Okay, a very slow start, back into study, and I have spent a focussed week, looking into part of the course MST121, entitled, Modelling with Sequences. I am currently studying the different units, of this course, out of sequence. I have dipped in and out of Vectors, Matrices and Sequences. I find, that this keeps my interest and also maintains a holistic view of the course, by not becoming too narrowly focussed on any one part.
So, studied this week:
Sequences and Limits
Sequences from recurrence Systems
Sequences from Sums
Recap of some mental arithmetic, including lots of fractions work (just felt like brushing up).
My daughter (now 6yrs old), has been studying Kumon Maths, for the last 2yrs now, and has achieved her Silver Medal this month (Silver medal is given for being 1yr ahead of your age group). It was seeing her, doing lightening fast, mental arithmetic of large 2 digit numbers, in one step, that led me to feel like I should brush up on some mental maths, myself!
She seems to have a natural ability and is amazing with numbers. However, when I asked her whether she wanted to be a mathematician or scientist, when she grows up, she simply told me straight,
'daddy, I want to look after ponies, and wear a glittery riding hat'.
Thursday, 31 March 2011
Wednesday, 30 March 2011
The Fibonacci Sequence
The Fib sequence, is one of those strange mathematical entities, that appears to reflect itself in nature. For those that don't know, the Fibonacci sequence is created, using the real numbers, from 1, 1, 2... to infinity. The numbers are added together in sequence, so that the previous two numbers in the sequence, add up to the next number.
For example, the first few numbers of the sequence are:
1,1,2,3,5,8,13,21,34, 55, 89 etc...
So 1+1 = 2
Then 1 +2= 3
2+3= 5
And so on.
But, for some reason, the ratios between the numbers in this sequence, as the sequence progresses, have some strange properties.
The ratios include, the so called Golden Ratio, of approx 1.618. This ratio, is used in creating, so called, perfect proportions, such as those found in 5th Century BCE, Greek architecture; or it is used by some plastic surgeons, when they are trying to create perfect facial proportions. The Fib ratios are also part of nature and are alleged to be found in the patterns of sunflower seed heads, or the chambers in the shell of a Nautilus.
The ratios are also heavily used by stock and Forex (foreign exchange) traders, as the stock market trends have a funny habit of starting or ending, near to key Fibonacci ratios, within their charts and graphs.
This strange sequence has also lead me to ponder the natural logarithms and the number 'e' where e is an irrational constant approximately equal to approx: 2.718281828
Whilst we tend to find the number 10, easier to work with, when trying to count or measure things; this number 'e', keeps cropping up in maths and in nature, in the strangest of places.
I have no idea why; but this absolutely fascinates me, and it is one of the aspects of maths, that I am going to now find out more about. How it fits into Physics, is, no doubt, going to be surprising and probably very elegant.
For example, the first few numbers of the sequence are:
1,1,2,3,5,8,13,21,34, 55, 89 etc...
So 1+1 = 2
Then 1 +2= 3
2+3= 5
And so on.
But, for some reason, the ratios between the numbers in this sequence, as the sequence progresses, have some strange properties.
The ratios include, the so called Golden Ratio, of approx 1.618. This ratio, is used in creating, so called, perfect proportions, such as those found in 5th Century BCE, Greek architecture; or it is used by some plastic surgeons, when they are trying to create perfect facial proportions. The Fib ratios are also part of nature and are alleged to be found in the patterns of sunflower seed heads, or the chambers in the shell of a Nautilus.
The ratios are also heavily used by stock and Forex (foreign exchange) traders, as the stock market trends have a funny habit of starting or ending, near to key Fibonacci ratios, within their charts and graphs.
This strange sequence has also lead me to ponder the natural logarithms and the number 'e' where e is an irrational constant approximately equal to approx: 2.718281828
Whilst we tend to find the number 10, easier to work with, when trying to count or measure things; this number 'e', keeps cropping up in maths and in nature, in the strangest of places.
I have no idea why; but this absolutely fascinates me, and it is one of the aspects of maths, that I am going to now find out more about. How it fits into Physics, is, no doubt, going to be surprising and probably very elegant.
Monday, 28 March 2011
TMA01 Result
I received back my result for TMA01, MST121, this week. I scored 93% which I am very pleased with, considering it was done whilst sick. However, I made some enquiries with the Open University, last week. The enquiries were about the post graduate courses in maths and physics, that they run. I was simply enquiring as to the types of courses and the likely future presentation of such courses.
