I am going to put a question out there, that I don't know the answer to at the moment.
Q. Are the mathematics courses offered by the Open University, both under and post graduate, of sufficient depth and breadth compared to other, traditional, University maths courses, in the U.K?
I ask this question, as I would be interested in debating this aspect about what is offered by the O.U. and whether it provides sufficient grounding for any budding mathematician, pure or applied.
I have found that their teaching material is very easy to follow and is challenging enough, to keep me interested and intellectually satisfied. It is both incremental in its content and yet I find that I am learning new concepts, each week.
However, I have noticed, that there are a lot of level 2 and 3 courses, that seem to start from the very basics, before moving into new material. For example, the Pure maths course M208, seems to go over abbreviated sections of the MS221 / MST121 material on graphs and numbers, for example.
Is this continual recap of basics at the beginning of each module, wasting time that could be spent fitting in more complex and deeper mathematics? Or, is it a necessary evil, for an institution that tries to cater for people who may dip in and out of their courses, and hence, need a quick recap of basic material, before they find their stride?
I wonder how much extra, and arguably important material, could be fitted into courses, without the slow start? One possible reason for this recap, could be that courses come and go, and often a pre-requisite course, may become unavailable after a few years. Therefore, the only way to fully prepare students for taking courses without these pre-requisites being available, is to provide the recap at the start.
As I read more mathematics for fun and in a scholarly way, I am discovering more and more amazing theorems such as Godel, Fermat and others. I know that the O.U are ditching their module that covered Godel's most famous theorem and I wonder how many other important parts of maths, are being left out?
I would be interested in hearing other people's views. I personally don't have an answer to this just yet.
Interesting question I would say that in general the Open University maths course equates to about 2/3 to 3/4 of a full degree. Obviously it depends on what options you choose. However if you compare with Cambridge for example it is clear that the OU does not offer as wide a range of choices as Cambridge or any Russell group university. What are the reasons for this is a long debate. However 1 would say that in general
ReplyDeletelevel 2 courses equate to the first year of a university Maths course and most level 3 courses equate to the second year of a university maths course.
Missing are Pure Maths
1) Differential Geometry
2) Functional Analysis
3) Rings/Fields and Galois Theory
4) Group Representation Theory
5) Advanced Complex Analysis
6) Topos theory/Category Theory.
7) Lebesgue Integration
Applied Maths/Mathematical methods
1) Any systematic account of Special Functions and their similarity to vector spaces.
2) Green's Functions and Integral equations
3) Numerical analysis computing projects
4) Any systematic account of the Frobenius method for solving differential equations.
Also I get the impression that the questions as you have commented on are generally (although at level 3 there are some exceptions) simpler than those at Cambridge. The Cambridge examples tend to test your ability to link concepts together and at least as far as say group theory is concerned tend to be at a more abstract level.
A Cambridge student sits 4 exams every year making a total of 12. They also start from a higher base. An OU student will sit at most 8 exams including 2 courses which are designed to get people upto speed.
I get the impression that it didn't use to be the case when the OU started and certainly in the past they used to offer courses on Lebesgue Integration, Differential Geometry, Functional Analysis and Linear Mathematics but these are long since gone.
But I think it's only going to get worse as the pressure to merge courses and drop content increases.
There does seem to be a switch in the ethos of the Open University to focus on young people and to be seen as a viable alternative to other universities and I would argue that is why challenging courses are slowly being squeezed out of the system. However those like me who are doing this mainly out of interest or to fill in gaps of my knowledge will become excluded.
If you do the MSc then some of the defects will be remedied but again there will still be gaps the most glaring ones being Representation Theory, Differential Geometry, Applied Functional Analysis and Lebesgue Integration.
Also it's a tragedy that neither the physics department or the maths department offer any courses at MSc level in quantum field theory, particle symmetries, or the foundations of quantum mechanics.
An interesting question and I agree somewhat with the previous comments by Chris, although my exposure might be a little different. For context I took a BA in Maths at Oxford (1967-70), an Msc in Maths at the OU (1991 - 97) and Part III of the Cambridge Tripos (now Master of Advanced Studies) (2010 - 2011).
ReplyDeleteI am not sure of the current OU options but when I studied for the MSc I took Level 3 modules in Galois Theory and Lebesgue Integration and the MSc included modules on Differential Geometry and Functional Analysis. I agree that Chris is right to mourn their passing. (However I am not sure that Topos Theory has a place in undergraduate or even MSc courses at the OU).
For comparison purposes I think we can leave out the Cambridge Part III as it is unlikely to be typical. The thing that struck me about the OU MSc is that it is very much "taught". i.e. each module was based on working through a given text book with supporting notes and TMAs. My Oxford (and Cambridge) experience was very much one of being left to one's own devices which is OK if you are engaged in full time study. I found the OU approach to be an excellent guidance and control system for part-time study (in conjunction with a full time job!).
