>> up to and including itself

PhD diary archives >> Research/progress

>> 13.04.05

Long haul starts here
Whilst my supervisor looks at re-drafting the paper I have been working on, he suggested I make a start on writing-up my thesis proper. It seems like quite a daunting task if you think of it in terms of writing down every thought of the last 18 months or so in an intelligible, concise form, but fortunately this is not the situation I am facing. For my annual review, I produced a substantial report, about which I had this to say: The document that I handed in will, after a... {>>}
Posted by rich at 16:22

>> 08.04.05

y'(0) = 0 paper — second draft
As promised last week, here is the second draft of the paper I am currently working on (it's a pdf file, around 192k). The main change contained within this draft is the statement of the fundamental theorem immediately, which can be found in section 2. Following that, examples are moved to section 3 to show how the fundamental theorem works and then some trickery that allows the theorem to work for a new class of equations is given in section 5. The "further work" section remains virtually the same. The... {>>}
Posted by rich at 16:29

>> 01.04.05

y'(0) = 0 paper — first draft
The paper I've been working on for a while is currently with my supervisor, who is making various changes to it. As an indication of how things are progressing, I thought I would post here the various drafts so that readers can have a look — if they are so inclined — at how a/the paper takes shape. To start this off, then, we have the first draft. It's a pdf file, around 180k, so shouldn't take too long to download. Overall, it contains a lot of information — in... {>>}
Posted by rich at 16:43

>> 14.03.05

Second draft submitted
Last week proved to be quite an intense period concerning my studies, working hard to try and get a decent second draft together for the paper I'm working on with my supervisor. As noted previously, the first draft had been fairly naff and was in need of a major overhaul. Although it took a great deal of juggling about and plenty of decisions concerning when to introduce things and when to leave it to a later point, the finished draft — which I handed in on Thursday — was something... {>>}
Posted by rich at 13:18

>> 03.03.05

Second draft
Following on from the submission of the first draft of the paper I'm working on at the moment, my supervisor had a nice meeting with me pointing out the very many ways in which the paper can be improved. The single biggest issue was one of structure, which was something I was expecting. The work we have completed so far takes one major breakthrough (thought of by my supervisor and on which he has written, submitted and had accepted for publication a paper) and extends it for various different cases.... {>>}
Posted by rich at 13:32

>> 24.02.05

First draft
The last few weeks have seen me writing the first draft of a paper my supervisor and I are going to submit on the work we have been considering. The experience has been a difficult one, trying to temper my writing style to the necessarily formal style required of a paper whilst remaining succinct and mildly understandable. Anyone that has read this diary for a reasonable period of time will realise that brevity is not one of my strong points; indeed, I could hardly defend myself against a charge of... {>>}
Posted by rich at 13:03

>> 08.02.05

There must be some way outta here
Over the course of the last few posts, I have outline the reasons for and feelings associated with leaving my PhD studies. This final post could be considered the legal proceedings: a what happens next in order to take me from the maths department to the Real World™. Recall that the three years of the PhD are actually split into two, almost distinct parts: the MPhil and the transfer to the PhD (an MPhil being a Master of Philosophy, as opposed to their PhD counterpart, the Doctor of Philosophy). Usually,... {>>}
Posted by rich at 12:08

>> 04.02.05

Feelings
Over the last few posts, I have tried to explain some of the reasons behind my decision to leave my PhD studies. These reasons have been ordered, in the loosest sense of the word, and brought together into roughly similar factors to convey some of the facts — as much as there are any — behind my decision. This post is concerned with much less tangible reasoning, based on how it feels to gradually realise and decide upon taking this particular decision. Primarily, I feel tremendously guilty. Although guilt is... {>>}
Posted by rich at 16:04

>> 18.01.05

Same old place
After discussing the issues of not wanting to pursue a career in academe and time informing my decision to leave the PhD, this post is concerned with environment. It is a fairly simple point I wish to make: I have been at the University of Surrey, in one form or another, since September 1998, when I joined as an undergraduate student. Six and a half years in the same place, during perhaps the most turbulent period of a young man's life, is a long time and I feel that my... {>>}
Posted by rich at 14:41