The person I spoke to on the phone, was a little negative. She promptly told me, that I had no business, thinking about doing a research degree in maths or physics, unless I was scoring at least 95% in my TMA's. I happen to think, that she is wrong. TMA01, is my first summative piece of course work, that I have completed for MST121, which, if replicated in the next 3 TMA's, should see a distinction grade. Why 93% would not be good enough for research work? I have no idea.
The lady I spoke to left me feeling a little deflated, however, following my bought of very bad sickness this last 2 months (I have pneumonia, which I can't shake off); that lady's comments, have just spurred me on, to put her in the pile of non-believers, and achieve my goals, in spite of opinions like hers.
The person I spoke to on the phone, was a little negative. She promptly told me, that I had no business, thinking about doing a research degree in maths or physics, unless I was scoring at least 95% in my TMA's. I happen to think, that she is wrong. TMA01, is my first summative piece of course work, that I have completed for MST121, which, if replicated in the next 3 TMA's, should see a distinction grade. Why 93% would not be good enough for research work? I have no idea.
The lady I spoke to left me feeling a little deflated, however, following my bought of very bad sickness this last 2 months (I have pneumonia, which I can't shake off); that lady's comments, have just spurred me on, to put her in the pile of non-believers, and achieve my goals, in spite of opinions like hers.
Wednesday, 23 March 2011
Feeling better!
Just a quick post. I'm back, fitting fit and ready to study. Posts will resume tomorrow. Hurray!
Thursday, 17 March 2011
Physics and Maths, Studied this Week.
My sickness has finally taken over and I have spent most of this week in bed, on all sorts of anti-biotics. Therefore, my study has been limited to a couple of videos and some light reading (I have a constant headache, so can't cope with anything cerebral).
The Teaching Company Calculus
Concavity and points of inflection
Curve Sketching and Linear approximations
The Teaching Company Cosmology
Conditions during the first million years
MST121 O.U Course
Recap on functions and trigonometry
Total time spent: 3hrs
--------------------------
I hope to be back on my feet soon and will look to try and post something when I am feeling more human! I am expecting the result from my TMA01, coursework piece, any day now, So i'll post the result as soon as it drops on the mat.
The Teaching Company Calculus
Concavity and points of inflection
Curve Sketching and Linear approximations
The Teaching Company Cosmology
Conditions during the first million years
MST121 O.U Course
Recap on functions and trigonometry
Total time spent: 3hrs
--------------------------
I hope to be back on my feet soon and will look to try and post something when I am feeling more human! I am expecting the result from my TMA01, coursework piece, any day now, So i'll post the result as soon as it drops on the mat.
Saturday, 12 March 2011
Mathcad Update
Following a very useful comment from Chris, I have had the good fortune to check out the latest offering of Mathcad. It appears to have a much more intuitive interface, than previous versions; and once the more functional 2.0 version appears in the autumn, I will seriously consider purchasing my own copy (I suspect the O.U may not catch up and use this version, until much later).
I am liaising with my tutor, to find out if the O.U are going to use the new version of Mathcad in the future. One blockage I can see, is that the O.U course text is written, integrating the current version of Mathcad (the one I'm not keen on). So, I would surmise, that the O.U, won't swap to a new version, until they are due to change the current presentation of course material (which could be several years for MST121).
It won't stop me lobbying the O.U, regarding the new Mathcad version. I see maths software as essential for higher maths courses. It allows you to do lots of smaller but tedious calculations, in an instant, whilst in pursuit of a much larger and important solution.
I am currently reading a book by Richard Feynman, detailing his memoires, about the time that he was at Los Alamos, engineering the first atomic weapons. He tells of warehouses, full of student physicists and technicians, punching cards into mechanical counting machines and iterating the answers many times over. It used to take them about 4 months to tackle any particular problem, concerning the energy release of different atomic fission models. We have come such a long way.
On reading this tale, it did make me stop and think; that even though I was struggling for 3hrs, to plot a graph and do some calculations, with mathcad; doing it with just a pencil and paper, would have taken a very long time, indeed.
I am liaising with my tutor, to find out if the O.U are going to use the new version of Mathcad in the future. One blockage I can see, is that the O.U course text is written, integrating the current version of Mathcad (the one I'm not keen on). So, I would surmise, that the O.U, won't swap to a new version, until they are due to change the current presentation of course material (which could be several years for MST121).
