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...
Saved in:
| Superior document: | Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 |
|---|---|
| VerfasserIn: | |
| Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2012] ©2012 |
| Year of Publication: | 2012 |
| Edition: | Course Book |
| Language: | English |
| Online Access: | |
| Physical Description: | 1 online resource (280 p.) :; 52 line illus. 16 tables. |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| id |
9781400841714 |
|---|---|
| ctrlnum |
(DE-B1597)447469 (OCoLC)922637586 |
| collection |
bib_alma |
| record_format |
marc |
| spelling |
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 |
| work_keys_str_mv |
AT ashavner elliptictalescurvescountingandnumbertheory AT grossrobert elliptictalescurvescountingandnumbertheory |
| status_str |
n |
| ids_txt_mv |
(DE-B1597)447469 (OCoLC)922637586 |
| carrierType_str_mv |
cr |
| hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 |
| is_hierarchy_title |
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 |
| author2_original_writing_str_mv |
noLinkedField noLinkedField |
| _version_ |
1806143563385274368 |
| fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>04399nam a22008055i 4500</leader><controlfield tag="001">9781400841714</controlfield><controlfield tag="003">DE-B1597</controlfield><controlfield tag="005">20210830012106.0</controlfield><controlfield tag="006">m|||||o||d||||||||</controlfield><controlfield tag="007">cr || ||||||||</controlfield><controlfield tag="008">210830t20122012nju fo d z eng d</controlfield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">(OCoLC)973401017</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781400841714</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/9781400841714</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-B1597)447469</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)922637586</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-B1597</subfield><subfield code="b">eng</subfield><subfield code="c">DE-B1597</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">nju</subfield><subfield code="c">US-NJ</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA343 .As987 2012</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT015000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">515.983</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 180</subfield><subfield code="2">rvk</subfield><subfield code="0">(DE-625)rvk/143222:</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ash, Avner, </subfield><subfield code="e">author.</subfield><subfield code="4">aut</subfield><subfield code="4">http://id.loc.gov/vocabulary/relators/aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Elliptic Tales :</subfield><subfield code="b">Curves, Counting, and Number Theory /</subfield><subfield code="c">Avner Ash, Robert Gross.</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Course Book</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Princeton, NJ : </subfield><subfield code="b">Princeton University Press, </subfield><subfield code="c">[2012]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">©2012</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (280 p.) :</subfield><subfield code="b">52 line illus. 16 tables.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="347" ind1=" " ind2=" "><subfield code="a">text file</subfield><subfield code="b">PDF</subfield><subfield code="2">rda</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="t">Frontmatter -- </subfield><subfield code="t">Contents -- </subfield><subfield code="t">Preface -- </subfield><subfield code="t">Acknowledgments -- </subfield><subfield code="t">Prologue -- </subfield><subfield code="t">PART I. DEGREE -- </subfield><subfield code="t">Chapter 1. Degree of a Curve -- </subfield><subfield code="t">Chapter 2. Algebraic Closures -- </subfield><subfield code="t">Chapter 3. The Projective Plane -- </subfield><subfield code="t">Chapter 4. Multiplicities and Degree -- </subfield><subfield code="t">Chapter 5. Bézout's Theorem -- </subfield><subfield code="t">PART II. ELLIPTIC CURVES AND ALGEBRA -- </subfield><subfield code="t">Chapter 6. Transition to Elliptic Curves -- </subfield><subfield code="t">Chapter 7. Abelian Groups -- </subfield><subfield code="t">Chapter 8. Nonsingular Cubic Equations -- </subfield><subfield code="t">Chapter 9. Singular Cubics -- </subfield><subfield code="t">Chapter 10. Elliptic Curves over Q -- </subfield><subfield code="t">PART III. ELLIPTIC CURVES AND ANALYSIS -- </subfield><subfield code="t">Chapter 11. Building Functions -- </subfield><subfield code="t">Chapter 12. Analytic Continuation -- </subfield><subfield code="t">Chapter 13. L-functions -- </subfield><subfield code="t">Chapter 14. Surprising Properties of L-functions -- </subfield><subfield code="t">Chapter 15. The Conjecture of Birch and Swinnerton-Dyer -- </subfield><subfield code="t">Epilogue -- </subfield><subfield code="t">Bibliography -- </subfield><subfield code="t">Index</subfield></datafield><datafield tag="506" ind1="0" ind2=" "><subfield code="a">restricted access</subfield><subfield code="u">http://purl.org/coar/access_right/c_16ec</subfield><subfield code="f">online access with authorization</subfield><subfield code="2">star</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">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.</subfield></datafield><datafield tag="530" ind1=" " ind2=" "><subfield code="a">Issued also in print.</subfield></datafield><datafield tag="538" ind1=" " ind2=" "><subfield code="a">Mode of access: Internet via World Wide Web.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">In English.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021)</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Counting.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Curves, Elliptic.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Elliptic functions.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Algebra</subfield><subfield code="x">Abstract.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Complex Analysis.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Mathematics</subfield><subfield code="x">Algebra</subfield><subfield code="x">Abstract.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Mathematics</subfield><subfield code="x">Complex Analysis.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Number theory.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / History & Philosophy.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Gross, Robert, </subfield><subfield code="e">author.</subfield><subfield code="4">aut</subfield><subfield code="4">http://id.loc.gov/vocabulary/relators/aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">Princeton University Press eBook-Package Backlist 2000-2013</subfield><subfield code="z">9783110442502</subfield></datafield><datafield tag="776" ind1="0" ind2=" "><subfield code="c">print</subfield><subfield code="z">9780691151199</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/9781400841714</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://www.degruyter.com/isbn/9781400841714</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="3">Cover</subfield><subfield code="u">https://www.degruyter.com/cover/covers/9781400841714.jpg</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">978-3-11-044250-2 Princeton University Press eBook-Package Backlist 2000-2013</subfield><subfield code="c">2000</subfield><subfield code="d">2013</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_BACKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_CL_MTPY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EBACKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EBKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ECL_MTPY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EEBKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ESTMALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_PPALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_STMALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV-deGruyter-alles</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA12STME</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA13ENGE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA18STMEE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA5EBK</subfield></datafield></record></collection> |