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!
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