Another week and apart from a miserable cold, I have managed to visit the O.U library, get a steer on what I should be studying, and adjusted my study load appropriately.
I found that I was getting too far into geometry and that I can leave some of my planned study in that subject, until next year and the year after.
I also reflected on some comments that were left on my blog this week, by a rather brilliant, learned and certainly not failed physicist, Chris. He said, tongue in cheek, that I was starting to transmogrify into a pure mathematician. I guess he based this astute comment on my recent fascination with some of the pure mathematics topics that I have recently encountered, and my lack of Open University physics courses that I plan to be examined in, over the next 3 years.
To answer this observation, I would say that my plan hasn't changed; rather, through detailed study and research, my approach has changed. Following my in-depth studies of the life and works of Rodger Penrose, and my experience of university level mathematics and physics; I feel, that to understand mathematical physics as easily as possible and with a wide range of knowledge and tools; whilst tackling the outlier abstract topics that exist; I believe that I will be best placed to succeed, by following the path below:
1. Absorb the building blocks of mathematics. E.g. not just learning the mechanics of an Einstein-Rosen Bridge, or Loop Quantum Gravity, but actually knowing how it all 'ticks' at the purist of mathematical levels.
2. Understand all undergraduate level, mathematics.
3. Learn both pure and applied mathematics at taught MSc level.
4. Then apply all of this knowledge to a theoretical physics PhD.
I believe that any plan to learn a bit of physics and a bit of applied maths at undergraduate level, will be okay; but wouldn't allow for the depth of understanding required, for a PhD in the field. Some may argue with that; but I know that I need to personally start at the basement, before moving up. One could argue that bothering with any pure maths topic is a waste of time when attempting an experiment such as mine. However, I would disagree with that assertion.
Don't get me wrong; I am not going to be neglecting physics over the next few years; rather, I will study it alongside the maths, until I know how to handle those numbers!
You only have to look at some of the most cutting edge theoretical or mathematical physics that is currently being worked on; and you will see that, to even understand it, you need a solid base of group theory, combinatorics, linear algebra, topology and a sprinkling of calculus.
If there is one thing that I have truly learnt from the first year of my experiment in perseverance by trying to convert my GCSE in Maths, into a PhD in Theoretical Physics; is that I love mathematics, I think I'm okay at it, and I can't wait to study all of the maths that I can squeeze in, over the next 10 years.
As my first-year sixth-form physics teacher once said, before his untimely death under the wheels of a lorry, 'mathematics is the language of physics; and without it, you are up S**t creek, without a paddle'.
Good old Mr. Curley.
Thursday, 29 September 2011
Tuesday, 27 September 2011
M208 and M337
I took another trip to the Open University Library in Milton Keynes, today. I wanted to closely examine the course material of M208 Pure Maths and also M337 Complex analysis. The purpose of doing so, was to try and get an idea of where my difficulties may lay with different units or topics, whether I need to brush up on anything that I'm not planning to study, make sure I am not studying too widely or deeply, and finally to estimate how long it is likely to take me to complete each unit booklet. This will then let me set my self-study plans for next year, without over burdening myself.
It was a morning very well spent. Not only do I love the O.U library as a place to sit and study, with its clean lines and light and airy spaces; but it is also interesting to leaf through other course materials, that are on display.
I was particularly interested in looking at courses such as M338 Topology, and a few other level 3 modules. The reason being, that some of the course materials from these dying level 3 courses, is being used in M303 Further Pure Maths, which I will be taking in October 2013. Again, it was a scoping exercise. I found the level 3 course material to be fairly accessible. And, although I don't have the required knowledge yet, to understand some of the topics and units; I know that they look very well written and certainly doable, if you have completed the pre-requisite courses.
Following my visit, I have decided to continue reading through the Brannan Intro to Analysis, but I am now reducing my study of Spivak's Calculus, to just reference checking topics such as the epsilon-delta, limit definitions etc. I am also going to reduce my Brannan Geometry reading, to now only include Conics, Quadric surfaces, transformations and some of the group theory that is contained within.
I am also going to replace some of that work, with some number theory practice, repeating exercises from Brannan and from online sources, as well as continuing to read the M221 units.
I also plan to re-visit a book that I picked up in August called, 'How to Prove It', by Daniel Velleman. This is because, the only part of the M208 that I feel I need the most practice at, is the minor use of theorem proving that features in the appendices and also in the units of Number theory and some of the analysis units.
I plan to confidently be able to prove some very minor results, by the time I complete M208, so this book will lay the foundations well and will actually go well beyond what M208 requires. Even so, I am always looking 3yrs ahead, to those post-graduate days which is really not that far away.
