Maths Uni Chat Watch

sonofdot
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#961
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#961
(Original post by Simplicity)
Don't you get example sheets?
They're not exactly easy supplies of elementary questions...
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Simplicity
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#962
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#962
(Original post by sonofdot)
They're not exactly easy supplies of elementary questions...
Do the hard problems not the easy ones.
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nota bene
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#963
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#963
(Original post by Swayum)
Is anyone finding it takes a lot longer for results/theorems to stick with you compared with at school? At school, something would be proven once and a couple of examples given and I'd probably remember it for at least a year. Where as now I can't even do questions identical to examples without looking it up again in the book and the proofs I forget almost entirely even though they don't seem much harder yet.

Maybe it's the gap year.
I find it alright as long as I understand what's going on in the proofs. Some (especially algebra) seem to come out of nowhere and I don't understand why elements are chosen etc. Those proofs I won't remember until I actually understand what's going on (and can more than see 'well this looks solid').
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nota bene
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#964
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#964
(Original post by Simplicity)
Do the hard problems not the easy ones.
Huh?

He's saying he needs to do quite a few easier questions to get his head around the topic, before proofs and harder questions become easily approachable; so I fail to see how "do the hard ones" is helpful...
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Simplicity
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#965
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#965
(Original post by nota bene)
Huh?

He's saying he needs to do quite a few easier questions to get his head around the topic, before proofs and harder questions become easily approachable; so I fail to see how "do the hard ones" is helpful...
Well, in a way if a problem is hard then its good as it makes you think about it. So yes do the hard ones.

I find the best way to get around a topic is to try and grasp the proofs even if they take weeks, which in some cases it can. You could argue easy question build up intuition, but normally people just want to mimic the argument or change it slightly instead of understanding it.

Hence, the fact that people try and memorise proofs instead of trying to understand them and wonder why it doesn't stick in the brain.

(Original post by Swayum)
It isn't about understanding - I can understand and follow what's happening just fine. It's about not being able to actually do the questions a few days later without referring back to the examples/proof because you forget completely what you learnt. I didn't find this happened to me at school. And it's not that the questions are hard or anything - they're often really easy - it's just... memory loss.
Well, I don't accept that. Certainly, I know a bit about memory tehniques and memory. If you have forgotten something then it more likely you didn't understand it i.e. couldn't do it in the first place even when putting down the book for a minute or you didn't associate it with other material. In the first case not using semantic processes and you could argue doing a proof when you haven't seen it in a awhile shows you actually understand the proof. In the second case not linking it with what you learnt so you can't trace back the memory, which even if you could would be bad as yeah memory isn't something you should depend on.

P.S. This reminds me of a funny blog post on neverendingbooks.
A majority of the students was unable to do this… Sure, the result was not contained in their course-notes (if it were I\’m certain all of them would be able to give the correct statement as well as the full proof by heart. It makes me wonder how much they understood of the proof of the Sylow-theorems.) They (and others) blame it on the fact that not every triviality is spelled out in my notes or on my \’chaotic\’ teaching-style. I fear the real reason is contained in the post-title…
http://www.neverendingbooks.org/inde...chat-line.html
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Totally Tom
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#966
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#966
(Original post by Simplicity)
I mean this lemma If there exists an injection f:N_n \rightarrow N_m then  m \leq n.

I remeber reading from Penrose that Euclid didn't define what straight meant and that was meant to be something that is obvious. But, yeah in the five postulates he doesn't mention shortest distance.

According to wikipedia this is true. It easy to generalise what a straight line is to higher dimensions as its just linear algebra. But, wouldn't defining a line that is straight to be what minimises distance be circular reasoning if you're trying to prove that its the shortest distance?
would you stop going on about that bloody lemma.

it's like you're planning on doing a PhD on it or something.
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My Alt
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#967
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#967
What's the intersection of 2 planes? The world trade centre, of course.
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Oh I Really Don't Care
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#968
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#968
(Original post by My Alt)
What's the intersection of 2 planes? The world trade centre, of course.
You are a sick person
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My Alt
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#969
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#969
Watching what is happening to my rep score after that statement is a very interesting social experiment.

