Elliptic Tales : : Curves, Counting, and Number Theory / / Avner Ash, Robert Gross.
Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics-the Birch and Swinnerton-Dyer Conjecture. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this...
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2012] ©2012 |
Year of Publication: | 2012 |
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Physical Description: | 1 online resource (280 p.) :; 52 line illus. 16 tables. |
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Ash, Avner, author. aut http://id.loc.gov/vocabulary/relators/aut Elliptic Tales : Curves, Counting, and Number Theory / Avner Ash, Robert Gross. Course Book Princeton, NJ : Princeton University Press, [2012] ©2012 1 online resource (280 p.) : 52 line illus. 16 tables. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Frontmatter -- Contents -- Preface -- Acknowledgments -- Prologue -- PART I. DEGREE -- Chapter 1. Degree of a Curve -- Chapter 2. Algebraic Closures -- Chapter 3. The Projective Plane -- Chapter 4. Multiplicities and Degree -- Chapter 5. Bézout's Theorem -- PART II. ELLIPTIC CURVES AND ALGEBRA -- Chapter 6. Transition to Elliptic Curves -- Chapter 7. Abelian Groups -- Chapter 8. Nonsingular Cubic Equations -- Chapter 9. Singular Cubics -- Chapter 10. Elliptic Curves over Q -- PART III. ELLIPTIC CURVES AND ANALYSIS -- Chapter 11. Building Functions -- Chapter 12. Analytic Continuation -- Chapter 13. L-functions -- Chapter 14. Surprising Properties of L-functions -- Chapter 15. The Conjecture of Birch and Swinnerton-Dyer -- Epilogue -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics-the Birch and Swinnerton-Dyer Conjecture. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem.The key to the conjecture lies in elliptic curves, which may appear simple, but arise from some very deep-and often very mystifying-mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and, in the process, venture to the very frontiers of modern mathematics. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) Counting. Curves, Elliptic. Elliptic functions. MATHEMATICS Algebra Abstract. MATHEMATICS Complex Analysis. Mathematics Algebra Abstract. Mathematics Complex Analysis. Number theory. MATHEMATICS / History & Philosophy. bisacsh Gross, Robert, author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 9783110442502 print 9780691151199 https://doi.org/10.1515/9781400841714 https://www.degruyter.com/isbn/9781400841714 Cover https://www.degruyter.com/cover/covers/9781400841714.jpg |
language |
English |
format |
eBook |
author |
Ash, Avner, Ash, Avner, Gross, Robert, |
spellingShingle |
Ash, Avner, Ash, Avner, Gross, Robert, Elliptic Tales : Curves, Counting, and Number Theory / Frontmatter -- Contents -- Preface -- Acknowledgments -- Prologue -- PART I. DEGREE -- Chapter 1. Degree of a Curve -- Chapter 2. Algebraic Closures -- Chapter 3. The Projective Plane -- Chapter 4. Multiplicities and Degree -- Chapter 5. Bézout's Theorem -- PART II. ELLIPTIC CURVES AND ALGEBRA -- Chapter 6. Transition to Elliptic Curves -- Chapter 7. Abelian Groups -- Chapter 8. Nonsingular Cubic Equations -- Chapter 9. Singular Cubics -- Chapter 10. Elliptic Curves over Q -- PART III. ELLIPTIC CURVES AND ANALYSIS -- Chapter 11. Building Functions -- Chapter 12. Analytic Continuation -- Chapter 13. L-functions -- Chapter 14. Surprising Properties of L-functions -- Chapter 15. The Conjecture of Birch and Swinnerton-Dyer -- Epilogue -- Bibliography -- Index |
author_facet |
Ash, Avner, Ash, Avner, Gross, Robert, Gross, Robert, Gross, Robert, |
author_variant |
a a aa a a aa r g rg |
author_role |
