Reflection and Renewal

Happy new year!

Having now spent the last two years(ish), blogging my path through maths and physics study; It is sometimes too easy to loose a little perspective.  The daily or weekly difficulties and bumps in the road, can make you think that you are not learning anything.

But, it only takes a glance back for me, through posts from 2011,  to help me realize that I could not have hoped for a better start to my journey into academia.

There have been kinks in the journey.  For starters, I based this experiment on some slightly shaky assumptions.  For example, who could have known that my interests and skills appear better suited to pure mathematics, rather than physics or applied maths?

It certainly took me by surprise, and I did have a period, in December, where I thought that I had cocked up my study path, messed up my plans and panicked about not being able to complete studies in quantum mechanics and electromagnetism, next year.  However, it often takes an outsider to make you realise, with fresh eyes, exactly how far you have come.

It was on speaking with a good friend, that I found myself maudlin about how I couldn't stomach two years of applied maths, and pined for some pure maths modules; but had left it too late to get on the courses for 2013.

At that point, my friend halted my diatribe; "let me get this straight.  You just scored distinction level marks on two university applied and pure maths course, after studying just a GCSE in maths, and you are f*****g moaning about it?"

Ah, point made!

You see, I remember a cold February night this year, when I was lying in bed, worrying and almost in tears, as I couldn't understand any of the M208 material on equivalence relations.  Yet, after 9 months, it is now second nature.  It just goes to show, that Perspective is everything; time is a wonderful teacher; and I am now reinvigorated and excited about 2013.

A very happy new year to you all.

Of Mice and Men

John Steinbeck, Of Mice and Men:

  

"[He] walked heavily, dragging his feet a little, way a bear drags his paws.  His arms did not swing at his sides, but hung loosely."

I revisited the O.U library last week, as I seemed to be loosing some sleep over my module choices for February (Electromagnetism and Quantum mechanics).

I am comfortable with the maths required for both courses, but I was just feeling really unsure about the physics.  Also, my gut was telling me that there was a disturbance within the force, and it is very rarely wrong, in that regard.

No, I hadn't been eating cheese before bed, or fallen asleep whilst watching a late night ITV re-run of Star Wars.  Something just didn't feel right.

So, I put on my hat and scarf, and braved the Ice and wind, to revisit the OU at Milton Keynes.  After I finally found a parking space (there was a Xmas lecture that day, so the car parks were full!), I found the reference copies of Electromagnetism and The Quantum World.  They were exactly where I had left them, so I guess no one else had looked at them since I was there, last.

And, after I tuned out the din from two O.U employees gossiping rather loudly about a co-worker, I sat down and studied the first two chapters of each book.

What did I find?  Well, I ended up with a gargantuan list of physics that I needed to study before attempting these two courses.  And that was just from the first few chapters.  So, it dawned on me, that I have completely underestimated the amount of physics that I don't know, and also the size of the task ahead of me, to learn it all sufficiently, before the end of January.

So, I went home, miserable.  I emailed Chris, my mentor, to seek his advice, and then I lost some more sleep.

This time, the thoughts running through my head were: you are not going to pass those two courses in January; you have only two other viable choices for Feb 2013, and they are both taxing, in their own ways.

Those other two courses are Astrophysics, and Cosmology (The Relativistic Universe).

Having read the reviews on both courses and also looked at the course materials for both, I have come to the conclusion that I could easily be ready for Astrophysics in Feb 2013.  I have already completed level 1 courses in this area, I have an active interest in Astronomy and I have planned a viable course of study that would cover all the physics and astronomy needed for this course, before Feb 2012. 

The Relativistic Universe looks a lot harder, it is anecdotally claimed to be the hardest of all level 3 OU physics courses, due to the mathematical and conceptual difficulties, combined with some poor set books.  I could also comfortably cover the additional material required before February, but the course is very difficult to obtain a grade 1 pass in, so it is on my maybe pile.

So, I have cancelled my Quantum and electromag modules, which I may pick up in October;  I have registered for Astrophysics in February; and I am waiting until January the 2nd, to decide whether I finally register for the cosmology course (depending on how my pre-study goes.)

This will mean that I then need to take 2 x 30 point modules in October, to complete this stage of my studies.  Whether they will be physics or maths, will be decided later on in the year.

K.B.O

Post-Results Blues

This last two weeks, I have been concentrating on  partial derivatives, gradient, curl etc,
as I delve (pun intended), into the murky waters of applied mathematics.

I have to say that I really have mixed feelings about this subject.   I know that I mentioned earlier this month, that applied mathematics is a lot of 'hand waving'; however, my tongue in cheek comments actually hide a little bit of fear and trepidation about this field of mathematics.

I though that doing pure mathematics first: analysis, groups and linear algebra; would have made the applied subjects an easy win on my study journey.

However, I am finding myself a little stressed as I self-study the  O.U course MST209 (Mathematical Methods and Models).

It isn't the difficulty of the material, since I believe that M208 is equally as taxing.  It is simply a case of my brain seemingly being better at abstract maths rather than applying the maths theorems to models, making assumptions and knowing which units the final answer should be expressed in.

This has caused me a small issue.  That is, in the back of my mind, I can feel a little bit of tedium creeping in; and, dare I say it, some boredom too, as I go through the applied examples in MST209.

This is causing me two problems.

Firstly, after the heady 92% pass in my pure maths exam, I have now lurched into a mild state of panic.  I have 18 months of applied maths modules ahead of me and if I am finding it a bit tedious now, how the hell am I going to be able to sustain my concentration when things get tough in June next year.

Secondly, I have a little voice at the back of my head that is whispering, "you don't like applied maths, do you?"  I don't know whether to believe that voice, or whether it is just some self-destructive thought pattern, trying to provoke me into shifting to a safe study path.

I know that I am going to be excited about studying quantum mechanics in February.  However, what if I can't shake this feeling of doubt and tedium?  Will I be able to cope with Electromagnetism, if I can't stand the sight of another damn Maxwell equation?

I do hope that these feelings pass.

M208 Exam Result

I am thrilled to say that I managed to pass the Open University's offering in Pure Mathematics, M208.

The email came today, stating that the results were in; and, after plucking up the courage an hour later, I checked my result.

Well, I managed to achieve a Distinction with 92% of the available marks, which has left me amazed, since I am sure I counted up at least 10 marks of 'known' errors in my exam script.

So, it just goes to show, that post-exam memory cannot be relied upon, as an accurate assessment of performance.

So, once I have soaked the news up, I will begin to plan with a little more security, the rest of my studies.

I am sticking with Quantum mechanics and Electromagnetism in February;  but I am now one step closer towards my wife supporting my MSc studies at a brick University, in October 2013.

MSc choices

I have been working hard this week, to convince my better half, to let me use some of our hard earned savings to pay for a part-time MSc next year, at a London University.  The course is 2yrs part-time and costs well over £12K!

I have been used to plodding through my Open University studies, each year, at a pace that is financially comfortable and is not too taxing in terms of time spent each week, studying.

However, the Open University simply do not offer me what I want at the postgraduate level.  I am also certain, that they never will either (going by the recent conversations that I have had with several tutors and course administrators).

Bottom line?  The O.U do not believe that it is financially viable for them to offer theoretical science MSc's.  This is despite them having a student base of over 250,000.

So, my potential choice of an MSc, with a very well known London university, is an intensive two year stint, with a minimum of 20hrs per week of studying and at the very least, a monthly trip to London for intensive lectures and study.

I already work in a traditional profession, and clock the occasional 56hr week, so any extra time spent studying, will almost certainly impact on my 'family time'.

So, it's a big ask; "darling, can I spend our savings so that I can see you and the kids even less for the next two years?"  Doesn't sound that attractive.

The course, which I have deliberately not mentioned the title of  yet, combines some pure and applied mathematics, with fairly advanced computer science and modelling.

It isn't a degree in physics, but then I am struggling to find one, that will allow me to complete it part-time, without having to visit a lab each week.

So, I will ponder, cogitate and digest this potential bifurcation point in my study path; whilst I sit and wait for my exam results for this year.

If I don't get a good pass in those exams, I will probably be fairly limited in my MSc options, anyway.

Lastly, why haven't I mentioned the title of the degree yet?  Because I want to settle on the decision myself, since it is such an important choice.  If it turns out to be wrong, then I want that decision to be on my shoulders only.

Rambling Matrices Revisited!

The title of this post is an intended homage to two particularly favourite blogs of mine, by  fellow students.

Matrices Reloaded

Ramblings of a Short Fat Failed Physicist

Having studied matrices as part of M208 Pure Mathematics, I feel I need a little refresher / revisit / reload of some basic manipulation and applications of them

I have thumbed through several books that I have which cover advanced mathematical physics; and it appears that matrices play a major, prominent role in many areas.

I don't have any particular issues with matrices and I found that Gauss elimination method was one of my best practised methods, as I prepared for the M208 exam.

However, I want to be able to fire through manipulation of matrices, vectors / tensors and other tools, at lightening speed and with pinpoint accuracy.  It just feels like it will be nice to have a security blanket going into quantum mechanics and electromagnetism, in February.