Whilst I was at the library, I also glanced at all of the MSc Mathematics modules. The only one that has taught materials in a style similar to OU undergraduate modules, is the M820 - Calculus of Variations and Advanced Calculus. It was tomb like and very heavy in places. Interestingly, the alternative 'pure' MSc module, M823 Analytical Number Theory (I), didn't look half as complicated as M820. It uses a set book as the main text and on reading the specimen exam paper and solutions provided, along with the TMA booklet; it looked a much more intriguing course than M820. I guess the shock would come when you study Analytical Number Theory (II), which looks like a beast!
Finally, whilst at the library, I happened to overhear a lively discussion between some faculty staff. They seemed to be discussing the unavoidable financial cuts and the possible effects on O.U content. The gist was, that they were discussing whether a paradigm shift from well written unit booklets and tutor supported learning, to one where students read set books and then presumably just took exams, would cut costs whilst keeping student numbers.
Interesting.
It was a morning very well spent. Not only do I love the O.U library as a place to sit and study, with its clean lines and light and airy spaces; but it is also interesting to leaf through other course materials, that are on display.
I was particularly interested in looking at courses such as M338 Topology, and a few other level 3 modules. The reason being, that some of the course materials from these dying level 3 courses, is being used in M303 Further Pure Maths, which I will be taking in October 2013. Again, it was a scoping exercise. I found the level 3 course material to be fairly accessible. And, although I don't have the required knowledge yet, to understand some of the topics and units; I know that they look very well written and certainly doable, if you have completed the pre-requisite courses.
Following my visit, I have decided to continue reading through the Brannan Intro to Analysis, but I am now reducing my study of Spivak's Calculus, to just reference checking topics such as the epsilon-delta, limit definitions etc. I am also going to reduce my Brannan Geometry reading, to now only include Conics, Quadric surfaces, transformations and some of the group theory that is contained within.
I am also going to replace some of that work, with some number theory practice, repeating exercises from Brannan and from online sources, as well as continuing to read the M221 units.
I also plan to re-visit a book that I picked up in August called, 'How to Prove It', by Daniel Velleman. This is because, the only part of the M208 that I feel I need the most practice at, is the minor use of theorem proving that features in the appendices and also in the units of Number theory and some of the analysis units.
I plan to confidently be able to prove some very minor results, by the time I complete M208, so this book will lay the foundations well and will actually go well beyond what M208 requires. Even so, I am always looking 3yrs ahead, to those post-graduate days which is really not that far away.
Whilst I was at the library, I also glanced at all of the MSc Mathematics modules. The only one that has taught materials in a style similar to OU undergraduate modules, is the M820 - Calculus of Variations and Advanced Calculus. It was tomb like and very heavy in places. Interestingly, the alternative 'pure' MSc module, M823 Analytical Number Theory (I), didn't look half as complicated as M820. It uses a set book as the main text and on reading the specimen exam paper and solutions provided, along with the TMA booklet; it looked a much more intriguing course than M820. I guess the shock would come when you study Analytical Number Theory (II), which looks like a beast!
Finally, whilst at the library, I happened to overhear a lively discussion between some faculty staff. They seemed to be discussing the unavoidable financial cuts and the possible effects on O.U content. The gist was, that they were discussing whether a paradigm shift from well written unit booklets and tutor supported learning, to one where students read set books and then presumably just took exams, would cut costs whilst keeping student numbers.
Interesting.
Monday, 26 September 2011
Calculus can be Simple
At times, I found the OU's treatment of differentiation, a little contrived. It was okay; and is probably the proper approach to learning the elements of calculus, preparing the way for Analysis at level 2 study.
However, I think much more emphasis should have also been given to teaching the mechanical, practical rules of differentiation and integration, in a much more utilitarian way.
I would like to have seen a separate booklet containing hundreds of progressive quick differentiation and integration problems, that could help towards mastery of the mechanical act of 'doing' the calculus. I believe that there are budding scientists or engineers who don't care for the minutia of Analysis, but instead need to use it as a tool in their trade, who may be put off by a lack of 'practical' exercises.
Anyway, I thought I would share an extract of the book 'Calculus Made Easy, by Thompson, Gardner. It just shows how simple calculus can be made. What is striking about this extract, is that the OU tried to explain the exact same element of learning, in about 800 words, whereas Gardner does it in about 100 words. Also, on first reading of the OU text, I didn't grasp the concepts and it took several hours of self study, to practice and attempt mastery of the technique. I read the Gardner extract in approximately 4 minutes and was able to apply it immediately. Here it is:
'Sometimes one is stumped by finding that the expression to be differentiated is too complicated to tackle directly.