It won't stop me lobbying the O.U, regarding the new Mathcad version. I see maths software as essential for higher maths courses. It allows you to do lots of smaller but tedious calculations, in an instant, whilst in pursuit of a much larger and important solution.
I am currently reading a book by Richard Feynman, detailing his memoires, about the time that he was at Los Alamos, engineering the first atomic weapons. He tells of warehouses, full of student physicists and technicians, punching cards into mechanical counting machines and iterating the answers many times over. It used to take them about 4 months to tackle any particular problem, concerning the energy release of different atomic fission models. We have come such a long way.
On reading this tale, it did make me stop and think; that even though I was struggling for 3hrs, to plot a graph and do some calculations, with mathcad; doing it with just a pencil and paper, would have taken a very long time, indeed.
Friday, 11 March 2011
An O.U Maths Epiphany
I had a small epiphany today when trying to tackle some extremely dull logistical model calculations, for my latest piece of coursework (TMA02), for the Open University Course MST121.
Just for the benefit of those who haven't had the soul-destroying pleasure of encountering logistical models (my personal opinion, but others may not agree); it is, basically, the use of sequences to model things. I don't think the maths itself is dull, but in fact, it is the examples that always seem to be used in text books, that send me to sleep. The example questions will normally ask you to work out how many geese are on some island at year (n), or how many ladybirds there are in a bush based on a starting population and a non-linear growth rate! Yawn. It's not as exciting as working out the thrust of a rocket or how many slits a particle goes through, at the same time!
Anyway, my epiphany came at 10:30hrs this morning, in my home office, whilst working on another boring geese population problem. Now, because of my dislike for modelling with sequences, I have to admit, that I just scan read the OU material for this section. It seemed straight-forward enough: count geese, put numbers into equation, count some more geese, ad infinitum... However, when I started the TMA question this morning, I was stumped. I couldn't do it. I scanned the study material again, and again and again. I just couldn't work out, not only the answer, but which equations I should even be using.
I sat slumped in my chair, poured a pot of hot coffee, and subjected my ears to 90db of 1980's electronic pop music. As I was drifting off into thining about what I was going to cook for dinner this evening, the answer suddenly struck me.
I switched off the Eurythmics track, halfway through, and grabbed my pencil. 20mins later, I had solved the problem, by an amalgamation of all of the previous pages of examples, combined with some fairly hefty algebra. I checked my workings, and they seemed good.
However, I had a problem. I couldn't help but feel uneasy about the whole event. Firstly, the O.U have a habit of giving you very formulaic questions, in all of their TMA's. Some of them are so similar to the course material, that you could just semi-copy a previous worked answer, just substituting your own values, into the equations. I don't like doing that, so I try and work it out and then check back to ensure completeness.
So, why was I uneasy? Well, I had been properly stumped by an ostensibly simple population model. This was a challenge to my world view: 'was my journey to theoretical physicist ending here?' 'Were wild birds going to dash my hopes of scholarly excellence?' 'was I destined for a poultry existence' (sorry, couldn't resist the pun). It shouldn't have stumped me, as this is, after all, a year 1 University course. But it had. So I started to dissect what had gone wrong.
That is when I finally had my epiphany! Whilst finishing my cup of Brazil's finest hot beverage, I began flicking through the rest of the study text.
And there it was, on a page towards the back; a page that I hadn't read properly; a page that made me frown, then grin, and then burst out laughing.
The page contained, a formulaic version of my TMA question! It looked exactly the same as my own working's out, that I had completed, independently of the study text. I had worked this very complicated set of equations out, all by my self. Without any guiding, worked example; I had created the model, worked out the equations and done the maths, all in my head, independently from the course material!
This made me realise, two serious points and also one, not so serious point:
1. I have begun to integrate all of my studies to date, into a semi-usable, intuitive method of maths problem solving.
2. I nearly gave up trying and was intending to ring my tutor for advice. I didn't give up and I was successful by not doing so.
3. I should have read the ******* text book properly!
To clarify the epiphany in its entirety: Today, I have realised that I can potentially learn, struggle and overcome, on my own, without assisting intervention. I think this may be one of the best life lessons, that I have learn't so far. Time will tell.
