1st degree (Bachelor)
Coordinator Office Hours:
Prof Ron Livne
In the course we discuss elliptic curves over the real and the complex numbers, and over number fields, in particular over the rational numbers. We will mainly look at their arithmetic properties and prove the Mordell-Weil theorem using Galois theory, and define ge Selmer and the Shafarevich-Tate groups.Time permitting, we will discuss additional topics that would take into account the preference of the students.
The goal will be to spark interest in the arithmetic of elliptic curves and some of the modern techniques in diophantine equations.
Learning outcomes - On successful completion of this module, students should be able to:
To continue the study of elliptic curves and their generalizations
Teaching arrangement and method of instruction:
See course description
The course notes
Additional Reading Material:
The books by Silverman and Koblitz on elliptic curves
End of year written/oral examination 0 %
Presentation 0 %
Participation in Tutorials 0 %
Project work 0 %
Assignments 0 %
Reports 0 %
Research project 0 %
Quizzes 0 %
Other 100 %
1) We will assume familiarity with functions of complex variable (eg 80519) and with field theory (eg 80446) According to the number of students requiring a grade, it will be decided in the beginning of the course how it will be determined (exam or lecture).