EDIT: Should point out it wasn't my joke...
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Totally Tom
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#970
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#970
(Original post by My Alt)
Watching what is happening to my rep score after that statement is a very interesting social experiment.
i would rep but i've used mine earlier
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majikthise
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#971
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#971
Ha, not heard that before! Can't wait for Boilerhouse.
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The Muon
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#972
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#972
(Original post by Totally Tom)
i would rep but i've used mine earlier
When I repped you before it was foresight for this post!


(Original post by My Alt)
Watching what is happening to my rep score after that statement is a very interesting social experiment.
I'll make up for it tomorrow. Tom stole me today rep :hmmm:
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ste0731
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#973
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#973
Bad start for me after reading week of setting myself the goal of "no more drinking, no more missing lectures, and do all work early"
Missed 2 lectures + 1 tutorial in 2 days xD And am doing work tonight due in tomorrow Although this is early, it's usually done at 2pm tomorrow!

ALTHOUGH we get our maths hoodies tomorrow I'll look super cool with my "i saying to pi be rational" and "Pi saying to i" be real (or other way around xD you get the hint) B)

(Original post by Simplicity)
The sets, numbers and function test was easy.

Basically, it stuff like what is a infinite set A. A set which is denurable with itself i.e. can be put in a bijection between a subset X of A.

Then, what is a predicate involving variables a and b.

Then some state the priniciple of induction and then prove that n!>2^n for n>3 where n is in Z.

P.S. Anyway, yeah easy.
P.P.S. I some how managed to turn up into the wrong room. I hope the paper doesn't get lost because of this.
Yeh exam wasn't too bad. How was you in wrong room? :p: Shouldn't make too much difference, they'll just go to your tutor.

I missed a few marks though, unsure what to expect as I didn't fully justify all my proof for part 2. so depends how generous they are

Take it you've finished stats cwk? Any tips for 3d and 5d?

What you think of the new lecturers, I'm struggling to hear and understand the new calc lecturer but he seems more understanding and willing to go slower (probably will upset you- but means I can sleep a bit more), and I didn't go to the sets after exam, but heard mixed reviews of him. :confused:

PS: did you find this weeks calc work REALLLLLLY easy. The first question I spent an hour on the night before and was using ITP three times combined with product/chain rule etc, then realise a simple substituion and you end up with e^u xD What a waste of an hour. Apart from that it was all straight forward IMO.
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Simplicity
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#974
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#974
(Original post by ste0731)
Bad start for me after reading week of setting myself the goal of "no more drinking, no more missing lectures, and do all work early"
Missed 2 lectures + 1 tutorial in 2 days xD And am doing work tonight due in tomorrow Although this is early, it's usually done at 2pm tomorrow!

ALTHOUGH we get our maths hoodies tomorrow I'll look super cool with my "i saying to pi be rational" and "Pi saying to i" be real (or other way around xD you get the hint) B)



Yeh exam wasn't too bad. How was you in wrong room? :p: Shouldn't make too much difference, they'll just go to your tutor.

I missed a few marks though, unsure what to expect as I didn't fully justify all my proof for part 2. so depends how generous they are

Take it you've finished stats cwk? Any tips for 3d and 5d?

What you think of the new lecturers, I'm struggling to hear and understand the new calc lecturer but he seems more understanding and willing to go slower (probably will upset you- but means I can sleep a bit more), and I didn't go to the sets after exam, but heard mixed reviews of him. :confused:

PS: did you find this weeks calc work REALLLLLLY easy. The first question I spent an hour on the night before and was using ITP three times combined with product/chain rule etc, then realise a simple substituion and you end up with e^u xD What a waste of an hour. Apart from that it was all straight forward IMO.
Yeah, so how is your probability going, lets just say 3.d. is causing me a headache. I been trying for ages but looking on the internet I don't know what to do. My last resort is basically learning how to do maths from tree diagrams.

