Introduction to Elliptic Curves and Modular Forms

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Springer Science & Business Media, May 3, 1993 - Mathematics - 248 pages
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This textbook covers the basic properties of elliptic curves and modular forms, with emphasis on certain connections with number theory. The ancient "congruent number problem" is the central motivating example for most of the book. My purpose is to make the subject accessible to those who find it hard to read more advanced or more algebraically oriented treatments. At the same time I want to introduce topics which are at the forefront of current research. Down-to-earth examples are given in the text and exercises, with the aim of making the material readable and interesting to mathematicians in fields far removed from the subject of the book. With numerous exercises (and answers) included, the textbook is also intended for graduate students who have completed the standard first-year courses in real and complex analysis and algebra. Such students would learn applications of techniques from those courses. thereby solidifying their under standing of some basic tools used throughout mathematics. Graduate stu dents wanting to work in number theory or algebraic geometry would get a motivational, example-oriented introduction. In addition, advanced under graduates could use the book for independent study projects, senior theses, and seminar work.
  

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Contents

III
1
IV
3
V
6
VI
9
VII
14
VIII
18
IX
22
X
29
XVIII
90
XIX
98
XX
108
XXI
124
XXII
147
XXIII
153
XXIV
176
XXV
177

XI
36
XII
43
XIII
51
XIV
56
XV
64
XVI
70
XVII
79
XXVI
185
XXVII
202
XXVIII
212
XXIX
223
XXX
240
XXXI
245
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About the author (1993)

Neal Koblitz is a Professor of Mathematics at the University of Washington in the Department of Mathematics. He is also an adjunct professor with the Centre for Applied Cryptographic Research at the University of Waterloo. He is the creator of hyperelliptic curve cryptography and the independent co-creator of elliptic curve cryptography. Professor Koblitz received his undergraduate degree from Harvard University, where he was a Putnam Fellow, in 1969. He received his Ph.D. from Princeton University in 1974 under the direction of Nickolas Katz.

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