>> 16.01.05

Too much time?
Another major factor contributing to leaving the PhD is the issue of time. If I were to be honest, I have been thinking about leaving since I completed my annual review last October. At that point, I began wondering whether I would be able to complete another two year of study. There were two aspects associated with this: my mathematical ability and any possible career I choose to pursue. The question of ability was this: do I have the mathematical creativity for the project I am working on? is the... {>>}
Posted by rich at 15:04

>> 13.01.05

A career in academe?
In the previous post, I finally revealed that I am to discontinue my PhD studies. This is the first in a series of posts detailing some of the reasons why I am not continuing, which will precede further posts based on the practicalities of what happens next. The first rule of getting a PhD is to want one. An essentially simple statement, but one that can easily catch people out: why would someone start a PhD if they didn't want one? how do they expect to stay motivated if they... {>>}
Posted by rich at 17:33

>> 07.01.05

Terminal decision
The new year provides me with the ideal opportunity to divulge some of the details of the last month concerning my progress and the PhD diary. Given that there has been very little activity here for some weeks now — and given the tone of some of the posts when there was some activity — it will be of little surprise that progress has not been terrific. Whilst the nature of postgraduate research is such that good times will follow bad and vice versa, it became increasingly apparent to me... {>>}
Posted by rich at 15:22

>> 05.11.04

Literature review (ix)
This is the last part of the literature review, as submitted in part for the annual review and which will eventually form the introduction to my thesis. For more details on this series, please see the first part. Although much research effort has been expended in both the classical and nonclassical formulations of Lie theory concerning B- and IVPs as outlined above, there is still no general, systematic procedure that a user can employ to find symmetries that satisfy conditions (i)-(iii). Instead of this being the fault of the various... {>>}
Posted by rich at 12:27

>> 04.11.04

Literature review (viii)
The remainder of the classical techniques currently available for dealing with BVPs also concentrate on classifying those initial conditions that, through the application of symmetry methods, will solve classes of associated IVPs. As a result, rather prescriptive methods have been developed in which B- and IVPs that can be solved have been classified according to their symmetries, instead of finding and using the symmetries of a given system in order to solve it. (Note that the terms boundary value problem and initial value problem are used synonymously. The relationship between... {>>}
Posted by rich at 14:04

>> 03.11.04

Literature review (vii)
This is the seventh part of the literature review, as submitted in part for the annual review and which will eventually form the introduction to my thesis. For more details on this series, please see the first part. The most successful use of the classical method has been employed in a series of works by Bluman and various co-authors. For a BVP for an nth order ODE, it has been shown that the reduction of order made possible through a multi-parameter solvable Lie group can lead to obtaining qualitative results... {>>}
Posted by rich at 12:21

>> 02.11.04

Literature review (vi)
This is the sixth part of the literature review, as submitted in part for the annual review and which will eventually form the introduction to my thesis. For more details on this series, please see the first part. The area of symmetry analysis is therefore a large and varied one, extending naturally when called upon to do so. Although Lie's approach and its many extensions has had great success in determining and classifying solutions of differential equations, it has proved much less successful in the treatment of boundary- and initial-value... {>>}
Posted by rich at 13:19

>> 01.11.04

Literature review (v)
This is the fifth part of the literature review, as submitted in part for the annual review and which will eventually form the introduction to my thesis. For more details on this series, please see the first part. Generalised symmetries do not act geometrically on the space of variables but are still considered to be symmetries; dissimilarly, there are a class of point transformations that are not at all symmetries but can lead to exact solutions of PDEs. Such "symmetries" are referred to as "nonclassical" symmetries and were introduced by... {>>}
Posted by rich at 16:17

>> 30.10.04

Literature review (iv)
This is the fourth part of the literature review, as submitted in part for the annual review and which will eventually form the introduction to my thesis. For more details on this series, please see the first part. The classification of symmetries, linearising transformations and invariant soltuions formed a great deal of the research effort once symmetry methods were reclaimed from pure mathematicians. Ovsiannikov paid much attention to constructing group-invariant solutions, whilst a reference book containing the symmetries etc. of many PDEs was developed by Ibragimov. Thus, in its classical... {>>}
Posted by rich at 16:16