Mathematical Modelling Software

I have now completed units 1, 2 and 3 of the Open University course MST209 (Mathematical Methods and Models).  This is self study and after a quick recap on vector algebra tomorrow and Tuesday; I will have set myself up for a few weeks of Vector Calculus practice, before Christmas creeps any closer.

Unit 3 mainly developed some basic calculus involving second order differential equations.  Time allowed me to manage about 75% of the example questions, selecting at least one example for each different 'issue' that arises when trying to solve these equations.

I found it particularly satisfying when the second order diff equations were used to model damping phenomena in oscillating systems.  I will probably look to try and use some of these example questions to test drive some different types of modelling software, before settling on one package to then master over the next two years.

However, I am quite unsure as to which software I should invest the time and effort into learning.

I have some experience of the algebra package Mathcad, but I found it quite difficult to use and didn't really warm to it. I know they are planning an easier product in the future, and I will test drive that software as part of my selection process. Other choices might be Mathematica, Matlab, Maple etc.

I need to do some research here, as I am unsure as to whether there is one package that is mainly used as an academic and industry standard, when modelling mathematical and physical systems or designs.

I suspect there isn't just one' best-fit' package, so it may just come down to personal preference, ease of use and checking that it has the scope to be used in my research and beyond.

My Annual Visit to the O.U Library

This morning, I braved the wind and rain to embark on my now traditional visit, to the Open University campus at Walton Hall.

As part of my preparation for the February modules, I like to visit the O.U library, which contains reference copies of all the O.U module materials, that I will be studying soon.

This has two distinct benefits:

1.  By leafing through the materials, I get a feel for the level of difficulty that awaits me.  Thus, my stress levels are minimized, as we approach February.

2.  I know exactly how much prep I need to do and in which areas of study.  This has already paid off, as I can see that I had planned to study my maths prep, in far too much detail.  I now plan to refine that plan this week, so that I can spend much more time on practising and becoming a differentiation and  integration Jedi!

So, for my two Feb courses, in Quantum mechanics and Electromagnetism; here are the areas of study for next year (Chris, I know you will salivate at the sight of some of these topics;-)


SMT359 (Electromagnetism)

Book 1

Electric forces and fields
Gauss law
Magnetic forces and fields
Vectors
Field coordinates
Partial derivatives
Volume and surface integrals
Divergence of a vector field
Line integrals
Curl of a vector field
Laplacian operators


Book 2

Foundations of electromagnetism
Electrical fields in materials
Magnetic fields in materials
Electrostatics
Magneto statics
Forces on particles
Resistance and induction
Super conductivity
Special relativity

Book 3

Electromagnetic waves in empty space
Generation of electromagnetic waves
Dielectrics
Conductors
Plasmas


SM358 (The Quantum World)

Book 1

Basics of quantum mechanics wave / particle discussions etc.
Schrödinger's equation and wave functions
Particles in boxes (more Schrödinger)
The Heisenberg uncertainty principle
Simple harmonic oscillators
Wave packets and motion
Scattering and tunnelling
Maths tool-kit including,
Complex numbers
Ordinary diffrential equations
Partial differential equations
Probability

Book 2

Dirac notation
Ehrenfest equations
Geometry of quantum mechanics
Angular momentum
Spin angular momentum
May particle systems
The Pauli exclusion principle
Bose Einstein condensate
Quantum entanglement
Quantum information
Quantum teleportation
Vectors
Abstract vector spaces
Matrices

Book 3

Angular momentum in atomic physics
The hydrogen atom
Time independent approximation methods
Hydrogen like systems
Putting quantum mechanics and relativity together
Many electron atoms
Hund's rules
Diatomic molecules
Solid state physics
Light and matter

Both courses seem to separate out the mathematics 'training' from the qualitative material and the application of the concepts.  This makes it easy to dip into the maths chapters first, so that there is less stop-start business going on.

I am so excited at the prospect of studying this material, that I am not sure I will sleep tonight. 

 Now, where's that anorak?

Quantum Mechanics and Electromagnetism Preparation

Okay, so I am now in full swing with my preparatory studying in preparation for the level 3 Open University mathematical physics courses, The Quantum World (SM358) and Electromagnetism (SMT359).

These are the main offerings at level 3 for physics.  There are another two courses that cover Astrophysics and also Relativity / Cosmology, which look very interesting, but I am not sure they fit in with my study plans.

That will leave me with two other, rather obvious courses, for me to choose in order to make up an appealing and ostensibly solid mathematical physics / applied maths background to my degree.  Those courses are, Waves Diffusion and Variational Principles (MS324) and the science project course Radiation and Matter (SXP390).

I have added this project module on my list of hot favourite modules for October 2013, simply because it will follow on nicely from the quantum and electro stuff that I will have just finished studying; and it appears to allow some research and writing in a substantial piece of work.  This will develop skills that I don't currently have and that I critically need, if I am to study a masters thesis module or even move straight onto a part-time MPhil or beyond.

It will also nicely consolidate my Feb 2013 study modules, as I will be applying them in the following 9 month period.  The project subjects available include work on quantum entanglement, so it certainly sounds challenging enough to whet the appetite.

Anyway, this week I have now studied the following prep materials:

recap on:
differentiation and integration
first order differential equations
solving linear equations

So I have managed to cover 32hrs worth of work, from the OU course MST209 (Mathematical Methods and Models), in 12hrs.  Having said that, much of it was a recap or advancement on work that I had done in MST121 or M208 in 2011 / 2012.

Next stop, second order differential equations and some recap on vector algebra, before, next week,  I launch into some Fourier Series and partial differential equations.

Awesome!

Biological Physics, An Introduction

I just spotted this; the Institute of Physics have a website that contains a load of  free modules that they have written, to introduce physicists to the subject of Biological Physics.

It looks fascinating and appears to be quite heavy in mathematical content, in parts.  The gist is, that this subject deals with how physics content is applied in understanding and developing areas such as bio-mechanics,  thermodynamics in organisms and molecular actions such as in molecular machines.

The modules are available to read on the site or for download as Powerpoint slides.

You can find them all here:  The Biological Physics Site

Settling Down After the Exam

I experienced a post exam high, that has not yet dissipated   I have never experienced such a phenomena  after any previous exams on other courses.

Interestingly, this high is not a reflection of how I think that I have done, in the exam.  It is more a sense of accomplishment from simply being able to study all of that university level pure mathematics, and actually understand most of it.  I feel nourished from the very act of pitting my brain against M208; a course that was a cruel mistress at times, but ultimately lovable.

On reflection, the whole experiment of trying to start out with a GCSE (school) level qualification in mathematics, and move into such higher mathematical study, seemed like a tall order; a flight of fancy; a pipe dream.

Yet, here we are, two years on from starting to study maths with the Open University; and I feel strangely calm, enthused and ready to tackle more.

To that end, I have finalised my next 12 months of study, and it looks something like this:


November 2012
MST209 course material-
Second Order differential equations
Vector Algebra recap
Fourier Series
Partial differential equations
Vector Calculus


December 2012
S207 course material-
Static Fields and potentials
Dynamic fields and waves


January 2013
A Student's Guide to Maxwell Equations.    Fleisch, Daniel.
A Student's Guide to Vectors and Tensors.      Fleisch, Daniel.

I'll also dip into the Unit 0 material for the Open University third year course,  MS324 Waves Diffusion and Variational Principles


This is all self study material, that looks exciting and a real change from the very abstract world of pure maths.

This is all in preparation for my next year of study which consists of:


February 2013 - October 2013

The Quantum World - 3rd year quantum mechanics module

Electromagnetism - 3rd year applied maths / physics module


That only then leave me one more 30 point level three module to do, in order to have enough points to claim a BSc Hons Open degree, at that point.  Even so, I am actually planning on taking 60 points in October 2013, as I want to enrich my knowledge in mathematical physics, sufficiently enough to allow an easier introduction into some post-graduate work in October 2014.

Also, I am trying to make use of my transitional arrangements for the university fees, which is a system that vastly reduces the costs of any additional undergraduate modules that I can squeeze in, before 2017.

Roll on February.

I can't wait!

M208 Post-Exam Review

I am exhausted!

I took the M208 exam today and I shall quickly make a few comments about how it went.

Firstly, I feel happy, simply because I don't think that I could have revised any more than I did, and I feel like I gave each question 100% effort, during the short time that I was in that room.

So the results, will not be able to upset me, if they turn out to be poor.

The part 2 questions that I chose were from Groups A , which ended up being quite a bit of writing.  The second one I chose was the Analysis A question.

I only glanced at the other three part 2 questions, so I don't know much about them; other than, they looked very tricky.

I know I made some errors, so I have no idea what score to expect.  If all the things that could have gone wrong, went wrong; then it could be dire.  On the other hand, if I was lucky and didn't make too many accuracy errors in the questions, then no score is off the cards.

I just simply and genuinely have no idea how it has gone.  Results are out in December.

Exam time

Well, here we are at last; 24hrs before the start of my M208 exam.  I just thought I would jot down a few things.