Just for the benefit of those who haven't had the soul-destroying pleasure of encountering logistical models (my personal opinion, but others may not agree); it is, basically, the use of sequences to model things. I don't think the maths itself is dull, but in fact, it is the examples that always seem to be used in text books, that send me to sleep. The example questions will normally ask you to work out how many geese are on some island at year (n), or how many ladybirds there are in a bush based on a starting population and a non-linear growth rate! Yawn. It's not as exciting as working out the thrust of a rocket or how many slits a particle goes through, at the same time!
Anyway, my epiphany came at 10:30hrs this morning, in my home office, whilst working on another boring geese population problem. Now, because of my dislike for modelling with sequences, I have to admit, that I just scan read the OU material for this section. It seemed straight-forward enough: count geese, put numbers into equation, count some more geese, ad infinitum... However, when I started the TMA question this morning, I was stumped. I couldn't do it. I scanned the study material again, and again and again. I just couldn't work out, not only the answer, but which equations I should even be using.
I sat slumped in my chair, poured a pot of hot coffee, and subjected my ears to 90db of 1980's electronic pop music. As I was drifting off into thining about what I was going to cook for dinner this evening, the answer suddenly struck me.
I switched off the Eurythmics track, halfway through, and grabbed my pencil. 20mins later, I had solved the problem, by an amalgamation of all of the previous pages of examples, combined with some fairly hefty algebra. I checked my workings, and they seemed good.
However, I had a problem. I couldn't help but feel uneasy about the whole event. Firstly, the O.U have a habit of giving you very formulaic questions, in all of their TMA's. Some of them are so similar to the course material, that you could just semi-copy a previous worked answer, just substituting your own values, into the equations. I don't like doing that, so I try and work it out and then check back to ensure completeness.
So, why was I uneasy? Well, I had been properly stumped by an ostensibly simple population model. This was a challenge to my world view: 'was my journey to theoretical physicist ending here?' 'Were wild birds going to dash my hopes of scholarly excellence?' 'was I destined for a poultry existence' (sorry, couldn't resist the pun). It shouldn't have stumped me, as this is, after all, a year 1 University course. But it had. So I started to dissect what had gone wrong.
That is when I finally had my epiphany! Whilst finishing my cup of Brazil's finest hot beverage, I began flicking through the rest of the study text.
And there it was, on a page towards the back; a page that I hadn't read properly; a page that made me frown, then grin, and then burst out laughing.
The page contained, a formulaic version of my TMA question! It looked exactly the same as my own working's out, that I had completed, independently of the study text. I had worked this very complicated set of equations out, all by my self. Without any guiding, worked example; I had created the model, worked out the equations and done the maths, all in my head, independently from the course material!
This made me realise, two serious points and also one, not so serious point:
1. I have begun to integrate all of my studies to date, into a semi-usable, intuitive method of maths problem solving.
2. I nearly gave up trying and was intending to ring my tutor for advice. I didn't give up and I was successful by not doing so.
3. I should have read the ******* text book properly!
To clarify the epiphany in its entirety: Today, I have realised that I can potentially learn, struggle and overcome, on my own, without assisting intervention. I think this may be one of the best life lessons, that I have learn't so far. Time will tell.
Thursday, 10 March 2011
Physics and Maths, Studied this Week.
This week has been tough. My cold is now a fully blown chest infection and it has been difficult to concentrate. However, it has been a useful testing ground, to see if I can maintain quality work production, even when struggling with illness.
As part of the learning process, as I progress via distance learning; I am always looking for ways to test my resolve. I need to know, that when I study at much harder levels or at much larger volumes; that I can cope if life throws an illness or personal problem, at me.
When ill, I actually try to push myself even harder, to test the edges of what is possible, what the limits are and what is my maximum capacity for work. (no pun intended, by using the words, 'limits' and 'maximum'!)
So, here is this week's completed study:
Open University MST121
Modelling with sequences
Constructing a model
Sums
The Exponential Model
The Logistical Model
Sequences and Limits
Matrices Intro videos
Addition and multiplication of Matrices
Vectors (geometric form)
Vectors (component form)
Completion and submission of TMA1 Part 2
The Teaching Company lectures. Calculus
Extrema on an Interval
Increasing and Decreasing Functions
Concavity and Points of Inflection
The Teaching Company lectures, Cosmology
The Cosmic Microwave Background
S196 O.U Course, Planets
Venus
Total study time: 16hrs
--------------------------------
I haven't completed any other outside work this week, due to my illness and lots of sleeping in between work and study. However, I have done some internet surfing, continuing to refine my possible future study modules and courses, in my attempt to become a Theoretical Physicist.
