MARC details
| 000 -LEADER |
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| fixed length control field |
02759 a2200277 4500 |
| 001 - CONTROL NUMBER |
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| control field |
136483 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
ISI Library, Kolkata |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20160127155620.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
160127b xxu||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783319185873 |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
ISI Library |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
516.352 |
| Edition number |
23 |
| Item number |
Si587 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Silverman, Joseph H. |
| 245 10 - TITLE STATEMENT |
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| Title |
Rational points on elliptic curves / |
| Statement of responsibility, etc |
Joseph H. Silverman and John T. Tate. |
| 250 ## - EDITION STATEMENT |
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| Edition statement |
2nd ed |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc |
Switzerland : |
| Name of publisher, distributor, etc |
Springer, |
| Date of publication, distribution, etc |
2015. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xxii, 332 p. : |
| Other physical details |
illustrations ; |
| Dimensions |
25 cm. |
| 490 0# - SERIES STATEMENT |
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| Series statement |
Undergraduate texts in mathematics |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references and index. |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Introduction --<br/>1. Geometry and Arithmetic --<br/>2. Points of Finite Order --<br/>3. The Group of Rational Points --<br/>4. Cubic Curves over Finite Fields --<br/>5. Integer Points on Cubic Curves --<br/>6. Complex Multiplication--<br/>A. Projective geometry--<br/>B. Transformation to weierstrass form--<br/>List of noataion--<br/>References--<br/>Index. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
This book 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 this book. 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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Elliptic Curves. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Rational points (Geometry) |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Tate, John T., |
| Relator term |
author |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Koha item type |
Books |
