Elliptic Curves (20cr)
| Code | School | Level | Credits | Semesters |
| MATH4084 | Mathematical Sciences | 4 | 20 | Autumn UK |
- Code
- MATH4084
- School
- Mathematical Sciences
- Level
- 4
- Credits
- 20
- Semesters
- Autumn UK
Summary
The course will start with several topics from the perspective of what can be explicitly calculated with an emphasis on applications to geometry and number theory. Topics for this course include:
- basic notions of projective geometry;
- plane algebraic curves including elliptic curves;
- addition of points on elliptic curves;
- results on the group of rational points on an elliptic curve;
- properties of elliptic curves and their applications.
Target Students
Only available to Single and Joint Honours of Mathematical Sciences students.
Classes
- Two 1-hour lectures each week for 11 weeks
- One 2-hour lecture each week for 11 weeks
Assessment
- 30% Coursework 1: Summative assessment based on in-class questions that are distributed through the semester
- 70% Exam 1 (2-hour): Written examination
Assessed by end of autumn semester
Educational Aims
This course is related to other courses within Pure Mathematics, specifically in number theory and algebra. The course develops the basic theory of mathematical notions in the topic of elliptic curves and includes many examples. It helps the students to gain an introduction to advanced topics through concrete examples and linking it to interesting applications. It develops facility in the understanding, use and study of appropriate geometric and algebraic notions, and number theoretical methods.Learning Outcomes
A student who completes this course successfully should be able to:
L1 - Use and apply concepts and methods from projective geometry;
L2 - Define and apply the basic geometric concepts related to algebraic curves;
L3 - Define and apply the main algebraic and number theoretic concepts related to elliptic curves;
L4 - Use and apply the addition law on elliptic curves over different fields;
L5 - Prove basic propositions in the theory.