Thus, the equation: \(y = {({x^2} + {a^2})^{\frac{3}{2}}}\) is awkward for a beginner.
Now the dodge to turn the difficulty is this:
Write some symbol such as 'u' for the expression \(({x^2} + {a^2})\)
then the equation becomes \(y = {u^{\frac{3}{2}}}\)
Which you can then easily manage; for \(\frac{{dy}}{{du}} = \frac{3}{2}{u^{\frac{1}{2}}}\)
Then tackle the expression \(u = ({x^2} + {a^2})\)
and differentiate it with respect to x, thus, \(\frac{{dy}}{{du}} = 2x\)
Then all that remains is plain sailing, for \(\frac{{dy}}{{dx}} = \frac{{dy}}{{du}} \times \frac{{du}}{{dx}}\)
\(\frac{{dy}}{{dx}} = \frac{3}{2}{u^{\frac{1}{2}}} \times 2x\)
\( = \frac{3}{2}{({x^2} + {a^2})^{\frac{1}{2}}} \times 2x\)
\( = 3x{({x^2} + {a^2})^{\frac{1}{2}}}\)
And so the trick is done.'
Calculus Made Easy (1998)
Wonderfully simple. Oh, how glad I am that I found this book.
Tuesday, 20 September 2011
'Real-World' Maths text books
The dust has now settled following the completion of MST121 Using Mathematics, and I have now begun to put together my study for the interim period between MST121 and M208 Pure Maths in late January. The main theme that is going to run through this period of revision, reflection and breaking new ground; is the use of 'real world' text books.
The Open University study materials are written like a set of very good lecture notes which are quite different from the type of text's that one encounters in mathematics text books. The text books often gloss over algebraic manipulations, as they plough through the solutions. This can mean that if your algebra manipulation is not very good, then you will struggle to understand the text and will not get very much out of it.
I say that OU notes are easy to use, however, I do sometimes find them rather laboured which can actually be at the expense of clarity. I have encountered several topics that I have not really understood in the OU text, only to then glance at my copy of Brannan or Spivak, and they have explained in one paragraph, what the OU has tried to explain in a whole chapter.
Sometimes, brevity can mean clarity.
The reason that I am practising reading other textbooks, is two fold. Firstly, it makes sense to use two or three approaches to learning a subject, as one of them is bound to make sense. Secondly, postgraduate maths, requires the ability to sift through other people's work, because they are either used as the set book, or when you are required to write your dissertation, you need to be able to scan quickly, large amounts of the stuff and understand it.
I have found the Brannan books (Intro to analysis and the Geometry text), to be short, to the point and relatively easy to follow. I understand that large parts of the Brannan text, are used in courses such as M208 and I am sure I recognise parts of his Geometry text, in the course notes for M336 Groups and Geometry, which I browsed at the O.U library last month.
Even so, it is helpful to study the style and brevity of these texts, for future proofing my skills. The only worry that I have, is the horror stories that I have heard, where massive mathematics texts are riddled with errata. I can just imagine me banging my head off of a large brick wall after trying to understand a problem for hours, only to find out that the solution was written incorrectly in the appendix!
Anyway, here is my study for this week. Total hours 16.
Brannan: A First Course in Mathematical Analysis - Pages 1 - 9 Real numbers.
Brannan: Geometry - pages 1 - 10 Conic sections.
Gardner: Calculus Made Easy - Pages 184 - 209 Partial differentials / integration
Practice maths skills:
Advanced factorisation
Expansion of polynomial products
Review of Linear functions
The Open University study materials are written like a set of very good lecture notes which are quite different from the type of text's that one encounters in mathematics text books. The text books often gloss over algebraic manipulations, as they plough through the solutions. This can mean that if your algebra manipulation is not very good, then you will struggle to understand the text and will not get very much out of it.
I say that OU notes are easy to use, however, I do sometimes find them rather laboured which can actually be at the expense of clarity. I have encountered several topics that I have not really understood in the OU text, only to then glance at my copy of Brannan or Spivak, and they have explained in one paragraph, what the OU has tried to explain in a whole chapter.
Sometimes, brevity can mean clarity.
The reason that I am practising reading other textbooks, is two fold. Firstly, it makes sense to use two or three approaches to learning a subject, as one of them is bound to make sense. Secondly, postgraduate maths, requires the ability to sift through other people's work, because they are either used as the set book, or when you are required to write your dissertation, you need to be able to scan quickly, large amounts of the stuff and understand it.
