After passing my two most recent exams with much better marks than I ever hoped for, I have decided to hit the big red button and go for the nuclear option for my next course - Complex Analysis M337 with the Open University.
I think that this (apart from the old Topology course) is probably the most challenging of the OU maths courses of recent years.
Looking at the preparation available for this course being Pure Maths and Mathematical methods, both level 2 courses with the OU - these don't seem to be very comprehensive prerequisite courses for tackling Complex Analysis.
Of course, there are other courses which are not analysis based which use calculus, or alternatively, provide practice at reading and producing complex proofs, such as the fluids dynamics course etc...
But I haven't taken those other courses and my own background comes from pure mathematical courses alone.
So, I have started planning some pre-course study, to get me back up to speed with analysis. The books that I am using are:
Calculus. Spivak
Complex Analysis. Gamelin
A First Course in Mathematical Analysis. Brannan
A Course of Pure Mathematics. Hardy
I won't study them in depth and also not in the order listed above. I will also be referring back to my trusty annotated M208 Pure Maths handbook from my course in 2012, which has all those handy little notes which now make no sense at all, two years on.
My preparation will consist of two strands.
1. An overview and recap of main concepts, starting with limits, bounds and series / sequences; leading on to continuity, epsilon-delta, properties of integrals, power series etc...
2. A sharp facility in the rapid calculation of most basic differentiation and integration problems with some memorization of basic derivatives and integrals.
Spivak has a nice section for practicing facility with derivatives and integrals - and I particularly like his humor as he describes this passage of work:
'Although rapid calculation is not the goal of mathematics, if you hope to treat theoretical applications of the chain rule with aplomb, these concrete applications should be child's play - mathematicians like to pretend that they can't even add, but most of them can when they have to'! Spivak.
On the bright side, I have now only signed up for 30 points this year; half of last years study time. I will be pushing for a distinction on this course, which should line me up nicely for a half decent grade on final graduation next Summer.
Because my OU studies will come to an end at that time- I have now started to look at all the available MSc courses which provide distance learning or part time options, which require a high mathematical content.
I will need to start applying for my MSc course, after this Christmas.
I'll try and give an in-depth critique of the options available for a distance learner, in a future post.
Saturday 2 August 2014
Thursday 24 July 2014
Thank the Lord. I Passed!
What a blogging hiatus, that has just been.
Four months... few!
Four months seems an age; but I have remained silent during this time, for two main reasons.
Firstly, I found myself so deep into studying and really struggling for time to even spend with my family; that I just decided to stop the posts for a while, and concentrate on what is most important.
Secondly, I was having a major melt down / ego readjustment, as It really dawned on me that there were large volumes of material within my two current courses, Number Theory / Mathematical Logic, and Groups / Geometry; that still left me sweating at night with not even a clue on how to navigate the material.
The simple human condition then took over - as in - it's simply not very pleasant to write about your impending implosion into failure, no matter how reflective your blog is supposed to be.
'Warts and all' can be an extraordinarily challenging blogging ethos, in times of real difficulties. I feel I have failed that test, this time around.
Fast forward to June - I took my exams in Birmingham. Two exams in two days. I stayed in a hotel, in between the exams, and up until the hour before the first exam, I was revising for 10hrs a day for three weeks solid (I took leave from work).
I just couldn't remember the material and produce it quickly enough under exam conditions. Help!
Anyway, I took the exams and having totted up my points, I had reckoned that I had achieved around the grade 3 area for Number Theory, and Grade 4 area, for Groups.
To my astonishment, I received my results email tonight, logged into my student home page, and promptly fell off my chair, Brie sandwich in hand.
I am pleased to report, that I scored the following results:
Number Theory and Mathematical Logic - 72% (Grade 2)
Groups and Geometry - 66% (Grade 2)
As my followers will appreciate; it is now time for me to attend a public house and imbibe a pint of - what has now become an exam results tradition for me - a pint of Bishops Finger.
Ooh Matron!
Four months... few!
Four months seems an age; but I have remained silent during this time, for two main reasons.
Firstly, I found myself so deep into studying and really struggling for time to even spend with my family; that I just decided to stop the posts for a while, and concentrate on what is most important.
Secondly, I was having a major melt down / ego readjustment, as It really dawned on me that there were large volumes of material within my two current courses, Number Theory / Mathematical Logic, and Groups / Geometry; that still left me sweating at night with not even a clue on how to navigate the material.
The simple human condition then took over - as in - it's simply not very pleasant to write about your impending implosion into failure, no matter how reflective your blog is supposed to be.
'Warts and all' can be an extraordinarily challenging blogging ethos, in times of real difficulties. I feel I have failed that test, this time around.