How do I feel?  Suprisingly calm. No butterflies, no last minute panic. Revision has been steady at average of 4hrs per day for the last 3 weeks. I have done each past paper many times and I am now happy that bar any catastrophic meltdown, that I should finish the paper on time.

I have worked out, that I am much better at Group Theory A, Analysis A, Group Theory B. I can manage most part 1 type questions although I do tend to make simple arithmetic all errors, which can throw things a little.

The part that I seem to struggle with the most, is some of Analysis B, which is the integrations stuff. Yet I am happy with tackling the power series topics and the Differentiation bits as well.

I am still quite unsure about a lot of the later Linear algebra stuff, under exam conditions, but I have annotated the odd example, to help me through the process.

I intend to blog about the exam itself and then will hopefully look to finalise my next 2yrs of study. As has become a bit of a tradition for me, I like to use the lead up to Christmas to get my results, review the year and then chop or change my next modules, as best I can

I am currently booked in to study Quantum Mechanics and Electromagnetism from February.

I think that if I can achieve a grade 2 pass for M208, then I will stick to that plan.

If I bomb tomorrow's exam?

Well, I see that my local community college does woodworking classes on a Tuesday night... I'll get my chisels.

TMA07 Passed; Revision in Full Swing!

Okay, so I thought that I had bombed TMA07, simply because I had decided to spend the time messing around with revision rather than trying to get a distinction mark on this TMA.  I was amazed to see that I scrapped a distinction with 87%.  Interestingly, yet again, I rushed through a TMA to find that despite spending about 40% less time completing it, I only dropped about 6% from my average marks.

Food for thought there, when it comes to next year's study schedule.

So, onwards, and upwards.  I have taken a few days off work, and really got stuck in to some past paper revision.  I have kept it simple and tackled questions in an exam style, under the clock.  I have then marked the results and spent the second half of the revision period checking where I went wrong; then making some notes in my handbook, of important stuff to remember.

It seems to be working well so far.  I started off with about 70% correct answers and I have moved that up to 78%, this week.

Having said that, I have only really been tackling the part one questions at this time.  I plan to begin introducing some part 2 next week and I will then make some additional notes in the handbook, to help me structure my answers.

There are some big gaps in my knowledge; for example, I skimmed through Analysis B, so my Integration needs some serious extra study, to be up to speed.

My goal is simple.

All I want, is to be able to walk out of that exam room, feeling that I couldn't have performed any better.

If I then get a disappointing result?

Eh bien...c'est la vie.

Don't Panic!

I've had a month off from blogging, as I found that I needed to reduce my focus on the day to day detail of OU work, and take a more strategic view of the course, as I started to think about the exam.

Well, during that time, I have managed to score 83% on TMA06 which was the second analysis paper.  I was pleased with that mark, since I really didn't understand some of it, partly due to the fact that I simply couldn't settle quickly enough, back into the subject.

I really do hate the way that some of the most interesting material, so often feels crammed into the end of each OU course.  But such is life at this University.

So, tonight, I have rushed like crazy, to try and get TMA07, completed.  I've managed to complete approximately 83% of the paper. There were two questions that I tried to do battle with, but I was spending so much time on them with not much progress, that I realised that it was time being wasted.

I should mention, that using the course score calculator, it seems that in order to reach distinction level with my TMA work, this year, I now only need to score 30% in this last TMA.

I therefore rationalised, that if I could score about 70% , then my ego would not take too much of a bashing, and this would then leave me several more precious days, to fit in some exam revision, whilst still leaving the door open for an overall distinction, if I have a good day during the exam.

On the subject of exams, I normally like them, but I really feel that I may have met my match, this time around.

Having worked through some of the TMA07 exam style questions, I realised just how shaky some of my most basic maths foundations actually are.  Silly mistakes in TMA06 caused lost marks such as arithmetic errors and other trivia.  Also, some of the part 2 questions on the past papers, look formidable.

We shall see, in due course, how the nerves of the exam, will affect my accuracy and focus.

O.M.G, I Actually Passed TMA05!

Well, I just don't believe it.  I submitted TMA05, part completed and with no hope of gaining over 50% of marks, in what has been a dreadful few months of illness.

You can imagine my astonishment, when my script arrived this morning, for me to find that I had scored 82%, overall.

I am dumbfounded.

Why?  Well, I had completed at least three-quarters of the paper, in the space of about 3hrs, and with no reference to any of the Unit texts.  You see, I had reached a point of resigned meltdown, and I couldn't bring myself to even open the books.

I think I did this, so that it would have then felt easier to accept a dismal mark, telling myself that if I had studied harder, then I might have done well.

Perversely, I actually scored 100% on that rushed section.  Work that one out?

Anyhow, to try and finish the course, I am having to employ some serious disaster tactics.  I have opened the Battle Bridge and separated the Saucer Section; and with Analysis Part B I am going straight to the TMA, and only reading the bits from the units that I need to, in order to complete that paper.

I will, of course, visit the Units again as I prepare for the exam; but needs must, and I just need to produce another two TMA's in the next 6 weeks.  Hopefully by then, I will have sufficiently recovered (health-wise), to put in some serious hours and pass that damn exam.

By the Power of Greyskull!!!

Group Theory B and TMA05

Umm,

What can I say about that car crash of a Unit.  I am sure it is wonderfully interesting, only, I haven't been able to study it in any real depth, due to my current medical difficulties.

I have an extension on TMA05, but I will send it on Wednesday this week (5 days late), with only 80% of the questions answered and a probable score of around 50%.  If this is the case, I need to score an average of 75% on the next two TMA's to gain a TMA overall score of 85%.

Oh, I will also be attempting an old waitress's trick, by enclosing a few boiled sweets and drawing a smiley face on my script, in the hope that I can get some extra credit from my tutor.

What I have learnt from Group Theory B, can be summarised as follows:

1.    Orb = 1990's electronic trance band
2.    Fix   = what my wife keeps asking me to do with our garage door handle.
3.    Stab = what I feel like doing to self, after studying this unit.

If I have missed anything, please let me know.

KBO

I am struggling.  Struggling to concentrate.  Struggling to organize myself.  Struggling to find the time to study.  Struggling to keep my office tidy.

I don't know what is going on.  But there you are.  I am about one week behind on my reading of Group Theory B book 3, and I have asked my tutor for an extension.

The good news is, that if I have a difficult time for the next few months, then according to the Open University final mark calculation algorithm; I would achieve a distinction grade for the TMA's, if I am able to score an average across the next 3 TMA's, of 72%.

I don't want to drop marks, but it is good to know that I could survive this disaster.

As a Scottish Physicist recently told me,

KBO.

An IQ Experiment

Just a bit of fun:

I was interested in how I am being affected by the different medications that I am taking following my back surgery.  They make me feel very foggy and I have difficulty thinking, so I am keen to know how much of this 'fog' is affecting my real performance.


I have a baseline IQ test result, as I joined Mensa some years ago.  I then took another Mensa IQ test today, about 3hrs after taking my 'meds'.  Both tests were the same type, so they are directly comparable.

So, drum roll pleas:

Baseline IQ       = 155
Medicated IQ   = 96

Medication is BAD, BAD, BAD.

Now, where are my pills?

A Day in the Life of a Dyslexic

8am - A day off work, so an O.U study day, for me.

9am - Get books out.  Can't remember where I got to yesterday, a typical dyslexic problem.  I need to also organize an exam study schedule.  Can't organize my thoughts though;  having a 'bad' dyslexia day, today.

10am - I have re-read the same three unit pages in the last hour.  As I get to the end of one subsection, I can't remember what I read at the beginning.  The words move and swirl on the page as I try to make out the proof.
11am - Reading with dyslexia, is exhausting.  I put the books down.  Quick cup of Nespresso (Indrya) and I settle down in front of the computer to do some more work on TMA05.

12pm - So I can see the screen without the text swirling around, I have changed the background to Turquoise colour and the text to dark purple in font 28.  It still moves about on the page, but I can now see what symbols I am getting out of Mathtype.  I have also shut all the curtains, as the light enters my eye and causes pains in my head (like when you eat ice-cream too fast). This symptom is courtesy of Irlen Syndrome, a condition which accompanies my Dyslexia and Dyspraxia.

1pm - Dinner time.  I dare not read the newspaper whilst I am eating, as reading saps my study energy for later.

2pm - Back to the grind.  Writing out flash cards with Theorems from the handbook - the cards are small and my lack of dexterity in the hands (Dyspraxia), means that it is a slow process.  As I try and fix my glance between the flash card I am writing and Handbook, I continually loose my place as the writing swirls and vibrates on the page.

3pm - I need a break.  I have another caffeine hit and I sit down to read (Hardy's - A Mathematicians Apology), but as I read on the Iphone, it hurts my eyes.  I remember I have a 'Text to Speech' app on my Iphone, so I open it, only to discover that the essay isn't read properly by the app and it is almost unintelligible (think - Steven Hawkins computerised voice - and you are near to what it is like).

3:30pm - I give up with the app and add the essay to my growing pile of - want to read, but can't - pile.

