Powered by MathJax From GCSE Maths, to Rocket Scientist...: June 2011

Tuesday 28 June 2011

Physics and Maths, Studied this Week.

Another week done and, this morning, I received my 1000th blog visitor, which is definitely a motivator for me, to keep writing about my journey from a GCSE in maths, to a PhD in Theoretical Physics.

I have taken this opportunity, to reflect on my likely path towards this lofty goal.  I believe that the easiest way to study physics is by doing as much 'brain-melting' maths first, before attempting heavy weight physics of any kind.

My chosen course for next year, is the first steps at the start of this path.  I am enrolled on MST209, Mathematical methods and models.  This is one of the true beginnings of mathematical physics with the Open University.  It is maths applied to physical models and offers a launch pad to higher level 3 courses.

I am definitely warming to the idea of doing at least some of the post-grad OU maths courses or even the full MSc Maths, before diverging into post-grad physics.  I am certainly excited about all that higher level calculus and other complex areas of maths and mathematical physics.  I need to do some research, but I believe that Rodger Penrose, and many other successful physicists, actually studied maths at undergraduate level, before doing physics later.  I'll confirm this and post later.  It's probably a good exercise to do anyway, as examining the study paths of great physicists, may help shape some of my future course decisions.

I was flicking through a book, last night, from another Open University course, S207, The Physical World.  The book was the intro to quantum mechanics.  As I turned the pages and tried to make sense of the Schrödinger equations, standing wave models and working out whether a particle is bound or unbound; I thought back to before I started studying maths, and I do believe that I just would not have understood, even qualitatively, any of the more unusual quantum physics concepts, if I hadn't studied the maths first.

However, there was a very interesting paragraph in the S207 book, that presented the argument that although many brilliant physicists and mathematicians can use maths to apply equations to quantum situations; many of them don't understand why quantum mechanics works, or indeed, how it works.

This started me thinking of perhaps how dangerous it could be, using theories that we can manipulate but don't understand, to change the world around us.  I am thinking in particular, about the attempts at creating a quantum computer.  It is said, that a quantum computer will be able to calculate in multiple states, simultaneously, so that (if you believe the many worlds theory), it could be using copies of itself in other universes, to multiply its processing power, almost infinitely.

And, although I don't believe that this type of future technological power, is intrinsically dangerous; I am not so sure about the humans that will wield that power.  I understand that the U.S and other military's, are already racing to develop quantum computing and other technologies, such as carbon nano-tubes.  What will the military do with this power?  Who knows?

Anyway, on that apocalyptic note, here is this week's completed study.

Total study time:  20hrs.

MST121
Finished, reviewed and posted TMA03.  (Answers checked, using Wolfram Alpha and Mathcad)
Differential equations: Euler's Method.
Slope Fields
Further integration practice
Separating variables practise
Vectors, practise questions

Probability: Game Theory
Independence and multiplication rule

The Teaching Company Lectures: Calculus
Inverse trigonometrical identities
Bases other than 'e'

The Teaching Company Lectures: Mastering Differential Equations
What is a differential Equation?
A Limited-growth population model


This week, I will be finalising my marked assignment for S197 (How the Universe Works), my' intro to astrophysics' course.  I will also be taking a well earned, few days off, going camping.  Lets hope it stays hot!

Friday 24 June 2011

MST121, TMA03 Finished

Thank goodness for that!  I have finished the TMA03 final draft and, apart from a last minute light touch review, it is ready for the postman.  I'll probably send it on Monday, which will be 10 days before it is due in.  I really enjoyed the challenge of completing some marked Integration and differential equation solving.  I have just also purchased a new 'The Teaching Company' set of video lectures entitled:  Mastering Differential Equations: A visual Approach.  The calculus lectures by Prof. Bruce Edwards, have been so useful, that I just couldn't resist the further calculus set.  Also, they are 20% off in the sale.

