Maths and Theoretical Physics Course Thread TR031 TR035

Maybe_Memories · 01-09-2011 6:39pm

Tears in Rain wrote: »

On an unrelated note, very nice Linear Algebra exam, it was almost too easy...

Out of extreme curiousity, for question 2, which of your vectors were part of the subspace?

Aoibheann · 01-09-2011 7:07pm

PurpleFistMixer wrote: »

That or I'm jealous that Vlad has been going around handing out gifts and I'm missing it.

I briefly thought that too.. >.>

What was so nice about the paper actually? Hope you guys got on well!

Maybe_Memories · 01-09-2011 7:20pm

Aoibheann wrote: »

I briefly thought that too.. >.>

What was so nice about the paper actually? Hope you guys got on well!

Jordan Normal question was a 2x2 matrix.

Sylvester's Criterion was on it, and showing a vector is part of a subspace (reducing a 5x5 matrix isn't very fun...).

Question 1 was difficult though.

CJC86 · 01-09-2011 7:31pm

PurpleFistMixer wrote: »

On the upside, there's a new and exciting TP course on the Standard Model! >.>

Just as the Standard Model has been, with reasonable confidence, falsified by the LHC. Nice.

Aoibheann · 01-09-2011 8:04pm

Maybe_Memories wrote: »

Jordan Normal question was a 2x2 matrix.
Sylvester's Criterion was on it, and showing a vector is part of a subspace (reducing a 5x5 matrix isn't very fun...).

Question 1 was difficult though.

2x2?! Seriously? That was very, very generous of Vlad. You can pretty much pass semester 2 on that question alone like, or you could with the marks assigned to it on our paper last year.

What was question 1, out of nosiness? You guys had separate papers for each this year, right?

Maybe_Memories · 01-09-2011 8:20pm

Aoibheann wrote: »

2x2?! Seriously? That was very, very generous of Vlad. You can pretty much pass semester 2 on that question alone like, or you could with the marks assigned to it on our paper last year.

What was question 1, out of nosiness? You guys had separate papers for each this year, right?

1. (a) Define the rank of a linear operator.
(b) Consider the vector space V of all 2x2 matricies. Show that for every 2x2 matrix A the mapping L:V->V given by the formula L(X) = AXA - 3X is a linear operator. Compute the rank of this operator for

A = 2 -1
``` 1 2

Showing that L was a linear operator was grand. But getting the rank wasn't. If L is the operator then surely L(X) is the image of some vector X? But that doesn't make sense because then the AXA part of the formula isn't defined...

Yup, we did.

Burkie.EXE · 01-09-2011 8:55pm

Well, second round offers came in this morning, so I guess I'll be hanging out with all you Theoretical Physics guys

Phil92 · 01-09-2011 9:06pm

Well, second round offers came in this morning, so I guess I'll be hanging out with all you Theoretical Physics guys

Same here! I'm amazed it dropped by a whole 30 points..

dabh · 01-09-2011 9:38pm

Maybe_Memories wrote: »

1. (a) Define the rank of a linear operator.
(b) Consider the vector space V of all 2x2 matricies. Show that for every 2x2 matrix A the mapping L:V->V given by the formula L(X) = AXA - 3X is a linear operator. Compute the rank of this operator for

A = 2 -1
``` 1 2

Showing that L was a linear operator was grand. But getting the rank wasn't. If L is the operator then surely L(X) is the image of some vector X? But that doesn't make sense because then the AXA part of the formula isn't defined...

The point to take on board is that the 'vector space V of 2x2 matrices' is a vector space, so the elements of V are the 'vectors'. Thus a 2x2 matrix X is a vector in this 4-dimensional space. Its components are given by the four components, say

X = ( p q )
( r s )

Compute the components of L(X) in terms of p,q,r,s. These components form a quadruple of real numbers, so you have the specification of a linear transformation from a 4-dimensional vector space to itself. This has a well-defined rank.

Basically, you should be unfazed by the fact that the space of linear operators on an n-dimensional vector space is a vector space of dimension n^2, whose components are the components of the matrices representing the linear operators. Thus linear operators acting on some vector space are vectors belonging to some other vector space. In particular a 2x2 matrix can be regarded as a 4-dimensional vector.

Fringe · 01-09-2011 9:54pm

PurpleFistMixer wrote: »

That or I'm jealous that Vlad has been going around handing out gifts and I'm missing it.

Vlad did give a book to someone in our year because he really liked their proof in the exam. He even latexed it up and sent it to everyone.

fh041205 · 01-09-2011 11:40pm

Fringe wrote: »

Vlad did give a book to someone in our year because he really liked their proof in the exam. He even latexed it up and sent it to everyone.

