Saturday, 20 November 2010

Decisions Decisions

As many people reading this blog will know one of the endless games one gets into as an OU student is planning ahead. This involves a combination of planning ahead and keeping an eye on what will be available years ahead, also constraints of time and finances etc.  My problem is compounded as I have ambitions in both philosophy and mathematics. The maths plan is fairly straightforward although I was dithering as to its final form. Anyway I think its more or less finalised. I aim to complete a degree in Mathematics and Statistics.
by end of 2012 and then embark on the MSc

To this end I need the following compulsory courses

MST121 and MS221 of which I've completed both see earlier blog 30 points each.

Statistics 4 courses
Level 2
M248 Analysing Data                           30  points     Completed 2008   Grade 3 pass
M249 Applied Statistics                       30 points       Completed 2008  Grade 2 pass
Level 3
M343 Probability                                  30 points     Completed 2009  Grade 4 pass (bombed exam completely)
M346 Linear Statisitical Modelling         Still to do.

These 4 courses form a diploma in Statistics

In 2012 there will be another statistics course M347 called mathematical statistics. However after a long correspondence on the First Class conference I found out that whilst M346 was deemed necessary for the degree M347 is optional. This somewhat dismayed me as M346 is essentially a computer based course with little or no explanation of the underlying mathematics as incidentlally M249 was. Also the programme used is GenStat the  licence of which runs out after the course so any skills learnt are not transferable. However after much soul searching bearing in mind I want the degree finished in two years to start the MSc in 2013. I've decided to do it this year. I will get a diploma at the end of 2011 and be put in a strong positon to finish the degree in 2012.

Then there is an option to pursus an Applied or Pure Track. For me the choice was obvious I need to understand pure maths for my other ambitions. Also I'm familiar with much of the content of the OU applied maths/ physics courses.

So its M208 Pure Maths (60 points)
         M337 Complex Analysis (30 points)
I have to do Complex Analysis this year as it's only presented in even years. So that with M346 fills my quota for the year (You are only allowed 120 points per year)

That leaves 2012 The other two Pure maths courses I can do this year are
         M336 Group Theory                                                           30
         M338 Topology (The last time its going to be presented)     30

I could then cheat and include one of my second level arts courses as a free option and get the degree but it seems a Cheat and also I want to revise some of  my mathematical modelling skills. So the obvious course to do is M326 Mathematical methods and Fluid dynamics. However after 2011 it doesn't run again until October 2012. That suits me as for reasons to be explained below I want to do the 3rd level Philosophy course Philosophy of Mind which would round off my OU Arts studies nicely. Technically that would mean doing 150 points in 2012 but given the shift of starts I'm sure I'll get away with it. So thats the Maths degree sorted.

Now for my philosophy ambitions to tidy up the Open university Arts Options

My situation is as follows I first started Open university studies 10 years ago by doing the diploma in music the courses I studied were

A214           Understanding  Music     2nd Level    Grade 2 pass  60 points    2001  
AA314         Studies in Musc             3rd Level     Grade 3 pass  60 points    2002

This led to a diploma in music. I then toyed with the idea of doing their MA in music but was put off by the fact that the MA did not allow for analysis of musical works but concentrated on the history of performance and the reception of works. Not really what I wanted. Due to other pressures I stopped my OU studies made some fitful starts on some courses but didn't finish them.

I then had the idea of doing the degree in Philosophy and Psychological Studies as a preliminary to doing postgraduate research in philosophy. I'll talk about this in more detail later but I've alternated as to what would be the best course for me to pursue this ambition within a reasonable time scale. Anyway as a result I did the Foundation course in Social sciences

DD100      Foundation Course in Social Sciences  (October 2006 - 2007)         Pass
DSE212    Introduction to psychology                    October 2007                      Grade 3

And then I would have alternated between Philosophy and the Human Condition, Cognitive Psychology and
Philosophy of the mind. Howver as a result of the psychology course which I didn't really enjoy I got into statisitcs which I did enjoy so started the Diploma in Statistics . Also I became suspicious of the relevance of the Open University philosophy courses to what I really wanted to do (a suspicion I still have but I've learnt to live with it). Ok so having abandoned psychology I concentrated on Statistics which lead to the fully fledged maths degree. I had planned to embark on the external London BA in Philosophy in 2008

With tuition available from Pathways

And if I were starting this journey again that would be the Path I would follow. However again time procrastination and so forth led to me putting it off. Also as it was easier to continue doing the OU courses I decided to do A211  Philosophy and the Human condition whilst concurrently building up a portfolio of courses which count as 10 points towards accreditation from the Depatment of continuing education at Edinburgh and Oxford University.

So far I've completed 30 points

Philosophy of language   Edinburgh     Jan   - Mar        2009      
Metaphysics                  Oxford          Apr - August     2009
Ethics                            Edinburgh      Sept - Dec        2009

And then did A211 this year. 