I have found the Brannan books (Intro to analysis and the Geometry text), to be short, to the point and relatively easy to follow. I understand that large parts of the Brannan text, are used in courses such as M208 and I am sure I recognise parts of his Geometry text, in the course notes for M336 Groups and Geometry, which I browsed at the O.U library last month.
Even so, it is helpful to study the style and brevity of these texts, for future proofing my skills. The only worry that I have, is the horror stories that I have heard, where massive mathematics texts are riddled with errata. I can just imagine me banging my head off of a large brick wall after trying to understand a problem for hours, only to find out that the solution was written incorrectly in the appendix!
Anyway, here is my study for this week. Total hours 16.
Brannan: A First Course in Mathematical Analysis - Pages 1 - 9 Real numbers.
Brannan: Geometry - pages 1 - 10 Conic sections.
Gardner: Calculus Made Easy - Pages 184 - 209 Partial differentials / integration
Practice maths skills:
Advanced factorisation
Expansion of polynomial products
Review of Linear functions
Wednesday, 14 September 2011
Physics and Maths, Studied this Week.
The last 2 weeks have been taken up primarily with completing TMA04 and CMA42, for MST121. Now that I have completed this course, I am very satisfied with how it has all gone and I am looking forward to starting M208 (Pure Maths), in January.
In preparation for that course, and to make good use of the time between now and January (Only 18 study weeks left), I have put together a study plan, which I have already started yesterday.
The plan consists of the following work each day:
3 pages of slow, detailed study and completion of the exercises in 'A First Course in Mathematical Analysis' Brannan.
1hr of repeated maths exercises of all maths that I have done to date, right from handling polynomials, through to calculus.
2 pages of detailed study and completion of exercise in 'Geometry' Brannan.
2 pages of detailed study and completion of exercises in 'Calculus 3rd Ed.' Spivak.
I know that 7 pages per day of textbook study, might not sound a lot, but I am really going for critical analysis and understanding the concepts, rather than a whistle-stop tour. Also, I find that reading maths textbooks, is an art that needs to be learned, before building up to any significant volume. I hope that this approach between module presentations with the OU, will stand me in good stead for future postgraduate work.
Also, each week, I will do some themed topic study on various sections of maths and physics, depending on what takes my fancy. For example, last night, I dipped my toe in the partial differential waters and did a small exercise on that topic.
I am just missing the groups books for MS221, which I had hoped to use to gently introduce my brain to the subject in a scholarly way. I'm not sure whether to buy those books or whether there is an alternative good intro textbook, that I could pick up instead.
I plan to also re-read Gödel's Proof, re-read the Hitch-hikers Guide trilogy of four books (had a weird dream last night about the three breasted whores from Eroticon 6, But I won't go into that here ;-). Finally, I'll be carrying on with the Feynman Lecture series.
This is going to be a wonderfully exciting period of enlightenment.
In preparation for that course, and to make good use of the time between now and January (Only 18 study weeks left), I have put together a study plan, which I have already started yesterday.
The plan consists of the following work each day:
3 pages of slow, detailed study and completion of the exercises in 'A First Course in Mathematical Analysis' Brannan.
1hr of repeated maths exercises of all maths that I have done to date, right from handling polynomials, through to calculus.
2 pages of detailed study and completion of exercise in 'Geometry' Brannan.
2 pages of detailed study and completion of exercises in 'Calculus 3rd Ed.' Spivak.
I know that 7 pages per day of textbook study, might not sound a lot, but I am really going for critical analysis and understanding the concepts, rather than a whistle-stop tour. Also, I find that reading maths textbooks, is an art that needs to be learned, before building up to any significant volume. I hope that this approach between module presentations with the OU, will stand me in good stead for future postgraduate work.
Also, each week, I will do some themed topic study on various sections of maths and physics, depending on what takes my fancy. For example, last night, I dipped my toe in the partial differential waters and did a small exercise on that topic.
I am just missing the groups books for MS221, which I had hoped to use to gently introduce my brain to the subject in a scholarly way. I'm not sure whether to buy those books or whether there is an alternative good intro textbook, that I could pick up instead.
I plan to also re-read Gödel's Proof, re-read the Hitch-hikers Guide trilogy of four books (had a weird dream last night about the three breasted whores from Eroticon 6, But I won't go into that here ;-). Finally, I'll be carrying on with the Feynman Lecture series.
This is going to be a wonderfully exciting period of enlightenment.
Monday, 12 September 2011
MST121, TMA04 Finished
Finally. After 9 months of work, it is done. TMA04 and CMA42 both completed and sent in to the OU. I have now officially completed MST121 and can now have a short break of a few days, before I kick start my prep work for M208 Pure Maths, in January 2012.
