This month, I have been taking a real interest in infinity and its effects on maths. It started out with me pondering the idea of the area approaching a limit, and the fact that you can have a finite area, split into infinite parts, represented by an infinite amount of real numbers.
From this, I picked up a copy of Godel's Proof, a book that tries to describe Godel's incompleteness theorem, in about 200 pages. And, I then discovered that Godel, among others, proposed the fact that if you identified sets of numbers, that were mind bogglingly large, you could just build new levels of infinity, on top of underlying numbers and then you could use these sets, to prove some of the maths problems that exist underneath.
It was then, that I stumbled on an article in the New Scientist periodical, this week. The piece was boldly entitled 'Ultimate Logic - so powerful it could wipe out mathematics as we know it.'
In a nutshell, the piece describes how a mathematician (Hugh Woodin), believes he has solved the continuum hypothesis (Is there an infinite set that sits between the countable infinity, such as counting the integers from 1 towards infinity and the 'continuous' infinity, such as when you split a sphere into infinite sections, when the whole is finite.)
The difference with his claim, is that he states that he has solved this maths problem, by using a new type of logic language and structure called 'ultimate L'. This method would allow extra steps of sets to be bolted on to the top of infinite sets, filling in gaps below sufficiently, to allow any lower mathematical problem to be solved. He makes the bold statement, that this new theory, allows him to provide 'a definitive account of the spectrum of subsets of real numbers and thus, proves Cantor's continuum hypothesis, as true; ruling out anything between the countable infinity and the continuum'!
Woodin, even claims, that this may overturn major parts of Godels incompleteness theorem and be a tool that actually, artificially, allows us to root out unsolvability in number theory. He doesn't go as far as saying that Godel's theories would be dead - but that you could 'chase it as far as you pleased up the staircase into the infinite attic of mathematics'.
This idea seems similar in theme, to the idea of calculus and limits. In that, yes, you might never be able to say what is actually happening at the limit its self, but you can get so close to it, that your results have the same effect as if you were actually at the limit.
This all reminded me of the amusing anecdote relating to Zeno's paradox. It is said, that when it was once explained to a student, that if you were trying to reach a girl on the other side of a room, that you would never actually get there, if you travel half of the previous distance travelled in discrete steps. The student's retort was thus;
'Well, I might not ever reach the girl, but I could get plenty close enough for all 'practical' purposes! It seems, that perhaps Woodin is saying; 'why try and reach infinity? when you can just get so close to it, that your results are almost the same, as if you were actually there?' He seems to believe, that he has created a new language for mathematicians, to solve these issue.
Could it be, that if we do end up with a radical departure from existing mathematical logic and ideas, to prove almost everything; that we will end up with two tiers of mathematics, such as happened in physics with 'classical' and 'quantum' theories?
Sunday, 31 July 2011
Wednesday, 27 July 2011
Life's ambitions.
Iv'e been a bit sick this week, hence the lack of posts. Anyway, it hasn't stopped me from ploughing ahead, with my MST121 final coursework.
I have now completed all of the readings of new material from the course; and I have now completed and submitted, the CMA covering the Statistics chapters. It is now all about finalising TMA04 and the other CMA that covers the whole course material.
Also, I had a bit of a wobble this week, as I found myself struggling to bring forth, from my memory, the rules and identities for integration. Specifically separating the variables, and differential equations involving double angle formulas and trig identities.
It led me to ponder the question, as to whether I should be economical with what I am covering or learning, i.e. learn what I need to, just to pass the exams and TMA's, without worrying about trying to commit the entire course to memory. Or, alternatively, whether I should be fastidiously digesting all examples, all proofs and all learning points, to the point of mastery.
I guess it all comes down to what the end goal is. My end goal, is not just to pick up qualifications, but then it got me thinking; what is my actual goal? It is not as easy to identify, as one would imagine.
I decided to examine the steps carefully, and try to extract my reason d'etre, in the process.
