volume also emphasizes the importance of these ballads in understanding the continuity of Hispanic epic poetry within the Sephardic diaspora. Through detailed analysis and scholarly commentary, the book sheds light on the dynamic, living tradition of balladry, demonstrating the creative and evolving nature of these oral narratives across generations. This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1994.
Judeo-Spanish Ballads from New York
Collected by Mair Jose Bernardete
AvSamuel G. Armistead,Joseph H. Silverman
Inbunden, Engelska, 2021
787 kr
Skickas inom 5-8 vardagar
In New York City during the winter of 1922 and the spring of 1923, Mair Jose Benardete recorded the texts of the thirty-nine traditional ballads published in this volume. His collection, the beginning of Judeo-Spanish ballad research in America, was assembled when the oral tradition was still rich and vigorous among immigrants to New York from the Sephardic settlements of the Eastern Mediterranean and North Africa. Among the ballads are a number of rare text types, some never again recorded in the Sephardic communities of the United States, In addition, many of the texts provide new insights into the origins of the thematic traditions they represent. Samuel G. Armistead and Joseph H. Silverman have edited the ballads collected by Benardete, offering an English abstract and exhaustive bibliography for each ballad. In addition to placing each ballad within the context of its Sephardic variants, the bibliographies refer to the most important collections in the modern Castilian, Portuguese, Catalan, and Hispano-American traditions, to earlier (fifteenth- to seventeenth-century) evidence, and to any known analogs in other European traditions. The volume also includes a general bibliography, a thematic classification of the ballads, several indexes, and a glossary of exotic lexical elements. In an introduction, professors Armistead and Silverman present a documented survey of Judeo-Spanish ballad scholarship with particular attention to fieldwork in teh United States and elsewhere. Benardete himself attributed the decline of ballad singing among the Sephardim to a growing preference for phonographic recordings over traditional family singers. The need for further field-work increases as "Sephardic folkspeech and folklore retreat before the irresistible onslaught of the English language and modern American mass-media culture" (from the Introduction). This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1981.
Folk Literature of the Sephardic Jews, Vol. III
Judeo-Spanish Ballads from Oral Tradition, II Carolingian Ballads, 1: Roncesvalles
AvSamuel G. Armistead,Joseph H. Silverman
Inbunden, Engelska, 2022
905 kr
Skickas inom 5-8 vardagar
Folk Literature of the Sephardic Jews: Judeo-Spanish Ballads from Oral Tradition offers a comprehensive exploration of the rich oral traditions within the Sephardic Jewish community, focusing on ballads that trace their roots to medieval epic narratives. Drawing from a collection of ballads recorded between 1957 and 1980 across Eastern and North African Sephardic communities, the book examines five key narrative types, particularly those connected to the French medieval epic Chanson de Roland and the historical event of Roncesvalles. The volume provides a deep dive into the relationship between these modern Sephardic ballads and their epic antecedents, comparing them with sixteenth-century romancero versions, and placing them within the wider context of Pan-European balladry. Through synthetic texts and an analysis of variants, it uncovers the creative evolution of these ballads within the oral tradition, offering a fresh perspective on their narrative structures and thematic elements.The book addresses ongoing debates in scholarship, particularly the contested connection between epic poetry and ballads. While some critics have downplayed or denied this link, the study presents ample evidence to confirm the genetic and oral-traditional relationship between the romancero and its epic origins. It highlights the preservation of medieval poetic forms and narrative motifs across centuries, particularly the survival of specific poetic features in the Sephardic ballads. The volume also emphasizes the importance of these ballads in understanding the continuity of Hispanic epic poetry within the Sephardic diaspora. Through detailed analysis and scholarly commentary, the book sheds light on the dynamic, living tradition of balladry, demonstrating the creative and evolving nature of these oral narratives across generations.This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1994.
Moduli Spaces and Arithmetic Dynamics
AvJoseph H. Silverman
Inbunden, Engelska, 2012
1 348 kr
Skickas inom 5-8 vardagar
This monograph studies moduli problems associated to algebraic dynamical systems. It is an expanded version of the notes for a series of lectures delivered at a workshop on Moduli Spaces and the Arithmetic of Dynamical Systems at the Bellairs Research Institute, Barbados, in 2010. The author's goal is to provide an overview, with enough details and pointers to the existing literature, to give the reader an entry into this exciting area of current research. Topics covered include: (1) Construction and properties of dynamical moduli spaces for self-maps of projective space. (2) Dynatomic modular curves for the space of quadratic polynomials. (3) The theory of canonical heights associated to dynamical systems. (4) Special loci in dynamical moduli spaces, in particular the locus of post-critically finite maps. (5) Field of moduli and fields of definition for dynamical systems.
Del 106 - Graduate Texts in Mathematics
Arithmetic of Elliptic Curves
AvJoseph H. Silverman
Häftad, Engelska, 2010
558 kr
Skickas inom 10-15 vardagar
The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. The book begins with a brief discussion of the necessary algebro-geometric results, and proceeds with an exposition of the geometry of elliptic curves, the formal group of an elliptic curve, elliptic curves over finite fields, the complex numbers, local fields, and global fields. The last two chapters deal with integral and rational points, including Siegel’s theorem and explicit computations for the curve Y^2 = X^3 + DX.
Rational Points on Elliptic Curves
AvJoseph H. Silverman,John Tate
Häftad, Engelska, 2010
567 kr
Skickas inom 5-8 vardagar
In 1961 the second author deliv1lred a series of lectures at Haverford Col lege on the subject of "Rational Points on Cubic Curves. " These lectures, intended for junior and senior mathematics majors, were recorded, tran scribed, and printed in mimeograph form. Since that time they have been widely distributed as photocopies of ever decreasing legibility, and por tions have appeared in various textbooks (Husemoller [1], Chahal [1]), but they have never appeared in their entirety. In view of the recent inter est in the theory of elliptic curves for subjects ranging from cryptogra phy (Lenstra [1], Koblitz [2]) to physics (Luck-Moussa-Waldschmidt [1]), as well as the tremendous purely mathematical activity in this area, it seems a propitious time to publish an expanded version of those original notes suitable for presentation to an advanced undergraduate audience. We have attempted to maintain much of the informality of the orig inal Haverford lectures. Our main goal in doing this has been to write a textbook in a technically difficult field which is "readable" by the average undergraduate mathematics major. We hope we have succeeded in this goal. The most obvious drawback to such an approach is that we have not been entirely rigorous in all of our proofs. In particular, much of the foundational material on elliptic curves presented in Chapter I is meant to explain and convince, rather than to rigorously prove.