Ha fair play. What was it? Any chance you could sent it to me? I'm curious to see it.

Aoibheann · 01-09-2011 11:57pm

PM'd you the link.

The guy whose solution it is, is our other resident genius, along with Fringe there.

PurpleFistMixer · 02-09-2011 1:06am

CJC86 wrote: »

Just as the Standard Model has been, with reasonable confidence, falsified by the LHC. Nice.

Now now, it's not a course on SUSY.

Tears in Rain · 02-09-2011 1:17am

Maybe_Memories wrote: »

Out of extreme curiousity, for question 2, which of your vectors were part of the subspace?

I can't remember...I'm woeful at reducing matrices without making arithmetic errors so I was very surprised when my first one turned out to be part of the subspace. Can't remember the rest though. That said, I'm pretty sure I got the reduction wrong and it shouldn't have been.

Good luck everyone who has Analysis tomorrow!!

Maybe_Memories · 02-09-2011 11:32am

dabh wrote: »

The point to take on board is that the 'vector space V of 2x2 matrices' is a vector space, so the elements of V are the 'vectors'. Thus a 2x2 matrix X is a vector in this 4-dimensional space.

Aaah! At least I'll know for next time.

Enkidu · 02-09-2011 6:47pm

CJC86 wrote: »

Just as the Standard Model has been, with reasonable confidence, falsified by the LHC. Nice.

No it hasn't!

KarlD93 · 04-09-2011 12:17am

Well, I'm starting maths this year and can't wait! By the sounds of it it should be interesting but hard! Bit confused by the timetable though... (Here: http://www.maths.tcd.ie/undergraduate/timetable/ttjf.html) Some periods have three subjects and also listed at different places like 12:00 on Tuesday, Wednesday and Friday! Any insight??? And one more question, when a period is listed as odd weeks only, does that mean there is no period at all on even weeks? Thanks!

PurpleFistMixer · 04-09-2011 12:23am

Not sure what's up with Friday at 12 (I'd guess it might mean the location of the lecture changes, since it's the same lecturer), but the other overlaps are all tutorials which probably means you'll be split up. If MA1261 is the 061 course I took in first year, it's a small computers thing with only 10 or so in the group, so you'd only have to attend one of those (and likely told which one).

Maybe_Memories · 04-09-2011 12:43am

MA1261 is C programming with Colm O'Dunlaing.

The thing on Friday at 12 is Pete splitting up his class for a tutoria one week and a lecture the other, presumably in different places.
Tuesday at 12 is the MA1261 tutorial, also clashing with the maths help room, but thats on at 11 as well.

KarlD93 · 04-09-2011 12:48am

How's the transition anyway from LC to College? I'm a bit nervous about it all oddly

. Should go smoothly I hope!

Maybe_Memories · 04-09-2011 12:58am

KarlD93 wrote: »

How's the transition anyway from LC to College? I'm a bit nervous about it all oddly . Should go smoothly I hope!

In terms of maths? The bring it in gradually like they dont throw you in the deep end straight away. They do however raise the standard a lot after christmas.

wantacookie · 04-09-2011 1:01am

I don't use boards for ages and come back and find we have a whole thread, about time!
anyone else looking forward to going back? third year should be interesting!

KarlD93 · 05-09-2011 3:01am

Could someone tell me what's the difference between a tutorial and a lecture. I'm going into JF maths

dabh · 05-09-2011 7:51am

KarlD93 wrote: »

Could someone tell me what's the difference between a tutorial and a lecture. I'm going into JF maths

The difference is pretty much what the individual lecturer thinks it ought to be for a particular module (or course).

The basic idea, though, is that some contact hours may be lectures, where the lecturer will develop theory, providing definitions, proving theorems, explaining and justifying methods to solve problems etc. Other contact hours may be tutorials, which are typically used for going over solutions to problems, which may often have previously been given to students as homework assignments.. If the class size is sufficiently large, the class may be divided up into several smaller groups for tutorials.

funkadelica · 05-09-2011 1:45pm

Just had a quick skim through this thread. Way to terrify the first years lads.