>> 29.10.04

Literature review (iii)
This is the third part of the literature review, as submitted in part for the annual review and which will eventually form the introduction to my thesis. For more details on this series, please see the first part. Once the symmetry group of a given differential equation has been calculated there are many possible applications. For ordinary differential equations (ODEs), invariance under a one-parameter Lie group of transformations means that the order of the equation can be reduced by one, complete with one quadrature. In the case of a first-order... {>>}
Posted by rich at 16:13

>> 28.10.04

Literature review (ii)
This is the second part of the literature review, as submitted in part for the annual review and which will eventually form the introduction to my thesis. For more details on this series, please see the first part. A symmetry of a differential equation is a transformation that maps solutions of the equation to other solutions; a Lie symmetry group of transformations is a group of transformations (which depend upon continuous parameters) that map any solution of the equation to another solution. These symmetries, examples of which are translations, rotations... {>>}
Posted by rich at 12:10

>> 27.10.04

Literature review (i)
This is the first part of the literature review, as submitted in part for the annual review and which will eventually form the introduction to my thesis. The reproduction of it here is provided for the interested reader, as a reference for others involved in the area of symmetry analysis and as an easily locatable reference for myself. There are nine sections (all of which will be linked to in each section) and a bibliography will be made available at a later point. Towards the end of the 19th century,... {>>}
Posted by rich at 16:06

>> 26.10.04

Completed annual review
The customary silence of the PhD diary will not have worried many people so we'll just pretend that it didn't happen and move on. The annual report was completed some time ago now and has been accepted by all the people it needed to be. I was pleased with the result, which included a detailed introduction to the area of symmetry methods and in particular the use of symmetry methods in the solution of initial- and boundary-value problems. I will post the literature review over the coming days in a... {>>}
Posted by rich at 13:07

>> 09.09.04

Annual report progress
I have been working hard on my end of first-year report and have been doing a lot of typing to try and get on top of things. I have split the process of writing the report into two main sections and subsections thereof: typing up the maths-y work that has been done and researching/writing the literature review. At this stage, both of those sections are complete in what I would consider to be their first draft, which is to say that everything I want to say is written down in... {>>}
Posted by rich at 15:50

>> 27.08.04

Annual report
Many thanks to Paul for his insights into the EngD research degree; I can't say I envy him whilst he is on his outward bound course camping in what is almost certainly wet and windy conditions. As for my recent break in France, I had a very productive time, due in part to the stormy conditions that lasted for four days in total. Now that I am back to the maths work, the reality of the impending annual report has started to manifest itself in a large pile of text... {>>}
Posted by rich at 11:28

>> 19.05.04

Sunny side up
A real change in fortunes today, despite the weather being exactly the same as it was yesterday (I'll have to remember not to blame the weather next time). The trials and jumbles of paper that accumulated on my desk finally produced something tangible and along the lines of what we were expecting and with great joy I have written up the 40 or so sheets into, erm, three sides of neat, structured argument. I was up early this morning to help invigilate and exam for my supervisor. It was a... {>>}
Posted by rich at 15:21

>> 18.05.04

The sun is shining
All day now I have had Finley Quaye's song Sunday Shining running through my head, because the weather is great and I am couped up in the "office". It is a familiar whinge of postgraduate students to moan about having to work whilst everyone else enjoys themselves (along with everyone that has a proper job for a living, I suppose) so I shall not indluge myself for too long, except that to say the work I am doing at present is very hard and I am getting precisely nowhere with... {>>}
Posted by rich at 16:45

>> 14.05.04

A serious hurdle
After handing me the preprint of a paper he will be submitting/has submitted to a journal recently, my supervisor asked me to come up with an equivalent analysis of another — though related — classification of problem we have been looking at. The last week has been spent trying to put together such an analysis and has led to many a moment of dispair as my understanding of the problem all came crashing down around me, only for me to spend literally hours slowly rebuilding it with fragments taken from... {>>}
Posted by rich at 13:43