It went something like this:
A. I Want to score maximum marks in all of my exams and TMA's.
Q. But why?
A. Because I want to be sure that I fully understand all of the concepts and material.
Q. But why? It's not required, to pass the course and gain a good (2.1) degree.
A. Because I want an excellent degree( 1st)
Q. Yes, but Why?
A. Because I want to know that I am intellectually capable enough, to study the subject at postgraduate level.
Q. But Why?
A. Because I want to eventually study a PhD.
Q. But Why? It's 10yrs of training, will cost a fortune to fund and the remuneration is not fantastic.
A. Because I want to produce something original, that no one else has ever produced. I also want to spend my twilight years, pottering about doing maths and physics research, surrounded by learned people; not retire, playing Golf and Sudoku.
Q. Ah, now we are getting somewhere! - So it is about creating unique legacy and also being part of a community of like minded people?
A. Yes - That's exactly it.
Q. So, most people feed that need to create something unique and to leave a legacy, by having a few kids - but you want to spend tens of thousands of pounds and thousands of hours, doing maths and physics that no ordinary person could give two hoots about?
It was at this point, that I told my inner voice to shut up, and I went down the pub, for a pint and a curry.
I have now completed all of the readings of new material from the course; and I have now completed and submitted, the CMA covering the Statistics chapters. It is now all about finalising TMA04 and the other CMA that covers the whole course material.
Also, I had a bit of a wobble this week, as I found myself struggling to bring forth, from my memory, the rules and identities for integration. Specifically separating the variables, and differential equations involving double angle formulas and trig identities.
It led me to ponder the question, as to whether I should be economical with what I am covering or learning, i.e. learn what I need to, just to pass the exams and TMA's, without worrying about trying to commit the entire course to memory. Or, alternatively, whether I should be fastidiously digesting all examples, all proofs and all learning points, to the point of mastery.
I guess it all comes down to what the end goal is. My end goal, is not just to pick up qualifications, but then it got me thinking; what is my actual goal? It is not as easy to identify, as one would imagine.
I decided to examine the steps carefully, and try to extract my reason d'etre, in the process.
It went something like this:
A. I Want to score maximum marks in all of my exams and TMA's.
Q. But why?
A. Because I want to be sure that I fully understand all of the concepts and material.
Q. But why? It's not required, to pass the course and gain a good (2.1) degree.
A. Because I want an excellent degree( 1st)
Q. Yes, but Why?
A. Because I want to know that I am intellectually capable enough, to study the subject at postgraduate level.
Q. But Why?
A. Because I want to eventually study a PhD.
Q. But Why? It's 10yrs of training, will cost a fortune to fund and the remuneration is not fantastic.
A. Because I want to produce something original, that no one else has ever produced. I also want to spend my twilight years, pottering about doing maths and physics research, surrounded by learned people; not retire, playing Golf and Sudoku.
Q. Ah, now we are getting somewhere! - So it is about creating unique legacy and also being part of a community of like minded people?
A. Yes - That's exactly it.
Q. So, most people feed that need to create something unique and to leave a legacy, by having a few kids - but you want to spend tens of thousands of pounds and thousands of hours, doing maths and physics that no ordinary person could give two hoots about?
It was at this point, that I told my inner voice to shut up, and I went down the pub, for a pint and a curry.
Friday, 22 July 2011
Physics and Maths, Studied this Week.
Okay, I have 3 pieces of work left for MST121, including two computer marked assignments. The first is CMA41, a 20+ multiple choice paper on Statistics, yawn. I have half completed this, but just need to read through MST121 Chapter D3 and D4, before I can finalise my responses this week.
The other pieces are papers on the whole MST121 course, covering all of the calculus, matrices, vectors, series etc.
I have also engaged in some fun diversions this week, including buying a Rubik's cube, which I plan to solve this month and then I will try and get my times down over the summer, to < 5min. I have also purchased a group theory book, that is based around using the theories, to solve the cube. It seems like a bit of a hoot, although a bit contrived in places. The book is called Adventures in Group Theory.