Next spring I hope to do a course on Hume at Edinburgh and then either an Oxford course or some of the Pathways courses

which although not credited have got quite a reputation. I want to study metaphysics and the philosophy of language in more depth.

I'll round all the philosophy off by doing the level three OU course in the philosophy of mind in 2012.That would mean my OU Arts courses would combine to give me an Open degree. If I were vain enough I could turn an Open degree into a named degree in humanities with music and philosophy but I would have to do another Arts course.

 I should then be in a  reasonable position to formulate a research proposal (of which more later) even though I would not have a fully fledged philosophy degree.  I hope to  start part time research in either 2013 or 2014. I might take advantage of Geoffrey Klempner's associateship and fellowship awards of the ISFP to help me formulate my research proposals better. The field I want to explore would be the relationship between current ideas in the philosophy of language epistemology and the interpretation of quantum mechanics. Specifically for those who know about it the research would explore the connection between Dummett's claim that realism is commited to bivalence (ie something is either true or false)  and the fact that the current mathematical formalism of quantum mechanics is not bivalent and hence intrinsically non-realist.  I'll expound more in another post. After long agonising this seems the best way forward, if I were to do the London BA it would be at least another five years before I could complete it and that would only postpone the ambition to do research in philosophy. I do feel slightly guilty that I wont be doing the best available qualification in philosophy available to me but I'm aware of its contents and have familiarised myself with the exams  and reading lists so I'll pursue those on my own anyway. 





Sunday, 14 November 2010

Preparation for M208 , and a bit on Latex and Mathbin

As part of my preparation for M208 I've been trying to grapple with the epsilon - delta definition of continuity. Open up any Old style textbook on analysis and you will find a definition which is almost incomprehensible anyway things have improved greatly. At the risk of boring those people I know from the OU forums I've been using a book by Brannan called A first course in mathematical Analysis published by Cambridge University Press. This covers the analysis part of M208 and I would recommend anyone who is contemplating doing M208 to invest in it.

I think I finally understand (after 30 years) how to use the definition of continuity  at least for simple cases. I've enclosed a basic summary on Mathbin

Duncan introduced me to Mathbin  as a consequence of some  work we are doing on the Cambridge Maths departments  example sheets for rotational motion of which more later.

Mathbin is great for exchanging posts which require mathematics. Its based on Latex which Nilo has kindly given me some hints how to use.  However it has it's own idiosyncracies in that for Internet explorer the previewer doesn't work and Latex copy doesn't copy across as mathematical text  is bracketed with [EQN]   [/EQN] instead of $  $ and it is a real pain to adjust LATEX files so that they work first time on Mathbin.  It took me about 10 iterations before I got it correct. Fairly soon following the hints that Nilo gave me I hope to incorporate Latex on this blog. For now as I'm just getting used to the whole Latex thing  then this hash will have to do. Eventually for my large projects I will use something like ScribTEX.

Monday, 8 November 2010

Review of MS221 and MST121

Hi first let me apologise for not posting earlier I'm currently working on the so called 'Straightforward but Tedious' process of deriving the Friedmann equations (the ones that form the basis of modern cosmology) from Einstein's Theory of relativity. The process is certainly tedious whether or not it is straightforward is another matter. I'll keep you posted. Anyway in the mean time here are my thoughts on the two maths courses I did this year. These were

MST121 Using mathematics and MS221 Exploring Mathematics.

As essentially entry courses for the degree in mathematics they try to cover most of the stuff that would be expected for an entry into a typical university. So roughly equivalent to the old A level Pure and Furthe Pure maths courses with a little mechanics and statistics thrown in. Without boasting for me most of the course material was revision  mainly to get back into thinking about stuff which I hadn't done for years. My colleagues Neil and Nilo have already described these courses in some detail and there is not much I can add to their descriptions. For those who want a blow by blow description I refer to their blogs.

However here is a quick overview. I think the courses are best taken together as a unit with MST121 in October and MS221

The courses are split into 4 blocks and the material in the MS221 blocks A, B and C build on the corresponding blocks in MST121. Whereas block D in MST121 covers basic statistics and block D in MS221 provides an introduction to pure maths of which I will be getting a lot more of when I do M208.

Block A is concerned with sequences, functions, coordinate geometry trigonometry and recurrence relations
the stuff on recurrence relations was new to me and one of the more interesting parts of the course especially the stuff about Fibbonacci series and the golden ratio. It's that sort of maths which on the one hand is quite straightforward but has amazing applications. However solving a second order recurrence relation can be quite tricky to get correct and I'm sure I lost a couple of marks in the exam.  For those contemplating doing MST221 next year it really is worth mastering the procedure for rotation of a conic section as this question always seems to crop up in the second half of the exam. (Of course I didn't heed this advice of which more later)

Block B is concerned with vectors matrices and their application to geometric  transformations and also another topic which was new to me the fixed points of an equation and how they govern the behaviour of a function when it is iterated. Again a fixed point question seems to come up all the time and it is worth getting to the stage where you can invert a 2x2 matrix, find it's inverse, eigenvalues and corresponding eigenvectors.