Fast forward to June - I took my exams in Birmingham. Two exams in two days. I stayed in a hotel, in between the exams, and up until the hour before the first exam, I was revising for 10hrs a day for three weeks solid (I took leave from work).
I just couldn't remember the material and produce it quickly enough under exam conditions. Help!
Anyway, I took the exams and having totted up my points, I had reckoned that I had achieved around the grade 3 area for Number Theory, and Grade 4 area, for Groups.
To my astonishment, I received my results email tonight, logged into my student home page, and promptly fell off my chair, Brie sandwich in hand.
I am pleased to report, that I scored the following results:
Number Theory and Mathematical Logic - 72% (Grade 2)
Groups and Geometry - 66% (Grade 2)
As my followers will appreciate; it is now time for me to attend a public house and imbibe a pint of - what has now become an exam results tradition for me - a pint of Bishops Finger.
Ooh Matron!
Wednesday 5 March 2014
Exam Revision - or - The Lack of it...
Hmm,
I really am struggling with the workload on these two courses. I just feel like I am glossing over the books, in order to answer the TMA's - with no real hope of a deep understanding of the material at hand.
Logic is fairly straightforward, if you don't mind the dryness of having to learn a new language - that of formal logic with all its odd symbols and squiggles! It's one of those subjects that you can read, understand and then apply without too much thought, though.
Now, Number Theory - that is completely different.
I have noticed that TMA03 (which I am writing at the moment) is seeming easier than the first two. But I have realized that I have started to pick up on the 'method' of proof for answering these blasted TMA's. It is more of an art form than a process, and it requires you to see the tricks that the OU employ, to baffle, beat and thrash you , with the NT questions. As mentioned before, many of the questions don't resemble any of the unit examples.
They are a cruel bunch, those course writers (Derek G, I'm looking at you!)
So, we come to Groups and Geometry. I thought I was fairly good at groups and awful at geometry. However, it seems that my tutor thinks it is the other way around! I have struggled with the algebra involved in the groups units - but I think this is just showing up my low level of algebra knowledge, which I most definitely missed out on, between GCSE and University level.
Anyway - I have now printed off all of the exam papers of past years, and I am slowly practicing exam style questions, in the hope that I can somehow be ready on those looming exam dates this June.
Help!
I really am struggling with the workload on these two courses. I just feel like I am glossing over the books, in order to answer the TMA's - with no real hope of a deep understanding of the material at hand.
Logic is fairly straightforward, if you don't mind the dryness of having to learn a new language - that of formal logic with all its odd symbols and squiggles! It's one of those subjects that you can read, understand and then apply without too much thought, though.
Now, Number Theory - that is completely different.
I have noticed that TMA03 (which I am writing at the moment) is seeming easier than the first two. But I have realized that I have started to pick up on the 'method' of proof for answering these blasted TMA's. It is more of an art form than a process, and it requires you to see the tricks that the OU employ, to baffle, beat and thrash you , with the NT questions. As mentioned before, many of the questions don't resemble any of the unit examples.
They are a cruel bunch, those course writers (Derek G, I'm looking at you!)
So, we come to Groups and Geometry. I thought I was fairly good at groups and awful at geometry. However, it seems that my tutor thinks it is the other way around! I have struggled with the algebra involved in the groups units - but I think this is just showing up my low level of algebra knowledge, which I most definitely missed out on, between GCSE and University level.
Anyway - I have now printed off all of the exam papers of past years, and I am slowly practicing exam style questions, in the hope that I can somehow be ready on those looming exam dates this June.
Help!
Saturday 8 February 2014
TMA02 Results
Okay, I did much better than I had imagined. I really felt that I had made a meal of the number theory paper; but after a last ditched attempt at two of the questions that I messed up; it all came good in the end.
So, here are the results:
Number Theory and Logic - 97%
Groups and Geometry - 98%.
In what has become a bit of a tradition for me, over the last 4yrs - I am now off down the pub for a celebratory pint of Bishops Finger.
Oohh Matron!
So, here are the results:
Number Theory and Logic - 97%
Groups and Geometry - 98%.
In what has become a bit of a tradition for me, over the last 4yrs - I am now off down the pub for a celebratory pint of Bishops Finger.
Oohh Matron!
Monday 3 February 2014
TMA's away, on time!
Just a quicky!
Both TMA's for M381 and M336 have now been completed and chucked in the post. They arrived on the cut off date, with my tutor, so I await the results...
The Number Theory TMA was a nightmare and I spent far to much time on it. Having said that, I did finally manage to put together some sort of coherent answer for each question, so I am in a better place than I was two weeks ago.
The Groups and Geometry TMA was typical O.U fare, with four large questions, one on each block of work. Going to the tutorial really helped, as I had made a couple of mistakes in my TMA, through a 'clanger' of a misunderstanding in the material 'counting with groups'.
