Maths Uni Chat
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Original post by shamika
I'd never even heard of an exterior wedge product until I looked it up... what else was in this 'Further Topics in Algebra' course?
Original post by Simplicity
Just wondering has everything appeared to made easier?
I remember a lecturer saying that they dumb down the course because of students having more power to complain if everything is hard.
I remember a lecturer saying that they dumb down the course because of students having more power to complain if everything is hard.
I don't know if 'dumbing down' is the correct term, but on the whole I would say that yes: university courses have got a little easier, at least in the first two years with the passage of time.
As I recall, when I started as an undergraduate (nigh on eight years ago now) real analysis from basic principles up to and including the Riemann Integral and its properties, was pretty much a corner stone of the first year.
Today, I've noticed quite a few mathematics course either defer analysis to the second year and/or replace it with a course on sequences and series or somesuch, with the bulk of the more difficult elements of the course being moved to a second year course (which typically results in either less time to cover traditional second year analysis material, or a 'squeeze' as the department tries to catch everyone up before the third year).
Edited to add: I'm conscious of appearing like I'm slagging off 'current degrees', which isn't my intention. Perhaps rather than talking about 'easier' or 'dumbing down' it would be better to view universities as offering a more gentle introduction to the subject in at least the first year. Whether or not a given department picks up the pace in later years, such that the degree covers more or less everything it used to is a matter for individual universities.
(edited 12 years ago)
Original post by SimonM
You should see a doctor.
Haha, i meant that its hard to catch up to their notes when they are flipping boards and that!
post because i accidentally stopped watching these
Original post by pappymajek
hi everyone,
I really need your recommendations for any simple easy to read books on number theory-especially with proofs -axioms, etc.
I'm in my first yr at uni and our number theory course is very new to me. Also any other useful resources would be really appreciated.
Thanks
I really need your recommendations for any simple easy to read books on number theory-especially with proofs -axioms, etc.
I'm in my first yr at uni and our number theory course is very new to me. Also any other useful resources would be really appreciated.
Thanks
Ask your lecturer to recommend one - you could get 500 recommendations from us and yet none of them may contain the entirety of your course in it.
Original post by DFranklin
Embarrassingly, I don't remember. I do still have my IB notes, so I checked, and there was a bit on Lie Algebras. Again, I remember absolutely nothing about that now.
That's insane... Lie Algebras in a second year course - no wonder you found it hard! Was anyone able to understand the course?
What were your Part II courses like then, and how do they compare to the current Tripos?
Original post by shamika
That's insane... Lie Algebras in a second year course - no wonder you found it hard! Was anyone able to understand the course?
If I remember correctly, the real killer with that course was that it was lectured in exam term. In my experience, if you teach anything "deep" in exam term there's little chance of it being absorbed until after the exams.
What were your Part II courses like then, and how do they compare to the current Tripos?
I do have to confess that it's a long time since I went to uni, and I find I have pretty good memory for the stuff I really understood, but the 'harder stuff' in Part II has largely slipped me by. (That is, I remember the overall concepts, but am woolly enough on details that I can hardly do any Part II questions any more).
So I'm not really "competent" to judge Part II difficulty that well to be honest.
Original post by shamika
That's insane... Lie Algebras in a second year course - no wonder you found it hard! Was anyone able to understand the course?
You could do a quite gentle, basic course and mostly just treat it as a work out in linear algebra.
For instance, you could talk about the classification of finite dimensional irreps. of SL(2,C) or so.
It is true that a lot of basic results are much easier with heavier machinery. For example, on my Lie Algebra course, we did a fairly longish proof of Weyl's theorem which would have been easier with the machinery of cohomology.
I'm sorry if this is in the wrong thread, but does anyone have any idea of how to find the volume of an object other than using double integration, given you know the function of the planes that bound the space whose volume you would like to find? thanks before!
Original post by Jake22
...which would have been easier with the machinery of cohomology.
...which would have been easier with the machinery of cohomology.
Isn't that so often the case? The stuff of my nightmares is one day finding that everything I've spent months of blood and sweat working on in a race to submit has been proved via homology or cohomology. And that it took less than a week and nine pages in which to do it.
I keep telling myself that my way has the advantage of being constructive, but nothing can completely eliminate the terror.
