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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2011/2012
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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Elliptic Curves and Applications (MATH10041)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Course typeStandard AvailabilityAvailable to all students
Credit level (Normal year taken)SCQF Level 10 (Year 4 Undergraduate) Credits10
Home subject areaMathematics Other subject areaSpecialist Mathematics & Statistics (Honours)
Course website https://info.maths.ed.ac.uk/teaching.html Taught in Gaelic?No
Course descriptionCourse 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 (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Algebra (MATH10021) AND Complex Variable & Differential Equations (MATH10033)
Co-requisites
Prohibited Combinations Other requirements None
Additional Costs None
Information for Visiting Students
Pre-requisitesNone
Displayed in Visiting Students Prospectus?Yes
Course Delivery Information
Not being delivered
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.
Assessment Information
Examination only.
Special Arrangements
None
Additional Information
Academic description Not entered
Syllabus Not entered
Transferable skills Not entered
Reading list Not entered
Study Abroad Not entered
Study Pattern Not entered
KeywordsEll
Contacts
Course organiserDr Tom Mackay
Tel: (0131 6)50 5058
Email: T.Mackay@ed.ac.uk
Course secretaryMrs Alison Fairgrieve
Tel: (0131 6)50 6427
Email: Alison.Fairgrieve@ed.ac.uk
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© Copyright 2011 The University of Edinburgh - 16 January 2012 6:24 am