I can now start to concentrate on the final TMA04 and other last bits of coursework.  I also have the final marked assignment to complete for ' How the Universe Works' S197, another of my physics modules, with the O.U.

Well, I'm off out tonight, to celebrate.  A nice olde worlde country pub beckons; along with several pints of Bishops-Finger.  Ooh matron!

Wednesday 22 June 2011

S196, Passed!

I received a letter in the post today, informing me that I have passed S196 (Planets, an Introduction).  Although I don't need any more year 1 University modules; I took this, as I am simply interested in knowing more about the cosmos.  The course was heavy on reading and the final marked assignment was a pain in the Uranus.

Although it is a level 1 course; I found, in a similar way to another level 1 course (Intro to Astronomy), that the question paper felt a little bit subjective and I really wasn't sure about some of the answers, as the questions had been a little woolly.

Anyway, a pass, is a pass.  I don't know the score, as it was just pass or fail; although I had a small amount of feedback to indicate that I probably scored a good to good/average score.

It's another 10 O.U points under my belt, for a rainy day.  Who knows, maybe I can do enough extra bits and bobs with the O.U, to cobble together an extra qualification, later on down the line.  It all helps...

Open University Tutorials

O.U Tutorials, hmmm, I have mixed feelings about them.  I have studied a total of 8 modules with the O.U, over the last 7 years.  These include both level 1, 2 and 3 courses in Science and Humanities.

From my own experience, I have noticed a difference in the quality of the tutorials, that the O.U offers with each course.  I have also noticed, that within those 8 modules, there has been some correlation between the academic level of the course, and the quality of the tutorial.

Firstly, let me qualify exactly what I am describing, when I speak of quality.  For me, quality in a tutorial consists of the following elements (other people's ideas of quality, will undoubtedly diverge).

Intellectual level, not too low.

More 'university lecture', than 'group chat'.

Not 'dumbed down', to the lowest common denominator.

Provides actual benefit and consolidates concepts, rather than just a few unconnected exercises done in small groups.

A  tutor with significant exposure to their field through either lecturing experience or research.

Takes place at a University, rather than in a village hall or dark, damp community college room.

Are of substantial length and content (typically a whole day or morning, rather than 45mins / 1hr at night - midweek).


All of these elements are, for me, important in making the experience of tutorials, worth having.  What I have found, is that most of my level one courses, have less of the above 'wish list', whilst some of my level 2 and 3 courses, have had very comprehensive tutorial programmes, held in the environment of a 'red brick' University, and some have been with leading professionals, in their field's.  For these types of tutorials / lectures, I have pre-booked annual leave from work, just so that I can attend.

I find that I very rarely attend more than the odd level 1 tutorial, half of my Level 2 lectures and nearly all of my level 3 tutorials.  I suspect that there are so many students at level 1, that there aren't enough quality venues and even less, experienced or learned professors, to cope with that level of students.  It seems that those courses with a small Nationwide interest, in very specialist fields, seem to benefit from some very interesting tutors and better structure and loci.

I am, of course, speaking in broad terms.  There are, as always, exceptions.  These include an exceptional level 1 French course that I studied in 2007 with a fantastic tutor who held very well designed and useful tutorials, that were full of opportunities to practice speaking and listening with other students.  Also, whilst my current MST121 tutorials don't meet most of  my criteria above; they are run by a tutor who is quite clearly an intelligent and capable scholar.

Sunday 19 June 2011

Physics and Maths, Studied this Week.

Okay,
Another week done and probably the most challenging so far.  I did a lot of integral practice, to try and make it all second nature.  I'm getting there, but I reckon that I need at least another 10hrs of solid practice, before I can call my self a derivative / integral king.

So, this week I have spent 24hrs total study time.

MST121
Differential equations
Lots and lots of integral practice
Finished full draft copy of TMA03.

