Post-Results Blues

This last two weeks, I have been concentrating on  partial derivatives, gradient, curl etc,
as I delve (pun intended), into the murky waters of applied mathematics.

I have to say that I really have mixed feelings about this subject.   I know that I mentioned earlier this month, that applied mathematics is a lot of 'hand waving'; however, my tongue in cheek comments actually hide a little bit of fear and trepidation about this field of mathematics.

I though that doing pure mathematics first: analysis, groups and linear algebra; would have made the applied subjects an easy win on my study journey.

However, I am finding myself a little stressed as I self-study the  O.U course MST209 (Mathematical Methods and Models).

It isn't the difficulty of the material, since I believe that M208 is equally as taxing.  It is simply a case of my brain seemingly being better at abstract maths rather than applying the maths theorems to models, making assumptions and knowing which units the final answer should be expressed in.

This has caused me a small issue.  That is, in the back of my mind, I can feel a little bit of tedium creeping in; and, dare I say it, some boredom too, as I go through the applied examples in MST209.

This is causing me two problems.

Firstly, after the heady 92% pass in my pure maths exam, I have now lurched into a mild state of panic.  I have 18 months of applied maths modules ahead of me and if I am finding it a bit tedious now, how the hell am I going to be able to sustain my concentration when things get tough in June next year.

Secondly, I have a little voice at the back of my head that is whispering, "you don't like applied maths, do you?"  I don't know whether to believe that voice, or whether it is just some self-destructive thought pattern, trying to provoke me into shifting to a safe study path.

I know that I am going to be excited about studying quantum mechanics in February.  However, what if I can't shake this feeling of doubt and tedium?  Will I be able to cope with Electromagnetism, if I can't stand the sight of another damn Maxwell equation?

I do hope that these feelings pass.

M208 Exam Result

I am thrilled to say that I managed to pass the Open University's offering in Pure Mathematics, M208.

The email came today, stating that the results were in; and, after plucking up the courage an hour later, I checked my result.

Well, I managed to achieve a Distinction with 92% of the available marks, which has left me amazed, since I am sure I counted up at least 10 marks of 'known' errors in my exam script.

So, it just goes to show, that post-exam memory cannot be relied upon, as an accurate assessment of performance.

So, once I have soaked the news up, I will begin to plan with a little more security, the rest of my studies.

I am sticking with Quantum mechanics and Electromagnetism in February;  but I am now one step closer towards my wife supporting my MSc studies at a brick University, in October 2013.

MSc choices

I have been working hard this week, to convince my better half, to let me use some of our hard earned savings to pay for a part-time MSc next year, at a London University.  The course is 2yrs part-time and costs well over £12K!

I have been used to plodding through my Open University studies, each year, at a pace that is financially comfortable and is not too taxing in terms of time spent each week, studying.

However, the Open University simply do not offer me what I want at the postgraduate level.  I am also certain, that they never will either (going by the recent conversations that I have had with several tutors and course administrators).

Bottom line?  The O.U do not believe that it is financially viable for them to offer theoretical science MSc's.  This is despite them having a student base of over 250,000.

So, my potential choice of an MSc, with a very well known London university, is an intensive two year stint, with a minimum of 20hrs per week of studying and at the very least, a monthly trip to London for intensive lectures and study.

I already work in a traditional profession, and clock the occasional 56hr week, so any extra time spent studying, will almost certainly impact on my 'family time'.

So, it's a big ask; "darling, can I spend our savings so that I can see you and the kids even less for the next two years?"  Doesn't sound that attractive.

The course, which I have deliberately not mentioned the title of  yet, combines some pure and applied mathematics, with fairly advanced computer science and modelling.

It isn't a degree in physics, but then I am struggling to find one, that will allow me to complete it part-time, without having to visit a lab each week.

So, I will ponder, cogitate and digest this potential bifurcation point in my study path; whilst I sit and wait for my exam results for this year.

If I don't get a good pass in those exams, I will probably be fairly limited in my MSc options, anyway.

Lastly, why haven't I mentioned the title of the degree yet?  Because I want to settle on the decision myself, since it is such an important choice.  If it turns out to be wrong, then I want that decision to be on my shoulders only.

Rambling Matrices Revisited!

The title of this post is an intended homage to two particularly favourite blogs of mine, by  fellow students.

Matrices Reloaded

Ramblings of a Short Fat Failed Physicist

Having studied matrices as part of M208 Pure Mathematics, I feel I need a little refresher / revisit / reload of some basic manipulation and applications of them

I have thumbed through several books that I have which cover advanced mathematical physics; and it appears that matrices play a major, prominent role in many areas.

I don't have any particular issues with matrices and I found that Gauss elimination method was one of my best practised methods, as I prepared for the M208 exam.

However, I want to be able to fire through manipulation of matrices, vectors / tensors and other tools, at lightening speed and with pinpoint accuracy.  It just feels like it will be nice to have a security blanket going into quantum mechanics and electromagnetism, in February.

Mathematical Modelling Software

I have now completed units 1, 2 and 3 of the Open University course MST209 (Mathematical Methods and Models).  This is self study and after a quick recap on vector algebra tomorrow and Tuesday; I will have set myself up for a few weeks of Vector Calculus practice, before Christmas creeps any closer.

