If I were a Springer-Verlag Graduate Text in Mathematics, I would be Kenneth Ireland and Michael Rosen's A Classical Introduction to Modern Number Theory.
Bridging the gap between elementary number theory and the systematic study of advanced topics, I am a well-developed and accessible text that requires only a familiarity with basic abstract algebra. Historical developement is stressed throughout, along with wide-ranging coverage of significant results with comparitively elementary proofs, some of them new. An extensive bibliography and many challenging exercises are also included. I have been corrected and contain two new chapters which provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curves.
Which Springer GTM would you be?
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