In total, I have completed 50 points this year, at level 1. This now gives me a grand total of 250 pts; of which, 30 are at level 3, 60 at level 2 and 160 at level 1.
2012 will see me taking on:
M208 Pure Mathematics (60pts at level 2)
M337 Complex Analysis (30pts at level 3)
Plus one 30pt Level 3 course (TBC)
2013 will consist of:
M303 'Further Pure Maths' (60pts at level 3)
This is just my O.U studies and doesn't include lots of other exciting maths and physics, that I have planned.
Regardless of anything else, my minimum expectation, is to complete my degree and kick start some post graduate maths in 2014.
As part of my prep for my next course, M208, I have obtained a copy of the course MS221 (Exploring Mathematics), which I intend to self-study for the next 16 weeks. I also plan to set up a daily regime of additional mathematics work based around the Analysis and Geometry books by Brannan, alongside some basic proof work from, 'How to Prove It', by Velleman.
I'm also going to try and crack a sub-5min Rubik's Cube!
In total, I have completed 50 points this year, at level 1. This now gives me a grand total of 250 pts; of which, 30 are at level 3, 60 at level 2 and 160 at level 1.
2012 will see me taking on:
M208 Pure Mathematics (60pts at level 2)
M337 Complex Analysis (30pts at level 3)
Plus one 30pt Level 3 course (TBC)
2013 will consist of:
M303 'Further Pure Maths' (60pts at level 3)
This is just my O.U studies and doesn't include lots of other exciting maths and physics, that I have planned.
Regardless of anything else, my minimum expectation, is to complete my degree and kick start some post graduate maths in 2014.
As part of my prep for my next course, M208, I have obtained a copy of the course MS221 (Exploring Mathematics), which I intend to self-study for the next 16 weeks. I also plan to set up a daily regime of additional mathematics work based around the Analysis and Geometry books by Brannan, alongside some basic proof work from, 'How to Prove It', by Velleman.
I'm also going to try and crack a sub-5min Rubik's Cube!
Sunday, 11 September 2011
Am I mad?
I know I talked about economising my study time, in a previous post. But I just can't seem to do it.
I mean, I have spent the last week of over 24hrs total study time, working on just 10 points worth of TMA questions for MST121, that don't gain me a grade that is any higher than the rather vanilla 'pass' that they hand out for all of your efforts on this course.
It's not that I am struggling with the content, although the calculus is a little more complex than I expected. No, it is that I just can't seem to 'let it go'. Writing this TMA, has been like nurturing a small child. I am terrified to let it go, before I have made sure that I have done everything within my power, to make it turn out well.
It just doesn't make any sense whatever.
I have worked out, that I could score just 59% on this assignment, and still gain an overall course score of 85%.
So why, oh why, do I have this drive, no, compulsion, to dissect every last mark and use all of my time, books and brain power, to milk it of its precious marks?
I think I might know the answer, above and beyond a simple neurotic tendency towards perfectionism. It is more to do with me wanting to prove to myself, that I am intellectually capable, of mastering mathematics. Not just some of it, but all of it. Every last polynomial.
I have this strange notion, lurking in my limbic system, that if I can't ace the TMA's on a level 1 mathematics course (give or take the odd arithmetic mistake or lapse of concentration); then I am unlikely to be capable of completing a PhD that is mainly mathematics based.
I have tried to finalise my TMA, be sensible, and spend my time preparing for M208 in January. But I just can't seem to let TMA04 go, without licking my finger to wipe its cheek, before tucking its shirt in and sending it to the OU.
I mean, I have spent the last week of over 24hrs total study time, working on just 10 points worth of TMA questions for MST121, that don't gain me a grade that is any higher than the rather vanilla 'pass' that they hand out for all of your efforts on this course.
It's not that I am struggling with the content, although the calculus is a little more complex than I expected. No, it is that I just can't seem to 'let it go'. Writing this TMA, has been like nurturing a small child. I am terrified to let it go, before I have made sure that I have done everything within my power, to make it turn out well.
It just doesn't make any sense whatever.
I have worked out, that I could score just 59% on this assignment, and still gain an overall course score of 85%.
So why, oh why, do I have this drive, no, compulsion, to dissect every last mark and use all of my time, books and brain power, to milk it of its precious marks?
I think I might know the answer, above and beyond a simple neurotic tendency towards perfectionism. It is more to do with me wanting to prove to myself, that I am intellectually capable, of mastering mathematics. Not just some of it, but all of it. Every last polynomial.
I have this strange notion, lurking in my limbic system, that if I can't ace the TMA's on a level 1 mathematics course (give or take the odd arithmetic mistake or lapse of concentration); then I am unlikely to be capable of completing a PhD that is mainly mathematics based.
