Maths Uni Chat Watch

Jake22
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#6981
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#6981
(Original post by shamika)
2) More seriously (and I ask this not having ever studied Lie Algebras), what are Lie Algebras good for? Are they interesting enough to be studied in their own right, or are they used only to study Lie Groups? If its for Lie Groups then that application is sophisticated to teach in the second year (in exam term of all times!)
They are interesting enough to also be studied in there own right. And in that setting, classification is a good enough motivation for machinery (and also, as I said, one could do a shorter, more basic course as an extended work out in linear algebra without having to develop too much extra machinery)

Think about group theory courses. These are often run without anything other than a small off the cuff passing reference to anything external yet in many first courses, one looks at classification of finite groups of certain orders.

One can do a basic Lie algebras course in an analagous fashion i.e. do some little bits of classification for an end unto itself.
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DFranklin
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#6982
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#6982
(Original post by shamika)
I was thinking about this...

1) This was a Cambridge course, and I'm fairly sure Cambridge doesn't do things by half-measures
Oh I think "half-measures" is entirely accurate in this particular case. One might even suspect they had 16 lectures, and 10 lectures of stuff they actually wanted to cover, and then thought "what can we use to fill the other 6 lectures?".

I'm not sure that's quite what really happened, but there were so few lectures for the last part (and as I said, this was also exam term, so the last few lectures were really when people were concentrating on exams) that I doubt there was much "lecturing with intent" going on...
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MrShifty
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#6983
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#6983
(Original post by Jake22)
Sometimes...
Thanks for that. I may dust off my long forgotten Homology, try and get proficient with all the stuff I've long ignored, and see if there's anything there which proves useful.

That said, the problem 'here' is that surprisingly little is known about the projectives.

That'ss exacerbated a bit by the fact that really I'm studying a family of algebras which is dependent on a couple of parameters, and finding concrete statements can very quickly be quite nightmarish - even classifying the simple modules involves dragging quantum algebras up, and even then the best we have is a recursive definition rather than a nice, closed expression.
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shamika
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#6984
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#6984
(Original post by Jake22)
They are interesting enough to also be studied in there own right. And in that setting, classification is a good enough motivation for machinery (and also, as I said, one could do a shorter, more basic course as an extended work out in linear algebra without having to develop too much extra machinery)
Fair enough. I now really want to learn more about Lie algebras. I'm guessing very few books cover the material at a sufficiently introductory level though...

(Original post by Jake22)
Think about group theory courses. These are often run without anything other than a small off the cuff passing reference to anything external yet in many first courses, one looks at classification of finite groups of certain orders.

One can do a basic Lie algebras course in an analagous fashion i.e. do some little bits of classification for an end unto itself.
Good point. I loved classification of finite groups of small order - its incredible how simple group axioms can create such an immensely rich theory, I think that's a nice highlight for a course

(Original post by DFranklin)
Oh I think "half-measures" is entirely accurate in this particular case. One might even suspect they had 16 lectures, and 10 lectures of stuff they actually wanted to cover, and then thought "what can we use to fill the other 6 lectures?".

I'm not sure that's quite what really happened, but there were so few lectures for the last part (and as I said, this was also exam term, so the last few lectures were really when people were concentrating on exams) that I doubt there was much "lecturing with intent" going on...
Wonder what was the motivation for the course - was it required for later courses in any way? If there's still a gap in the Tripos for the material, either push it into Lent or treat as non-examinable?
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DFranklin
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#6985
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#6985
(Original post by shamika)
Wonder what was the motivation for the course - was it required for later courses in any way? If there's still a gap in the Tripos for the material, either push it into Lent or treat as non-examinable?
It's 20 years ago now, so it's somewhat moot. Courses in exam term were always regarded as problematic in terms of "you can't expect anyone to know it next year", so I expect there was a certain amount of "wouldn't do people harm to have seen this, but it's only a taster".
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around
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#6986
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#6986
(Original post by DFranklin)
It's 20 years ago now, so it's somewhat moot. Courses in exam term were always regarded as problematic in terms of "you can't expect anyone to know it next year", so I expect there was a certain amount of "wouldn't do people harm to have seen this, but it's only a taster".
This is most problematic with the Metric and Topological Spaces course in 1st year - only now, in 3rd year, are we actually building up on stuff we did in Easter 1st year.

of course, a lot of 2nd year courses were helped by taking that course, but none could expect knowledge of met+top.
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assmaster
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#6987
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#6987
(Original post by Oh I Really Don't Care)
I get the urge to slam someones head on the desk when they correct somebody else
Yeah, that's me. Need to kick what is rapidly becoming a habit. It happened again today, but at least this time the person was actually asking a question to the air, and I was sat near enough that it wasn't weird to answer it (unlike that time I saw a guy stretch over two rows to point at what he was talking about... that was weird. Wouldn't have been that bad if he was stretching forward and down, but it was backwards and up the lecture hall, which just looked painful and made his eagerness all the creepier).

