I'm posting rather than studying at the moment. Procrastination rules...
I have to say that the fourth book of the Mathematics module Groups and Geometry with the OU, is a lovely rehash of some safe, comforting basic group theory. I never thought I would be so glad to meet this material again, after M208 (Pure Mathematics). I had struggled, at times, with the concepts on Cosets and Normal subgroups; so it wasn't exactly a passion of mine, at the time.
But, coming back to it with fresh and slightly more capable eyes, I am actually enjoying this unit. It is basic, but it is abstract and axiomatic, two aspects I very much enjoy. But mainly, this is a welcome interlude from the relentless TMA onslaught of this course and the Number Theory course M381.
However, I see from Duncan's posts, that this is the calm before the storm, for this particular module.
Wednesday 20 November 2013
Tuesday 19 November 2013
M381 TMA, away...
Just a quicky!
I have completed and sent off my first TMA for Number Theory and logic. It was very tough; but, already, on reviewing the answers, I am starting to feel a familiarity for some of the tools and techniques used in them.
So, it's bitter-sweet really. I have put in far to many difficult hours on this TMA; but I am feeling an enormous sense of satisfaction in its completion. I have no idea how I have done, but the challenge was good.
I have completed and sent off my first TMA for Number Theory and logic. It was very tough; but, already, on reviewing the answers, I am starting to feel a familiarity for some of the tools and techniques used in them.
So, it's bitter-sweet really. I have put in far to many difficult hours on this TMA; but I am feeling an enormous sense of satisfaction in its completion. I have no idea how I have done, but the challenge was good.
Thursday 14 November 2013
Tricky Number Theory
Oh Lord.
I am managing to understand number theory - (none of it is so difficult, that you are unable to follow the proofs with very careful reading) - but every time I come across another example problem in the book, It is clear that I would never have thought of answering it in the way described within the text.
What's more, having read the answer, I still can't understand how a number theory novice is supposed to know the answers to these things, from the sparse collection of theorems that are provided in the set books.
I reckon that with many extra hours of study and utilizing a rather handy technique that I have recently picked up for learning new material, I should be able to rote learn the minor theorem proofs, some key example solutions and a few other bits, in time for the exam. But, I don't actually think that this is going to get me through the damn exam; however, it might just keep the blood pressure low enough to avoid going on Statins before June.
As my friend Chris would say.
K.B.O.
I am managing to understand number theory - (none of it is so difficult, that you are unable to follow the proofs with very careful reading) - but every time I come across another example problem in the book, It is clear that I would never have thought of answering it in the way described within the text.
What's more, having read the answer, I still can't understand how a number theory novice is supposed to know the answers to these things, from the sparse collection of theorems that are provided in the set books.
I reckon that with many extra hours of study and utilizing a rather handy technique that I have recently picked up for learning new material, I should be able to rote learn the minor theorem proofs, some key example solutions and a few other bits, in time for the exam. But, I don't actually think that this is going to get me through the damn exam; however, it might just keep the blood pressure low enough to avoid going on Statins before June.
As my friend Chris would say.
K.B.O.
Friday 1 November 2013
Reflecting on Number Theory
I think that both Chris and Duncan, were spot on, when they identified that the level of thought and abstraction involved in level 3 number theory, is much more thought provoking and much less formulaic, when it comes to answering problems based on the material.
On first examination, many of the number theory theorems presented in the course material are, ostensibly, elementary; and one can be fooled into thinking that they are, almost, trivial. But this would be underestimating the power of such elementary building blocks on which all of mathematics is essentially laid.
Most of the worlds most beautiful architectural buildings are built using the basic materials that you can find in any common builders yard; but the ways that they are combined, built upon, measured and used as an expression of human thought, are essentially infinite.
Number theory is such a construction. It is based on simple, axiomatic, undeniable truths, which lead to some very complex and thought provoking conclusions. Glancing ahead, the strength in such constructions, is probably going to be both confirmed and blown apart at the same time, as I eventually discover what Herr Gödel had to say about these matters.
I can't wait. The work will have been so worthwhile.
On first examination, many of the number theory theorems presented in the course material are, ostensibly, elementary; and one can be fooled into thinking that they are, almost, trivial. But this would be underestimating the power of such elementary building blocks on which all of mathematics is essentially laid.
Most of the worlds most beautiful architectural buildings are built using the basic materials that you can find in any common builders yard; but the ways that they are combined, built upon, measured and used as an expression of human thought, are essentially infinite.
Number theory is such a construction. It is based on simple, axiomatic, undeniable truths, which lead to some very complex and thought provoking conclusions. Glancing ahead, the strength in such constructions, is probably going to be both confirmed and blown apart at the same time, as I eventually discover what Herr Gödel had to say about these matters.
I can't wait. The work will have been so worthwhile.
Subscribe to:
Posts (Atom)