Block C on calculus was my favourite but that is because I have loved calculus ever since I first came across it when I was about 15 or 16. I think anyone who hasn't got a basic understanding of calculus at the level of this course doesn't deserve to be called properly educated. A bit strong perhaps but without a grasp of calculus you have no idea how physics or engineering works. Those in the Arts world often call  physicists and engineers philistines as they aren't familiar with the main works of Shakespeare are just as philistine themselves if they don't know how calculus works . If I have a slight criticism of this unit I feel that they could have made an attempt to include material on Second order differential equations instead of Taylor series. It is second order differential equations which form the backbone of most physics modelling enshrined in the simple harmonic oscillator, The thing that made me really interested in mathematical physics was the realisation that the same basic differential equation described both mechanical and electrical oscillations. Taylor series whilst important could really be left to a level two course whereas an introduction to second order differential equations with an explanation of some of their applications would be much more useful. Especially for those people for whom MS221 will be their last maths course.  Anyway those who want a taste should down load the units of MST209 available on Open Learn. Anyway despite getting my best marks for the TMA's in this part I totally bombed the long exam question as I had a mental block. So whilst calculus is interesting doing it under pressure is not so good and it is not recommended to do the long calculus question.

MST121 Block D Statistics Most people found this boring however I have to say I thought it gave a good overview of the process of hypothesis testing. This has had quite significant social implications in recent years especially when it comes to testing the efficacy of certain proposed medical statistics. In brief hypothesis testing is a method whereby tests can be devised to test the validity or otherwise of a certian proposed treatment. It enables a statistic such as the mean from two samples to be compared, In medical tests two groups of people of  the same size are compared one is given a new drug say whilst the others are given a placebo. If the number of people who improve after being given the drug is significantly higher than those who are just given the placebo then the efficacy of the drug treatment is deemed worthy of further investigation. More often or not there is no statistically significant difference between the two samples and thus the treatment can be ruled out. In the current climate their appear to be all sorts of quack remedies such as homeopathy or other so called alternative medical treatments. By performing a hypothesis test the validity of these claims can be rigourously checked, Needless to say when these tests are performed the treatment is generally deemed statistically insignificant. The point is that this methodology is a powerful tool and politicians and people who make policy decisions should be aware of this. Had a proper analysis of the claims of Dr Wakefield who claimed that there was a link between the MMR vaccination and autism been undertaken much needless scaremongering and agony for many parents would have been avoided. However as a consequence of the claim many people were put off subjecting their children to the MMR jab and as a consequence we are now facing the rise in measeles a disease which had been effectively erradicated.
The point being that with tools like hypothesis testing soft sciences such as the social sciences can be raised to the status of real science as they have a method of falsifying claims. Unfortunately the unit in MST121 did not really mention this application of statistics. Had it done so then perhaps people would not have found it so boring.

Unit D MS221 Introduction to Pure Maths this covered complex numbers a brief introduction to number theory group theory and methods of proof including induction

This is an attempt to introduce some of the thinkning behind pure mathematics I was familiar with complex numbers, group theory and  mtethods of proof. As a taster the group theory was Ok but (and I suspect) this will become more so when I do M208 and M336 there was no real rationale behind why group theory is important. Yet it has had a profound impact in physics via the use of representation theory as applied to particle physics and quantum mechanics. However the part that is necessary for this is representation theory and this I believe is not taught in any of the OU maths courses. However group theory as a mathematical structure is quite profound in iteself I refer you to Nilo's site for those interested in this aspect.

As for number theory I really don;t get it and the course did not really convince me give me a complicated integral and I'll get my pen out and do my best to solve it. Show me the analogy between vector spaces and function spaces (of which more later ) and I'll be really impressed, On the other hand I just can't get excited by relationships between prime numbers or congruences. The application to coding given in this unit was quite tricky easy to make mistakes and fiddly. I'm afraid I couldn't resist at a tutorial getting my tutor to work through an example on the board I was relieved to find that he made more or less the same errors that I would have done.

Ok so overall impressions as a warm up to the real stuff and practice in doing TMA's these courses are great however the real stuff starts at level two I can't wait. As a sideline I was really lucky in having a really good tutor and a friendly tutorial group I have made lots of friends including Nilo (who I got to know via a link on Neils blog) , Duncan and Neil this is the first OU course where I became convinced of the value of tutorials and the friendships that follow. I would like to thank my tutor Alan Borthwick and all the friends I made on MS221.


Block B