Undergraduate Course: Elliptic Curves and Applications (MATH10041)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 10 (Year 4 Undergraduate) 
Availability  Available to all students 
SCQF Credits  10 
ECTS Credits  5 
Summary  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. 
Course description 
Not entered

Information for Visiting Students
Prerequisites  None 
Course Delivery Information
Not being delivered 
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.

Contacts
Course organiser  Dr Tom Mackay
Tel: (0131 6)50 5058
Email: T.Mackay@ed.ac.uk 
Course secretary  Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk 

