M208 Pure Mathematics

I still have the plague (man flu) and I am having to take some heavy duty painkillers for a chest infection.  This has caused a certain haziness which has made any mathematics study difficult, but not impossible.

I have continued to try and refine my study methods that I will deploy when M208 begins in January 2012.  The books should arrive at the end of December, around xmas time, but I have managed to find enough of the unit materials, to not only get a small head start, but also to allow me to prime any areas that I may find difficult next year.

If I were to say which are my favourite areas of M208 mathematics, they would probably be, in the following order, (favourite first):

Group Theory
Analysis
Linear Algebra

I find all the groups stuff very interesting and with such amazing applications from discovering new particles to solving the Rubik's cube.

Just a general note about M208.  I fear that if one were to stumble across the OU website and take the 'Are You Ready for M208' diagnostic knowledge check; then one could very easily get caught in an elephant trap, if one then assumed that the test is a fair representation of the mathematical maturity required, to study the course.

It is true that you can start the course with the knowledge from a good A level, but having looked at all the M208 study material in detail, last month; there are some very challenging topics and it goes into wonderful depth and breadth, around these topics.

I am not sure I would have coped, had I not started reading Brannan et al, last month and therefore turning a 9 month course into a 12 month course by getting a head start.

The rough list of main topics covered is as followed:

Real functions and graphs
Graph sketching
Hybrid functions
Curves from parameters
Sets
Functions
Proof
Binomial theorem
Geometric series identity
Number systems
complex numbers
Modular numbers
Equivalence relations
Symmetry in R^2
Representing symmetries
Group Axioms
Proofs in group theory
Symmetry in R^3
Groups and subgroups
cyclic groups
isomorphisms
groups and modular arithmetic
Permutations
Conjugacy
Subgroups
Cayleys theorem
Cosets and Lagrange's theorem
Vectors and conics
Matrices and vectors
Vector Space etc
Linear transformations
Eigenvectors
Conics and Quadrics
Inequalities
Bounds upper and lower etc
Sequences
Series
Continuity
Conjugacy
Homomorphisms
Kernels and images etc
Group actions
Orbits and stabilisers etc
Limits and continuity
Differentiation
Integration
Power series

Wow, all that in 9 months, 7 coursework assignments and one 3hr exam.

I can't wait!