So what did everyone sign up to at freshers' fair this year?
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Simplicity
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#6988
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#6988
(Original post by assmaster)
Yeah, that's me. Need to kick what is rapidly becoming a habit. It happened again today, but at least this time the person was actually asking a question to the air, and I was sat near enough that it wasn't weird to answer it (unlike that time I saw a guy stretch over two rows to point at what he was talking about... that was weird. Wouldn't have been that bad if he was stretching forward and down, but it was backwards and up the lecture hall, which just looked painful and made his eagerness all the creepier).

So what did everyone sign up to at freshers' fair this year?
I don't know why you guys get so angry about people asking questions. It's like if you can't ask stupid questions then what is the point of going to lectures? you could just sit at home and figure it for yourself. However, hearing other give stupid answer is what makes lectures worth it.

I signed up to type theory reading course. Think about computer science students stereotypes and then times it by ten.

(Original post by around)
This is most problematic with the Metric and Topological Spaces course in 1st year - only now, in 3rd year, are we actually building up on stuff we did in Easter 1st year.

of course, a lot of 2nd year courses were helped by taking that course, but none could expect knowledge of met+top.
How much topology do you know? Haudorff spaces? product topology? I always feel I'm lagging behind everyone in this thread.

I hope you guys haven't done stuff like Artin-wedderburn theorem in algebra.
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Oh I Really Don't Care
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#6989
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#6989
I think you're really behind as well too Simplicitly - it's absolutely vile and I would suggest even more study.

Don't focus on basic courses or even pinning down fundamentals.

If I were you I would get a book on first order logic and the axioms of ZFC then write down all theorems (without proof) from every pure subject of the third year.

Formally prove each one and explore any links. Good luck with your catching up to the real mathematician's goals in 2012!

P.S. the Artin-wedderburn theorem was covered in our second week. Enthralling.

P.P.S. I am back after the new year so have not officially joined though rugby and cross country. Of course I am interested in more but time is so scarce with effectively 7 week terms.
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My Alt
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#6990
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#6990
(Original post by Oh I Really Don't Care)
blah blah look at me clever + funny oh yes ladies
I swear ripping on simplicity went out of fashion years ago. Oh wait, yeah people got bored of ripping on his posts that make less sense, and now it's cool to rip on the completely normal posts, that are actually reasonably contributing to the conversation. My bad.
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Oh I Really Don't Care
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#6991
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#6991
(Original post by My Alt)
I swear ripping on simplicity went out of fashion years ago. Oh wait, yeah people got bored of ripping on his posts that make less sense, and now it's cool to rip on the completely normal posts, that are actually reasonably contributing to the conversation. My bad.

I do not personally get involved with Simplicity's life - but from what I can gather -he can probably laugh at a funny response on the internet and relax in the knowledge he was worrying about something he need not. The course at Manchester is far more than adequate and Jake something or other [who is a member on this site] did the course Simplicitly is doing now and is of similar ability to those who are equally as progressed in their Career at Oxford.

Firstly, I don't believe that was a serious question. However, even if it was I hope the reply would have covered how foolish it would be to linger on such a thought - even if another University was two years ahead, he is still doing mathematics. It is not like University A teaches anything 'new' while University B is stuck in the dark ages still roaming around Vector spaces and Topological spaces. Whatever is excluded in his course he will soon cover and it will be exactly the same as whatever uni was 'ahead'.

Clearly I have mistook the obvious seriousness of TSR.



a picture that nicely sums up my feelings.

EDIT: I am sure
(Original post by Jake22)
Yeah, its nice. The close Dmaj tunings DADGDF# and DADF#AD are also pretty nice.
will have a much more accurate portrayal on the speed and content of the course at Manchester and how it does compare to courses found elsewhere.