Unit 3 mainly developed some basic calculus involving second order differential equations.  Time allowed me to manage about 75% of the example questions, selecting at least one example for each different 'issue' that arises when trying to solve these equations.

I found it particularly satisfying when the second order diff equations were used to model damping phenomena in oscillating systems.  I will probably look to try and use some of these example questions to test drive some different types of modelling software, before settling on one package to then master over the next two years.

However, I am quite unsure as to which software I should invest the time and effort into learning.

I have some experience of the algebra package Mathcad, but I found it quite difficult to use and didn't really warm to it. I know they are planning an easier product in the future, and I will test drive that software as part of my selection process. Other choices might be Mathematica, Matlab, Maple etc.

I need to do some research here, as I am unsure as to whether there is one package that is mainly used as an academic and industry standard, when modelling mathematical and physical systems or designs.

I suspect there isn't just one' best-fit' package, so it may just come down to personal preference, ease of use and checking that it has the scope to be used in my research and beyond.

My Annual Visit to the O.U Library

This morning, I braved the wind and rain to embark on my now traditional visit, to the Open University campus at Walton Hall.

As part of my preparation for the February modules, I like to visit the O.U library, which contains reference copies of all the O.U module materials, that I will be studying soon.

This has two distinct benefits:

1.  By leafing through the materials, I get a feel for the level of difficulty that awaits me.  Thus, my stress levels are minimized, as we approach February.

2.  I know exactly how much prep I need to do and in which areas of study.  This has already paid off, as I can see that I had planned to study my maths prep, in far too much detail.  I now plan to refine that plan this week, so that I can spend much more time on practising and becoming a differentiation and  integration Jedi!

So, for my two Feb courses, in Quantum mechanics and Electromagnetism; here are the areas of study for next year (Chris, I know you will salivate at the sight of some of these topics;-)


SMT359 (Electromagnetism)

Book 1

Electric forces and fields
Gauss law
Magnetic forces and fields
Vectors
Field coordinates
Partial derivatives
Volume and surface integrals
Divergence of a vector field
Line integrals
Curl of a vector field
Laplacian operators


Book 2

Foundations of electromagnetism
Electrical fields in materials
Magnetic fields in materials
Electrostatics
Magneto statics
Forces on particles
Resistance and induction
Super conductivity
Special relativity

Book 3

Electromagnetic waves in empty space
Generation of electromagnetic waves
Dielectrics
Conductors
Plasmas


SM358 (The Quantum World)

Book 1

Basics of quantum mechanics wave / particle discussions etc.
Schrödinger's equation and wave functions
Particles in boxes (more Schrödinger)
The Heisenberg uncertainty principle
Simple harmonic oscillators
Wave packets and motion
Scattering and tunnelling
Maths tool-kit including,
Complex numbers
Ordinary diffrential equations
Partial differential equations
Probability

Book 2

Dirac notation
Ehrenfest equations
Geometry of quantum mechanics
Angular momentum
Spin angular momentum
May particle systems
The Pauli exclusion principle
Bose Einstein condensate
Quantum entanglement
Quantum information
Quantum teleportation
Vectors
Abstract vector spaces
Matrices

Book 3

Angular momentum in atomic physics
The hydrogen atom
Time independent approximation methods
Hydrogen like systems
Putting quantum mechanics and relativity together
Many electron atoms
Hund's rules
Diatomic molecules
Solid state physics
Light and matter

Both courses seem to separate out the mathematics 'training' from the qualitative material and the application of the concepts.  This makes it easy to dip into the maths chapters first, so that there is less stop-start business going on.

I am so excited at the prospect of studying this material, that I am not sure I will sleep tonight. 

 Now, where's that anorak?

Quantum Mechanics and Electromagnetism Preparation

Okay, so I am now in full swing with my preparatory studying in preparation for the level 3 Open University mathematical physics courses, The Quantum World (SM358) and Electromagnetism (SMT359).

These are the main offerings at level 3 for physics.  There are another two courses that cover Astrophysics and also Relativity / Cosmology, which look very interesting, but I am not sure they fit in with my study plans.

That will leave me with two other, rather obvious courses, for me to choose in order to make up an appealing and ostensibly solid mathematical physics / applied maths background to my degree.  Those courses are, Waves Diffusion and Variational Principles (MS324) and the science project course Radiation and Matter (SXP390).

I have added this project module on my list of hot favourite modules for October 2013, simply because it will follow on nicely from the quantum and electro stuff that I will have just finished studying; and it appears to allow some research and writing in a substantial piece of work.  This will develop skills that I don't currently have and that I critically need, if I am to study a masters thesis module or even move straight onto a part-time MPhil or beyond.

It will also nicely consolidate my Feb 2013 study modules, as I will be applying them in the following 9 month period.  The project subjects available include work on quantum entanglement, so it certainly sounds challenging enough to whet the appetite.

Anyway, this week I have now studied the following prep materials:

recap on:
differentiation and integration
first order differential equations
solving linear equations

So I have managed to cover 32hrs worth of work, from the OU course MST209 (Mathematical Methods and Models), in 12hrs.  Having said that, much of it was a recap or advancement on work that I had done in MST121 or M208 in 2011 / 2012.

Next stop, second order differential equations and some recap on vector algebra, before, next week,  I launch into some Fourier Series and partial differential equations.

Awesome!