Elliptic Curves (Record no. 60264)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 02254nam a22002297a 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240509b 2024|||||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9798886130843 (PB) |
| 041 ## - LANGUAGE CODE | |
| Language code of text/sound track or separate title | eng |
| 080 ## - UNIVERSAL DECIMAL CLASSIFICATION NUMBER | |
| Universal Decimal Classification number | 514 |
| Item number | MIL |
| 100 ## - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Milne, James S |
| 245 ## - TITLE STATEMENT | |
| Title | Elliptic Curves |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 2nd ed. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Name of publisher | World Scientific |
| Year of publication | 2024 |
| Place of publication | New Jersey |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | x, 308p. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE | |
| Bibliography, etc | Includes References (297-304) and Index |
| 505 ## - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 1. Algebraic Curves<br/>2. Basic Theory of Elliptic Curves<br/>3. Elliptic Curves over the Complex Numbers<br/>4. The Arithmetic of Elliptic Curves<br/>5. Elliptic Curves and Modular Forms |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory. It assumes only a knowledge of the basic algebra, complex analysis, and topology usually taught in first-year graduate courses. An elliptic curve is a plane curve defined by a cubic polynomial. Although the problem of finding the rational points on an elliptic curve has fascinated mathematicians since ancient times, it was not until 1922 that Mordell proved that the points form a finitely generated group. There is still no proven algorithm for finding the rank of the group, but in one of the earliest important applications of computers to mathematics, Birch and Swinnerton-Dyer discovered a relation between the rank and the numbers of points on the curve computed modulo a prime. Chapter IV of the book proves Mordell's theorem and explains the conjecture of Birch and Swinnerton-Dyer. Every elliptic curve over the rational numbers has an L-series attached to it.Hasse conjectured that this L-series satisfies a functional equation, and in 1955 Taniyama suggested that Hasse's conjecture could be proved by showing that the L-series arises from a modular form. This was shown to be correct by Wiles (and others) in the 1990s, and, as a consequence, one obtains a proof of Fermat's Last Theorem. Chapter V of the book is devoted to explaining this work. The first three chapters develop the basic theory of elliptic curves. For this edition, the text has been completely revised and updated. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Analytic Geometry |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Modular Forms |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) | |
| Topical term or geographic name as entry element | Mathematics |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | BOOKS |
| Withdrawn status | Lost status | Damaged status | Not for loan | Home library | Current library | Shelving location | Full call number | Accession Number | Koha item type | Owner (If the Item is Gratis) |
|---|---|---|---|---|---|---|---|---|---|---|
| IMSc Library | IMSc Library | First Floor, Rack No: 30, Shelf No: 36 | 514 MIL | 77807 | BOOKS | NBHM through KNR |