I have also now finalised my next year's Open University, course choice. I have decided to study, (drum role).....
M208 Pure Maths
This is instead of doing MST209, first. A fellow O.U student and blogger, Chris, has helped me with this next decision and was kind enough to send me some samples of the M208 course, to assist.
I have also done some in depth analysis of my skills, needs and plans, for the next 3yrs, and realised the following things:
1. I seem to find it much easier to understand maths applications, if I, know / master, the abstract maths theories behind those applications.
2. I know that I am wired up a little differently to most normal people (what ever normal is? / Is this part of my Asperger's or Dyslexia? / who knows?). As such, I have discovered this week, that I can rotate / translate and manipulate objects, in my head, whilst reading through the stuff on Group Theory. I don't know if many people can do this, but it seems to make that subject quite straight forward, for me. Thus, it is probably a nice quick win intro to honours level maths.
3. Doing applied calculus, without first doing the analysis behind the methods, is personally difficult for me. I just can't grasp the rules all that well, without de-constructing the nuts and bolts behind integration / differentiation etc.
4. Finally, I am almost certainly going to complete some of the O.U Maths MSc modules, as part of my studies; which, at the very least, means that I need to study M208 Pure Maths, M337 Complex Analysis and M303 Further Pure Maths. I can then fit in some applied stuff, after these modules.
I did think about possibly not doing M303 and replacing it with the final presentations of Number theory and Logic, with Groups and Geometry. Thus, by doing so, being able to work on the proofs of Godel's Incompleteness theorem. However, I am just not sure that this Brucie bonus, justifies the extra 3hr exam that would occur, if I replaced M303. Also, is such self indulgence in Godel, distracting me from making progress towards PhD? Never say never, but 303 looks favourite.
Anyway, this week's study has been:
Total 20hrs.
MST121
Chapter D2 Modelling Variation
CMA41 questions 1 - 16
Recap on Trigonometry identities
Other Reading
The Calculus Lifesaver, Banner Functions, Graphs, Lines, Review of Trig.
Feynman, Lectures Vol 1. Chapter 8. Motion.
Adventures in Group Theory Chapters 1-4.
M208 Intro part 1. Group Theory part 1.
S197 How the Universe Works
Finished and sent off EMA. Course now complete.
Last night, I watched, 'A Beautiful Mind', the story of Schizophrenic Mathematician John Nash. It was really sad!
Next week, Starting my EMA for MST121.
The other pieces are papers on the whole MST121 course, covering all of the calculus, matrices, vectors, series etc.
I have also engaged in some fun diversions this week, including buying a Rubik's cube, which I plan to solve this month and then I will try and get my times down over the summer, to < 5min. I have also purchased a group theory book, that is based around using the theories, to solve the cube. It seems like a bit of a hoot, although a bit contrived in places. The book is called Adventures in Group Theory.
I have also now finalised my next year's Open University, course choice. I have decided to study, (drum role).....
M208 Pure Maths
This is instead of doing MST209, first. A fellow O.U student and blogger, Chris, has helped me with this next decision and was kind enough to send me some samples of the M208 course, to assist.
I have also done some in depth analysis of my skills, needs and plans, for the next 3yrs, and realised the following things:
1. I seem to find it much easier to understand maths applications, if I, know / master, the abstract maths theories behind those applications.
2. I know that I am wired up a little differently to most normal people (what ever normal is? / Is this part of my Asperger's or Dyslexia? / who knows?). As such, I have discovered this week, that I can rotate / translate and manipulate objects, in my head, whilst reading through the stuff on Group Theory. I don't know if many people can do this, but it seems to make that subject quite straight forward, for me. Thus, it is probably a nice quick win intro to honours level maths.
