Elliptic Curves Over Finite Fields.
Masters thesis, National University of Ireland Maynooth.
This thesis provides a self-contained introduction to elliptic curves accessible
to advanced undergraduates and graduate students in mathematics, with
emphasis on the the theory of elliptic curves over finite fields.
In Chapter 1, affine and projective planes are introduced. Chapter 2
introduces the theory of algebraic curves and the Weierstrass Normal Form
of a cubic curve is derived. In Chapter 3 we define derivations on arbitrary
polynomial rings, and prove the group law for elliptic curves. Chapter 4
discusses elliptic curves over finite fields and proves some results on counting
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