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?
Tuesday 24 April 2012
Monday 16 April 2012
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.
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.
Saturday 14 April 2012
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.
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.
Wednesday 11 April 2012
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.
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.
Friday 6 April 2012
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.
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.
Wednesday 4 April 2012
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.
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.
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