I have now stepped up another gear, and in the last week I have completed the unit that uses formal logic language, to construct formulas and tautologies. I found that very enjoyable, as it is right up my street - all that coding of symbols and working out truth tables, appeals to my twisted brain. I have also managed to complete, in full, the TMA questions for this unit, already.
If the rest of the logic books are of a similar nature, then I will be very happy, indeed.
I won't talk about Unit GR3, Decomposition of Abelian groups as, well, it's a bit of a car-crash. I knew I was going to have trouble, when I opened the book and had to go back to the earlier units and my glossary, to remember what the terms, 'word' and 'free group' meant, in the context of Abelian groups.
I am moving through this book at a snails pace, not really understanding it, globally. All I can do is rote learn the Theorems and some examples, and hope it starts to make sense, by next week.
ps: for those of you on the Groups course, you may have noticed that I am about 2 weeks behind on my schedule, too...
Oh the joys of concatenation, reduction, generators and quotients!
Both TMA's for M381 and M336 have now been completed and chucked in the post. They arrived on the cut off date, with my tutor, so I await the results...
The Number Theory TMA was a nightmare and I spent far to much time on it. Having said that, I did finally manage to put together some sort of coherent answer for each question, so I am in a better place than I was two weeks ago.
The Groups and Geometry TMA was typical O.U fare, with four large questions, one on each block of work. Going to the tutorial really helped, as I had made a couple of mistakes in my TMA, through a 'clanger' of a misunderstanding in the material 'counting with groups'.
I have now stepped up another gear, and in the last week I have completed the unit that uses formal logic language, to construct formulas and tautologies. I found that very enjoyable, as it is right up my street - all that coding of symbols and working out truth tables, appeals to my twisted brain. I have also managed to complete, in full, the TMA questions for this unit, already.
If the rest of the logic books are of a similar nature, then I will be very happy, indeed.
I won't talk about Unit GR3, Decomposition of Abelian groups as, well, it's a bit of a car-crash. I knew I was going to have trouble, when I opened the book and had to go back to the earlier units and my glossary, to remember what the terms, 'word' and 'free group' meant, in the context of Abelian groups.
I am moving through this book at a snails pace, not really understanding it, globally. All I can do is rote learn the Theorems and some examples, and hope it starts to make sense, by next week.
ps: for those of you on the Groups course, you may have noticed that I am about 2 weeks behind on my schedule, too...
Oh the joys of concatenation, reduction, generators and quotients!
Saturday 18 January 2014
3yrs - Almost 200 Blog Posts - KBO
Well, after a fast and furious Christmas where my studying actually stepped up a gear, to try and catch up; I have finally, almost got back to where I should be in my studies of groups and number theory.
I have just this minute, put the finishing touches on TMA02 for the groups and geometry streams, and printed the script off. I will post it on Monday.
However, I am having a lot of difficulty with the number theory TMA. I think that I have just about managed to complete the logic stream, without too much drama. However, I am getting my knickers in a real twist with the numbers part.
For example, despite me spending upwards of 10hrs, trying to answer a particular section of a question, I am still stumped. I even had some hints and tips from a fellow number theorist, in the recent day school at Aston University; but I am still a long way off from producing a cogent proof.
I only have to prove that d=210! What could be so difficult about that?
I have read and re-read x10, the unit book on congruence's; and I know that I have the answer in front of me. It just won''t coalesce.
Well, I will spend another 5hrs on it this weekend and whatever state that TMA is in, on Monday morning, that is how it is being sent off.
Realistically, I think I may be headed for 70% territory, for that one. But I'm not sad. I've taken on-board Chris's advice about just getting the job done and not trying to get 100% out of everything. It will end up driving me insane, if I carry on at the level of intensity that I have mustered, so far in these courses.
I have just this minute, put the finishing touches on TMA02 for the groups and geometry streams, and printed the script off. I will post it on Monday.
However, I am having a lot of difficulty with the number theory TMA. I think that I have just about managed to complete the logic stream, without too much drama. However, I am getting my knickers in a real twist with the numbers part.
For example, despite me spending upwards of 10hrs, trying to answer a particular section of a question, I am still stumped. I even had some hints and tips from a fellow number theorist, in the recent day school at Aston University; but I am still a long way off from producing a cogent proof.
I only have to prove that d=210! What could be so difficult about that?
I have read and re-read x10, the unit book on congruence's; and I know that I have the answer in front of me. It just won''t coalesce.
Well, I will spend another 5hrs on it this weekend and whatever state that TMA is in, on Monday morning, that is how it is being sent off.
Realistically, I think I may be headed for 70% territory, for that one. But I'm not sad. I've taken on-board Chris's advice about just getting the job done and not trying to get 100% out of everything. It will end up driving me insane, if I carry on at the level of intensity that I have mustered, so far in these courses.
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