Elliptic Curves

Time: the third semester

Credit: 3 hours

Period: 54 hours 

Previous courses: Elementary Number Theory, Abstract Algebra

Syllabus:

(1) Algebraic Curves

(2) Basic Theory of Elliptic Curves

(3) Elliptic Curves over the Complex Numbers

(4) The Arithmetic of Elliptic Curves

(5) Elliptic Curves and Modular Forms

References:

(1) J. W. S. Cassels, Lectures on Elliptic Curves, Cambridge University Press, Cambridge.

(2) J. S. Milne, Elliptic Curves, available at http://www.jmilne.org/math/.

(4) H. Silverman, The Arithmetic of Elliptic Curves, GTM 106, Springer-Verlag. 

(5) H. Silverman, Advanced Topics in the Arithmetic of Elliptic Curves, GTM 151, Springer-Verlag.