Original post by MrShifty
Isn't that so often the case? The stuff of my nightmares is one day finding that everything I've spent months of blood and sweat working on in a race to submit has been proved via homology or cohomology. And that it took less than a week and nine pages in which to do it.
I keep telling myself that my way has the advantage of being constructive, but nothing can completely eliminate the terror.
I keep telling myself that my way has the advantage of being constructive, but nothing can completely eliminate the terror.
(Co)homological methods can sometimes be constructive too!
A lot of the time the difference is entirely one of language though. I mean, look at the history of group cohomology for example - people were talking about extension problems etc. 50 years before they were using the word cohomology. They were dealing with cocycles but they just called them factor sets instead.
Original post by desy.kris
I'm sorry if this is in the wrong thread, but does anyone have any idea of how to find the volume of an object other than using double integration, given you know the function of the planes that bound the space whose volume you would like to find? thanks before!
Or triple :P I wouldn't have thought so in the general case - although in a specific special case you may be able to do something. What did you have in mind?
Original post by My Alt
Or triple :P I wouldn't have thought so in the general case - although in a specific special case you may be able to do something. What did you have in mind?
I'm doing a mathematical modelling investigation for my IB Extended Essay... modelling a taco :/ I'm using double integration, lol :P
Original post by Jake22
Apologies: I didn't mean to give the impression that homological methods can't be constructive.
Even so, please don't destroy the one thing that justifies my working existence
Original post by MrShifty
Apologies: I didn't mean to give the impression that homological methods can't be constructive.
Even so, please don't destroy the one thing that justifies my working existence
Even so, please don't destroy the one thing that justifies my working existence
Well, I am working on trying to understand at the moment when one can make stuff even at the derived level constructive so it can go even higher then that.
Obviously, this is all pretty vague but a good example that I like to think about is from algebraic topology:
You want to talk about stable homotopy classes of maps between spheres. The cohomology algebra doesn't distinguish between each stable homotopy class but then you view it as a module over the Steenrod Algebra, chuck it through the Adams Spectral Sequence et voila (under nice circumstances) all of the stable homotopical information is realisably cohomologically.
Original post by desy.kris
I'm doing a mathematical modelling investigation for my IB Extended Essay... modelling a taco :/ I'm using double integration, lol :P
oh cool. Yeah, there's no easy way in general. If you're finding volume, surely you should be integrating over 3 dimensions, or are you just trivialising one in some way, and therefore not counting it?
Original post by Zuzuzu
Any other freshers not really enjoying their maths course? Mechanics, vectors and matrices for 3/4s of the week is not good. 
I avoid this by cunningly not doing mechanics
But I know what you mean! Methods is basically FP4 all over again with a couple more proofs in there, and while I actually quite like Algebra, I'm really not a fan of matrices in general. At least we have Analysis
Which is exactly like I hoped 'university maths' would be - problem sheets that take you a while and things you actually have to think about.It's really bothering me that they just blithely hand out the answers to the homework whenever people ask. We get the Analysis problem sheets on Monday, and I have the tutorial for it on Wednesday, in which he pretty much told us how to do the homework, thus ruining the second half of it for me, because I hadn't got around to doing it yet
Original post by SimonM
This. In fact, answering questions in general.
Or taking lots of time out of the lecture to insult people who asked stupid questions.
Original post by kerily
Or taking lots of time out of the lecture to insult people who asked stupid questions.
At least then people will think twice before asking another question.
Original post by SimonM
At least then people will think twice before asking another question.
We're all too scared to go to his office hour/ask relevant questions/etc now, so he's doing something right
To be fair, I don't think there are many circumstances under which questions are appropriate. If there's a mistake on the board, yes, but other than that, not really... if you don't understand, you should probably go away and try to work it out on your own before you waste 5 minutes of 200 people's time.
Original post by kerily
We're all too scared to go to his office hour/ask relevant questions/etc now, so he's doing something right
To be fair, I don't think there are many circumstances under which questions are appropriate. If there's a mistake on the board, yes, but other than that, not really... if you don't understand, you should probably go away and try to work it out on your own before you waste 5 minutes of 200 people's time.
To be fair, I don't think there are many circumstances under which questions are appropriate. If there's a mistake on the board, yes, but other than that, not really... if you don't understand, you should probably go away and try to work it out on your own before you waste 5 minutes of 200 people's time.
Even then, the mistake has to be significant, and something others might miss.
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