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
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Information for Visiting Students
| Pre-requisites | 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.
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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 |
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