>> 06.05.04

On the road to publishing a paper
The momentum gained from my attendance at the BAMC a couple of weeks ago has continued and my work has yielded many small victories. Currently, I am working on one of two cases concerning initial value problems; the other problem has been cracked by my supervisor and he is currently in the process of submitting a paper to a journal. He has given me a copy of the paper and asked me to perform a similar feat for the study that I am working on, which is proving to be... {>>}
Posted by rich at 16:56

>> 04.05.04

NPC online survey
Arriving at the most appropriate time imaginable, given that I have just completed my own six-month review, the National Postgraduate Committee have released an online survey intended to find how useful progress review procedures are for research students. The survey seems slightly — and I do mean slightly — biased towards the view that progress reports are somewhat bureaucractic, but is quite thorough in its questions. The first, and perhaps most informative question, asks the participant what they think the purpose of a review is; it is informative in the... {>>}
Posted by rich at 22:52

>> 22.04.04

BAMC 2004 (iv)
The final day of the conference saw the late nights and early mornings — along with the constant talk of maths and sheer effort of concentration — finally catch up with me and I fell asleep in at least one of the small talks. Altogether, this morning saw six such talks and the final plenary lecture. Since today has been similar to the others in many details aside from the mathematical ones (those being exactly the ones I can't really talk about), I shall concentrate on the overall impressions the... {>>}
Posted by rich at 23:00

>> 21.04.04

BAMC 2004 (iii)
The days are starting to go quicker, with today being the last full day of the conference. The structure of the schedule was such that talks were timetabled until lunchtime and the afternoon left as free time, before the main social event of the grandly titled "banquet", which was held in the "medieval splendour" of Saint Andrews Hall in Norwich city centre (images). The day's mathematical content comprised of six talks and a plenary lecture. Certainly, having listened to a lot of mathematics over the last couple of days, I... {>>}
Posted by rich at 23:00

>> 20.04.04

BAMC 2004 (ii)
One or two glasses of wine too many at the reception last night made this morning a potentially hazardous area; fortunately, the breakfast was especially satisfying and the dull ache that was to be present in my head all day had the positive effect of increasing my ability to concentrate. This acute concentration proved to be of great benefit, for the day contained no less than eight talks and three 1 hour plenary lectures. The majority of the talks I attended fell into the rough subject heading of bio-fluids ('fluids'... {>>}
Posted by rich at 23:00

>> 19.04.04

BAMC 2004 (i)
British Applied Mathematics Colloquium (BAMC) 2004 University of East Anglia, Norwich Note: I have been at my first mathematical conference for the last four days; what follows is a brief diary of those four days. I have edited the date of entry for each day such that it appears as though I was keeping the diary up to date each day whilst away. Images are on this page. The British Applied Mathematics Colloquium (BAMC) is an annual gathering of the UK's applied mathematicians, designed to provide a platform at which... {>>}
Posted by rich at 23:00

>> 06.04.04

Successful return
I'm back from holiday and have some great work to get my teeth stuck into. On the last day of the undergraduate term, the meeting with my supervisor turned out to be something of a breakthrough: having added what we thought were necessary complications to the method we were employing, it turns out that the main added complication was in fact redundant. By removing it, the method suddenly transforms into a more reasonable problem to tackle and it is that on which I am working now. The main problem we... {>>}
Posted by rich at 12:32

>> 02.04.04

Literature review (viii)
This is the eighth part of the literature review, as submitted in part for the annual review and which will eventually form the introduction to my thesis. For more details on this series, please see the first part. The remainder of the classical techniques currently available for dealing with BVPs also concentrate on classifying those initial conditions that, through the application of symmetry methods, will solve classes of associated IVPs. As a result, rather prescriptive methods have been developed in which B- and IVPs that can be solved have been... {>>}
Posted by rich at 13:23

>> 15.03.04

Skills training for mathematicians
Nearer the end of last semester, I was moaning away about the sheer uselessness of the research skills lectures all new postgraduate students had to attend. Or rather, I was bemoaning the fact that — though in principle a good idea — the research skills lectures as they stood were of no relevance to maths students and were far too heavily geared to engineers and physicists. In order to demonstrate how I felt about things, I didn't treat one of my assignments as I should have done and ended up... {>>}
Posted by rich at 23:12

