Open University - M303 Further Pure Mathematics

It has begun. This is my fifth year with the OU and this is the proper start of what would be third year if I was full time. This particular course has something of a reputation already in it's short life (this is the second presentation). It consolidates a number of previously independant courses into one 60 point - that's basically a whole year part time or half a year full time equivilant. The main topics covered are:

  • Number Theory - congruence equations, quadratic reciprocity, prime number theorems
  • Group Theory - Sylow theorems, classification, finite fields, introductory Galois Theory
  • Rings & Fields - extensions, elliptic curves (& crypto)
  • Metric Spaces & Topology

As this is probably the most complicated and deep module I've studied yet I'm attempting to actually take notes. I update the following as I work through the material. I recommmend having a look and bookmarking the resources over at Shirleen Stibbe's site, it's a great collection of additional material!

Number Theory

  • Mindmap (using MindNode2): PDF. I find mind maps a nice way to get a good feel for the overall topics.
  • General notes: HTML; I've listed out the learning outcomes from each chapter into a single list. This is stuff that you should be able to look at and just "know".