Open University Module MS221: Exploring Mathematics

This block starts by taking the ideas of squences further. It introduces the golden ratio and the fibonacci sequence.

These are explained in a good manner with the accompanying video files and audio helping a great deal. This part was a good and interesting start to the course. With Marcus Du Satoys TV series the code running on the BBC, which mentioned many of the ideas of this part of the module, adding to the interest.

The block then moves onto the idea of conic sections, Hyperbolas, Ellipses and parabolas. These, for me at least, were intially quite had to get my head around, however once it clicked i found these were the part of the course that I remembered best once I got to revise for the exam.

The block ends by taking the ideas of conics further and explains how they can be moved from standard postion and rotated, reflected etc by functions.

This was an interesting start to the course and turned out to be, for me the most memorable part.

I attained a pass mark of 96% in TMA01, which is the first course work assement and is associated with this block only.

Interating functions is simply put entering an inital number into the function to find the following term. Then repeating to find each following term. This is explained really well especially with the addition of graphical iteration. Which makes it much easier to visualise how an iterated sequence works and it's future behavour.

More matricies, this takes the idea of vectors and matricies a little further than in MST121. It also ings in the idea of eigen vectors and lines.

A good block in my opinion although describing the long term behavour of iteration sequences is quite boring.

This was my favourite section and I received 98% in the TMA which was my best result of the course.

This block again takes the idea's introduced in MST121 further.

It takes differentiation slightly further and fully explains first priciples. Introcing the limits which enable differentiation.

The same is true with integration, bringing in integration by parts and by substitution. Also introduced is the idea of volumes of revolution which are simply the volume produced when the graph of a function is revolved around the x-axis. It is possible to use integration to work out the voulme of the shape created.

The third section of this block is different to MST121 and introduces Taylor polynomials as a way of estimating the value of a function.

This section is completely different to MST121. The majority of the ideas were completely new to me.

Complex numbers are introduced in the first part of this block. This brings in i as a number, reffered to as an imaginary number. As we know you can not take the square root of negative numbers and so some quadratic equations are un solveable. However if we introduce an new numbering system i where i = root -1. This then allows us to find answers to previousley unsolveable equations, with an answer that is a mixture of real and imaginary numbers, referred to as complex.

Number theory was again new to me, the majority of this section is fairly straight forward bringing in simple ways to find remainders of division. Also bringing in new operations which add to the standard multiplication, addition, division and subtraction, that we are used to.
the section then moves on to use these for simple cryptographic applications.

Groups yet agian new to me, this allows us to draw up tables where groups of numbers are acted upon to produce an element of the table. This then leads to various patterns and properties.

Finally we finish with proof and reasoning. This brings in logic, much of which you may have met in basic programming courses or even just basic IT. However it is seen from a much more mathematical perspective. I rushed this section a bit as I wanted to get revising for the exam.

As stated I tended to fush this block a little to try and give myself a bit more time for revision. This ended up showing slightly as my TMA result for this block was 94% my lowest of the course.

Mathcad is used much less in this module. In fact I would say that you can get away without using it for the whole of the second half of the course.

That said it can be very handy in checking working etc throughout the module.

For more info on mathcad see my lens on module MST121.

Ok so I have finished the exam, but don;t have my result yet. Despite finishing off this lens I am trying my best not to think about the exam.

I think that I have done fairly well, I should get a grade of somewhere around 90%, as my best guess. So hopefully I have a grade 1 which is the top grade and generally should have a break point of around 85%. So i am hoping to be just above this fingers crossed.

The key to this exam IMHO is practicing past papers both timed and at leasure. I only did 2 papers one timed and one not. This was definately a mistake. With time very short in the exam, despite it being 3 hours long, if you have practiced well you can get the simpler questions out of the way quickly. This then allows you to relax and take a little extra time on questions that are a little more confusing.

Revising using the activity books, which is what I did mostly, is helpful but I did find that the exam questions were worded very differently to the course questions. This is why I would say to get as many past papers as possible and concentrate on them, I would try to do 10 including the specimin exam which is provided. doing 2 of these timed.

I found that the majority of the exam questions were extremely similar to past exam questions, with only 2 being different enough to momentarily put me off. I think had I done more past papers I wouldn't have found they were all similar to past questions.

All that said it was not a bad exam, a good balance of simple questions and more taxing ones. But again I haven't received my result yet and so I may change my mind.

Good luck to anyone who takes this in the future!

I have now received my result 86% which was just inside the cut off for a distinction. I am very happy and a little lucky. My advise to everyone is that with enough revision of old exam papers everyone can get a similar result.

Now on to M208!!!!