>> 12.03.04

British Applied Maths Colloquium 2004
As part of the routine that university departments and their academics follow, each Friday sees the non-linear mathematics seminars, a phenomenon that I have spoken about before. Not only do these seminars provide an opportunity to find out about current research in different areas, they also allow academics to establish links with other university departments and for postgraduate students to meet other academics outside of the department. Seminar seasons such as the ones in the maths department basically form a subset of conferences and provide a good idea of what... {>>}
Posted by rich at 23:03

>> 10.03.04

Good week, bad week, good week...
Embarking on the Funding Focus a month ago seemed like a good idea at the time; it is still probably a good idea now, but it has meant that the PhD diary as a report of my progress and lifestlye has suffered somewhat. There is a list of topics to cover that I have collected over the month, though, so I will endeavour to cover those over the next few days. The Funding Focus has actually highlighted an aspect of my approach to learning that has always been troublesome: as... {>>}
Posted by rich at 12:09

>> 09.02.04

Prize questions
The momentum of writing entries in the PhD diary has diminished over the last few days due to an increase in application. The majority of my time has been spent scrawling busily on a piece of paper trying to solve the mysteries of initial value problems, the sum total of my application leaving things — as they stand — exactly where they were before I started. Never the less, I am not to be deterred and am confident something will happen soon. As a small diversion from my work, I... {>>}
Posted by rich at 17:36

>> 04.02.04

Which comes first?
For an unknown reason, I haven't been sleeping too well of late, but despite this — or perhaps in spite of it — my work has been progressing well. Tiredness is a state that provides your brain with more capability to concentrate for shorter periods of time and it is in those periods that I have been at my most fruitful, moving to the point where I am equipped (mathematically speaking) to lunge into the major challenge of my PhD. It may turn out that this preparation will prove to... {>>}
Posted by rich at 11:46

>> 20.01.04

Depth
I've been struggling to contain my excitement at being back in lectures of late; in order to bring things back to a mathematically acceptable level of emotion, I thought I would discuss what has changed in the lecture theatre since I was there last (which is around 19 months ago). By "change", I do not mean physically, more how being a postgraduate has affected my approach to lectures As an undergraduate, a student displays a justifiable reverence towards the lecturer: there is the required state of trust, which is to... {>>}
Posted by rich at 23:44

>> 14.01.04

Frustrating inability
The majority of today has been spent trying to avoid checking e-mails as a result of my continually banging my head against a brick wall and thus progressing at a rate similar to that of a static caravan. Things started off well enough, until I realised that the result I had meant that either everyone who had come before me was wrong or else I was; it seemed only fair to assume it was the latter. From that point on, belief in my abilities dwindled to the point where I... {>>}
Posted by rich at 19:35

>> 15.12.03

Christmas holidays
The final week before the university closes down for christmas looks like it's going to be one of those in which very little gets achieved. As ever, there are the rounds of social activities, including at least two leaving parties and the maths christmas dinner on Thursday; it is in terms of work, however, that the week will prove to be frustrating and — much as it pains me to keep going on about it — it's the research skills lectures (which I've talked about at great length, here, there... {>>}
Posted by rich at 11:45

>> 13.12.03

A good meeting
Having written about having a meeting every day, little else has been written in this diary about something that is really quite rare at the level of PhD. In truth, I don't think it is worth expanding upon because the meeting is one of the things (like most of them, actually) that are determined by the supervisor. Thus, me writing about the merits of daily meetings might be of no assitance whatsoever to someone that meets their supervisor weekly and might serve only to aggravate a student that already thinks... {>>}
Posted by rich at 19:36

>> 11.12.03

Obviously, it's evident
Having spent a lot of time reading through papers on symmetry methods of late, I'm starting to feel a little out of my depth. It seems that the language of maths is really one that takes a while to acquire and - languages not being my strong point — I'm finding it a little difficult. The difficulties are a combination of many things: a lack of familiarity with the subject matter (it is new, after all), a lack of knowledge of some other fields of maths, an inability to spot... {>>}
Posted by rich at 13:25