Advanced Topics in the Arithmetic of Elliptic Curves
AvJoseph H. Silverman
E-bok
PDF, Engelska, 2013
868 kr
Läs direkt efter köp
In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate''s algorithm, and Ogg''s conductor-discriminant formula. V. Tate''s theory of q-curves over p-adic fields. VI. Neron''s theory of canonical local height functions.
Diophantine Geometry
An Introduction
AvJoseph H. Silverman,Marc Hindry
E-bok
PDF, Engelska, 2013
1 393 kr
Läs direkt efter köp
This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.
Modular Forms and Fermat's Last Theorem
AvGlenn Stevens,Joseph H. Silvermanm. fl.
E-bok
PDF, Engelska, 2013
1 413 kr
Läs direkt efter köp
This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 through 18, 1995 at Boston University. Contributor''s includeThe purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi-stable) elliptic curve over Q is modular, and to explain how Wiles'' result can be combined with Ribet''s theorem and ideas of Frey and Serre to show, at long last, that Fermat''s Last Theorem is true. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of Wiles'' proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serre''s conjectures, Galois deformations, universal deformation rings, Hecke algebras, complete intersections and more, as the reader is led step-by-step through Wiles'' proof. In recognition of the historical significance of Fermat''s Last Theorem, the volume concludes by looking both forward and backward in time, reflecting on the history of the problem, while placing Wiles'' theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this volume to be an indispensable resource for mastering the epoch-making proof of Fermat''s Last Theorem.
Arithmetic of Elliptic Curves
AvJoseph H. Silverman
E-bok
PDF, Engelska, 2013
1 136 kr
Läs direkt efter köp
The preface to a textbook frequently contains the author''s justification for offering the public "another book" on the given subject. For our chosen topic, the arithmetic of elliptic curves, there is little need for such an apologia. Considering the vast amount of research currently being done in this area, the paucity of introductory texts is somewhat surprising. Parts of the theory are contained in various books of Lang (especially [La 3] and [La 5]); and there are books of Koblitz ([Kob]) and Robert ([Rob], now out of print) which concentrate mostly on the analytic and modular theory. In addition, survey articles have been written by Cassels ([Ca 7], really a short book) and Tate ([Ta 5J, which is beautifully written, but includes no proofs). Thus the author hopes that this volume will fill a real need, both for the serious student who wishes to learn the basic facts about the arithmetic of elliptic curves; and for the research mathematician who needs a reference source for those same basic facts. Our approach is more algebraic than that taken in, say, [La 3] or [La 5], where many of the basic theorems are derived using complex analytic methods and the Lefschetz principle. For this reason, we have had to rely somewhat more on techniques from algebraic geometry. However, the geom etry of (smooth) curves, which is essentially all that we use, does not require a great deal of machinery.
Rational Points on Elliptic Curves
AvJohn Tate,Joseph H. Silverman
E-bok
PDF, Engelska, 2013
558 kr
Läs direkt efter köp
In 1961 the second author deliv1lred a series of lectures at Haverford Col lege on the subject of "Rational Points on Cubic Curves. " These lectures, intended for junior and senior mathematics majors, were recorded, tran scribed, and printed in mimeograph form. Since that time they have been widely distributed as photocopies of ever decreasing legibility, and por tions have appeared in various textbooks (Husemoller [1], Chahal [1]), but they have never appeared in their entirety. In view of the recent inter est in the theory of elliptic curves for subjects ranging from cryptogra phy (Lenstra [1], Koblitz [2]) to physics (Luck-Moussa-Waldschmidt [1]), as well as the tremendous purely mathematical activity in this area, it seems a propitious time to publish an expanded version of those original notes suitable for presentation to an advanced undergraduate audience. We have attempted to maintain much of the informality of the orig inal Haverford lectures. Our main goal in doing this has been to write a textbook in a technically difficult field which is "readable" by the average undergraduate mathematics major. We hope we have succeeded in this goal. The most obvious drawback to such an approach is that we have not been entirely rigorous in all of our proofs. In particular, much of the foundational material on elliptic curves presented in Chapter I is meant to explain and convince, rather than to rigorously prove.
Introduction to Mathematical Cryptography
AvJeffrey Hoffstein,Jill Pipherm. fl.
Inbunden, Engelska, 2014
780 kr
Skickas inom 10-15 vardagar
This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. This text provides an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online.The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include:classical cryptographic constructions, such as Diffie–Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, anddigital signatures;fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms;an in-depth treatment of important cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem.The second edition of An Introduction to Mathematical Cryptography includes a significant revision of the material on digital signatures, including an earlier introduction to RSA, Elgamal, and DSA signatures, and new material on lattice-based signatures and rejection sampling. Many sections have been rewritten or expanded for clarity, especially in the chapters on information theory, elliptic curves, and lattices, and the chapter of additional topics has been expanded to include sections on digital cash and homomorphic encryption. Numerous new exercises have been included.
Introduction to Mathematical Cryptography
AvJoseph H. Silverman,Jill Pipherm. fl.
E-bok
Engelska, 2014
997 kr
Läs direkt efter köp
This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. This text provides an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online.
The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include:
classical cryptographic constructions, such as Diffie–Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, anddigital signatures;fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms;an in-depth treatment of important cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem.
The second edition of An Introduction
to Mathematical Cryptography includes a significant revision of the material on digital signatures, including an earlier introduction to RSA, Elgamal, and DSA signatures, and new material on lattice-based signatures and rejection sampling. Many sections have been rewritten or expanded for clarity, especially in the chapters on information theory, elliptic curves, and lattices, and the chapter of additional topics has been expanded to include sections on digital cash and homomorphic encryption. Numerous new exercises have been included.
Introduction to Mathematical Cryptography
AvJeffrey Hoffstein,Jill Pipherm. fl.
Häftad, Engelska, 2016
780 kr
Skickas inom 10-15 vardagar
This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. This text provides an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online.The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include:classical cryptographic constructions, such as Diffie–Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, anddigital signatures;fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms;an in-depth treatment of important cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem.The second edition of An Introduction to Mathematical Cryptography includes a significant revision of the material on digital signatures, including an earlier introduction to RSA, Elgamal, and DSA signatures, and new material on lattice-based signatures and rejection sampling. Many sections have been rewritten or expanded for clarity, especially in the chapters on information theory, elliptic curves, and lattices, and the chapter of additional topics has been expanded to include sections on digital cash and homomorphic encryption. Numerous new exercises have been included.
Judeo-Spanish Ballads from Bosnia
AvSamuel G. Armistead,Joseph H. Silverman
Inbunden, Engelska, 2016
1 029 kr
Skickas inom 10-15 vardagar
The Judeo-Spanish folk literature of the Sephardic Jews of Bosnia, and with it their uncommonly rich balladry, has remained largely unknown to Western scholars. Since their move to Sarajevo in the sixteenth century, Serob-Croatian has displaced their original Spanish, and the entire culture is rapidly approaching extinction.This book preserved for posterity three fundamentally important groups of these rare ballads: Kalmi Baruch's Spanski romanse; ballads collected from the readers of the Sarajevo newspaper Jevrejski Glas; and five previously unedited eighteenth-century Bosnian ballads from a manuscript in the Jewish National and University Library in Jerusalem.Notes, abstracts in English, reproductions of the music itself, and other scholarly aids serve to make this colorful and strangely modern literature fully accessible to Hispanists, folklorists, and all students of comparative literature and Judaic culture.
Judeo-Spanish Ballads from Bosnia
AvSamuel G. Armistead,Joseph H. Silverman
E-bok
PDF, Engelska, 2016
1 724 kr
Läs direkt efter köp
The Judeo-Spanish folk literature of the Sephardic Jews of Bosnia, and with it their uncommonly rich balladry, has remained largely unknown to Western scholars. Since their move to Sarajevo in the sixteenth century, Serob-Croatian has displaced their original Spanish, and the entire culture is rapidly approaching extinction.This book preserved for posterity three fundamentally important groups of these rare ballads: Kalmi Baruch''s Spanski romanse; ballads collected from the readers of the Sarajevo newspaper Jevrejski Glas; and five previously unedited eighteenth-century Bosnian ballads from a manuscript in the Jewish National and University Library in Jerusalem.Notes, abstracts in English, reproductions of the music itself, and other scholarly aids serve to make this colorful and strangely modern literature fully accessible to Hispanists, folklorists, and all students of comparative literature and Judaic culture.
Rational Points on Elliptic Curves
AvJohn T. Tate,Joseph H. Silverman
E-bok
PDF, Engelska, 2015
718 kr
Läs direkt efter köp
The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This volume stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergraduate curriculum. This accessibility, the informal writing style, and a wealth of exercises make Rational Points on Elliptic Curves an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry.
Most concretely, an elliptic curve is the set of zeroes of a cubic polynomial in two variables. If the polynomial has rational coefficients, then one can ask for a description of those zeroes whose coordinates are either integers or rational numbers. It is this number theoretic question that is the main subject of Rational Points on Elliptic Curves. Topics covered include the geometry and group structure of elliptic curves, the Nagell–Lutz theorem describing points of finite order, the Mordell–Weil theorem on the finite generation of the group of rational points, the Thue–Siegel theorem on the finiteness of the set of integer points, theorems on counting points with coordinates in finite fields, Lenstra''s elliptic curve factorization algorithm, and a discussion of complex multiplication and the Galois representations associated to torsion points. Additional topics new to the second edition include an introduction to elliptic curve cryptography and a brief discussion of the stunning proof of Fermat''s Last Theorem by Wiles et al. via the use of elliptic curves.
Rational Points on Elliptic Curves
AvJoseph H. Silverman,John T. Tate
Häftad, Engelska, 2015
551 kr
Skickas inom 10-15 vardagar
The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This volume stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergraduate curriculum. This accessibility, the informal writing style, and a wealth of exercises make Rational Points on Elliptic Curves an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry.Most concretely, an elliptic curve is the set of zeroes of a cubic polynomial in two variables. If the polynomial has rational coefficients, then one can ask for a description of those zeroes whose coordinates are either integers or rational numbers. It is this number theoretic question that is the main subject of Rational Points on Elliptic Curves. Topics covered include the geometry and group structure of elliptic curves, the Nagell–Lutz theorem describing points of finite order, the Mordell–Weil theorem on the finite generation of the group of rational points, the Thue–Siegel theorem on the finiteness of the set of integer points, theorems on counting points with coordinates in finite fields, Lenstra's elliptic curve factorization algorithm, and a discussion of complex multiplication and the Galois representations associated to torsion points. Additional topics new to the second edition include an introduction to elliptic curve cryptography and a brief discussion of the stunning proof of Fermat's Last Theorem by Wiles et al. via the use of elliptic curves.