I have been looking, in some depth, at the research degrees offered by the O.U. In particular, I notice that they run Ph.D's in mathematical physics, such as quantum theory. Sounds right up my street, so I'll keep researching the options and will update my plans, as I elucidate them, in my own mind!
As part of the learning process, as I progress via distance learning; I am always looking for ways to test my resolve. I need to know, that when I study at much harder levels or at much larger volumes; that I can cope if life throws an illness or personal problem, at me.
When ill, I actually try to push myself even harder, to test the edges of what is possible, what the limits are and what is my maximum capacity for work. (no pun intended, by using the words, 'limits' and 'maximum'!)
So, here is this week's completed study:
Open University MST121
Modelling with sequences
Constructing a model
Sums
The Exponential Model
The Logistical Model
Sequences and Limits
Matrices Intro videos
Addition and multiplication of Matrices
Vectors (geometric form)
Vectors (component form)
Completion and submission of TMA1 Part 2
The Teaching Company lectures. Calculus
Extrema on an Interval
Increasing and Decreasing Functions
Concavity and Points of Inflection
The Teaching Company lectures, Cosmology
The Cosmic Microwave Background
S196 O.U Course, Planets
Venus
Total study time: 16hrs
--------------------------------
I haven't completed any other outside work this week, due to my illness and lots of sleeping in between work and study. However, I have done some internet surfing, continuing to refine my possible future study modules and courses, in my attempt to become a Theoretical Physicist.
I have been looking, in some depth, at the research degrees offered by the O.U. In particular, I notice that they run Ph.D's in mathematical physics, such as quantum theory. Sounds right up my street, so I'll keep researching the options and will update my plans, as I elucidate them, in my own mind!
Wednesday, 9 March 2011
The Trouble with Mathcad...
Mathcad is a piece of software that I am currently using, with the Open University. It is essentially a computer programme that does algebraic manipulation, graphs, matrices, calculus and lots of other useful stuff. As part of course MST121 (Using Mathematics), and also many other O.U courses at level 2; Mathcad, is an integral part of the course and you have to provide printouts, for some of the marked TMA (coursework) questions.
Now, I am not technophobic, by any means! However, I just cannot get my head around Mathcad. It is very counter-intuitive compared to other digital interfaces, that we now use. Most of us are used to windows, Word, Excel or the Apple equivalents. Many people have apple I-phones or Blackberry smart-phones, myself included; and what all of these trappings of modern life, have in common, is that they all have an intuitive, easy to use, functional format, that even my 5yr old, appears to have no difficulty in working out.
So, why oh why, is Mathcad so difficult to use? It is certainly not intuitive. For example, I sat down last night, and tried to plot a simple graph, with a point shown on that graph and also a line across the Y axes. But this took me nearly 3hrs. I had to muddle through some ropey instructions, without much clue, other than trial and error, helping me along the way. Even the end result, was utterly uninspiring. My feeble point, plotted on the screen, hardly seemed worth all of the effort! However, it was a requirement for my current TMA, so it needed to be done.
It's as if the software is from a bygones age. The OU were nostalgically famed, (in the U.K), for their 1970's late night BBC films, featuring bearded professors, adorned with corduroy, kipper ties and flares. I almost feel that I should be wearing those items, when tackling Mathcad. Although, I wouldn't worry too much about growing a beard, as it seems to take care of itself, as you spend countless hours fumbling around with the software!
Mathcad feels years behind, in producing a user friendly, enjoyable, intuitive experience.
I know, from looking at other student comments, in the Open University forums; that it is not just me, having difficulties with the software. It does surprise me, that the O.U haven't developed their own after all these years. With all of those world-class computer science and maths graduates floating around, it would make a nice project for someone, or even present a good business opportunity.
All in all, the use of Mathcad is difficult. I'm not sure it is going to make maths easier, as I progress through the next 2yrs.
Now, I am not technophobic, by any means! However, I just cannot get my head around Mathcad. It is very counter-intuitive compared to other digital interfaces, that we now use. Most of us are used to windows, Word, Excel or the Apple equivalents. Many people have apple I-phones or Blackberry smart-phones, myself included; and what all of these trappings of modern life, have in common, is that they all have an intuitive, easy to use, functional format, that even my 5yr old, appears to have no difficulty in working out.
