Mathematics undergraduate - TCD or UCD ?

Smythe

I was just wondering if anyone had any comments on the Mathematics undergraduate courses offered at Trinity College Dublin compared to University College Dublin?

Is one course produced, in any way, to a better standard?

Or alternatively, do employers prefer one course over the other?

I'd be interested to hear any comments about either. Thanks

sponsoredwalk

I'll add a small addendum that anyone who knows the answer could just tack
on at the end It's a related question thus not deserving it's own space:

Assuming employers & statistics are not even the least of your worries
because you see both as the devil incarnate, is there a way to construct
a course in either TCD or UCD in such a fashion as to do enough physics
that a theoretical physicist would do all the while doing deeper math than
a TP would do? It's my understanding that math is more of a tool for a
TP & while that's great I physically can't learn math unless I learn the
theory, theorem proofs etc... Plus I want to learn it because it's extremely
interesting in it's own right. it's been a concern of mine for some time
& reading the TCD site has me a bit confused, a point in the right
direction would help

antiselfdual

sponsoredwalk wrote: »

Assuming employers & statistics are not even the least of your worries
because you see both as the devil incarnate, is there a way to construct
a course in either TCD or UCD in such a fashion as to do enough physics
that a theoretical physicist would do all the while doing deeper math than
a TP would do? It's my understanding that math is more of a tool for a
TP & while that's great I physically can't learn math unless I learn the
theory, theorem proofs etc... Plus I want to learn it because it's extremely
interesting in it's own right. it's been a concern of mine for some time
& reading the TCD site has me a bit confused, a point in the right
direction would help

Yes, do the Mathematics degree in TCD and pick all the TP options. Simple!

I can't really comment on the differences between the UCD and TCD degrees having only done one of them; I was going to make some partially informed statements after looking at the UCD course programme website, but then I saw they have a Mathematics degree, a Mathematical Science degree and a Mathematical Studies degree, which confused me too much to continue...

sponsoredwalk

antiselfdual wrote: »

Yes, do the Mathematics degree in TCD and pick all the TP options. Simple!

I can't really comment on the differences between the UCD and TCD degrees having only done one of them; I was going to make some partially informed statements after looking at the UCD course programme website, but then I saw they have a Mathematics degree, a Mathematical Science degree and a Mathematical Studies degree, which confused me too much to continue...

Thanks, is that what you did? I'm pretty concerned though, It's been my
plan all year to do TP but since my appreciation of math has grown I'm
leaning to doing math, but I honestly loath statistics & probability,
especially when applied to business situations which seems to me to be
a big focus because math courses churn out people going into these jobs.
From my glances it seems there is a heavy slant to these subjects in a
math course. Also, is there a big reduction in the physics if I choose just
math & do the TP choices? I'm really enjoying analysis & the inklings of
abstract algebra I have are only of clarity.
Basically my thoughts are that if I choose TP I'll be given a lot of
hand-wavey math, i.e. quantum mechanics without a deep & proper study
of functional analysis, general relativity without deep diff geom, manifolds,
forms etc... If I choose math I'll lose out on a lot of E&M, QM, QCD,
GR, particle physics...
My thoughts are that if this is the actual situation I face, i.e. a choice
between major losses, I'll just do TP & supplement it with a hell of a
lot of my own study.

And in keeping with the tone of the thread, comments on the differences
in TCD & UCD with regard to this situation would be really helpful.
I assume the OP would be more interested in the probability & statistics
stuff so comments on the positives and negatives of these devil
subjects would be great (Yeah QM uses a lot of both subjects, I'll learn them
properly of course & we *may* see a change in attitude but I doubt it).

antiselfdual

Yeah I did TP for 2 years than saw the errors of my ways and switched. The Maths modules for TCD are listed here. It's important to realise that the the Maths department teaches the "proper" quantum mechanics, quantum field theory and general relativity courses, also that in TP you do the majority of the first and second year Maths courses (excluding stats, primarily, and some miscellaneous pure courses like number theory and Lebesgue integral) before doing QM, Classical Fields, Stat Phys, QFT, General Relativity in the last two years. Differential Geometry is a prerequisite for Gen Rel.