I have tried to finalise my TMA, be sensible, and spend my time preparing for M208 in January. But I just can't seem to let TMA04 go, without licking my finger to wipe its cheek, before tucking its shirt in and sending it to the OU.
Saturday, 10 September 2011
S197 How the Universe Works
I received a pass result this morning, for this Open University module. It was a 10 point level 1 course in elementary cosmology and particle physics. It was a very exciting course and went into more depth than I would have imagined for a level 1 course. I didn't receive any specific feedback from the results of S197, other than a pass, so I am not sure how well I did; but it was probably one of the most enjoyable course that I have completed, to date.
I have counted the course towards my certificate of higher education, which is now complete. I will claim it once the University offer it formally to me, which means that I then only have M208 Pure maths to complete, to achieve my diploma in higher education (I have previous humanities courses at levels 1, 2 and 3). I then only need 30 more points at level 3 (probably complex analysis), for a BSc and then another 60pts (M303 Further Pure maths), to complete one of my BSc Hons.
I did a quick calculation last night, on the back of a fag packet; and it looks like I should be into my postgraduate maths courses by October 2014, whilst continuing to study some physics and mathematical physics, at undergraduate level. I still haven't formulated how I will structure my study from 2014 onwards; but one possible option would be to continue to take an MSc in mathematics either with the OU or another college, such as Kings in London; whilst also taking undergraduate courses of study either formally, via self study, or both, along side the formal mathematics training.
Whether I need to complete an MSc in full (I suspect I will + it will give me a chance to cover all the physics I need to, alongside); or whether I can do a postgraduate diploma in maths and then hop onto an MPhil; I will need to think about that and seek some professional advice at the time.
One thing I am not short of is options, and there are so many permutations, that it is going to be lots of fun, which ever way I do it.
I have counted the course towards my certificate of higher education, which is now complete. I will claim it once the University offer it formally to me, which means that I then only have M208 Pure maths to complete, to achieve my diploma in higher education (I have previous humanities courses at levels 1, 2 and 3). I then only need 30 more points at level 3 (probably complex analysis), for a BSc and then another 60pts (M303 Further Pure maths), to complete one of my BSc Hons.
I did a quick calculation last night, on the back of a fag packet; and it looks like I should be into my postgraduate maths courses by October 2014, whilst continuing to study some physics and mathematical physics, at undergraduate level. I still haven't formulated how I will structure my study from 2014 onwards; but one possible option would be to continue to take an MSc in mathematics either with the OU or another college, such as Kings in London; whilst also taking undergraduate courses of study either formally, via self study, or both, along side the formal mathematics training.
Whether I need to complete an MSc in full (I suspect I will + it will give me a chance to cover all the physics I need to, alongside); or whether I can do a postgraduate diploma in maths and then hop onto an MPhil; I will need to think about that and seek some professional advice at the time.
One thing I am not short of is options, and there are so many permutations, that it is going to be lots of fun, which ever way I do it.
Friday, 9 September 2011
TMA04
TMA04, is a pain in the backside. 50% of it needs to be carried out using OU Stats and Mathcad. And, because of a software issue, my Mathcad just wouldn't behave itself. I therefore spent 3 or 4 days, trying to battle my way through it and sent a pleading email to my Tutor, for some advice. She couldn't give it, but did suggest a re-install. I un-installed, re-installed and... it works!!
All that wasted time faffing about. Anyway, I think I am now 75% of the way through the paper, with the Mathcad bit now complete.
The other problem with TMA04, is that they have put in, what I think, is an unfair question. Not quite a trick question, but not far off it.
I can't go into the detail, for fear of breaching University regs, but what I will say, is that the some of the answers require more algebra, trigonometry and problem solving skills, than I would have expected in a level 1 course of this nature. I do wonder whether it has been done purposely, to identify those that really have properly mastered ALL of the course concepts.
A horrible TMA and I'll be glad to see the back of it.
All that wasted time faffing about. Anyway, I think I am now 75% of the way through the paper, with the Mathcad bit now complete.
The other problem with TMA04, is that they have put in, what I think, is an unfair question. Not quite a trick question, but not far off it.
I can't go into the detail, for fear of breaching University regs, but what I will say, is that the some of the answers require more algebra, trigonometry and problem solving skills, than I would have expected in a level 1 course of this nature. I do wonder whether it has been done purposely, to identify those that really have properly mastered ALL of the course concepts.
A horrible TMA and I'll be glad to see the back of it.