4pm - Try and gain some inspiration from a book called 'The Dyslexic Advantage'.  I get to page two and put it down.  The text is too small and it swirls so much that I get motion sickness.  How Ironic, considering the title of the book!

5pm - Teatime - Fish and Chips.

9pm - I pick up the books again and try to make progress through the unit.  Because it is now almost dark outside, I can reduce the light in the room I am in to complete darkness and use a desk lamp and coloured overlays on the pages.  This reduces the swirl of text and lets me gain some ground.

1am - Bed - exhausted.  15 pages studied, all but forgotten, and a draft question for TMA05, pencilled out.


Most people think that dyslexia is just problems with spelling or grammar.  This couldn't be further from the truth.

Dyslexia can cause:

Visual disturbances
Memory loss
Organization difficulties
Distracting thought patterns
Overwhelm if more than one or two tasks are in hand
Spelling problems
Loss of confidence / feeling ashamed.

Dyslexia is a spectrum of symptoms and difficulties, with each dyslexic having often a unique set of difficulties.  Dyslexia is often accompanied by Dyspraxia or Irlen /  Mears-Irlen Syndrome, ADD and other specific learning difficulties.

This was a typical day, in the life of a typical Dyslexic.

Thank you.

[For more info - check out these links:  ADD/ADHD association/ Dyslexia association / Dyspraxia association / Irlen association]

Getting Bogged Down

As I am working my way through GTB, the second Group Theory offering for M208 with the Open University, I have started to formulate my revision plan, in ernest.

The plan is simple enough;

note down all of the important sections in the handbook onto flash cards and learn them backwards over the next 12 weeks;

take a selection of exercises from the end of each unit and learn the structures of the answers, of each type;

Learn, verbatim, the answers to 3 past papers, so that the structure of the answers, is engrained;

Use two past papers as unseen tests,. One of them, timing of each individual answer and then stopping to reflect, before moving on to the next. The other paper, as a mock exam, one week prior to the exam, itself.

I hope that is enough.

However, I am just struggling to move through GTB, at the moment. It is taking hours to revise GTA, before absorbing the new material. We then have Analysis part B, to contend with at the end of July.

I know what I want to achieve, but I really am struggling to fit in all of the study of new material, writing TMA's and preparing and executing my revision plan.

I have started my flash cards, with GTA all complete, LA1 and LA2 half done. But it is only when one looks back through the handbook, that one can fully appreciate the mountain that stands in front of that golden, ephemeral glimpse, of a Distinction grade.

Why do we put ourselves through it?

Groups B, TMA05. Lord, Give Me Strength!

Oh Lordy, what a nightmare this TMA is. Rotate this, congugate that, Fix this, Kernel that. Now, I class myself as a bit of a '3D specialist', being able to spin objects around in my head easier, it seems, than most. I am told, that this is often the case with people who have Dyslexia, such as myself. However, TMA05 requires 4D IMAX, surround sound With full 1080p HD and Blue Ray capability, to answer parts one and four. (Chris, you'll know what I'm talking about!) Anyway, I must get back to my calculations, as I can see that this one is going to require some midnight coffee and Orio's.

M208 TMA04 Passed!

Thank goodness! With all of the testing events of the last two months, I genuinely thought that my journey on M208, was over. I had written TMA04 under the influence of opiates, tricyclics, barbiturates and a bucket of caffeine.

After a few 'all nighters', I managed to stay on track and submitted my script, only two days over the submission date.

My score was 87% with dropped marks from a circular proof and the odd typographical mistake or omission when setting out my proofs

The knock on effects of getting this TMA submission in on time, is keeping on track with the relentless programme of TMA production and unit material study.

I think that if I had dropped even a week behind, then it might have finished me, such was the low level of belief, last month.

Well, this keeps the dream alive, and in a strange way, i suspect it has shown me what my actual level of 'ability', really is.

What I mean is, throughout my OU Maths studies, I have polished and perfected TMA's, often to the point of neurotic obsession. And, whilst this has allowed me to gain marks in the 90's, I did often feel that it was a false achievement. False, because it is probably possible for anyone to score well on a TMA, given enough time.

So, by having my time squeezed and my senses dulled by medication, I believe that this has allowed my 'raw' TMA scores, to reveal themselves. I suspect these scores are my 'true' level of mathematics ability.

Is this level of ability enough to achieve a PhD and beyond in mathematical physics?

Well, I have heard two views on this.

Firstly, last year, I was told by a Learning Advisor at the OU, that I had no business thinking about postgraduate maths work, unless I was scoring an average of 93%+ on my TMA's.

Another view from Prof. De Garis, is that one needs to have an intelligence level within the top 1% of the population, to cope with PhD level mathematical physics.

Well, with a raw TMA score, it seems that my ability is probably around the 86% mark. With polish, it is nearer 95%.

I believe that beyond intelligence, there is one factor that is the most important in deciding as to whether success is part of your life. And that is: good old fashioned elbow grease.

The Midnight oil has never been such a valuable resource!

Group Theory,You Tube and Prof. de Garis

This week, I have been ploughing through some seriously deep and lengthy revision of Group Theory, including Symmetries, Conjugacy, Cosets, Normal and Quotient Subgroups etc....

Now, I have struggled to warm to Group Theory, as it is abstract, to say the least, and there is a lot of technical jargon to learn.  However, I often find that to learn a subject that is rich in 'bits' of information, as well as concepts; I often learn best from repeatedly (Old School), revising the definitions and doing exercises.

To do this, I have made circa 200 flash cards, with all the definitions etc, on them.  On one side is a question, and on the other is the solution or theorem that is being tested.  It's boring, but it works.  What more can I say?  I now know more Group Theory 'off-the-cuff', than I did a week ago.

Even so, that type of revision can become a little tedious.  So this week, I started surfing the Web, looking for any video lectures, that may assist in making my understanding of Groups a little deeper.

And, I came across a rather interesting if not, unconventional, Professor, whom I have been in correspondence with via email, this week.

He is Professor Hugo de Garis, currently based in China, and his newest online project, is a compendium of  You Tube based video lectures for Pure Mathematics, Mathematical Physics and some Advanced Computer Science.

Now, my own project is to move me from just a GCSE in Maths to a PhD in Mathematical Physics, using a lot of self- learning and also some courses from institutions such as The Open University.  Hence, why this blog has been created.

Having studied towards this goal for two+ years, I have realised that there is a severe lack of available part-time or distance learning courses in Mathematical Physics, beyond the odd module offered by U.K Universities, at first, second or third year Undergraduate level.

This means that a lot of my study needs to be 'self taught'.  The only problem with this style of learning, is that it is difficult to know which subjects to learn, without getting bogged down in interesting but irrelevant 'forks in the road'.  Also, some of the subjects at masters / PhD level, are difficult to follow for a lonely distance learner, with no real support from a supervisor.

A big problem!  And one, I suspect, that would put off all but the most tenacious and bloody minded of individuals, hoping to educate themselves among the boundaries of current physics and mathematical knowledge.

Enter - Professor de Garis.  The reasons I mention, are exactly why the Professor's video lectures caught my eye.

His plan, is to record 600 video lectures that are progressive, starting at 3rd year undergraduate level, taking a progressive path through the mathematical background needed to be able to tackle beyond PhD level physics.

His aim is to cover each and every level / area of knowledge that is needed, in 3rd year Undergraduate, 1st, 2nd and 3rd year masters study and then, as he describes it, Phd level 1 (what you would learn during a PhD) and also PhD level 2 (well beyond post doctoral studies).

There is an introductory page / pdf available that explains his project, which can be found HERE.

What is different about these lectures, is that they are no frills, recorded in HD in a drawing room with a white board.  They are of a conversational style and are not like the fast moving and difficult to follow lectures that one often finds with some of the MIT lectures etc, that are available on line.

The introduction lecture does stray from maths and physics in the later third, but only to give context as to why this project is being conducted.  It also goes some way to explaining why Prof. de Garis has decided to dedicate such a large amount of time towards this endeavour.

He does have some very unconventional views about a lot of things.  He is also rather brave, describing the Chinese government in his intro lecture as, 'a brutal dictatorship'; although hedoes assure the viewer that they would only be interested in his views, if he was broadcasting them in the Chinese language.  Still, I'm not sure I would take the chance!

However, I believe that to understand his politics and ethics through examining his interests; mathematical, philosophical and geopolitical; does allow one to understand why he is embarking on this project; and also, why watching its progress will be all the more compelling.

He plans to have completed all of the core videos within a few years and then plans to spend another 10-20yrs, providing further enrichment material on video, to supplement the core of the study programme.

It's all free, and he even provides details of where a student can obtain all of the books needed for free, on the internet, if required.  This opens the door to those in the world who are living below the poverty line, which I like the thought of.

The videos can be found at this Link - Professor Hugo de Garis.

Anyway, I'm now off to play with my new iPad that arrived this morning, which should make watching online study material, that much easier.  I hope that my new purchase will take my study practices to a whole new level.  We shall see!

An Efficient Study Schedule

I reckon, that I have been studying in a rather inefficient way over the last few months, despite having the best intentions to be as near to 100% efficient, as possible.

