As a relief from all the angst about Pure maths and Topology which seems to be getting quite a few of us down. Radio 3 has decided to spend the whole of this week playing continuous Schubert.

http://www.bbc.co.uk/radio3/

Schubert is amongst my favourite composers. Some years ago I wrote this little biography and I share it with my friends

http://dl.dropbox.com/u/16049029/Schubert_bio_cdf.pdf

For those who don't know Schubert then you don't know what you've been missing. I would recommend starting with the last 3 piano sonatas preferably played by Alfred Brendel.

http://www.amazon.co.uk/Schubert-Piano-Works-Franz/dp/B00000417C/ref=sr_1_1?ie=UTF8&qid=1332792862&sr=8-1

The last quartets and String quintet by the Lindsay quartet

http://www.amazon.co.uk/Schubert-Late-String-Quartets-Quintet/dp/B0001Z2RSW/ref=sr_1_1?s=music&ie=UTF8&qid=1332792942&sr=1-1

Finally the three great song cycles with Fischer Dieskau and Gerald Moore.

http://www.amazon.co.uk/s/ref=nb_sb_noss?url=search-alias%3Dpopular&field-keywords=Fischer+Dieskau+schubert+song+cycles+

Anyway I hope you enjoy exploring Schubert as much as I have. Take the opportunity to listen to Radio 3 this week especially the main evening concerts. I've just finished hearing a performance by Paul Lewis, one of Alfred Brendel's pupil's of the two A major sonata's.

It's quite surprising just how quickly time flies I can't believe it's almost 10 years since I wrote the short biography. Hopefully it wont be another 10 years before I write another one.

## Monday, 26 March 2012

## Thursday, 22 March 2012

### That sinking feeling

Help, I think topology must be one of the densest subjects to get into. I have to say I'm really struggling with this one as it's quite alien to anything I've come across. Still I'm not alone that does seem to be the consensus of a number of people on the forum.

I think part of the problem, is that one is dealing with general relations between functions, which aren't specified at all. In the analysis sections of M208 there was usually a function which was specified and it was possible, no matter how strange the function to say something about it. For example, the notorious Blancmange function of M208, yes proving it's continuous is a real pain in the neck (See the discussion I've been having with Duncan on this )

http://matrices-reloaded.blogspot.co.uk/2012/03/all-downhill-from-now-on.html

but at least you had something to get your teeth into. The function is defined, I more or less know the epsilon delta defintion of continuity and how to test if a function is differentiable or not. OK I might not grasp all the details of the proof but I can get the gist and I hope finally to consolidate my understanding with a few pints with Duncan next week.

With topology it's quite different, the definitions are about relations, between relations, between relations (alright I exaggerate a bit). It's very often definitiion 1, definition 2, combine definition 1 and 2 to get theorem 1. Definition 3 definition 3.1 Definition 3 and Definition 3.1 gives us theorem 2 and on and on, unfortunately there is no real road map as to where all this is going so it seems like wading through treacle.

Having said that, I think I've finally developed some sort of strategy to cope with this course. (a bit too late for the second TMA due in a couple of weeks time), but I think the only way to get a handle on this course is to try and learn the defintions by heart, at least in the first instance, testing yourself at odd moments during the day once those are grasped then you can begin to follow the theorems. This seems to have worked so far for unit A2. At first I was totally baffled, by the defintion of continuity for metric spaces, in terms of balls, (Indeed one can legitimately say topology or at least metric is a load of balls !!) A ball is essentially a generalisation of an open interval around a point in two or higher dimensional space. However having written it out a few times and more or less learnt it off by heart, it now begins to make sense and I can move on. Hopefully I've not left it too late to catch up. Fortunately we have a tutorial on Saturday and that should give me confidence to tackle the TMA over the next week. In the mean time I'll keep plodding away.

On a brighter note, I got my first TMA back from the Waves course, grade 1, but I dropped a few marks because of silly sign errors and also I had totally missed out a small section of one of the questions. TMA02 of this course is tempting, but as the school teacher said in the Pink Floyd's the Wall, "You can;t have your pudding until you've had your meat, how can you have your pudding if you don't eat your meat? "

So I have to eat the meat of TMA02 for the topology course before I can have my pudding of the waves course.