Dear Junior Freshmen,

As long as you're reasonably good at maths and physics, and happen to have half a brain (enough to realise you can't actually coast through without going to a single lecture, trust me, I tried), then you will quickly discover that first year is NOT HARD! (Take it from someone who has done it twice :P) Have a bit of cop on, do the work, and most of all, don't take it all too seriously, you'll be graaaaand

Love Nikki x

P.S I am, of course, only talking about first year, second year looks like a b***h :DD

fh041205 · 05-09-2011 3:02pm

Oh Nikki, we do love you so. But yea she's right lads. Personally I found 1st and 2nd year both hideously boring, but they are entirely necessary for all the cool stuff that follows. (sorry to be blunt about it)

Also, maths classes can be very reserved sometimes, don't be afraid to shout up or ask questions. Normally you'll just be saying what 90% of the class are thinking. The other 10% are me, Rob and Cathal, who are trying to falsify the concept of backwards time travel using a 4x4 rubik's cube and a magic 8 ball. Ah harmonic.....

Tears in Rain · 05-09-2011 3:11pm

fh041205 wrote: »

Oh Nikki, we do love you so. But yea she's right lads. Personally I found 1st and 2nd year both hideously boring

Ugh, well that's depressing (going into 2nd year)

Maybe_Memories · 05-09-2011 3:25pm

Tears in Rain wrote: »

Ugh, well that's depressing (going into 2nd year)

It'll still be more interesting than first year though hopoefully

FishyS · 05-09-2011 5:26pm

Maybe_Memories wrote: »

It'll still be more interesting than first year though hopoefully

First year was boring, second a little better. Hopefully third year will be interesting.

p.s. for first years, if you ask kovacs a question during the lecture he will go over the whole lecture again and you can get a little sleep

fh041205 · 05-09-2011 6:52pm

Maybe_Memories wrote: »

It'll still be more interesting than first year though hopoefully

Yes it is I suppose. Sorry I didn't mean to be a downer! But look at it his way. If you don't think first and second year were actually that bad, then by my logic sophister years will blow your f*cking mind!!!:D

Maybe_Memories · 05-09-2011 6:55pm

FishyS wrote: »

p.s. for first years, if you ask kovacs a question during the lecture he will go over the whole lecture again and you can get a little sleep

This is true.

Also, you don't really need to go to the first two mechanics lectures, unless you want to listen to Kovacs ramble on about how classical mechanics fails in a variety of circumstances, all of which are completely irrelevant to the course. :pac:

FishyS · 05-09-2011 7:12pm

Maybe_Memories wrote: »

This is true.

Also, you don't really need to go to the first two mechanics lectures, unless you want to listen to Kovacs ramble on about how classical mechanics fails in a variety of circumstances, all of which are completely irrelevant to the course. :pac:

Also absolutely nothing he did in the second half of the year was on the exam. He finished the course just after christmas.

PurpleFistMixer · 05-09-2011 7:16pm

I liked first and second year well enough (though I found the physics somewhat boring). So many nay-sayers... Third year is better because you start doing things which more closely resemble "real" theoretical physics, and that's always nice.

I missed the bit where people were saying it's really difficult, though. It's not a dos of a course, but you don't have to be a crazy genius to do well or anything... just do the work.

Podge_irl · 05-09-2011 7:48pm

PurpleFistMixer wrote: »

On the upside, there's a new and exciting TP course on the Standard Model! >.>

Who's teaching that?

The Standard Model is, in many ways, essentially just a course on Group Reps. Which is unfortunate as I hate group reps.

PurpleFistMixer · 05-09-2011 8:21pm

Sint. Then Shatashvili is doing Yang Mills Theory in the second semester. It's gonna be awesome.

mulciber · 05-09-2011 8:34pm

Hi, just a little 5th year here who's aspiring to do theoretical physics in TCD.

I was just wondering: is there anything I can do now to prepare for theoretical physics? Also, is there a way that you could join maybe theoretical physics and maths together or theoretical physics and computer science together?

Also, what job opportunities are there after you finish the course.

I just though I would ask the questions before I venture out into the course and before I put it down as No. 1 on my CAO form next year.

Any info would be appreciated.

Thanks,

~Mulicber

Maybe_Memories · 05-09-2011 8:43pm

mulciber wrote: »

Hi, just a little 5th year here who's aspiring to do theoretical physics in TCD.

I was just wondering: is there anything I can do now to prepare for theoretical physics? Also, is there a way that you could join maybe theoretical physics and maths together or theoretical physics and computer science together?

Also, what job opportunities are there after you finish the course.

I just though I would ask the questions before I venture out into the course and before I put it down as No. 1 on my CAO form next year.

Any info would be appreciated.

Thanks,

~Mulicber

Hey!

Right, firstly, you need to actually enjoy doing maths. There's a load of people in my class who are like "Yeah I was good at maths for the LC. I'll go off and do a maths degree shur! Be grand like!" The majority of them really regret their decision. A few people in maths have already dropped out. No idea what the story with TP is.