What do I mean exactly?  Well, a typical study week, currently consists of me reading the Unit for that week, do a few exercises and write a rough draft for the TMA questions, that the Unit covers.  What I haven't been doing, is any real revision of previous units or exercises.  I have done a few, but they have been very much a token effort.

So, I have decided to be a little more rigid with my allocated study time, from now on, until the exam in October.  I also tend to find some activities much more mentally taxing than others, and I tend to find myself less able to cope with the more difficult material, at night.  I have penned a list below, of what I personally  find the most mentally taxing activities (most difficult at the top):

1.    Read New Unit Material
2.    Formulating answers to TMA questions
3.    Tackling Unit Exercises for the first time
4.    Re-reading previously learnt Unit material
5.    Revision exercises from previous Units.

I don't know how others find these activities?  I may be a little unusual, since because of my Dyslexia and Irlen Syndrome, I find the act of reading to be a more time consuming activity, than most people probably would.


With this in mind,  I plan to split my studying as follows:

Read New Unit Material -  3/4hr per day
Formulating answers to TMA questions  - 1/2hr per day
Tackling Unit Exercises for the first time - 1/2hr per day
Re-reading previously learnt Unit material - 1/2hr per day
Revision exercises from previous Units. - 1/2hr per day

Total 19-20hrs per week.

So far, I have been spending this amount of time on just points 1,2 and 3, above.

Anyway, lets just see how it goes.  As John Steinbeck once said, '...of mice and men... '!

Where Are We Now?

Okay, I haven't been able to blog recently.

In fact, I haven't been able to do much, other than lay on my back following spinal surgery at the end of May.  One blood clot later, I am morphine soaked, immobile and miserable.  Walking with a crutch is not much fun.

As far as M208 is concerned; for the first two weeks of June, I was unable to do anything, as the medication prevented me from even being able to read a newspaper.  However, nil desperandum.  I did have, what turned out to be a very good exercise in disaster management.  Following difficulties in the prior eight weeks with a bereavement, I was on the back foot but had managed to keep up with studying and my TMA's.

I forgot to mention, that I scored 85% for TMA03, last month; a distinction grade, but well away from what I had scored in the previous two, TMA's.  The marks were dropped because, due to time constraints, I literally had to use my draft paper, as my actual final submission; so I did not have the chance to review my work, which is what I usually like to do.

So, fast-forward to early June, I put a call through to my tutor, who was very helpful on this matter.  He spent twenty minutes, discussing some mathematical points of order, and then he allowed me to have a two week extension on the submission date for TMA04, should it be needed.

Well, I have managed to reduce my medication sufficiently, to allow me to do some studying in the last ten days.  I have read the first three analysis units and completed three quarters of TMA04.  As it stands, today, I am one third of the way through the fourth unit book of analysis and due to start the TMA questions for this unit, on Friday.

All told, I think I should be able to submit my TMA, only 3 days over the published submission date, in time for starting the Group Theory B, sections.

I am becoming a little anxious about the exam, already.  It is due in the second week of October, and I had planned to do some revision on Linear Algebra and Group Theory over the last eight weeks, but it just didn't happen.

But, If I can come out of this last three months with a Grade Two pass for the course, then I will be happy, such has been the 'disaster' of ill health and outside influences.

It is truly turning out to be my annus horribilis.

A Quick Binomial Interlude

I just thought I would quickly share with you, what I consider to be a lovely way to demonstrate what polynomials actually represent, geometrically.

For some reason, until I saw this image, I never really fully understood how it all fits together, as you approach higher powers.  I have lifted this image from Wikipedia, which you can find here.



I think it's wonderful.

David Brannan Versus M208

I have now ploughed through the first two units of Analysis A; which is part of M208 Pure Mathematics, with the Open University.  Now that I am off work sick, awaiting back surgery, I have managed to consume an entire Unit in two days (should take about 16hrs per unit); so things are going okay at the moment.

As I was studying, I picked up my wonderful copy of David Brannan's 'A First Course in Mathematical Analysis'.  Now, the uninitiated may not actually know, but approximately 95% of the Analysis section of M208, is a direct lift from the pages of Brannan.  Shock, horror, you say!  I think that they have just left it mainly unaltered, because of the simple, sequential way that he expands on series and continuity, before launching into differentiation and integration, making the subject easier to follow.

This is not dissimilar to the way that Spivak, approaches the subject in his book, 'Calculus', the title of which may throw one a little, as the book actually covers much more than the simple mechanical aspects of calculus; as it weaves through series, limits, vectors, conics, planetary motion and plenty of rigour to whet the appetite of any purist.  I have the third edition, and I thoroughly recommend owning it, even if it's for nothing else other than the beautiful way he explains the basic theories of numbers in chapter one; or the way he makes one chuckle, by entitling the seventh chapter 'Three Hard Theorems'.  You certainly know what to expect from that chapter!

Now, one thing that struck me, about the M208 Units, whilst I was leafing through Brannan, is that each M208 unit is an A4 size booklet, of, say 40-60 pages of text.  Each one, sometimes, feels, like a 'pamphlet', an easy read option, almost like lecture notes, purposely written to give a student an easy life.  Yet, they are actually very deceiving!

It only took a few moments to realise, that just 8 of these 'pamphlets' actually cover the entire Brannan Analysis Textbook.  I found this surprising, as when you look at Brannan, it looks pretty scary in size.  So, maybe M208 isn't all that light on reading, after all.  The only problem with that assertion, is that one of the tutors at day school (an insanely brilliant mathematician), recently described M208, as Pure Maths 'lite'.  Well, it feels pretty 'full-fat' to me.  Time will tell, as to whether it will provide enough background to cope with any future studies.

An Errata?

I, like some of my esteemed peers and colleagues in the Mathematics world, have a penchant for pedantry (never thought i'd ever use those two words in the same sentence).

I don't do it for the sake of just 'doing it' (if so, is it still pedantry?); rather, I find that sometimes a little error, can actually throw you off and prevent some of the more subtle understanding that is needed in mathematics; especially in pure mathematics.

I was reading Unit AA1 of M208, Pure Mathematics, and spotted what I believe might be an error; but I am second guessing myself, as to whether it is just my limited understanding of the subject.

The possible errata I refer to, is on page 28, Example 4.3.  In the solution it describes the inequality \[1 - {\textstyle{1 \over {{n^2}}}} \le 1\] for n = 1,2,....

However, I would have thought that as n tends to infinity, that \[1 - {\textstyle{1 \over {{n^2}}}}\]  would approach 1 but never actually reach it.  So, therefore, that inequality should be just \[1 - {\textstyle{1 \over {{n^2}}}} < 1\]

Do I have that right?  I know it is a small thing, but I really must make sure, that my understanding is solid.

ps: if the latex above is not displaying, do let me know.  I am testing out Mathtype 6.7.

Blind-sided by LA5, Pure Mathematics.

I thought I would just quickly comment on the difficulty of the later units of the M208 section on Linear Algebra.  It was a real shock, how quickly it all became so abstract and a little bit counter intuitive in some parts (matrix arithmetic when diagonalising).

The whole Linear Algebra offering, was a really good example of a time where you, absolutely, must master the first 3/4 of the material, before even hoping to understand the last 1/4.

I did enjoy it, but I think it may take me the next year or so, to re-read, think about, and then finally absorb some of the finer subtleties of this subject.

I hope it doesn't take too long though; as I will probably need to apply it all, next year, if I finally register for Quantum Mechanics (The Quantum World) with the O.U in October 2013.

I am already on the look out for any interesting / classic Linear Algebra reference texts, to add to my creaking bookshelves.  I think, as with most of these subjects; that enrichment by reading widely, without necessarily increasing the difficulty of the material, is the key to understanding.

TMA03, Away...

Finally, after an extremely difficult week, I have managed to get TMA03 finished and in the post.  It was a little late, with a 3 day extension, but I am glad to say that I was able to finish late on Friday, post it Monday morning and make headway with the new shining, wonderful, solid and oh so delicious, Analysis Units for M208.

I don't know why, but I love Analysis.  Having said that, I have already pre-studied Brannan's, 'A First Course In Analysis', which the O.U Analysis Units, are broadly based on.  I found it exciting and elegant.  Much better than Group Theory at the beginning of the year (I still have nightmares).

I have also taken some good advice from my friend Chris, who suggested that I print off the audio transcripts for the course, rather than go through the pain of listening to some stranger, attempting to lead me through the material.  It's working well, so far, as I have nearly finished Unit AA1 and will start AA2 on Thursday.

Anyway, I sort of have some bad news that could also be slightly fortunate, in a strange way.  I am just about to go under the knife, for a herniated spinal disc.  Bottom line?  I will be off work for at least 2 months.  What's good about that?  I'll have about 12hrs a day to read mathematics, finish off Tolstoy's War and Peace, get my Rubik cube times down; and last but not least, catch up on some exciting enrichment material in Calculus (Spivak).

Summer, here we come!

Normal Service to Resume Shortly

Just a quick post.  I am working hard towards completing TM03 of M208, and now just have the last question to answer, which is all about working out standard form quadrics.  I am a bit behind on my reading (still half of Unit LA5 to read; as, due to a family bereavement, I have been quite distracted this week.