The Teaching Company: Calculus Lectures
The Chain Rule
Differential equations and slope fields
Applications of differential equations
Natural Logarithmic Integrations

Other reading


Calculus. 3rd edition Michael Spivak.
Chapter 1(basic properties of numbers)
Chapter 9 (derivatives)
Chapter 10 (differentiation)

Quantum Electrodynamics.  Richard Feynman
Lectures 1,2,3 and 4

Other maths
Revision of trigonometric identities
Revision of line and circle equations


Wow, a full on week of study, watching and reading.  Plenty of practice questions done and a lot of confidence built.

Looking forward to next week.

Thursday 16 June 2011

Rocket Science and Dyslexia.

I am currently steaming ahead through TMA03 (coursework paper for my Open University Course MST121, Using Mathematics).

Yesterday, all was going well, until, I hit a 'word' maths question, involving a Space Rocket.  This is the type of question that proposes a problem, in words alone, and then you need to apply equations that you have learnt, to solving the problem.  This is instead of the more usual: here is an equation, solve it for X, type of question.

Now I have, so far,  been coping better than I personally expected, with the maths at University.  It seems that the further away from 'calculating' and the more into learning 'concepts' and theorems that I move; the more I seem to be gaining a real and deep understanding, of the equations.

Anyway, I have dyslexia and I know, from years of living with it, that I have a serious problem with decoding written words.  This includes word problems in maths.

Now, for the first time, I reached one of those questions in TMA03, yesterday.  It was a taste of modelling a Rocket Science problem involving a space vehicle launch.  The question expected the use of calculus to derive a selection of important distances and velocities, at key times.  Enter Mr. Newton, his calculus, gravity and other important equations.

Well I sat yesterday, for nearly 4 hours, and I just couldn't work out what the question was asking.  The calculus, I can do.  I mean, I have been practising some pretty complicated problems, over the last few weeks.  But this one really stumped me.  It wasn't involving difficult maths; I just couldn't decode the words and work out what the question was asking.  This wasn't a problem with the maths; this was a problem with word comprehension.

Anyway, after sulking for 4 hours and then having an early night; I got up this morning, returned to my books and started to search my growing collection of maths texts and DVD's, to see if any of them could offer some hint of how to proceed.

Jackpot:  I remembered that my Teaching Company, Calculus Lectures, by Professor Bruce Edwards, contained a lecture that used an example involving a particle in motion.  The Lecture was entitled: Basic Differentiation Rules, and the example was at the end of the lecture.  It described a Swimmer, diving off a dive-board.  I watched the example and then, the penny dropped (Jedi stirrings)?  I now knew how to proceed.

I ran (literally) back to my books and started scribbling furiously.  Within 40 minutes, I had a credible answer to the TMA question.  Now, none of my DVD examples or maths texts gave an exact replica of my TMA question; but just the act of putting down the books, sleeping, returning with fresh eyes and searching available maths sources; allowed me to work it all out, for my self.

This is probably the best I have felt about my Maths journey, to date.  The maths wasn't difficult, it was just nice that everything came together, at the last minute, to solve a problem that was more personal than mathematical, in nature.  It was that dyslexic 'shadow' that has a habit of trying to beat you down, but in doing so, it sometimes has the opposite effect.

So, bring on more of those Rocket Science problems!  I have my books, Isaac Newton and Bruce Edwards by my side.  What could possibly go wrong?

Monday 13 June 2011

Can Mathematicians Add up? Part 2

Earlier this year, I discussed whether there was any real evidence to support the urban myth, that professional Mathematicians, as a group of individuals, are hopeless at basic mental arithmetic.

I have been searching books, and the internet, to see if there is any hard evidence that could prove this myth, as fact; or alternatively, to discover exactly when and why the myth began.

I have since been reading a book by Karl Sabbagh, called Dr Riemann's Zero's.  The book, details the search for a proof, related to prime numbers.

In that book, I discovered a few passages, that help towards perhaps proving that some very well known mathematicians couldn't add up!  The extracts below are lifted from chapter 7 (The Bieberbach Conjecture):



'The popular idea of mathematics, is that it is largely concerned with calculations.  What many people don't realize - and mathematicians at parties have given up correcting them - is that mathematicians are often no better calculators, and sometimes worse, than the average non-mathematician'.