>> 10.12.03

Catching worms
An early morning today means that things will either go well and my brain will be a hive of activity, or that things might not go so well and my brain will be a haze of inactivity. Since I will be invigilating in the early afternoon, the morning needs to be at least somehwat productive so that I can show my supervisor, Dr Peter Hydon, some of my work from the last couple of days. We did not have a meeting yesterday, which is somewhat of a luxury given that... {>>}
Posted by rich at 08:51

>> 05.12.03

The competition
Today was spent working through a paper that discusses initial value problems so that I could present the general gist of it to my supervisor, who wasn't familiar with the method the paper advocates. It was an enjoyable and challenging experience, one that both put in perspective where the research I am working on fits in with the symmetry scene and how to present an academic paper. Though I am attempting to write otherwise in this diary, my writing style is normally quite informal, with plenty of little comments here... {>>}
Posted by rich at 19:36

>> 04.12.03

Athens versus library services
In order to get back on track, the majority of the day has been spent searching for papers on initial value problems and their solution using symmetry methods. The main tool for this was MathSciNet, which proved to be both useful and frustrating in equal measure. The basic premise of MathSciNet is a very good one: perform a search for a required paper/author, choose the required paper and then download/print it. Easy enough. The difficulty arises when you are directed to the journal in which the paper appears: roughly half... {>>}
Posted by rich at 17:43

>> 30.11.03

Programming (successfully) in Maple
After several hours of deleting commas, replacing semi-colons with colons and basically playing with punctuation, I've managed to get the programme for finding symmetry generators of IVPs working. It has been quite a frustrating, though ultimately satisfying experience and I've been finding generators of IVPs left, right and centre simply because I can. It hasn't all been fun, though: in order to help the interested reader understand what IVPs are, there is now a small paper over in the research section of arbitrary constant that will hopefully make things a... {>>}
Posted by rich at 00:22

>> 28.11.03

Programming in Maple
My attempts to program in Maple have proved to be as successful as I thought they would be, which is to say they haven't been successful at all. This is partly due to a complete lack of experience with Maple as a mathematical package (which we can be registered as being a fairly major obstacle, i'd say) and a general inability to think "in computers." (I do, on occasions, talk in maths, though). At such times of defeat, it is always worth considering what you are trying to achieve and... {>>}
Posted by rich at 12:58

>> 27.11.03

IVP 'success'
After some time adjusting to the demands of research 'proper', work is moving in a positive direction. Having read the majority of the literature on symmetry methods, I am now working with my supervisor on the symmetries of initial value problems (IVPs). (A brief introduction to IVPs can be found elsewhere within the diary, although a better introduction to this part of the research will be available in the research section of arbitraryconstant soon). This basically boils down to us trying to find a systematic way of finding the symmetry... {>>}
Posted by rich at 23:08

>> 26.11.03

Adaptation
Adapting to true research is proving to be more difficult than I imagined it would be. As I have mentioned before, my PhD had until now entailed working through an introductory text on symmetry methods and working through the exercises/concepts to form a solid basis for future work. (Fortunately, the field of symmetry methods does not contain hundreds of ambiguous papers and text books that contain small, unfathomable results that serve to bog a reader down instead of educate them; as a result, the reading of one text should do... {>>}
Posted by rich at 10:13

>> 25.11.03

The end of the book
Today has seen the end of the first phase of my studies: I have finished working through Peter Hydon's book and will now be working on something that cropped up a while ago but no-one has yet figured out an answer/approach to. In as much as you can define so surely the end of a "phase" of a PhD, I feel like I have settled down well into the routine of things and am looking forward to the new challenges my work will now present. I will be working on... {>>}
Posted by rich at 14:34

>> 18.11.03

A big blank where my mind should be
Today has been by far the worst day of my studies: everything I have tried has gone decidedly wrong and, as it turns out, my grasp of a particular method is not so much a grasp as an attempt to hold on to a greasy pole having washed my hands with olive oil. The day has not been helped by my late-ish night last night, which was late because of the marking I chose to do. Although the money will come in useful, it provided a timely reminder that I... {>>}
Posted by rich at 15:50