Anyway, I will complete TMA03 and start the Analysis section next week, on time; after a short period of solitary reflection.

Audio Sections; Contributing to Confusion.

I am 3/4 of the way through writing TMA03, using Mathtype for word.  I have to say, that having spent approximately 20hrs using Mathtype, now;  it is becoming very much a breeze, to use.  The results of using it are nicely typed, automatically well formatted maths equations.

With regards to the content of TMA03, I did find it a real mixed bag of difficulty.  I found most of it relatively straight forward, except for the question on orthogonality.  I found myself in a real twist for about 6hrs, before working out what I needed to do, in order to find an orthogonal basis for a subset, that they had given.

I think what really threw me, was the increasingly annoying way that the O.U secrete an 'audio' section into the units, with cryptic accompanying notes, to guide your path.   I am not a purist, by any means.  I do enjoy occasionally learning in ways that are not connected with reading dusty old text books; but these audio sections are driving me insane.

I could understand the use of them, if they were needed to describe intricately subtle ideas, that wouldn't be apparent from just reading a text book; but my experience of the O.U's treatment of this format, leads me to the conclusion that they are just used to read out what is already written on the page of notes.  Hardly helpful!

They are an unnecessary distraction, in my view.  I believe that the use of an audio section in the 'Orthogonality of subspaces' section, has contributed to my confusion on TMA03; and I fear that there are more audio sections, to come.

Linear Algebra: Hard, But Great Fun

Well, I am now more than half way through the linear algebra offering from M208, The Open University's general pure mathematics course.  I am about 20 pages into book 4 of 5, and I am starting to now understand how it all fits together, very nicely.

I have always enjoyed matrices and simultaneous equations; but until I studied M208, I never understood that these areas of mathematics were just the tools that are required to study Linear Algebra, which I now regard as the 'science' of manipulating finite subspaces in n-dimensional vector spaces and also mapping transformations between them.  Not forgetting that what we actually seem to be doing (I think), is finding isomorphisms, between subspaces and also between vector spaces.

If you want a very good preci of what Linear Algebra actually is, in about a side of A4; just look on Wikipedia under Linear Algebra.  I particularly like the graphic at the right hand, top of the page.

Anyway, Linear Algebra: good.

Also, I am now just over 50% of the way through TMA03, for M208, which is all being completed on Mathtype and Word 2010.  So, onwards, and upwards.  I am planning to get all of Linear Algebra studying and TMA03, completed before the 7th of May, when I am hoping to take a few days off with the family.

Looking back over the last few years, it seems incredible that I started all of this off with just a GCSE in mathematics, as my highest level of maths study.  As an exercise in morale boosting last week, I glanced back over my unit books from MST121 last year.  I was really surprised to find, that the units appeared relatively simple and very light in content, compared to how I remember them.

I was particularly intrigued by the fact that there was one particular calculus exercise that I didn't understand last year during my study of MST121; but when I looked back at that particular problem last week, I completed it in about 30 seconds, without any need to review the subject matter.  Boy, how things have come on in just one year. Who knows what 2013 will hold?

Using Mathtype for TMA's

Today, I have had my first proper go at using the mathematics equation software, Mathtype, in producing a TMA.  I am using it to produce TMA03, and I have, so far, completed question 1, worth 10 marks on the subject of Linear Algebra.

I have spent most of the day fiddling around with hot-keys, short-cuts and watching You Tube videos, trying to pick up hints and tips on its use.  Although it has taken most of the day to produce such a small amount of work, I am already 300% faster in using Mathtype now, than I was just 12hrs ago.

I have decided to put myself through the pain of learning a new piece of software, mid-course, for several reasons.

Firstly, the amount and level of study that I am doing over the next 4 months, is relatively low, compared to what is on the horizon.   This is because,  from September and beyond,  I ramp up my self-study in physics and maths, and also my official O.U study, to what will amount to the equivalent of 180 points of level 2 and 3 study, within 18 months.

Also, I want to be up, running and using Mathtype (which is fully integrated with my Microsoft Word 2010), well before I need to produce typed coursework for the first time (October 2014, if I take M820 Calculus of Variations).

You see, all MSc TMA's need to be submitted electronically, and Mathtype is a good piece of software, to get me doing this, well before I need to.

Another reason for wanting to practice typing maths, is that I am finding it very tedious handwriting so called 'final' drafts, which I often repeatedly re-write, costing me hours each month.

Also, my current tutor gives a lot of very valuable feedback on each TMA, regarding formatting, content, presentation and conciseness.  I therefore want to hone my Mathtype use, whilst I still have access to this tutor.  In my 8yrs experience with the O.U, tutors who give excellent feedback, are a rare breed.

And finally, there is another more basic reason for wanting to type my mathematics:

It looks great and feels professional.

M208, TMA02, Passed!

I received my results back today, for TMA02 of the Open University course M208, Pure Mathematics.  I received the results via text, from my wife, who kindly opened the envelope for me, whilst I was Aston University for the O.U day school.

Well, the score was 99%, which I am deeply thrilled about, especially as I really did not fall in love with Group Theory, and it was a real test of my 'metal', in completing the TMA.

The mark that I dropped was for forgetting to mention that a group operation  x o y = e  was also true for
y o x = e.  Silly mistake, but an important lesson learned; so no hard feelings.

So far, so good.  I now have a 100% and a 99% from the first two TMA's, which should buffer me against any difficulties that are likely to occur in Analysis B or Group Theory B, which are looming large.

So now, as appears to be turning into a bit of a tradition, I am off to partake in a bottle of Bishops Finger or two; before carrying on with Vector Spaces, tomorrow.

Linear Algebra and Some Musings on Distance Learning

I am finding the Linear Algebra units for M208, an absolute dream to work through!

They started by treading some old familiar ground with vectors and matrices; before proving a few bits and pieces from those two areas; followed by some work on vector spaces, n-dimensional space and some yummy vector combinations.

I am now 1/3 of the way through, Unit 3 of 5, and it is proving to be the most enjoyable part of M208, so far.

After having a boost of confidence (falsely?), by scoring 100% on TMA01, I have found my work rate has really started to pick up, without much evidence of added fatigue, from day-to-day.

The upshot of this boost, is that I steamed through TMA02 in plenty of time (I await the score, any-day now); and I have also started, in earnest, studying some material from MST209 and also S207.  This has included running through Unit 1 of MST209 (which was surprisingly dull:  O.U, why have you tried to make such interesting topics, such as Calculus, so tedious?); and also I started to read the S207 Unit, Dynamic Fields and Waves, before realising, that I may need to read Static fields and potentials, first.  So, I have been clicking on Amazon at the weekend, and that pre-requisite unit, should arrive tomorrow.

This week has also marked the start of me doing some serious internet and phone research, into the scope of  maths and physics related postgraduate options, that are currently available, or due to be available soon.  I have noticed a theme developing, in that many Universities, including U.C.L, Liverpool and other fine institutions, are now starting to plan or offer taught masters in science or mathematics, via distance learning; or, at the very least, part-time.

It is a sign of the times, I guess, that Universities are finally starting to catch on to the fact, that distance learning provides them with another excellent stream of revenue as mature students are such an untapped group, who are generally able to pay their own fees and who require lower University overheads, to teach.

But the big difference is, that the internet is just so accessible now, compared to even just 5yrs ago; that experiments, tutorials and team collaboration work, can easily be completed on line, (just look at this excellent course offered by the OU:  SXP288 ).

Also, I think the O.U's current strategy is possibly causing their market position to weaken, allowing other Universities to fill the void, by providing affordable, high quality distance learning courses.  When I say their current strategy, I refer to the almost unbelievable decision to increase their fees to ostensibly unaffordable levels.  This has probably ended the vast swathes of learners who have studied with the O.U, for pleasure, over the years.  Will the O.U survive, without these students?  I know myself, that I would probably have never started studying with the O.U, had the fees been set to the new, proposed levels.  It is such a shame.

On a completely different topic; I very much appreciate all of the comments that have been left on my blog, since it began.  They are all read and thought about, very carefully; and I have gained some real help and guidance, as a direct result of them.  So thank you, to those kind soles, who have taken the time to write.

Study Timetable Dilemma

I am currently pondering the possibility of shortening my O.U undergraduate studies, by doubling up on modules in February 2013.

I am currently planning on taking M337 Complex analysis in October 2012, followed by SM359 Electromagnetism in February 2013.  This would give an overlap maximum of 60 points between February and June 2013.  This would then be followed by one or two, Level 3 maths / physics courses, in October 2013.

I would then finish all undergraduate studies and then be due to start MSc studies in Autumn 2014.

That is the conservative plan.

The 'mile-a-minute' slightly nutty plan, would be to start Complex Analysis in October 2012 and then in February 2013 taking both SMT359 Electromagnetism and also SM358 The Quantum World, with all three courses running alongside each other.  I would then have enough points by October 2013, to claim the BSc Hons Open degree with the OU.