3. Doing applied calculus, without first doing the analysis behind the methods, is personally difficult for me. I just can't grasp the rules all that well, without de-constructing the nuts and bolts behind integration / differentiation etc.
4. Finally, I am almost certainly going to complete some of the O.U Maths MSc modules, as part of my studies; which, at the very least, means that I need to study M208 Pure Maths, M337 Complex Analysis and M303 Further Pure Maths. I can then fit in some applied stuff, after these modules.
I did think about possibly not doing M303 and replacing it with the final presentations of Number theory and Logic, with Groups and Geometry. Thus, by doing so, being able to work on the proofs of Godel's Incompleteness theorem. However, I am just not sure that this Brucie bonus, justifies the extra 3hr exam that would occur, if I replaced M303. Also, is such self indulgence in Godel, distracting me from making progress towards PhD? Never say never, but 303 looks favourite.
Anyway, this week's study has been:
Total 20hrs.
MST121
Chapter D2 Modelling Variation
CMA41 questions 1 - 16
Recap on Trigonometry identities
Other Reading
The Calculus Lifesaver, Banner Functions, Graphs, Lines, Review of Trig.
Feynman, Lectures Vol 1. Chapter 8. Motion.
Adventures in Group Theory Chapters 1-4.
M208 Intro part 1. Group Theory part 1.
S197 How the Universe Works
Finished and sent off EMA. Course now complete.
Last night, I watched, 'A Beautiful Mind', the story of Schizophrenic Mathematician John Nash. It was really sad!
Next week, Starting my EMA for MST121.
Monday, 18 July 2011
Exciting Mathematics
Earlier on tonight, I had a quick chat on the phone, with my tutor. I wanted some advice on future course choices, as my tutor has extensive first hand experience of studying O.U maths and science courses, over the last few years, whilst also studying for a PhD.
As we were chatting, something she mentioned, got me thinking deeply about distance learning and the absorption of subjects that are as intellectually demanding as honours level mathematics. My tutor used an adjective to describe maths home study, that I have never heard used in that context before. The word that she used, was 'Exciting'.
I didn't pay much attention to such an unusual use of this word, during our conversation; but once I sat down for dinner, I pondered its use.
Exciting?..Yes...I agree!
Sitting on my own at night, with my books, my pencil and my exercise books; the thing that keeps me coming back for more, is that every time I learn a new piece of knowledge (especially an intellectually demanding one), I am excited by this.
I love learning new stuff. I guess that it seems a little counter-intuitive, though, to call it exciting. We all know that studying mathematics, is probably last on the list of classic past-times, that could be classed as exciting. Bungee jumping, yes; roller-blading, yes; Severn of Nine's Star-Trek uniform, yes; but studying?... Well, yes.
And besides, from that excitement also comes the risk of addiction, which any long-term distance learner will appreciate.
Should there be a public health warning on the side of each O.U textbook cover, such as: 'Warning, regular use may cause dependency.'? Maybe.
However, using a critical eye, I know that this 'excitement', can be short lived, particularly if the work is too easy or far too difficult. If the work is too easy, then this can be remedied by supplementary exercises and such like; but too difficult? Well, I guess that all of my outside reading, away from core O.U courses, has all been done as a - sort of - cushion. A buffer to ease any jolts of future difficulty, that may try and make the excitement, a distant memory.
Exciting, we like.
Brain melting, like a Pan-Galactic-Gargleblaster, we don't.
As we were chatting, something she mentioned, got me thinking deeply about distance learning and the absorption of subjects that are as intellectually demanding as honours level mathematics. My tutor used an adjective to describe maths home study, that I have never heard used in that context before. The word that she used, was 'Exciting'.
I didn't pay much attention to such an unusual use of this word, during our conversation; but once I sat down for dinner, I pondered its use.
Exciting?..Yes...I agree!
Sitting on my own at night, with my books, my pencil and my exercise books; the thing that keeps me coming back for more, is that every time I learn a new piece of knowledge (especially an intellectually demanding one), I am excited by this.