Finally in a slightly amusing way, I've left my small mark in Edinburgh. I was out drinking with some colleagues from work in the Blue Blazar a local pub just off Lothian Road, when a new guy who's just joined went to the toilet. He came up and said "Thats what I really like about Edinburgh, where else would you see Maxwell's equations scrawled next to some graffiti slagging off Hibs supporters". What is really amusing is that I had scribbled those on the toilet door about six years ago after a rather boozy Christmas do. I was amazed that they are still there.

Hopefully the mist will begin to clear vis a vis topology and I can't wait till my pudding but I must be careful not to gobble it all down quickly otherwise I'll drop some marks for silly mistakes.

I think part of the problem, is that one is dealing with general relations between functions, which aren't specified at all. In the analysis sections of M208 there was usually a function which was specified and it was possible, no matter how strange the function to say something about it. For example, the notorious Blancmange function of M208, yes proving it's continuous is a real pain in the neck (See the discussion I've been having with Duncan on this )

http://matrices-reloaded.blogspot.co.uk/2012/03/all-downhill-from-now-on.html

but at least you had something to get your teeth into. The function is defined, I more or less know the epsilon delta defintion of continuity and how to test if a function is differentiable or not. OK I might not grasp all the details of the proof but I can get the gist and I hope finally to consolidate my understanding with a few pints with Duncan next week.

With topology it's quite different, the definitions are about relations, between relations, between relations (alright I exaggerate a bit). It's very often definitiion 1, definition 2, combine definition 1 and 2 to get theorem 1. Definition 3 definition 3.1 Definition 3 and Definition 3.1 gives us theorem 2 and on and on, unfortunately there is no real road map as to where all this is going so it seems like wading through treacle.

Having said that, I think I've finally developed some sort of strategy to cope with this course. (a bit too late for the second TMA due in a couple of weeks time), but I think the only way to get a handle on this course is to try and learn the defintions by heart, at least in the first instance, testing yourself at odd moments during the day once those are grasped then you can begin to follow the theorems. This seems to have worked so far for unit A2. At first I was totally baffled, by the defintion of continuity for metric spaces, in terms of balls, (Indeed one can legitimately say topology or at least metric is a load of balls !!) A ball is essentially a generalisation of an open interval around a point in two or higher dimensional space. However having written it out a few times and more or less learnt it off by heart, it now begins to make sense and I can move on. Hopefully I've not left it too late to catch up. Fortunately we have a tutorial on Saturday and that should give me confidence to tackle the TMA over the next week. In the mean time I'll keep plodding away.

On a brighter note, I got my first TMA back from the Waves course, grade 1, but I dropped a few marks because of silly sign errors and also I had totally missed out a small section of one of the questions. TMA02 of this course is tempting, but as the school teacher said in the Pink Floyd's the Wall, "You can;t have your pudding until you've had your meat, how can you have your pudding if you don't eat your meat? "

So I have to eat the meat of TMA02 for the topology course before I can have my pudding of the waves course.

Finally in a slightly amusing way, I've left my small mark in Edinburgh. I was out drinking with some colleagues from work in the Blue Blazar a local pub just off Lothian Road, when a new guy who's just joined went to the toilet. He came up and said "Thats what I really like about Edinburgh, where else would you see Maxwell's equations scrawled next to some graffiti slagging off Hibs supporters". What is really amusing is that I had scribbled those on the toilet door about six years ago after a rather boozy Christmas do. I was amazed that they are still there.

Hopefully the mist will begin to clear vis a vis topology and I can't wait till my pudding but I must be careful not to gobble it all down quickly otherwise I'll drop some marks for silly mistakes.

## Sunday, 4 March 2012

### Progress

Well sorry for not posting for a while anyway progress of sorts has been made on M338 I got my first TMA back and did reasonably well but lost a few marks for taking short cuts. Also there was some difficulty in notation hopefully the wrinkles will be ironed out in time for the exam. Have to admit some of this course seems like wading through treacle and it's difficult to see the point of a lot of it. Still just keep carrying on I know a knowledge of topology is an essential pre-requisite if one wants to understand things like the singularity theorems of General Relativity proved by Penrose and Hawking so mustn't get too disheartened.

