Rational Points on Elliptic Curves

Front Cover
Springer Science & Business Media, Jun 24, 1992 - Mathematics - 281 pages
0 Reviews
In 1961 the second author deliv1lred a series of lectures at Haverford Col lege on the subject of "Rational Points on Cubic Curves. " These lectures, intended for junior and senior mathematics majors, were recorded, tran scribed, and printed in mimeograph form. Since that time they have been widely distributed as photocopies of ever decreasing legibility, and por tions have appeared in various textbooks (Husemoller [1], Chahal [1]), but they have never appeared in their entirety. In view of the recent inter est in the theory of elliptic curves for subjects ranging from cryptogra phy (Lenstra [1], Koblitz [2]) to physics (Luck-Moussa-Waldschmidt [1]), as well as the tremendous purely mathematical activity in this area, it seems a propitious time to publish an expanded version of those original notes suitable for presentation to an advanced undergraduate audience. We have attempted to maintain much of the informality of the orig inal Haverford lectures. Our main goal in doing this has been to write a textbook in a technically difficult field which is "readable" by the average undergraduate mathematics major. We hope we have succeeded in this goal. The most obvious drawback to such an approach is that we have not been entirely rigorous in all of our proofs. In particular, much of the foundational material on elliptic curves presented in Chapter I is meant to explain and convince, rather than to rigorously prove.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

V
9
VI
15
VII
22
VIII
28
IX
32
X
38
XI
41
XII
47
XXX
147
XXXI
152
XXXII
157
XXXIII
165
XXXIV
168
XXXV
171
XXXVI
174
XXXVII
177

XIII
49
XIV
56
XV
58
XVI
63
XVII
68
XVIII
71
XIX
76
XX
83
XXI
89
XXII
99
XXIII
102
XXIV
107
XXV
110
XXVI
121
XXVII
125
XXVIII
138
XXIX
145
XXXVIII
180
XXXIX
185
XL
193
XLI
199
XLII
205
XLIII
213
XLIV
220
XLV
225
XLVI
233
XLVII
242
XLVIII
251
XLIX
254
L
259
LI
263
LII
267
Copyright

Other editions - View all

Common terms and phrases

Popular passages

Page vi - Mordell's theorem, which says that the group of rational points on an elliptic curve is finitely generated...

References to this book

All Book Search results »

Bibliographic information