This would then allow me to start some Postgraduate studies in October 2013, (or Jan 2014, if taking the O.U MSc Maths), a year ahead of what I had already planned.

The upsides?  Truncation of the study plan, and quicker entry onto Postgraduate studies (none of us are getting any younger!)

The downsides?  I will only then be taking three level 3 maths / physics courses, instead of four; and the monster workload of  90, level 3 points, between February 2013 and June 2013, is a lot.  Not to mention an equivalent level of 90 points of self study and prep work for Electromagnetism and Quantum Mechanics, alongside Complex Analysis, between Oct 2012 and Jan 2013.

I am not sure what to do.  I do worry that studying 90 at the same time, will mean me having no chance of ever gaining a 1st class degree.  It might just be too much work to gain 85% on each level 3 module.

I will ponder this over the summer.

M208, TMA02, away...

Well, I managed to complete TMA02, about 3 days ago; and on the whole, I am fairly happy with it. However, I did feel the need, to complete a rather intensive and mature assessment of the Group Theory units, after the TMA.  This was because I just didn't feel that I understood the theories in sufficient detail, to be able to extrapolate the key themes, into unseen exam questions.

I have therefore spent my 'spare' minutes of each day, this week, copying the Group Theory A content from the handbook, into my 'Moleskine Journal'.  I have then carried this about with me and revised the key elements, at random points in the day.

It is a bit of an old fashioned way of learning (copying verbatim and then just reading repeatedly), but it can be a solid technique, for times when the content just won't stay in your head.  For me, studying Group Theory, is just one of those occasions.

Anyway, what a breath of fresh air, the Linear Algebra units have been.  I have launched into studying this rather satisfying topic, and completed the first unit, Vectors and Conics.  I am now also half-way through the second unit, Linear Equations and Matrices.

I do find Linear Algebra, to be a deeply interesting topic, which requires a certain amount of accuracy and attention to detail.  When I first studied this topic, I didn't really enjoy it.  Looking back, I now think that it was because my introduction consisted of just being shown a few 'processes', to crunch numbers with and obtain the solutions to some linear equations.

This type of approach, would probably be called 'hand-waving', by my current M208 tutor, Mr Jina; and I would probably agree with him.  You see, before M208, I had never explored Linear Algebra from first principles.  As such, I never really understood it, and so in order to learn it, I had to 'rote' learn the techniques.  Something which can be very difficult, for a dyslexic learner to do.

But now, M208 has introduced the techniques in a clear and concise way, allowing me to have complete understanding, with little in the way of hand-waving, going on!

I did initially have one gripe, which was this seemingly nutty way of solving simultaneous equations using row-reduction,  Gaussian techniques, or whatever they call them?  I couldn't believe how over complicated, it seemed to make the whole thing.  'How dare they', I said; 'what are they thinking?', I bleated.

That was, until I turned the pages, and realised that it is actually a rather clever way of sorting out big matrices, with lots of unknowns.  So, I take back the swearing that I uttered, whilst studying the first unit of LA2.  All is now forgiven.

So, I now await the result of TMA02 and I am already starting to look at TMA03, the first part of which, I may start to sketch out, on Monday morning.

Physics prep-material obtained: MST209 and S207

Okay, quick post.

I have now obtained hard-copies of several units from the Open University courses MST209 Mathematical Methods and Modelling, and S207 The Physical World; which I believe will top up my M208 Pure Mathematics, MST121 Using Mathematics and M337 Complex Analysis studies; to allow me to launch into SMT359 Electromagnetism, and other applied mathematical physics courses, as the next 2 years unfold.

The units that I will be studying between October 2012 and Feb 2012, are:

First-Order Differential Equations (MST209)

Second-Order Differential Equations (MST209)

Partial Differential Equations (MST209)

Fourier Series (MST209)

Scalar and Vector Fields (MST209)

Vector Calculus (MST209)

Fields that Vary with Time (S207)

Waves and Electromagnetic Radiation (S207)

Static Fields and Potentials (S207)



I am struggling to get hold of MST209 Unit 25, Multiple Integrals; so if anyone knows where I can find a hard-copy or PDF, then please let me know.  Likewise, if anyone thinks I am missing any important content out, then please let me know, so I can add it to my list of self-study items.

This studying should all fit in nicely between M337 and SMT359, as long as Christmas doesn't interfere!

M337 Complex Analysis and SMT359 Electromagnetism

I had pre-registered with the OU on two courses that are due to start in October 2012, which are Complex analysis and Number theory.  However, I received an email from the O.U stating that because of transitional arrangements with fees; that my registrations had been cancelled and that I needed to re-register this week.

It isn't too much of a drama, as I always pre-register on the course I think i will probably do, and then I do a final check, before committing to them.  This approach has worked well in the past, as I often hone my path, depending on my experiences of that year's study.

So far, I have enjoyed M208, even if Group Theory was a bit dull.  I have started the Linear algebra units and they are much more satisfying and easier to conceptualise.

So, today, I have done my final checks, before registering on my next two courses that follow M208, which is due to finish in October 2012.

I have chosen:

M337 Compex analysis starting Oct 2012

SMT359 Electromagnetism starting Feb 2013

This staggered presentation actually works very well for me.  It allows me to get a real head start in cracking complex analysis, and aim for that level 1 pass, before applying some of its content, in the course that starts in February.

This means that the exams will be staggered as well, and that I will then be able to study for the electromagnetism exam, without distraction.

Why am I dropping number theory this year?  Well, there are several very solid reasons.  But primarily, because of the transitional fee arrangements, all O.U students are now restricted in picking and choosing modules.  For me, this means that my plan to complete some pure maths at level 3, before going on to do applied maths; would have taken me over my allowed 360 points, that I can claim reduced fees.

Bottom line?  I can't afford the luxury of meandering my way through the whole maths syllabus, offered by the O.U at undergraduate level.

So now, it has forced me to be much more focussed.  So, in line with my plans of reaching the dizzying heights of mathematical physics; I will take the complex analysis course (essential in my opinion) and start my first mathematical physics course, with the O.U, earlier than I had planned to.

In a way, it probably makes much more sense, and may even force me to move through my studies, a lot quicker than I had planned.

I am missing some applied maths at level 2, by not taking MST209, but I plan to remedy this, by trying to get hold of the PDF's for MST209, that specifically cover any content required for SMT359.

What are my preliminary plans for Oct 2013?  Well, hot favourite at the moment, is The Quantum World and another level 3 maths / physics course.  I do have to be careful though, to ensure that I can still claim transitional fees, for the courses I choose, so watch this space.

Groups and Geometry M336

After careful consideration, I won't ever be taking this course...

That is all.

Grrrrrroups

I seem to be having great difficulty in recalling any of the Group Theory that  I have learnt over the last 4 weeks. It has been particularly difficult to decipher some of the questions and what they are asking for, as the use of special meanings for everyday words, is just piling up.  Symmetry, means something different if it is a symmetric group; order, isn't what you do at a restaurant and index is not a catalogue shop. Hmmm!

So I have had the strange experience of learning a unit and then have got to the examples at the end, only to find that it doesn't bear any resemblance to what I have just read.  So I have started going through all the exam questions from 2008 onwards, to get a flavour for what I absolutely have to know, to pass the Groups bit of the paper.

I shall learn the question structures and hopefully it will start to make sense.

Goodness knows what Group Theory B has in store for me.

Progress so far...

I am sorry, but I think Group Theory is dull.  Dull as ditch water, in fact.  I thought I might like it, on account of me being horribly dyslexic and having a knack for visualising 3d shapes and their permutations.  But, Group Theory has been made sufficiently boring by the O.U, that any fun, for me, left the building about three weeks ago.

So, I am finding that I am having to drag myself through the Groups material, which means that I haven't studied it in as much depth, as the intro materials.  I understand, from the day school discussions, that the O.U's method of presenting Group Theory, is just one of many ways of presentation and approach.  Another, method being; the understanding that Groups have to be constructed exactly how they are, otherwise without them, we couldn't make algebra work, for example.

To explore that aspect of Groups, would have been interesting and the tutor made a good attempt to do so, last month at the day school.  But, the O.U's general treatment of this subject is still B.O.R.I.N.G.

Even so, my enthusiasm for discovering more about Groups, has not been diminished; as I own a book called Adventures In Group Theory, which is all about the applications of theory, to solving the Rubik Cube.  Much more satisfying!  Check the above link for a freely available PDF of this book, courtesy of Durham University.

My one concern, is that I am planning to study Groups and Geometry, at level 3.  I am not sure I could sustain yawning that much, for a whole nine months; so I will keep that decision under review.

Study Methods, M208

I tend to find that my study methods evolve over a module's lifetime, and even from week to week.  When I first took on M208, I began by doing a pre-read of each unit book omitting the exercises, before returning to complete the exercises, selecting a handful from each sub-section, at the end of the week.

The problem with such an approach, is that when the subject gets very abstract, such as when you start to examine conjugacy's of this, and permutations of that; you often find that you lose the thread of what is going on, halfway through a sub-section.  The issue with doing so, of course, is that much of the OU's style, is to build on earlier concepts, with increasing complexity.