I love learning new stuff. I guess that it seems a little counter-intuitive, though, to call it exciting. We all know that studying mathematics, is probably last on the list of classic past-times, that could be classed as exciting. Bungee jumping, yes; roller-blading, yes; Severn of Nine's Star-Trek uniform, yes; but studying?... Well, yes.
And besides, from that excitement also comes the risk of addiction, which any long-term distance learner will appreciate.
Should there be a public health warning on the side of each O.U textbook cover, such as: 'Warning, regular use may cause dependency.'? Maybe.
However, using a critical eye, I know that this 'excitement', can be short lived, particularly if the work is too easy or far too difficult. If the work is too easy, then this can be remedied by supplementary exercises and such like; but too difficult? Well, I guess that all of my outside reading, away from core O.U courses, has all been done as a - sort of - cushion. A buffer to ease any jolts of future difficulty, that may try and make the excitement, a distant memory.
Exciting, we like.
Brain melting, like a Pan-Galactic-Gargleblaster, we don't.
S197 Finished! Cert H.E studies complete
At last, I have now completed and submitted my EMA for S197 How the Universe Works. It was an extremely enjoyable course and one, from which, I have learnt a lot.
The course really does give a whistle-stop tour of the Universe from its first few moments of Planck time, through to postulating the future of cosmology and the M-theory that is currently being worked on.
Considering that this was a level 1 course, It didn't dumb down the concepts or the detail needed on topics such as primordial nucleosynthesis or cosmic expansion. Of course, these topics were covered qualitatively, rather than with any mathematical rigour; but none the less, it was a very enjoyable diversion from my calculus studies.
A nice added bonus is that, if passed, it will complete another university certificate for me, on the very long journey towards a PhD. Although it will be superseded by a Dip H.E and a B.A, at the end of next year, it is still a nice one to put in the back pocket and to fill the baron, white space on a C.V.
The total of Cert H.E modules included for this qualification, are (nb: not full module titles):
A103 Humanities
L192 French
S194 Astronomy
S196 Planets
S197 Cosmology / Astronomy
That is 120 points at year 1 level
I have purposely aimed for a nice balance of the liberal arts rather than just a one sided science qualification at level 1. I am hoping that it looks better to any future employer and shows that I have a more rounded education.
I know, upon speaking earlier this year, to the course director of the BSc Astronomy at Lancashire; that she is one of many academics, who actively encourage students to make good use of any free choice modules in a degree profile, by exploring other non-science subjects. This is in the belief that it produces a more well-rounded student and person. I would certainly agree with that hypothesis.
(It has also helped me shout out more correct answers when watching University Challenge. My wife is mildly impressed)
Onwards and upwards. It is now full-on MST121 until September, with a little sprinkling of self generated maths study, in between.
The course really does give a whistle-stop tour of the Universe from its first few moments of Planck time, through to postulating the future of cosmology and the M-theory that is currently being worked on.
Considering that this was a level 1 course, It didn't dumb down the concepts or the detail needed on topics such as primordial nucleosynthesis or cosmic expansion. Of course, these topics were covered qualitatively, rather than with any mathematical rigour; but none the less, it was a very enjoyable diversion from my calculus studies.
A nice added bonus is that, if passed, it will complete another university certificate for me, on the very long journey towards a PhD. Although it will be superseded by a Dip H.E and a B.A, at the end of next year, it is still a nice one to put in the back pocket and to fill the baron, white space on a C.V.
The total of Cert H.E modules included for this qualification, are (nb: not full module titles):
A103 Humanities
L192 French
S194 Astronomy
S196 Planets
S197 Cosmology / Astronomy
That is 120 points at year 1 level
I have purposely aimed for a nice balance of the liberal arts rather than just a one sided science qualification at level 1. I am hoping that it looks better to any future employer and shows that I have a more rounded education.