My assessment is that the depth of study in each OU module (Level 3 and some MSc) was certainly comparable with the first two years at Oxford although the breadth was greater in the later case. (However if I remember correctly Differential Geometry and some of the Commutative Algebra did not appear until year 3).
Although I suspect it is not economically attractive for the OU to develop more advanced modules to include in the MSc options, I would support Chris' case for Representation Theory and wouldn't it be nice to include some Algebraic Geometry and Algebraic Number Theory and perhaps something on Lie Algebras to push the boundaries a bit?
Noel I am very interested in your part III experience - I am guessing you were a bit more 'mature' than most other students. How was the whole experience?
ReplyDeleteJ
Hi J,
ReplyDeleteSince you ask I was nearly 60 when I took Part III and with very limited objectives: viz to try and sample the current curriculum (in Pure Maths) and to provide a basis (i.e. my notes) for further study during retirement. To avoid the danger of letting things slide (after all I was paying for everything!) I also set myself the objective of somehow passing the final exam.
Not surprisingly it was very hard. There were many gaps in my detailed background knowledge in most topics (except Commutative Algebra and Differential Geometry which I had prepared before hand) and I was trying to cover a lot of ground for future use. So although I could usually follow the general drift sufficiently to ensure that my notes made some sense, in most cases I could not keep up with the detail.
This was not a problem as I had anticipated this and it didn't put my objectives too much at risk. There were three issues about age that I could do nothing about though:
1. Speed of thought was now quite slow (particularly in relation to the magnificently bright other students from around the world), but I could get there in the end. Not much good in exams though, but I didn't mind too much and just kept my targets realistic.
2. Memory, which was never that good, was shown now to be pitiful. OK with time to keep looking things up again but not great for exams.
3. Fatigue. Even though I was happy to devote nearly all my spare time to study (after all I no longer had student social angst problems to deal with!) I was physically unable to do so (e.g. falling asleep at 9.00 pm).
Having said this, I loved every minute of it (well perhaps not so much the self catering in graduate student accommodation, but I could drive home for the weekends and be looked after!). The concentration in an almost monastic way on mathematics. The magnificent library at the Mathematical Institute and the dark corners of the old University Library like something from Umberto Eco. The excitement of the lectures (I went to a few more advanced ones where I understood almost nothing of the techniques but was enthralled by the process of watching a story unfold).
In my case, I had the real bonus of no fear of failure (it was not exactly career defining!). I was doing it for the love of the subject. I also had my share of amusing moments such as waiting in the crowd to go in to one of the exams and being asked by a worried post-doc if I was the invigilator. (I said that I had in fact come to take the exam but I was happy to do both if required!).
Finally not to lose sight of the Cambridge experience (very different from my recollection of Oxford). I had the great fortune to be accepted by Kings and one of the bonus pleasures was that my son was there at the same time working on his PhD. So I could enjoy the magnificnce of the architecture at lunch as well as the carol concert at Christmas.
So J, I hope that gives you a flavour. If you wanted to know anything more specific I would be happy to oblige.
PS I forgot to mention the fun with the essay question. With the arrogance of age I chose a topic (Etale Cohomology) that was almost impossibly difficult for me just for the challenge. I had no help from my allocated tutor (no name ...) other than being referred to SGA 4 1/2, which was of course in French!
ReplyDeleteWell, suffice it to say I enjoyed the challenge, adopted my own style and scope and produced an essay for which (as is usual in Part III) I got my best marks. Great!
Noel,
ReplyDeleteSounds like a wonderfully rich experience at Cambridge. How did you find the quality of the lectures and tutorials, compared to those that you experienced at Oxford?
Dan
Hi Dan,
ReplyDeleteNo tutorials for PartIII, you are on your own! It is a bit difficult to compare back to the 60s, but broadly the Oxford lectures were definitely of the undergraduate type (as they should ahve been) and more explicit with respect to technique. You could (just,if you were foolish enough as I sometimes was) lean back and follow them all in realtime (and pay the price at exam time when you had no notes). Only the elite few I guess would attempt this for Part III.
In both cases there were some awful lecturers (no names ..) but this is unavoidable with a subject that can sometimes attract and nurture people not quite in the middle of the autistic spectrum.
My frequent feeling at the Cambridge lectures, particularly the younger lecturers, was listening to experts at the top of their game skipping from peak to peak and leaving you to fill in the detailed trail. OK by me! As far as I can judge, the level of mathematics for Part III is really quite high (which is the intention, after all).
In some cases at Oxford I had the impression that some of the older dons were giving the same lecture year after year, with shall we say a limit to their enthousiasm. It may of course be all very different now.
It is, of course invidious to compare a three year undergraduate course with a three term essentially post graduate course. I suspect that Cambridge undergraduates would tell a different story, not that much different from that told by Oxford undergraduates today.