So, why oh why, is Mathcad so difficult to use? It is certainly not intuitive. For example, I sat down last night, and tried to plot a simple graph, with a point shown on that graph and also a line across the Y axes. But this took me nearly 3hrs. I had to muddle through some ropey instructions, without much clue, other than trial and error, helping me along the way. Even the end result, was utterly uninspiring. My feeble point, plotted on the screen, hardly seemed worth all of the effort! However, it was a requirement for my current TMA, so it needed to be done.
It's as if the software is from a bygones age. The OU were nostalgically famed, (in the U.K), for their 1970's late night BBC films, featuring bearded professors, adorned with corduroy, kipper ties and flares. I almost feel that I should be wearing those items, when tackling Mathcad. Although, I wouldn't worry too much about growing a beard, as it seems to take care of itself, as you spend countless hours fumbling around with the software!
Mathcad feels years behind, in producing a user friendly, enjoyable, intuitive experience.
I know, from looking at other student comments, in the Open University forums; that it is not just me, having difficulties with the software. It does surprise me, that the O.U haven't developed their own after all these years. With all of those world-class computer science and maths graduates floating around, it would make a nice project for someone, or even present a good business opportunity.
All in all, the use of Mathcad is difficult. I'm not sure it is going to make maths easier, as I progress through the next 2yrs.
Sunday, 6 March 2011
Maths with the OU
I've noticed, over the last few years of checking, that the Open University maths course, have been reducing in number. I remember about 4yrs ago, that they offered an undergraduate MMath degree, which consisted of 4yrs worth of full time work, with some hefty 3rd year courses.
Now, having studied the current maths courses, particularly at level 3, I notice that options are limited to 3 or 4 either pure or applied courses, and that some of the courses that are offered, are actually science courses in disguise e.g. Wave diffusion...
I have now found out, that some of the 3rd year options such as Complex Analysis, are only running once every two years.
What are the implications for a distance learner such as my self? Well, it's going to be a fine balancing act to ensure that I don't have a year of study that is light on content and. by definition, lengthen the time that it takes to do my degrees.
Looking at one of my possible options of post graduate study, on my way to becoming a theoretical physicist, there is the taught masters in maths, that is offered by the OU. For some strange reason, they seem to have made it even harder to complete it in a short period of time. I personally find that I prefer to cram in lots of study, into perhaps a few years, rather than stretching study out, over 5yrs+. The rules governing the masters course, state that, out of the 180 credits required to complete it, only 30 of those can be taken in year 1, as opposed to the norm which would be 60 per year. The first year course is calculus / advanced calc, so I don't see what is so special about this presentation, that would make studying more difficult.
I am going to seek some answers from the OU, about all of these issues i.e, reducing maths course numbers, excessively long time to study the MSc. Once I have a response, I'll post the reply.
Now, having studied the current maths courses, particularly at level 3, I notice that options are limited to 3 or 4 either pure or applied courses, and that some of the courses that are offered, are actually science courses in disguise e.g. Wave diffusion...
I have now found out, that some of the 3rd year options such as Complex Analysis, are only running once every two years.
What are the implications for a distance learner such as my self? Well, it's going to be a fine balancing act to ensure that I don't have a year of study that is light on content and. by definition, lengthen the time that it takes to do my degrees.
Looking at one of my possible options of post graduate study, on my way to becoming a theoretical physicist, there is the taught masters in maths, that is offered by the OU. For some strange reason, they seem to have made it even harder to complete it in a short period of time. I personally find that I prefer to cram in lots of study, into perhaps a few years, rather than stretching study out, over 5yrs+. The rules governing the masters course, state that, out of the 180 credits required to complete it, only 30 of those can be taken in year 1, as opposed to the norm which would be 60 per year. The first year course is calculus / advanced calc, so I don't see what is so special about this presentation, that would make studying more difficult.
I am going to seek some answers from the OU, about all of these issues i.e, reducing maths course numbers, excessively long time to study the MSc. Once I have a response, I'll post the reply.
Thursday, 3 March 2011
Physics and Maths, Studied this Week.
Okay, another week done and I still can't shake this virus / cold!
Anyway, I have concentrated, this week, on doing a lot of practice questions to consolidate some basic maths skills. I often find, that by keeping the basic tools sharpened, such as algebraic manipulation, factorisation, handling logs, exponentials, roots, complex numbers and even practising my times tables; it takes a lot of strain out of dealing with complex pencil and paper exercises, that require lots of small mathematical steps, to achieve an answer.
