Bureau: 6153 André Aisenstadt, Tel: 343-6583; Courriel: andrew@dms.umontreal.ca

Course Book: *The Arithmetic of Elliptic Curves* by Joe Silverman is the standard reference in the subject and should be owned by every number theorist. It takes an approach that is well in-line with modern arithmetic geometry, which is not exactly how this course will proceed. You will find this available in the U de M bookstore

Alternatives: *Rational Points on Elliptic Curves* by Joe Silverman and John Tate is more elementary but covers many of the key introductory issues from as elementary a viewpoint as possible. We will use the approaches from this book in much of the first half of the semester.

*Introduction to Elliptic Curves and Modular Forms* by Neal Koblitz was an early book on precisely the subject of this course. It is a beautiful coherent account of many ideas leading up to some extraordinary developments with modular forms.

I am providing some notes entitled *Rational and Integral points on curves*.

Classtimes: Monday 10h30-12h30; Wednesday 10h30-12h30, in Andre-Aisenstadt 5183.

Class dates: From Sept 7 to Dec 7, 2011