So, you can find yourself struggling to understand relatively straight forward concepts at the back of the book, just because you haven't fully grasped an earlier concept.

So,  when tackling the Group Theory units this month, I have adopted an adjusted method, which consists of reading a unit through without doing any exercises, at first; but then, at the point of loosing track of what is going on or getting confused, I put a mark in the margin, and quickly return to the beginning of that sub-unit when I then tackle one or two exercises, in that sub-unit.

I can then quickly move on without too much disruption and with full understanding.

It's a little like the Feynman Method, which I have discussed in a previous post (can't remember which one), and it works very well.  It is a good method to use, if you are short of time, as I have found that I can blast through a first unit's reading, within two study sessions, leaving the exercises for revision at the end of each week.

The key is to just do enough exercises to ensure understanding, on the first pass of the material.

M208 TMA01, Parts I and II Passed!

I am thrilled to be able to say, that I have passed my first TMA of the Open University Course M208.  I scored 100% for the whole paper.  Even so,  I was very pleased to see that my tutor still had plenty of very useful comments to make, on all aspects of the piece.

The main highlighted theme of learning seemed to be, brevity.  There were one or two answers where I had used about a page to provide the explanation; but my tutor gave an alternative answer, which took up two lines.  I have to admit, I was being so careful to include all of the detail, that I have clearly started to add too much superfluous information, in the process.

So, I move forward with a smile and a fair idea of where I need to be, in the coming months.

Now, I'm going for a drink!

M208 TMA02, Q1 - 3 complete.

Fifty five out of one hundred marks, completed, and it is feeling deceptively straight forward.  I just don't  understand why this is so.  The intro units were taxing, to the point where I actually woke up at 2am, one cold winter's night, convinced that my journey was over; when I couldn't even work out, what the equivalence question 7a) in TMA01,  was asking me to do.

Fast-forward one month.  I have just completed half of the Group Theory paper, and it felt like treading an old path.  The symbols were familiar.  The method of laying out an answer, straight forward.  The completion, pure joy.

What exactly, is going on?

I haven't a clue.  Any thoughts are gladly welcome...

Group Theory versus Analysis

I don't know about anyone else, on the O.U course M208; but I am finding the topics of Group Theory and Analysis, so far apart from each other, in terms of mathematical flavours; that I am beginning to feel like Analysis is not dissimilar to a wonderfully stodgy, bread and butter pudding (quintessential, robust and ever so yummy); whilst Group Theory feels like more of a Monday lunchtime, fish-paste sandwich.

They are just so different; that I find myself wondering how it can be possible to love both areas of mathematics. I mean, Group Theory kind of feels a little bit like messing around with puzzles in the back of the Sunday newspapers.  Don't misunderstand me here; I don't mean that Group Theory is easy, by any stretch.  Rather, it just feels like messing around with stuff, for its own sake.  This approach is supported by my day school tutor, who said this weekend, "don't ask why Group Theory is that way; just have fun with it, and enjoy it for its own sake".

Analysis, on the other hand,  is just breathtakingly beautiful. You only have to thumb through the unit books of AA1 and beyond, to see that Analysis can be studied both for the pleasure of enjoying the pure aspect of its construction - and also for practical applications, that can present themselves at the end of the subject.

So far, I'm with Analysis, all the way; although I am yet to properly taste Linear Algebra.  So, who knows?  I might have time to clean my palette, before opening a new bottle of dessert wine, to wash down that second bowl of pudding.

M208 TMA02

I have started on question 1 of this TMA, which covers group theory from the units GTA, M208.  One thing I have noticed about the start of this TMA, is that it feels a lot easier than the second part of TMA01, which covered a lot of introductory concepts and areas, in preparation for the rest of the course.

In analysing it, I don't think that it is any easier; I just think that my brain has adapted to the types of information and rigour that is needed, to answer the questions well.

When I was completing TMA01, I just couldn't remember how to include all of the information needed, to answer the question and pick up the marks.  I think this has been commented on in many places recently, and it is because the rigour that is needed, can turn the most simple of answers, into three pages of waffle, where you feel as if you are repeating yourself.

It reminds me of when I began my O.U journey, studying art history and the humanities.  My, then tutor, told me that in order to do well in an essay question; you needed to state your answer in the introduction, restate it with explanation and evidence in the main body of the question and then finally to restate it again, in the summary and conclusion section.

This wash, rinse and repeat method, certainly looks like the method that is needed to answer a rigorous pure mathematics question.

First Real Dip in Performance

For the last two weeks, I have been experiencing what all distance, adult learners dread and fear.  It is the overtaking of life events, family, work and business, that all add untold pressure to the long-time adult learner.

I normally get at least one or two periods in each year, when I experience a nasty combination of events, that cause a drop in study motivation or performance.  And for me, my first of this year, has just occurred.

Thankfully, I have managed to pull through the back end of it and plan to get well back on track with my study hours.  The effects have been minimal, in that, when I kick started the Groups units, I was four weeks ahead of the course's suggested study timetable.  I am now nearer only two - three weeks ahead, as due to some horrible work problems along with dreadful sciatica causing me to take brain-melting painkillers, I have only managed 6hrs of study per week, for the last two weeks.

But, it is only temporary, as I am now used to the medication and the work issues have subsided.

The good news is that I have finished TMA01; I am finding the Groups units relatively straight forward; and I am able to attend the next three day schools.  So, barring any other disasters, I should get back on track and I look forward to leaving Groups temporarily at the end of March and moving onto Linear Algebra, which looks exciting.

How important it has proved, to be ahead of the curve, when studying independently.

The Joys of Group ...Theory!

So far, I am about half way through the M208 Unit GTA2, having completed unit 1, in the last 9 days.  And it's so far, so good.  I have found that Group Theory has actually felt more straight-forward, than some of the Introduction units that launched M208.  However, having read another blog, http://matrices-reloaded.blogspot.com/, I fear that Group Theory may take a turn for the complicated, later this year.

But this is just an introduction to Group Theory, rather than some heavy tomb covering the finer aspects of this vast subject, so I am hoping that it is not too problematic.

I am also possibly planning to study the level 3 course Groups and Geometry M336 in 2014, alongside an MSc mathematics module, so a thorough understanding of M208, is essential.

It is a shame, that apart from M208, it appears that M336 is the only other O.U course, that seems to cover Geometry or groups, in any real depth (apart from the MSc Dissertation, that covers some geometry).  So I feel that it is probably important that I have a go at M336; in order for me to have a more rounded mathematical field of view, before I decide to specialise further, beyond the MSc.

Having said all that, I have found the first two books of Group Theory in M208 a little bit, dare I say it, dull, and not very intellectually stimulating.  But on reading ahead, it does seem to pick up a bit, in the next two books.  Here's hoping so.

M208 TMA 01 Part 1, passed.

Okay,

Just a quick post, as I have received my results and feedback from TMA01 part 1, for M208 Pure mathematics.

I am thrilled to say that I managed to pick up 100% of the marks available, for this first 'toe in the water'.  However, I am also acutely aware, that sketching a few graphs, does not, a mathematician, make!

But it is still 35 marks in the back pocket, which should hopefully compensate for when things get tough and those TMA marks get dropped, in later units - Analysis B: I'm looking at you!

Next on the list, is posting Part 2 of TMA01 which I have now completed.

Now, where did I put that dodecahedron?

Obsessing about Mathematics

Hmm, this week, I struggled with a TMA question regarding equivalence relations.  I won't go into the details, for fear of breaching Uni regs; but all I will say, is that the question asks you to prove certain aspects of a relation.  Now, there are some relatively difficult parts of the question, but these weren't the parts that I had trouble with.  No,  it was more of a mental block and some slightly rusty, algebraic skills that caused my issues.  The marks that I was chasing, were only probably worth about one or two out of a  possible one hundred, in the whole paper.

So, one could argue that on the balance of things,  I should have had a go at the part that I struggled with, and not spent more than perhaps an hour on it, before moving onto some of the 'low hanging fruit', in the rest of the paper.

But, as I found when studying MST121, I can't let go of a TMA, unless I know that I have made every effort to understand the maths and produce reasonable answers.  I think if I ever found myself having to make-do by submitting a half-complete TMA; I may end up in a mental institution.

This is a concern as, apart from taking a slightly obsesive approach to O.U Maths study; I worry that if things get out of hand, that I may end up falling behind on study material, whilst chasing those last TMA marks.

In total, this week, I have spent 6hrs, chasing those one or two marks.  I don't know how good that is going to be, long term.  However, one good thing came out of it.  That is, I was forced to spend time with my brain, a pen and a white board.  I went down about 20 blind alleys, using all sorts of crazy methods, testing and probing.

And the outcome?  I think I have solved the problem and in the process of doing so, I have done so much thinking about the study materials, that I feel like I have a much better understanding of the more subtle ideas, that weren't aparant on my first study of the material.

So, it was time well spent, but I am exhausted and may well turn to a few pints of Bishop's Finger tonight.
I think I'll post part 2 of the TMA on Monday and then really start concentrating on Group Theory; only to do it all again at the end of March, via TMA 02!