VerfasserIn VerfasserIn VerfasserIn |
author2 |
Gross, Robert, Gross, Robert, |
author2_variant |
r g rg |
author2_role |
VerfasserIn VerfasserIn |
author_sort |
Ash, Avner, |
title |
Elliptic Tales : Curves, Counting, and Number Theory / |
title_sub |
Curves, Counting, and Number Theory / |
title_full |
Elliptic Tales : Curves, Counting, and Number Theory / Avner Ash, Robert Gross. |
title_fullStr |
Elliptic Tales : Curves, Counting, and Number Theory / Avner Ash, Robert Gross. |
title_full_unstemmed |
Elliptic Tales : Curves, Counting, and Number Theory / Avner Ash, Robert Gross. |
title_auth |
Elliptic Tales : Curves, Counting, and Number Theory / |
title_alt |
Frontmatter -- Contents -- Preface -- Acknowledgments -- Prologue -- PART I. DEGREE -- Chapter 1. Degree of a Curve -- Chapter 2. Algebraic Closures -- Chapter 3. The Projective Plane -- Chapter 4. Multiplicities and Degree -- Chapter 5. Bézout's Theorem -- PART II. ELLIPTIC CURVES AND ALGEBRA -- Chapter 6. Transition to Elliptic Curves -- Chapter 7. Abelian Groups -- Chapter 8. Nonsingular Cubic Equations -- Chapter 9. Singular Cubics -- Chapter 10. Elliptic Curves over Q -- PART III. ELLIPTIC CURVES AND ANALYSIS -- Chapter 11. Building Functions -- Chapter 12. Analytic Continuation -- Chapter 13. L-functions -- Chapter 14. Surprising Properties of L-functions -- Chapter 15. The Conjecture of Birch and Swinnerton-Dyer -- Epilogue -- Bibliography -- Index |
title_new |
Elliptic Tales : |
title_sort |
elliptic tales : curves, counting, and number theory / |
publisher |
Princeton University Press, |
publishDate |
2012 |
physical |
1 online resource (280 p.) : 52 line illus. 16 tables. Issued also in print. |
edition |
Course Book |
contents |
Frontmatter -- Contents -- Preface -- Acknowledgments -- Prologue -- PART I. DEGREE -- Chapter 1. Degree of a Curve -- Chapter 2. Algebraic Closures -- Chapter 3. The Projective Plane -- Chapter 4. Multiplicities and Degree -- Chapter 5. Bézout's Theorem -- PART II. ELLIPTIC CURVES AND ALGEBRA -- Chapter 6. Transition to Elliptic Curves -- Chapter 7. Abelian Groups -- Chapter 8. Nonsingular Cubic Equations -- Chapter 9. Singular Cubics -- Chapter 10. Elliptic Curves over Q -- PART III. ELLIPTIC CURVES AND ANALYSIS -- Chapter 11. Building Functions -- Chapter 12. Analytic Continuation -- Chapter 13. L-functions -- Chapter 14. Surprising Properties of L-functions -- Chapter 15. The Conjecture of Birch and Swinnerton-Dyer -- Epilogue -- Bibliography -- Index |
isbn |
9781400841714 9783110442502 9780691151199 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA343 |
callnumber-sort |
QA 3343 A S987 42012 |
url |
https://doi.org/10.1515/9781400841714 https://www.degruyter.com/isbn/9781400841714 https://www.degruyter.com/cover/covers/9781400841714.jpg |
illustrated |
Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
515 - Analysis |
dewey-full |
515.983 |
dewey-sort |
3515.983 |
dewey-raw |
515.983 |
dewey-search |
515.983 |
doi_str_mv |
10.1515/9781400841714 |
oclc_num |
922637586 |
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AT ashavner elliptictalescurvescountingandnumbertheory AT grossrobert elliptictalescurvescountingandnumbertheory |
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(DE-B1597)447469 (OCoLC)922637586 |
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hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 |
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Elliptic Tales : Curves, Counting, and Number Theory / |
container_title |
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 |
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