I know, upon speaking earlier this year, to the course director of the BSc Astronomy at Lancashire; that she is one of many academics, who actively encourage students to make good use of any free choice modules in a degree profile, by exploring other non-science subjects. This is in the belief that it produces a more well-rounded student and person. I would certainly agree with that hypothesis.
(It has also helped me shout out more correct answers when watching University Challenge. My wife is mildly impressed)
Onwards and upwards. It is now full-on MST121 until September, with a little sprinkling of self generated maths study, in between.
Thursday, 14 July 2011
TMA03 Result
I passed! 95% score with marks dropped for:
A rounding error
Truncation of a hand written graph
Over simplification of an answer
A calculation mistake
So, I am very happy with the result; but having listened to Richard Feynman's audio book 'Surely You must be joking Mr Feynman...'; Feynman tells of a realisation that he discovered during his Princeton years, which I shall share here.
He describes how he believed that there are two types of knowledge.
1. Solid, adaptable and useful knowledge.
2. Knowledge that is learned, but yet it is brittle, non-malleable and difficult to apply.
He explains a situation when he was chatting with another Grad student and he posed a question about relativity. He asked the student how he would work out the maximum amount of distance that an object could move from a gravitational body, in the shortest amount of time, with an initial velocity given.
The Grad student struggled with the problem and couldn't work out how to answer it. Feynman explained, that to answer the question, simply involved working out the maxima of a function, created for the object. This is undergraduate calculus, at best, and yet the student couldn't apply the knowledge he already had.
The reason I mention this interesting example, is that the calculus that I created for the TMA03, managed to score me 95%, yet I still don't feel that I 'own' the subject. I am still having to keep referring back to the mechanical 'rules' of integration, each time I attempt a problem.
And, whilst I am a realist and understand that knowledge takes time to sink in. It is still a nervous time, waiting for it to happen.
The time between first attempting a difficult new skill, and mastering it, can be a time of self doubt and wonder. "Will I ever understand it?", "am I intelligent enough to cope with the course?"
Whilst these unanswered questions can be unnerving; they also provide the basis for the greatest feelings of triumph and accomplishment. Because, after all that hard work, once you do master something that you once found almost impossible; you now know that you have a set of tools and techniques that you can use, to study, learn and achieve.
I'm not quite there yet, but I keep trying everyday. Lets see what happens!
A rounding error
Truncation of a hand written graph
Over simplification of an answer
A calculation mistake
So, I am very happy with the result; but having listened to Richard Feynman's audio book 'Surely You must be joking Mr Feynman...'; Feynman tells of a realisation that he discovered during his Princeton years, which I shall share here.
He describes how he believed that there are two types of knowledge.
1. Solid, adaptable and useful knowledge.
2. Knowledge that is learned, but yet it is brittle, non-malleable and difficult to apply.
He explains a situation when he was chatting with another Grad student and he posed a question about relativity. He asked the student how he would work out the maximum amount of distance that an object could move from a gravitational body, in the shortest amount of time, with an initial velocity given.
The Grad student struggled with the problem and couldn't work out how to answer it. Feynman explained, that to answer the question, simply involved working out the maxima of a function, created for the object. This is undergraduate calculus, at best, and yet the student couldn't apply the knowledge he already had.
The reason I mention this interesting example, is that the calculus that I created for the TMA03, managed to score me 95%, yet I still don't feel that I 'own' the subject. I am still having to keep referring back to the mechanical 'rules' of integration, each time I attempt a problem.
And, whilst I am a realist and understand that knowledge takes time to sink in. It is still a nervous time, waiting for it to happen.
The time between first attempting a difficult new skill, and mastering it, can be a time of self doubt and wonder. "Will I ever understand it?", "am I intelligent enough to cope with the course?"
Whilst these unanswered questions can be unnerving; they also provide the basis for the greatest feelings of triumph and accomplishment. Because, after all that hard work, once you do master something that you once found almost impossible; you now know that you have a set of tools and techniques that you can use, to study, learn and achieve.