Also finished the first assignment for MS324 which was on the whole a joy to do I'm definitely an Applied mathematician. The questions were essentially a review of mathematical techniques one should be aware of with one or two wrinkles thrown in. The first question was a question on Partial Fractions and an integration based on taking the limit of the integral to infinity. This involved some tricky manipulations of Logartihms but I think I got there. The second question was a straightforward and pleasurable solution of an inhomogeneous second order differential equation. The third question was a straightforward but tedious question on multivariable calculus and finding the stationary points. What made this question a bit tedious was the fact that the nature of the points varied for a wide range of conditions and you had to be careful not to miss out any combinations. The final question was on the deformation of springs more of a modelling question than a mathematics question I think I got most of it correct but I admit the very last part seemed badly phrased so I'm not sure if I got it correct or not. Still it's only 3 marks so should be on target for a good stab at this.

Both courses haven't really got started yet I really hope I can penetrate the fog of definition and theorem that is plaguing the topology units but at the minute I really can't see the wood for the trees. Conversely I know that the first real block of MS324 is on one of my favourite topics namely the wave equation and it's solutions I and feel reasonably confident I can polish off the next TMA in the next two weeks. The problem is it would be like a kid who eats his dessert before his main course instead of leaving it to last but what the heck.

As a final point at the risk of overloading people I've found yet another book on mathematics as applied to physics.

http://www.amazon.co.uk/Mathematics-Classical-Quantum-Physics-Dover/dp/048667164X/ref=sr_1_1?ie=UTF8&qid=1330880090&sr=8-1

Although quite old it covers all the branches of mathematics (apart from Topology) and their direct relevance to physics. It has quite an accessible introduction to the Hilbert space formulation of quantum mechanics stresses the key analogy between geometric and vector spaces which is so important to physics as well as having lots of concrete and challenging examples. I intend to try at least some of the questions which involve the separation of variables of pde's in spherical coordinate systems something not really covered in MS324 but which plays an important part in both classical and quantum physics. Anyway nice to see a book covering both classical and quantum physics in the same volume. A bit less abstract than say Szekres

http://www.amazon.co.uk/Course-Modern-Mathematical-Physics-Differential/dp/0521829607/ref=sr_1_sc_2?s=books&ie=UTF8&qid=1330880446&sr=1-2-spell

but not just another recipe book, Szekres and Byron complement each other nicely in my honest opinion.

Also finished the first assignment for MS324 which was on the whole a joy to do I'm definitely an Applied mathematician. The questions were essentially a review of mathematical techniques one should be aware of with one or two wrinkles thrown in. The first question was a question on Partial Fractions and an integration based on taking the limit of the integral to infinity. This involved some tricky manipulations of Logartihms but I think I got there. The second question was a straightforward and pleasurable solution of an inhomogeneous second order differential equation. The third question was a straightforward but tedious question on multivariable calculus and finding the stationary points. What made this question a bit tedious was the fact that the nature of the points varied for a wide range of conditions and you had to be careful not to miss out any combinations. The final question was on the deformation of springs more of a modelling question than a mathematics question I think I got most of it correct but I admit the very last part seemed badly phrased so I'm not sure if I got it correct or not. Still it's only 3 marks so should be on target for a good stab at this.

Both courses haven't really got started yet I really hope I can penetrate the fog of definition and theorem that is plaguing the topology units but at the minute I really can't see the wood for the trees. Conversely I know that the first real block of MS324 is on one of my favourite topics namely the wave equation and it's solutions I and feel reasonably confident I can polish off the next TMA in the next two weeks. The problem is it would be like a kid who eats his dessert before his main course instead of leaving it to last but what the heck.

As a final point at the risk of overloading people I've found yet another book on mathematics as applied to physics.

http://www.amazon.co.uk/Mathematics-Classical-Quantum-Physics-Dover/dp/048667164X/ref=sr_1_1?ie=UTF8&qid=1330880090&sr=8-1

Although quite old it covers all the branches of mathematics (apart from Topology) and their direct relevance to physics. It has quite an accessible introduction to the Hilbert space formulation of quantum mechanics stresses the key analogy between geometric and vector spaces which is so important to physics as well as having lots of concrete and challenging examples. I intend to try at least some of the questions which involve the separation of variables of pde's in spherical coordinate systems something not really covered in MS324 but which plays an important part in both classical and quantum physics. Anyway nice to see a book covering both classical and quantum physics in the same volume. A bit less abstract than say Szekres

http://www.amazon.co.uk/Course-Modern-Mathematical-Physics-Differential/dp/0521829607/ref=sr_1_sc_2?s=books&ie=UTF8&qid=1330880446&sr=1-2-spell

but not just another recipe book, Szekres and Byron complement each other nicely in my honest opinion.

Subscribe to:
Posts (Atom)