Sunday, 4 September 2011
The Pareto Principle
After my CMA result this week; I had a chat with my wife. We discussed the result and I explained that it was low, compared to my other results, because I didn't like the statistics units (block D), within the course MST121.
As we discussed this issue, she asked me how long had I spent on studying Block D and completing the CMA. I told her that it had taken me 10hrs to read through all 4 books of block D and then a further 3hrs, to complete the TMA.
This was a total of 13hrs for studying rather than the 60hrs that the Open University timetable recommended (The block D and CMA, were given 7.5 weeks recommended study time, which is equivalent to 60hrs of study).
My wife then went on to ask me about the grading system that the OU runs. I explained that to score an equivelent to a 1st class degree, you must score 85% or above, average on your assignments and any exam taken.
My wife then asked me, what level of degree I needed, to be accepted onto a masters level degree programme. I explained that most of them for maths or physics, require a 2.1 honours degree but some, including the Open University, will accept a 2.2, but most employers or academic circles, would normally expect a 2.1.
My wife then asked me what this 'dropped' and rushed mark for the stats units, would ultimately get me, if it was translated into an end of course result. I explained that 88% would be equivalent to a solid grade 1 pass.
She then asked me how much study time I had spent on a set of units, that had achieved my TMA average of 94%, for the rest of the course. I reckoned that the study time required to read and pass, for example, the TMA02 with this score, had been in the region of 112hrs (not including my other non MST121 studies).
My wife then told me that she thought I was a little daft and how could I hope to pass a maths degree, if I couldn't see the blindingly obvious.
What she was suggesting, of course, is that I should evaluate what benefit I have derived from working for an additional 14hrs per week, to score an additional 6% in a TMA, when it would make no difference to the final outcome of the module or degree classification.
Hmm, she had a point. It then got me thinking about why I had spent so many hours slaving over this course. Well, I think it is for a few reasons. Firstly, I love studying. But as my father used to say, 'busyness is a symptom of laziness', meaning that sometimes we fill our hours with interesting yet unproductive tasks or events, to avoid the difficult or important. I wouldn't say that any of my studying has been wasteful or any form of procrastination, but I do accept that I have skewed on occasion into a few indulgences, that have perhaps distracted me from the task in hand.
This all got me thinking about the 'Pareto principle', or the '80% of the benefit, from 20% of the effort', theories.
Now, I love studying, it is what I do and will continue to do, so any 'fat trimming', will not be about reducing the time that I spend studying. Indeed I hope to one day, do it full time. No, this is more about maximising the next few years' output of work, whilst still achieving the same result (a good degree and acceptance onto a masters / PhD programme).
I have trawled the internet and looked at many University websites. Nearly (in fact, all bar one or two) ask for, what they describe as a good degree. They qualify the use of the word 'good', to mean a 2.1 Honours award.
In Open University world, that equates to a minimum score of 70% in the TMA's and the exams. Well, I know that by spending only 11% of the suggested time, I have managed to pass a CMA, with 88% of the marks. So, what is the benefit of me slogging unneccessarily over TMA's, to score in the 90's? I know that one of the other main reasons that I tend to do this, is that I am a perfectionist and that any dropped marks, feel like a failure (I'm sure a psychiatrist would have a field day with that little gem!)
But, I need to decide, what benefits I could derive, from reducing my study time per module, to even 50% of its current level:
1. I could take more modules per year and get it all done a lot quicker. If I took an extra 30 pt module this October, overlapping it with M208 Pure maths in January 2012. I would have an overlap of 6 months where I studied 90pts, and then an exam in June 2012, followed by an exam in October 2012. Doable!
2. I could shave off time taken to complete the degree and also tot up additional points, to take a Diploma, BA and a BSc Hons, by the end of 2013.
My only worry, is that potential PhD supervisors, may pick students with top drawer marks in the 90's, rather than in the 70's or 80's. Would they question a sudden dip in average TMA scores?
This is all certainly food for thought. And, I know that with my methods of using 100's of practise exam style questions and flash cards, that I can shut myself away and study well for an exam, without too much drama.
So the only question left really is, do I want to get a 'good' degree quickly and move onto more interesting post-grad stuff quicker? Or, do I want to score in the 90's for my own well-being and satisfaction, and take the slower route to success?
As we discussed this issue, she asked me how long had I spent on studying Block D and completing the CMA. I told her that it had taken me 10hrs to read through all 4 books of block D and then a further 3hrs, to complete the TMA.
This was a total of 13hrs for studying rather than the 60hrs that the Open University timetable recommended (The block D and CMA, were given 7.5 weeks recommended study time, which is equivalent to 60hrs of study).
My wife then went on to ask me about the grading system that the OU runs. I explained that to score an equivelent to a 1st class degree, you must score 85% or above, average on your assignments and any exam taken.