I'm not quite there yet, but I keep trying everyday. Lets see what happens!
Tuesday, 12 July 2011
Physics and Maths, Studied this Week.
Another crazy week done and I have now recovered from the mental scars of Chapter D1 in MST121! I have really started to now explore, other supplementary study materials, trying to expand and fill in gaps in my basic knowledge of maths and Physics.
I have headed some rather excellent and welcome advice from a learned, fellow blogger, Chris; who is very well qualified to make comments on topics such as study content and future paths.
I have purchased the Feynman Physics Lectures part 1, and am managing a chapter every few days. This gives a nice easy going recap and re-introduction to some key physics concepts. Also, I have purchased A First Course in Mathematical Analysis, David Brannan.
I have started to work through this exploration of real analysis / advanced calculus, but have needed to recap on some rusty algebra, including some not so deft handling of inequalities. About 2yrs ago, I had gotten my mental arithmetic and algebraic manipulations, so that they were lightning fast. However, I have notice a massive drop off in speed and my memory is occasionally failing me.
So, my brief start on analysis has also kicked me into practising more algebra and general maths skills, which is always worth doing.
I have also nearly drawn my End of Course Assignment, to a close, for S197, How The Universe Works. I hope to finish it and send it off before Monday.
I am nicely into a rythm at the moment, with a nice balance of practise questions and new material.
Total study Time this week: 31hrs.
MST121
Chapter D1, Chance. CMA questions completed for this chapter.
Recap on Chapter C1, Differentiation.
Other Study
Cambridge University practise Integration questions (Intro to Maths Tripos)
Practise questions on seperation of variables from internet: http://www.intmath.com/differential-equations/2-separation-variables.php
Other Reading
Lectures on Physics Volume 1, Richard Feynman: Chapters 1-7 (light touch review)
Mathematical Analysis David Brannan: Chapter 1.1 - 1.3
S197
Completion and submission of EMA part A.
Completion of part B question 1.
Audiobooks
The Modern Scholar: Astronomy II, Stars, Galaxies and the Universe
Surely You're Joking, Mr Feynman!
A great bit of diversity this week and I am looking forward to blitzing the last 3 books of MST121, before preparing my final coursework for this maths course. It's then a look forward to the autumn when I am pondering studying a few module books from other OU courses, such as M208 (probably, the Brannan book will suffice); also an early look at MST209 and some external maths stuff from Cambridge University, such as the advised reading lists for their pre- tripos course applicants.
Also, I may be on the cusp of getting my wife's permission, to let me work part-time and take on more study modules!
Busy, Busy, Busy!
I have headed some rather excellent and welcome advice from a learned, fellow blogger, Chris; who is very well qualified to make comments on topics such as study content and future paths.
I have purchased the Feynman Physics Lectures part 1, and am managing a chapter every few days. This gives a nice easy going recap and re-introduction to some key physics concepts. Also, I have purchased A First Course in Mathematical Analysis, David Brannan.
I have started to work through this exploration of real analysis / advanced calculus, but have needed to recap on some rusty algebra, including some not so deft handling of inequalities. About 2yrs ago, I had gotten my mental arithmetic and algebraic manipulations, so that they were lightning fast. However, I have notice a massive drop off in speed and my memory is occasionally failing me.
So, my brief start on analysis has also kicked me into practising more algebra and general maths skills, which is always worth doing.
I have also nearly drawn my End of Course Assignment, to a close, for S197, How The Universe Works. I hope to finish it and send it off before Monday.
I am nicely into a rythm at the moment, with a nice balance of practise questions and new material.
Total study Time this week: 31hrs.
MST121
Chapter D1, Chance. CMA questions completed for this chapter.
Recap on Chapter C1, Differentiation.
