Elliptic Curves and Applications (U03422)

? Credit Points : 10 ? SCQF Level : 10 ? Acronym : MAT-4-Ell

Course for final year students in Honours programmes in Mathematics.

1. Elliptic curves: where they come from.
2. Elliptic functions: poles, zeroes,
3. Various forms (Weierstrass, Theta functions) and their algebraic structure.
4. Some projective geometry.
5. The addition formula for the elliptic curve.
6. Elliptic curves over finite fields.

Applications:
Cryptography, number theory and mechanics.

The course is to make use of PAA, CVD in the analytic description of functions; the structure of finite abelian groups made use of, and lattices from the algebra course.

Entry Requirements

? Pre-requisites : U01616 Algebra, U03107 Complex Variable and Differential Equations

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Honours), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 4th year

? Delivery Period : Semester 2 (Blocks 3-4)

? Contact Teaching Time : 2 hour(s) per week for 11 weeks

All of the following classes

Type	Day	Start	End	Area
Lecture	Wednesday	09:00	10:50	KB

Summary of Intended Learning Outcomes

1. An understanding of elliptic curves as projective cubic equations for arbitrary fields; that these possess a group structure; an ability to calculate this group for finite fields.

2. To understand elliptic functions over the complex numbers and to be able to relate these to elliptic curves.

3. Appreciation of elliptic functions and curves arising in applications such as number theory, cryptography and dynamics.