MATH70064 - Elliptic Curves
- Lecture times and place : Tuesday 12-13 HXLY 340, Thursday 11-12 HXLY 130 (except on week six HXLY 642), Friday 10-11 HXLY 144.
- Office: HXLY 625
- Office hours: Tuesday 15-16
- References: These are some of the books that I will be drawing from for the lectures
- J. W. S. Cassels - Lectures on Elliptic Curves
- J. H. Silverman, J. T. Tate - Rational points on Elliptic Curves (Second Edition)
- J. H. Silverman - The Arithmetic of Elliptic Curves (2nd Edition)
- To receive the announcements related to the course, please send me an e-mail if you are going to continue with this course.
Lecture notes
Here are the lecture notes. They are mostly taken from the above references. I will be updating these as we go along.
Exercises
We will go through most of the exercises from Cassels' book. I will post my solutions here as we cover the chapters (I expect to cover 2/3 of the book).
You should first attempt to solve the exercises yourself. If you struggle to come up with a solution, then you can read the solutions that I provide.
Some problems took me several hours to solve and it does feel good when you solve it.
If any errors (even typos) are detected, please send a query to the course email list.
Coursework
There will be 2 problem sets which will be posted here.
Each problem set will constitute %5 of your final grade.
Please submit your solutions as a PDF.
Exam
The exam constitutes %90 of your final grade.
Everything in the lecture notes (unless marked otherwise) is examinable.
The exam questions will be solvable with the material covered in the lecture notes.
Alternatively, if you have mastered the books listed above, you should be set for the exam.
In the exam, unless you provide the proof, you are not allowed to use results that we have not proved in the class (for example, Mazur's theorem cannot be used).
Extra