If you can, do Applied Maths for the LC. Some of the questions are at the same standard you'll be doing in Mechanics in TP, especially the ones in the 80s and 90s. Oddly enough the 70's aren't bad at all. Although there is that interesting question with the rod on in inclined plane... So do Applied Maths, and do your best to understand what's going on. Struggle through the problems and you'll get to a stage where you can do them with your eyes closed.

I've just realised you're in 5th year so will have to do Project Maths. This is bad. I've no idea how the maths department will change the introductory syllabii to make up for this, but I'd imagine they will. :pac:

mulciber · 05-09-2011 8:51pm

Maybe_Memories wrote: »

Hey!

Right, firstly, you need to actually enjoy doing maths. There's a load of people in my class who are like "Yeah I was good at maths for the LC. I'll go off and do a maths degree shur! Be grand like!" The majority of them really regret their decision. A few people in maths have already dropped out. No idea what the story with TP is.

If you can, do Applied Maths for the LC. Some of the questions are at the same standard you'll be doing in Mechanics in TP, especially the ones in the 80s and 90s. Oddly enough the 70's aren't bad at all. Although there is that interesting question with the rod on in inclined plane... So do Applied Maths, and do your best to understand what's going on. Struggle through the problems and you'll get to a stage where you can do them with your eyes closed.

I've just realised you're in 5th year so will have to do Project Maths. This is bad. I've no idea how the maths department will change the introductory syllabii to make up for this, but I'd imagine they will. :pac:

Thanks for the quick reply.

Yeah, I love maths, always have. It's my favourite subject in school. I'm a really logical person and I see maths as the world just broken down into it's most simplistic form. Everything can be described with maths.

I've already chosen to do applied maths as an extra subject. I'm even giving up my Wednesday afternoons to do it.

Yeah. I had a look at some of the project maths syllabus and it looks really bad to me. It looks as if they're trying to relate maths more to everyday life while I like the pure maths more.

PurpleFistMixer · 05-09-2011 9:55pm

mulciber wrote: »

Also, is there a way that you could join maybe theoretical physics and maths together or theoretical physics and computer science together?

In TCD, not officially. I think in NUIM or UCD you can do them together in some kind of Science thing, not entirely sure.

However:
Re maths and TP: TP is already >50% maths (ie taught in the maths department, courses open for pure maths students). You don't do as much pure maths as the mathematicians (simply because there is only so much time in a day...) but you certainly have a mathematical outlook/approach to physics. Also, it's fairly common/easy for TPs to transfer into maths in 1st/2nd/3rd year. (Not the other way around though, or science into TP.) Also, there is always (timetables permitting) the option of simply attending maths lectures if you want (which is what I do).

Re CS and TP: Not as simple as maths and TP, since TP has no association with the CS department. However, as part of the physics you do in TP you have to do computational stuff, so you do get an introduction to programming and numerical methods. That's about it though, I'm afraid. Though you do have the opportunity to do a computational project in 4th year (as well as computational labs in earlier years).

CS and Maths (I know you didn't ask but this may be useful): Much more possible. Maths students can take some (I've heard people say "any", but only some are advertised, so I'm not sure) courses from the CS department, particularly in 3rd and 4th year. There are also pure mathematics courses in things like algorithms and coding theory. Obviously it has a different emphasis though (more theoretical where CS is more applied, I suppose).

Maybe_Memories · 05-09-2011 10:15pm

PurpleFistMixer wrote: »

Also, there is always (timetables permitting) the option of simply attending maths lectures if you want (which is what I do).

This wont count for anything though unless you make arrangements with the head of the school of maths. Either way there's nothing in first year worth doing for TP, unless you really want to do stats and C programming...

In second year it might be a good idea to see if you'd be allowed do the differential equation module in second year, since for some bizarre reason TPs dont do that one.

PurpleFistMixer · 05-09-2011 10:26pm

Maybe_Memories wrote: »

This wont count for anything though unless you make arrangements with the head of the school of maths. Either way there's nothing in first year worth doing for TP, unless you really want to do stats and C programming...

Well, yes, but I mean, if you want to learn the maths, you can do so. You just won't be examined on it. And maybe they don't like this so I shouldn't be publicising it too much...

Maybe_Memories wrote: »

In second year it might be a good idea to see if you'd be allowed do the differential equation module in second year, since for some bizarre reason TPs dont do that one.

TPs do ODEs/PDEs as part of Methods in second year, which is why (I assume) we don't do the real course. I think we used to though, back when the course was a bit insane...

dabh · 05-09-2011 11:51pm

Second year TP.