>> 17.11.03

Original work
The whole point of a PhD is to contribute original material to your chosen field: if you do not add any new knowledge to your chosen subject matter, then the likelihood of receiving the title of "doctor" diminishes greatly; to zero, in fact. I am approaching the point where I shall no longer be familiarising myself with the discipline of symmetry methods and will be working with my suprevisor, Dr Peter Hydon to develop some new techniques. Though I am slightly apprehensive at the prospect of doing some sums that... {>>}
Posted by rich at 16:32

>> 13.11.03

LaTeX assignment
As part of the research skills course that is compulsory for all new PhD students, I have to produce a LaTeX document displaying various skills. This seems to be the perfect opportunity to employ what would otherwise be a pointless module and write a brief introduction to symmetry methods for the research section of arbitraryconstant. It is due for week 14, which in real moeny is something like the end of November; there will be a link to the paper (and perhaps even a picture to please the punters) from... {>>}
Posted by rich at 16:56
Concentrated effort
Now that I have settled down a bit more, my progress has improved steadily. The current preoccupation is with Dr Hydon's book, Symmetry Methods for Differential Equations, and involves a crash-course in symmetry methods. It's not so much a crash-course as a fairly rapid refresher, because symmetry methods formed a fourth year module as part of my undergraduate studies (and is now, interestingly, only available for MSc students), thus I am familiarising myself with concepts such that they come as second nature. The book itself is split into eleven chapters.... {>>}
Posted by rich at 16:48

>> 07.11.03

Symmetry methods for differential equations
Enough of the walk and talk: there is a need for some facts. My PhD is concerned with Structure Preserving Symmetries of Differential Equations which begs many questions: 1) What are differential equations? 2) What are symmetries of differential equations (or, perhaps more pertinently, what is symmetry)? 3) Should such details really be included in this PhD diary? The last question is perhaps the best starting point: as far as possible, I will not be going into too much detail concerning my actual work within this environment. This is for... {>>}
Posted by rich at 15:53

>> 03.11.03

Dr Peter Hydon
The most important individual associated with a PhD is the supervisor: they determine subject matter, groom learning, offer advice, experience and ability, and basically drag students kicking and screaming through three years of intensive, difficult study. The success of a PhD is down to hard work, which is all channelled in the right direction by a supervisor keeping a close eye on every letter and calculation produced. I think you get the idea. Upon deciding I wanted to continue after graduation with academic study, my thoughts immediately turned to symmetry... {>>}
Posted by rich at 19:50

>> 02.11.03

Research skills
Since the server is down in the BB block (the 'sister' department of maths, where the school reception is located) and I cannot find enough material to show my supervisor in the best possible light, a little more information concerning the conditions of the bursary are called for. There was a time when postgraduates were simply given their money and a supervisor, with the goal of walking away three years later with a PhD. Though that it is still effectively the case (at a very basic level), the demands of... {>>}
Posted by rich at 17:27

>> 31.10.03

MPhil and the transfer report
The first year of a PhD is not strictly "the first year of a PhD"; instead, students are registered on an MPhil (Master of Philosophy) course and then submit a transfer report at the end of the first year in order to upgrade their degree course to that of Doctor of Philosophy, or PhD. It is usually at this point that a student will produce their first large piece of work — sometimes in the form of a paper and supporting project, sometimes just a project — and a judgement... {>>}
Posted by rich at 19:06

>> 30.10.03

Settling into the Chair of Inspiration(TM)
The first day was spent in a temporary office whilst some sound-proofing was installed in the new-ish PhD office. In a previous life, the new "office" was the undergraduate computing laboratory, from which — in a different previous life — I acquired the room number placard during some departmental redecorating. I suppose my new position within the department should really prompt me to return the sign to it's rightful place, but that would be to take away a valued possession from the wall of my room and with it some... {>>}
Posted by rich at 22:28

>> 29.10.03

Induction day
Now that some of the formalities have been dealt with, we can move on to what actually goes on from day-to-day. UniS is separated into eight different "schools", one of which is the School of Engineering and Physical Sciences (SEPS). Somehow, it is assumed that maths falls into this school, and as such, the induction day for maths postgraduates was with about 200 students from physics and all of the engineering disciplines (civil, mechanical, chemical and electrical). It was quite an interesting mix of individuals, although it was relatively easy... {>>}
Posted by rich at 21:26
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