So if you do TP you miss out on some additional analysis (including fun anal, I am extremely dubious this course would be helpful for TCD's QM though and somewhat perturbed you realise it's important in QM at large, which was only pointed out to us by a lecturer in 4th year explaining how lacking our degree is, don't ask), group reps, and a mixed bag of other pure courses.

If you do Maths you miss out on labs (yay) and a pile of physics courses like optics, electromagnetism, various condensed matter and material physics (ugh) courses in the last couple of years. You certainly don't miss out on the chance to do QM, particle physics (ie QFT) and general relativity properly because that's done in the School of Mathematcs (admittedly it may be done terribly there anyway if you're unlucky with eg lecturers/retirement/whatever. But still). I'm pretty certain you can avoid probability and statistics completely after first year.

I hope someone who can talk about UCD as well as TCD comes along at some point...

sponsoredwalk

Wow, so my main loss would be thorough E&M & Optics then?
Well I know a book by Jackson is the gold standard in E&M & ultimately
conquering that book is the main goal over 4 years or so as I'm not overly
interested in it per se at the moment but I'll push myself to get through
that book before I decide anything major about E&M.
But everything you've said is exactly what I wanted to avoid I'll put
more effort into checkng this stuff out now, thanks for the help Any
further comments by anyone are graciously and vociferously hoped for

As for QM, I was reading the comments on a book here a while
ago for that book & one comment particularly stuck out:

This book is divided into two parts. The first part is devoted mainly to
metric and normed spaces. There are too a chapter on the essentials of
set theory, an addendum on generalized functions, and a chapter on
linear operators. The second part is devoted to measure theory, the
Lebesgue integral, the theory of square integrable functions(L2) and
Hilbert spaces. The second part incorporates exercises to the reader.
The clarity of exposition and the elegancy of this book is notorious !
This book can be recommended not only for mathematicians, but for
theoretical physicists. Do you know why the Heisenberg picture of
quantum mechanics is equivalent to the Schrodinger picture of
quantum mechanics ? Mathematically, Heisenberg theory uses the
space l2, while Schrodinger theory uses the space L2. A consequence
of the Riesz-Fisher theorem is that the spaces l2 and L2 are isomorphic,
a result proved in this book. The two theories leads to the same
physical results, and in consequence are equivalent, although
different in the mathematical content ! You need to buy this book !

To you this may be elementary but to me it's such a motivating factor
for learning otherwise obscure things like Lebesgue integration etc...
Motivation is hard to come by for some of these topics so a little is a
lot

Michael Collins

sponsoredwalk wrote: »

To you this may be elementary but to me it's such a motivating factor
for learning otherwise obscure things like Lebesgue integration etc...
Motivation is hard to come by for some of these topics so a little is a
lot

Ha I remember reading that particular quote myself, after which I added that book to my Amazon Wish List - I'm not allowed buy anymore books till I read the ones I have.

Enkidu

If you like rigorous Quantum Mechanics Michael Collins, then read Chapter VIII of Reed and Simons "Methods of Mathematical Physics" Volume 1.

Then, if you're really into it, you could read Volumes 2 and 3!

Fremen

I'd go with TCD, but that's my personal preference in mathematics showing through. UCD is arguably stronger in algebra, TCD in analysis. I don't think there's a course in topology in UCD, which is a gaping hole. It seems like neither offer number theory courses, which I found surprising.

Sponsoredwalk, I wouldn't be so quick to dismiss probability. Ok, the introductory stuff is pretty dull, but later on it gets fascinating. For instance, how would you construct a continuous function on [0,1] which is not differentiable at any point? Does such a function even exist? Probability will tell you...

Oh, and you'll need it in spades for QM.

Anonymo

I'd go along with what Fremen's point about TCD being stronger at analysis and UCD at algebra. As for the theoretical physics courses, if you're thinking of going down the string theory route eventually TCD is probably best. However UCD is certainly stronger for General Relativity and you'll get a broader basis in theoretical physics (fluid dynamics, astrophysics etc. are quite strong there). Though biased I would recommend UCD for an undergrad. I'd also recommend to go into the science course since through that you can pick as many maths, math physics and physics courses as you like. The 'problem' with theoretical physics in UCD is the lack of pure maths while the 'problem' with maths science is that you're constrained to pick some stats courses while it seems your interest is in physics/maths.