An example of this, is the Open University TMA 1 part 2 questions for course MST121, Using Mathematics. I have been writing my draft presentation of this marked piece of coursework. The questions are based on defining a circle, with reference to 3 fixed points and also some manipulation of quadratics in working out where a circle and line meet. There are lots of little steps (about 10), that must be done in order to solve the equations and I find that none of the steps, if practiced, are very difficult. The skill actually comes, in working out what the question is asking you to do.
I do find this with maths questions, that they seem to sometimes throw at you, an equation that requires some moving about and re-arranging, before you can identify what it is e.g. quadratic / equation of a circle / inverse function etc. When you get one of these odd looking equations, the ability to quickly 'play around' with the expression, using pre-calculus skills, is extremely important.
I actually think that most people perhaps struggle with the basics and this leads them to think that they can't cope with higher maths courses. Learning your times tables (up to 20 times table), allows you to glance at an expression and instantly recognise perfect squares, factors etc. Learning how to manipulate fractions, allows you to instantly re-arrange numerical equations, to make them easier to work with. There are many ways to make things easier for yourself, and I suspect, that practising the basics, is the key!
This weeks study:
Open University MST121
Functions!
Manipulation of functions
8hrs of self-made practice worksheets - Complex number manipulation / fractions / quadratics / factorisation / roots and exponentials / times tables.
Draft completion of question 1, TMA1 Part 2.
The Teaching Company Lectures, Calculus
Implicit differentiation and related rates
The Teaching Company Lectures, Cosmology
Cosmic acceleration
Audio book
The Modern Scholar: Astronomy I (Unabridged) (I'll post about this awesome series, later)
Entanglement: Amir D. Acze (quantum physics)
Total study time this week = 17hrs
I forgot to put on the total time for last week, which was 13hrs.
I am discovering more free study material, all the time, so I'll cover some of it, later. I also have a theory about successful study, using different sources, which I'll expand on in another post.
Anyway, I have concentrated, this week, on doing a lot of practice questions to consolidate some basic maths skills. I often find, that by keeping the basic tools sharpened, such as algebraic manipulation, factorisation, handling logs, exponentials, roots, complex numbers and even practising my times tables; it takes a lot of strain out of dealing with complex pencil and paper exercises, that require lots of small mathematical steps, to achieve an answer.
An example of this, is the Open University TMA 1 part 2 questions for course MST121, Using Mathematics. I have been writing my draft presentation of this marked piece of coursework. The questions are based on defining a circle, with reference to 3 fixed points and also some manipulation of quadratics in working out where a circle and line meet. There are lots of little steps (about 10), that must be done in order to solve the equations and I find that none of the steps, if practiced, are very difficult. The skill actually comes, in working out what the question is asking you to do.
I do find this with maths questions, that they seem to sometimes throw at you, an equation that requires some moving about and re-arranging, before you can identify what it is e.g. quadratic / equation of a circle / inverse function etc. When you get one of these odd looking equations, the ability to quickly 'play around' with the expression, using pre-calculus skills, is extremely important.
I actually think that most people perhaps struggle with the basics and this leads them to think that they can't cope with higher maths courses. Learning your times tables (up to 20 times table), allows you to glance at an expression and instantly recognise perfect squares, factors etc. Learning how to manipulate fractions, allows you to instantly re-arrange numerical equations, to make them easier to work with. There are many ways to make things easier for yourself, and I suspect, that practising the basics, is the key!
This weeks study:
Open University MST121
Functions!
Manipulation of functions
8hrs of self-made practice worksheets - Complex number manipulation / fractions / quadratics / factorisation / roots and exponentials / times tables.
Draft completion of question 1, TMA1 Part 2.
The Teaching Company Lectures, Calculus
Implicit differentiation and related rates
The Teaching Company Lectures, Cosmology
Cosmic acceleration
Audio book
The Modern Scholar: Astronomy I (Unabridged) (I'll post about this awesome series, later)
Entanglement: Amir D. Acze (quantum physics)
Total study time this week = 17hrs
I forgot to put on the total time for last week, which was 13hrs.
I am discovering more free study material, all the time, so I'll cover some of it, later. I also have a theory about successful study, using different sources, which I'll expand on in another post.
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