Complexity, Clocks and Study Time.

For those familiar with M208, they will probably guess from the title of this post, that I am in the midst of studying I3 (Number systems).  Specifically Complex numbers and Modular arithmetic.

It has been an interesting week, as coming off of the back of a good 2 weeks studying of Functions and Graphs and Mathematical language units I1 and I2; I am already starting to try and guess, which parts I will need to know perfectly, to make the exam easier in October.

With these units, there seems to be a theme whereby, the study material starts off with basic concepts, before descending into some crazy depth involving some nasty looking proofs, that will probably be extensively tested in the TMA's, but perhaps not so deeply in the exam.  They are the sort of proofs that you can imagine took some poor mathematician, a life's work to figure out.  So, I won't be too hard on my self, for not learning the proofs back to front in approximately 15 - 20hrs of weekly study.  However, I am taking extra care, to ensure that I can follow the exercises in each sub-unit, that tests the use of such proofs in a practical question.

I did get a little bogged down this week in the middle of the complex numbers sub unit.  I got muddled up when trying to work out other arguments of complex numbers, when given just   Z^n = a

It's not that I don't understand the maths; I fully understood it at first reading.  It is more that, following through a relatively complicated set of processes, to arrive at an answer, contains its own pitfalls when one is studying it late at night, after a busy day at work.  I have just about got the hang of doing questions on this topic now;  but, it has eaten into nearly 1/2 of my allotted study time this week.  That has not left me much time to conquer clock arithmetic and equivalences; or to do another quick revision of I1 and I2.

I have obtained copies of all of the previous M208 exam papers since 2006, with some example solutions as well.  It is comforting to see, that they all seem to follow the same pattern, with a high probability of certain questions or topics, being given their own question space.  These include, manipulating some complex numbers to find the Argument, drawing some graphs and labelling correctly, some equivalence work and also doing a basic proof based on a logical statement about some numbers.

It does give one a little bit of hope, that the exam almost looks doable and certainly written to be passed by those that put in some work.  Fingers crossed.