My wife then asked me, what level of degree I needed, to be accepted onto a masters level degree programme. I explained that most of them for maths or physics, require a 2.1 honours degree but some, including the Open University, will accept a 2.2, but most employers or academic circles, would normally expect a 2.1.
My wife then asked me what this 'dropped' and rushed mark for the stats units, would ultimately get me, if it was translated into an end of course result. I explained that 88% would be equivalent to a solid grade 1 pass.
She then asked me how much study time I had spent on a set of units, that had achieved my TMA average of 94%, for the rest of the course. I reckoned that the study time required to read and pass, for example, the TMA02 with this score, had been in the region of 112hrs (not including my other non MST121 studies).
My wife then told me that she thought I was a little daft and how could I hope to pass a maths degree, if I couldn't see the blindingly obvious.
What she was suggesting, of course, is that I should evaluate what benefit I have derived from working for an additional 14hrs per week, to score an additional 6% in a TMA, when it would make no difference to the final outcome of the module or degree classification.
Hmm, she had a point. It then got me thinking about why I had spent so many hours slaving over this course. Well, I think it is for a few reasons. Firstly, I love studying. But as my father used to say, 'busyness is a symptom of laziness', meaning that sometimes we fill our hours with interesting yet unproductive tasks or events, to avoid the difficult or important. I wouldn't say that any of my studying has been wasteful or any form of procrastination, but I do accept that I have skewed on occasion into a few indulgences, that have perhaps distracted me from the task in hand.
This all got me thinking about the 'Pareto principle', or the '80% of the benefit, from 20% of the effort', theories.
Now, I love studying, it is what I do and will continue to do, so any 'fat trimming', will not be about reducing the time that I spend studying. Indeed I hope to one day, do it full time. No, this is more about maximising the next few years' output of work, whilst still achieving the same result (a good degree and acceptance onto a masters / PhD programme).
I have trawled the internet and looked at many University websites. Nearly (in fact, all bar one or two) ask for, what they describe as a good degree. They qualify the use of the word 'good', to mean a 2.1 Honours award.
In Open University world, that equates to a minimum score of 70% in the TMA's and the exams. Well, I know that by spending only 11% of the suggested time, I have managed to pass a CMA, with 88% of the marks. So, what is the benefit of me slogging unneccessarily over TMA's, to score in the 90's? I know that one of the other main reasons that I tend to do this, is that I am a perfectionist and that any dropped marks, feel like a failure (I'm sure a psychiatrist would have a field day with that little gem!)
But, I need to decide, what benefits I could derive, from reducing my study time per module, to even 50% of its current level:
1. I could take more modules per year and get it all done a lot quicker. If I took an extra 30 pt module this October, overlapping it with M208 Pure maths in January 2012. I would have an overlap of 6 months where I studied 90pts, and then an exam in June 2012, followed by an exam in October 2012. Doable!
2. I could shave off time taken to complete the degree and also tot up additional points, to take a Diploma, BA and a BSc Hons, by the end of 2013.
My only worry, is that potential PhD supervisors, may pick students with top drawer marks in the 90's, rather than in the 70's or 80's. Would they question a sudden dip in average TMA scores?
This is all certainly food for thought. And, I know that with my methods of using 100's of practise exam style questions and flash cards, that I can shut myself away and study well for an exam, without too much drama.
So the only question left really is, do I want to get a 'good' degree quickly and move onto more interesting post-grad stuff quicker? Or, do I want to score in the 90's for my own well-being and satisfaction, and take the slower route to success?
Friday, 2 September 2011
CMA41 Result
I have received my MST121 Open University CMA41 result back, today. I scored 88%, which considering that I rushed through it because it was all about statistics (I hate statistics); then I am more than happy with that result. It is still in the pass 1 realms (85%+), which is where I need it to be.
When you actually add up all the stats work of MST121 including CMA41, part of TMA04 and part of CMA42; then it actually accounts for a large proportion of this course. A lot more than I imagined.
It still doesn't detract from my enjoyment of MST121, so far. Once I have completed TMA04 and CMA51 (very soon), then I will provide a critical evaluation of the entire course and some thoughts on how it sets one up, for further mathematics at University.
When you actually add up all the stats work of MST121 including CMA41, part of TMA04 and part of CMA42; then it actually accounts for a large proportion of this course. A lot more than I imagined.
It still doesn't detract from my enjoyment of MST121, so far. Once I have completed TMA04 and CMA51 (very soon), then I will provide a critical evaluation of the entire course and some thoughts on how it sets one up, for further mathematics at University.
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