Other Study
Cambridge University practise Integration questions (Intro to Maths Tripos)
Practise questions on seperation of variables from internet: http://www.intmath.com/differential-equations/2-separation-variables.php
Other Reading
Lectures on Physics Volume 1, Richard Feynman: Chapters 1-7 (light touch review)
Mathematical Analysis David Brannan: Chapter 1.1 - 1.3
S197
Completion and submission of EMA part A.
Completion of part B question 1.
Audiobooks
The Modern Scholar: Astronomy II, Stars, Galaxies and the Universe
Surely You're Joking, Mr Feynman!
A great bit of diversity this week and I am looking forward to blitzing the last 3 books of MST121, before preparing my final coursework for this maths course. It's then a look forward to the autumn when I am pondering studying a few module books from other OU courses, such as M208 (probably, the Brannan book will suffice); also an early look at MST209 and some external maths stuff from Cambridge University, such as the advised reading lists for their pre- tripos course applicants.
Also, I may be on the cusp of getting my wife's permission, to let me work part-time and take on more study modules!
Busy, Busy, Busy!
Friday, 8 July 2011
Modelling Uncertainty
Please, somebody help me. I have just lost the will to live! I've spent 4hrs tonight, studying and completing the MST121 block unit entitled, Chance.
What a load of old tosh. I have never been so bored. I actually nodded off in the middle of reading it. I just can't get excited about stats and the tired way that most books seem to treat the subject. I would like to have seen much more emphasis on applications in maths and science, rather than examples of parlour tricks, gamblers and rolling x amount of dice.
There is one good outcome of all this, though. I was able to sit and complete all of the CMA questions, whilst doing my first reading of the unit material. That means, I don't have to go back to it any time soon.
Tomorrow, I'm moving onto 'Modelling variation', which I hope is more interesting.
Note to self: don't get drunk one night, and register for an O.U stats course - the hangover would be just too much to bare...
What a load of old tosh. I have never been so bored. I actually nodded off in the middle of reading it. I just can't get excited about stats and the tired way that most books seem to treat the subject. I would like to have seen much more emphasis on applications in maths and science, rather than examples of parlour tricks, gamblers and rolling x amount of dice.
There is one good outcome of all this, though. I was able to sit and complete all of the CMA questions, whilst doing my first reading of the unit material. That means, I don't have to go back to it any time soon.
Tomorrow, I'm moving onto 'Modelling variation', which I hope is more interesting.
Note to self: don't get drunk one night, and register for an O.U stats course - the hangover would be just too much to bare...
Thursday, 7 July 2011
Richard Feynman and the Open University
I have now returned from my week off and feel raring to go again with some hardcore maths and physics.
Over the weekend, I ordered the first volume of Richard Feynman's infamous lectures on physics. It arrived today and whilst leafing through the worn brown pages of the preface in my newly aquired second hand book, I had cause to pause and think, about some of Feynman's own opinions on the teacher and student relationship.
Feynman discusses how the student - teacher relationship, is the most important factor, in whether or not a student will be successful in learning physics. This, he describes, is when a student discusses ideas, talks about ideas and thinks about ideas, with their tutor. Ostensibly he extolls that this is the time when the learning happens.
I raise these points as it made me think about being an Open University student. Those solitary hours, just me, my books and my thoughts. I know that the tutors are there to support; but I personally don't normally have contact with them, unless I have serious issues or as part of the TMA process. I'm sure other people have much more contact and find it useful. But I don't.
However, what I have noticed about the Open University texts is that they are written in a way that is 'just-so'. I often find that if I'm reading and a question or confusion springs into my head; my problem is usually answered nicely, in the next few pages. These are student orientated texts; they are easy to follow and they put some mainstream textbooks, to shame.
I believe that the voices of all those editors (most of whom are, or have been, O.U tutors), seep through the pages and speak to the reader, as the pages are slowly digested and enjoyed.
I am very happy with my O.U texts, and I suspect that Robert Feynman would probably have agreed with me, in this respect.
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