Dear David and Charlotte,

  Attached is the pdf file of a handout I've been working
on for the last few weeks, which at some point I'll be making
available to everyone who intends to attend the Elliptic
Curves lecture course. I've gathered together most of
the main prerequisites from Years 1,2,3, starting at a very
basic level (with groups), but then moving fairly quickly
through: quotient groups, rings, fields, field extensions,
elementary Number Theory, valuations, completions, resultants,
and some basic ideas from Geometry (such as singularities
on a curve and multiplicity of intersection). The idea
is that intending students can read it and fill in any
gaps, particularly students who have not taken all of
the related lecture courses in Years 1,2,3. The last few
pages (pages 33-39) give roughly what I'll be covering in
the first week of the course itself. Quite aside from being
preliminary reading for the Elliptic Curves course, it is
sometimes intereting to see topics from introductory Algebra,
Number Theory and Geometry, gathered together into a single summary.
  Anyway, please feel free either to read it or ignore it as
you prefer! If you do read it, then naturally I'd be interested
to know if you notice any typos.

  Best regards, Victor