Joseph H. Silverman – författare

Abstract Algebra

Rational Points on Elliptic Curves

Arithmetic of Elliptic Curves

Arithmetic of Elliptic Curves

Advanced Topics in the Arithmetic of Elliptic Curves

Advanced Topics in the Arithmetic of Elliptic Curves

Modular Forms and Fermat's Last Theorem

Rational Points on Elliptic Curves

Diophantine Geometry

Modular Forms and Fermat’s Last Theorem

Judeo-Spanish Ballads from New York

Folk Literature of the Sephardic Jews, Vol. III

Folk Literature of the Sephardic Jews, Vol. III

Judeo-Spanish Ballads from New York

Folk Literature of the Sephardic Jews, Vol. III

Moduli Spaces and Arithmetic Dynamics

Arithmetic of Elliptic Curves

Rational Points on Elliptic Curves

Advanced Topics in the Arithmetic of Elliptic Curves

Diophantine Geometry

Modular Forms and Fermat's Last Theorem

Arithmetic of Elliptic Curves

Rational Points on Elliptic Curves

Introduction to Mathematical Cryptography

Introduction to Mathematical Cryptography

Introduction to Mathematical Cryptography

Judeo-Spanish Ballads from Bosnia

Judeo-Spanish Ballads from Bosnia

Rational Points on Elliptic Curves

Rational Points on Elliptic Curves