MA2321 + MA2322 (Analysis in several real variables + Calculus on Manifolds)

-> Differential geometry, General Relativity, classical Yang-Mills,
instantons, compactified dimensions, Calabi-Yau manifolds, string theory...

-> also symplectic geometry, Hamiltonian systems...

MA2325 (Complex analysis)

-> If you cannot evaluate integrals by 'completing the contour in the upper half plane'
(or lower half plane) and applying the Cauchy Residue Theorem,
Samson Shatashvili will not be impressed, when he gets to cover
'dimensional regularization' in quantum field theory.

-> Also important for string theory are Calabi-Yau manifolds and mirror symmetry,
and these Calabi-Yau manifolds are Kaehler manifolds that carry a complex
structure, and to understand what all this entails, you need to know some
complex analysis.

-> on a more classical level, if you were interested in why airplanes are able to
fly through the air, you might look into the theory of the Joukowsky aerofoil...

MA1214 (Introduction to Group Theory)

-> Well a lot of quantum mechanics is applied group theory, where these groups
may be discrete groups or may be Lie groups. The structure of the periodic
table (orbitals and energy levels of hydrogen atoms etc.) follows from the
consequences of rotational symmetry. And many phenomena in quantum
mechanics and elementary particle theory are consequences of symmetry.
Group theory is the study of symmetry. For discrete groups, consider symmetries
of an ammonia molecule (say), and apply group representation theory to derive
information about the energy levels of the electron orbitals (quantum chemistry).

The 'standard model' is U(1) x SU(2) x SU(3) + Higgs. And the U(1), SU(2) and
SU(3) are ... groups.

MA2331, MA2332, MA2341, MA2342: these speak for themselves?

PurpleFistMixer · 06-09-2011 12:07am

Just in case anyone had the mild heart attack I had on first skimming dabh's post, what he's listing is not the syllabus for 2nd year TP, but is instead a list of things that follow on from it... Though we did Hamiltonian systems and touched on symplectic manifolds in 2nd year advanced mechanics.

Thinking back on it, second year was great. As was third year, though. And first year to a lesser extent.

Tears in Rain · 06-09-2011 1:44am

PurpleFistMixer wrote: »

Just in case anyone had the mild heart attack I had on first skimming dabh's post, what he's listing is not the syllabus for 2nd year TP, but is instead a list of things that follow on from it...

Ha...I was wondering :[

asdfghjz · 08-09-2011 12:54am

New lecturers and courses are up, including this... http://www.maths.tcd.ie/pub/official/Courses11-12/MA2201.pdf

fh041205 · 08-09-2011 1:21am

asdfghjz wrote: »

New lecturers and courses are up, including this... http://www.maths.tcd.ie/pub/official/Courses11-12/MA2201.pdf

This....will....be.....epic. **** it I'm gonna go to that.

PurpleFistMixer · 08-09-2011 3:37am

*rocks back and forth*
oh god not the maths olympiad anything but that

However, sophister course in Lie Algebras? Verrrry interesting. I just hope it doesn't clash with my TP timetable. This modular forms course also looks promising, from the 2 second trip to the wiki page on modular forms I just took...

Also haha, another lecturer giving algebraic and projective geometry? Maybe I can attend it this year, and successfully manage to attend the same course in three consecutive years with three different lecturers.

Tears in Rain · 08-09-2011 10:53am

asdfghjz wrote: »

New lecturers and courses are up, including this... http://www.maths.tcd.ie/pub/official/Courses11-12/MA2201.pdf

Not that I know anything...but a full problem solving lecture for the entire Maths class seems kinda weird, especially if they're expecting any kind of useful input from the class during it. It seems like the kind of thing that's perfectly suited for say a small tutorial group or something (like what the TP's do).

asdfghjz · 08-09-2011 11:00am

Tears in Rain wrote: »

Not that I know anything...but a full problem solving lecture for the entire Maths class seems kinda weird, especially if they're expecting any kind of useful input from the class during it. It seems like the kind of thing that's perfectly suited for say a small tutorial group or something (like what the TP's do).

It's an optional module, and doing it precludes you from the number theory course and either the algebraic course in hillary or part II of advanced mech/stats in hillary. I don't know how big the incoming second year class is but if it's the same as others you'll only have 4 or 5 taking this.

Tears in Rain · 08-09-2011 11:14am

asdfghjz wrote: »

It's an optional module, and doing it precludes you from the number theory course and either the algebraic course in hillary or part II of advanced mech/stats in hillary. I don't know how big the incoming second year class is but if it's the same as others you'll only have 4 or 5 taking this.

Ah...well that makes more sense then

Maths and Theoretical Physics Course Thread TR031 TR035

Comments