Sent to: Volodya Guletskii in April, 2007. [N.B. I have emailed him the 7 Liverpool problem sheets with solns, and the 2005 exams with solns]. Dear Volodya, Yes indeed, I lectured MATH444 Elliptic Curves at Liverpool in the year 2004/05. I've adapted it to a similar course which I am now lecturing at Oxford, for which I have word processed the notes. If you go to the course webpage: www.maths.ox.ac.uk/current-students/undergraduates/ lecture-material/C/elliptic-curves/ you will find the pdf files for: - the Course Synopsis - Preliminary Reading - Lecture Notes - Problem Sheets The final problem sheet (Sheet 8) includes the 2006 examination and a further "Mock Examination" for the Oxford course (each consisting of 4 questions, as it is combined with 4 questions from another lecture course). For the Oxford course, there are only 16 lectures. I expected the Oxford students already to know the Preliminary Reading before the course began (either by having taken relevant courses in Geometry, Algebra and Analysis beforehand, or by reading through the Preliminary Reading beforehand). Then I lecture the "Lecture Notes" in 16 lectures. The main difference in Liverpool was that I could not expect the Liverpool students to know as much at the start of the course (but, in compensation, 33 lectures were available at Liverpool, plus 3 lectures for revision at the end, so there was more time available), and so in the first few weeks of the course I lectured a summary of the Preliminary Reading document, followed by a slightly watered-down version of the Lecture Notes (I did not, in Liverpool, include Formal Groups - they took the integrality of torsion points on faith - or the full version of Hensel's Lemma - just a special case for x^2 - a). I didn't keep the Liverpool lecture notes, but you can essentially reconstruct them by gluing together the later topics of the Preliminary Reading, followed by a slightly watered-down version of Lecture Notes. Also attached are the 7 problem sheets I gave out for the Liverpool version of the course, as well as the 2005 Liverpool examination. This was 2.5 hours, and the students were expected to answer 4 questions out of the 7 available. Note that the exam is in latex, but the problem sheets are in plain tex. I've also attached the Liverpool syllabus. Best wishes, Victor