'Louis De Branges [...] discussing the idea that mathematicians did all their best work when they were young, and I asked him when he made some particular insight.  'Let's see', he said, 'It happened in 1984 and I was born in 1932.  So was I fifty?  How old was I then...?'


'Ernst Kummer, another professional mathematician [...] was also bad at elementary arithmetic: 'one story has him standing before a blackboard, trying to compute 7 times 9. "Ah," Kummer said to his high school class, "7 times  9 is eh, uh, is uh..."  "61," one of his students volunteered.  "Good," said Kummer, and wrote 61 on the board.  "No," said another student, "it's 69."  "Come gentlemen," said Kummer, "it can't be both.  It must be one or the other."



And finally, a lovely description of Mathematics by an unknown American Mathematician in the 19th Century:


"Mathematics is no more the art of reckoning and computation than architecture is the art of making bricks or hewing wood, no more than painting is the art of mixing colours on a palette, no more than the science of geology is the art of breaking rocks, or the science of anatomy the art of butchering".

Saturday 11 June 2011

Physics and Maths, Studied this Week.

This is my only post this week, as I am at the MotoGP at Silverstone, for four days, until Sunday night.  It's just a quick update about my study so far...

Total hours studied:  14

MST121
Finalised questions 1,2,3,4 for TMA03.
Definite Integrals
Optimization
The Fundamental Theorem of Calculus
Differential equations

Other Maths reading
Dr Riemann's Zero's

More posts, once I recover from this weekend's motor racing event, and my ears finally stop ringing!

Saturday 4 June 2011

Physics and Maths, Studied this Week.

Okay, so this week has been centred around tackling some advanced integration, by hand.  I can tell you, that it is not easy.  I have noticed that most intro calculus courses, give you tables of common  integration values; and MST121, is no exception.  I did spend a lot of time, trying to gain a deeper understanding of double angle formulas and general trigonometry rules, so that integration of these functions, is a little easier to grasp.

I have also touched on some differential equations, involving modelling a particle in two dimensions.  There is a whole book in MST121, dedicated to these equations, which I should start to study in July.

For now, I will continue to practise differentiating and integrating, until they become second nature.

I have also been supplementing my Open University study, with the Calculus lectures, from the Teaching company.  It was, 'Professor Edwards to the rescue', as his lecture on integration by substitution helped clarify a point that was really confusing and not explained well, by the O.U text.

I was struggling with a rather hashed description in the text, about the addition of constants to integrals e.g.

If you have an integral such as:   x(x^2 - 1)^3 dx                      you need to multiply the whole thing by 1/2 when working backwards, so that you end up with the correct answer.  It isn't immediately obvious why you would need to do this, and the OU text didn't explain it well.  However, the video lecture gave a wonderful explanation, that made it click straight away.

Total time studied this week: 18hrs


MST121

Integration by inspection
Algebraic manipulation before integration
Position, velocity and acceleration
Completed Final draft of TMA03 question 3, using Mathcad print-outs


The Teaching Company Calculus Course

Integration by substitution

Wednesday 1 June 2011

New Version of Mathcad

I am very excited.  It looks like the testing for the new 2.0 version of Mathcad, is about to begin in July 2011.

I have applied via email to the company, to be one of the testers, so 'fingers crossed', and maybe I'll get to test it first hand?

It sounds great and such a wonderful advance on the previous version 14, that I am currently running.  I understand, that any clunkiness, has been removed, for a more web 2.0 feel to the interface.

If it is as good as I think it will be; then It will really take my studying to the next level.  If I can shave off an extra 30mins a week study time, through a better user interface, then that will really make a difference to my grades.

You can find the Mathcad producers, Planet PTC, here.  They are a community for PTC customers and everyone is dedicated to product development excellence.  Hence, the new version of Mathcad.

Here's hoping, that it lives up to expectations.