Spoiler:
Show
Jake, I have been meaning to ask you - though always forgotten - what amps and guitars do you own?
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Jake22
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#6992
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#6992
(Original post by shamika)
Fair enough. I now really want to learn more about Lie algebras. I'm guessing very few books cover the material at a sufficiently introductory level though...
It is true that many books covering Lie Algebras also cover scary Geometry and/or Physics but there are some easier 'pure' Lie Algebra books, for example: Introduction to Lie Algebras by Karin Erdmann and Mark J. Wildon which is in the Springer Undergraduate Mathematics Series (SUMS) and has no prerequisites other than a basic familiarity with linear algebra. Essentially, the book introduces Lie Algebras and then leads up to a classification of the complex finite-dimensional reductive Lie Algebras (which are essentially everything you would see in practice).
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qgujxj39
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#6993
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#6993
(Original post by Oh I Really Don't Care)
and is of similar ability to those who are equally as progressed in their Career at Oxford.
That's probably because Oxford is ****

edit: yay at how putting a winking emoticon avoids getting negged
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Oh I Really Don't Care
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#6994
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#6994
(Original post by tommm)
That's probably because Oxford is ****
I suppose I should have said all other unis - I was just basing things on graduate students I actually know though.

I don't want to suggest Oxford, Cambridge, Warwick, York or x,y,z has more capable graduate students than anywhere else. I believe firmly that the top students at each University will be all on the same level; however I don't know any graduate students from Cambridge, Warwick or York (aside from my personal tutor who is not a fair representation due to him being a professor practically).

EDIT: I should perhaps point out this is still in reference to Simplicitly's post, not some kind of retraction or reply to your point, I know you were making a joke.

FWIF the graduates for art subjects who come from Cambridge have a rough initiation down here.
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Jake22
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#6995
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#6995
(Original post by Oh I Really Don't Care)
EDIT: I am sure Jake22 will have a much more accurate portrayal on the speed and content of the course at Manchester and how it does compare to courses found elsewhere.
It is difficult to say really. In a nutshell, it is pretty comparable to everywhere apart from Cambridge. One good thing about Manchester is that being one of the larger (the largest?) maths departments outside of Oxbridge - there is a wide variety of courses that one can take that would be pretty hard to find elsewhere. For example, when I did my undergrad, I did a course on so called quasi-toric manifolds and I sincerely doubt you would find such an undergraduate course anywhere else in the UK. There are also courses on non-standard logics and soforth that you wouldn't find in many other places.

To be honest though, university is just a resource for your mathematical education. At Manchester you have everything you need and staff on hand to cover pretty much most mathematical interests. The students I knew who were really interested and went on to do PhDs for example didn't just learn what was covered in the courses but followed their interests and supplemented that by choosing appropriate courses and particularly in the final year, chose the right project subject. I really think that the last year, there is less onus on courses and more the feeling that you should just learn some interesting maths. That is how I treated it anyway. By that stage, you have fewer courses to do as your project takes up most of your 'credits' so you essentially do what you want and the courses are easily manageable alongside that.

(Original post by Oh I Really Don't Care)
Jake, I have been meaning to ask you - though always forgotten - what amps and guitars do you own?
I have never really had particularly decent gear. I have a Schecter Omen 6 (which is nice enough to play but has crappy hardware) and a 1980s Marshall Valvestate which is ok if not a bit glassy and unreliable.
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Jake22
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#6996
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#6996
For what it is worth, in my department, I would say that about half of the grad students went to Cambridge (either doing the Tripos or just Part III) and there doesn't seem to be any clear distinction in ability or knowledge between them and people who went elsewhere.

Once you get to the PhD stage, it really doesn't matter where you did your undergrad - even if some people start off with more background knowledge, it all levels out pretty quickly. You probably learn more general background material in your first year or so then in 2 years of undergrad (even if some of this is a bit 'rougher' then the kind of learning you do at undergrad).

(Original post by Tomm)
(Original post by Oh I Really Don't Care)
(Jake22)... is of similar ability to those who are equally as progressed in their Career at Oxford.
That's probably because Oxford is ****
Cheers mate :rolleyes: I don't see how anyone is able to appraise my mathematical ability (or lack thereof) in any sense anyway.
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My Alt
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#6997
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#6997
To be fair, I think you probably find that average income has a fairly large dependence on the university one studies at (if you take on those who are maths students.)

I didn't want all this anger - I was just pointing out how unfunny your previous post was
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Oh I Really Don't Care
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#6998
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#6998
(Original post by My Alt)
I didn't want all this anger - I was just pointing out how unfunny your previous post was
I was aiming for passive aggressive sarcasm so I'm glad.

Do you even lift?
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My Alt
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#6999
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#6999
(Original post by Oh I Really Don't Care)
I was aiming for passive aggressive sarcasm so I'm glad.

Do you even lift?
lift? no comprende
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around
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#7000
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#7000
(Original post by Oh I Really Don't Care)
I was aiming for passive aggressive sarcasm so I'm glad.

Do you even lift?
person a: hey i do steroids

person b: hey me too

girl: i can't believe you guys are taking drugs

persons a&b: no we don't
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