MARC details
| 000 -LEADER |
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| fixed length control field |
02585nam a2200289Ia 4500 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
OSt |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20240130183228.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
231229s9999 xx 000 0 und d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783319307572 |
| 040 ## - CATALOGING SOURCE |
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| Transcribing agency |
IISER BPR |
| 041 ## - LANGUAGE CODE |
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| Language code of text/sound track or separate title |
Eng |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
516.352 |
| Item number |
SIL |
| Edition number |
23rd |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Silverman, Joseph H. |
| 245 #0 - TITLE STATEMENT |
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| Title |
Rational points on elliptic curves |
| 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 international Publishing, |
| Date of publication, distribution, etc |
c2015. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xxii, 332p. : |
| Other physical details |
ill (pbk). ; |
| Dimensions |
22cm. |
| 440 ## - SERIES STATEMENT/ADDED ENTRY--TITLE |
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| Title |
Undergraduate texts in mathematics |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
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.<br/><br/>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.<br/><br/>Includes illutrations, list of notations, references and index. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematics |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Geometry and Arithmetic |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Points and Curves |
| 700 ## - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Tate, John T. |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Koha item type |
Books |
| Source of classification or shelving scheme |
Dewey Decimal Classification |
| 947 ## - LOCAL PROCESSING INFORMATION (OCLC) |
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| a |
4384.967831 |
| 948 ## - LOCAL PROCESSING INFORMATION (OCLC); SERIES PART DESIGNATOR (RLIN) |
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| Series part designator, SPT (RLIN) |
0.22 |