I'm not getting a maths hoodie. If they put a fractal on the back I would, but not a joke that isn't funny:p:

Induction. I'm lucky that most of my revision is based on understanding induction. Yeah, I would mention more but then Totally Tom will tell me off about a problem I'm obessed with.

I was coming on here to ask you for a tip on 3d. All the people I have talked don't know how to do it. Well, I'm probably going to get the anwser so yeah I will tell you later. Every other question I got the correct anwser.

He seems really good. I heard that Mark Coleman is meant to be good, he can write pretty fast on blackboards. Calculus and vectors is on weird times so its hard not to fall asleep.
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ste0731
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#975
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#975
(Original post by Simplicity)
Yeah, so how is your probability going, lets just say 3.d. is causing me a headache. I been trying for ages but looking on the internet I don't know what to do. My last resort is basically learning how to do maths from tree diagrams.

I'm not getting a maths hoodie. If they put a fractal on the back I would, but not a joke that isn't funny:p:

Induction. I'm lucky that most of my revision is based on understanding induction. Yeah, I would mention more but then Totally Tom will tell me off about a problem I'm obessed with.

I was coming on here to ask you for a tip on 3d. All the people I have talked don't know how to do it. Well, I'm probably going to get the anwser so yeah I will tell you later. Every other question I got the correct anwser.

He seems really good. I heard that Mark Coleman is meant to be good, he can write pretty fast on blackboards. Calculus and vectors is on weird times so its hard not to fall asleep.
Probability is good apart from 3d. Definitely shoot me the answer if you get it I'll owe you big time Any hints for 5d? My friends got some answer for 3d, ill send over what she has when she sends it me in 5mins and see if it helps you at all. I doubt she has it correct.

Haha @ That problem :p:
Fast writing o.O Argh :woo:
Do you find it strange the lecturer randomly walks halfway up the lecture theartre xD and why must ALL lecturers do weird lunges and steps while speaking :p: extremely offputting. (even worse when i have jack for supervisions as well xD)
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Simplicity
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#976
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#976
(Original post by Totally Tom)
would you stop going on about that bloody lemma.

it's like you're planning on doing a PhD on it or something.
But, why I know how to prove it.

Lemma, if there exist an injection f:N_m \rightarrow N_n therefore m \leq n.

Base case n=1, if m>n, then there is atleast two elements in N_m that map to the single element in N_n. So, f(1)=f(2)=1, which isn't a injection, contradictions.

Inductive hypothesis, is that if there exist an injection f:N_m \rightarrow N_k then m \leq k.

Consider two cases, either f(i)<k+1 for all i in N_m. Then, considering m \leq k it must be true that m \leq k+1, as from f(i) everything injectively maps to N_k and so if m \leq k+1( if this was false than there must be an element mapped to k+1, which would mean a contradiction.)

Now consider the other case i.e. f(i_{0})=k+1 where i_0 is in N_(m). Consider a function g where g(i)=i if i&lt;i_0 and g(i)=i+1 if i_0 \geq i, where g:N_{m-1} \rightarrow N_m.

Lastly, consider the composite function
f \circ g:N_{m-1} \rightarrow N_k, this is an injection since its a composite of injection, since f is a injection and g is a injection(if, I wanted to be spammy I would prove this). So m-1 \leq k, therefore m \leq k+1.

In both cases, m \leq k+1 and since these are the only two cases, QED.

P.S. Yeah, pretty impressed that I can prove it. Even in both cases i.e. induction on co domain, which is a bit easier as all you defined is a flip function. But, yeah I know how counting works and I don't know if there is branch of maths that is as obessively good as this I might do a PhD in it, I thought this was combinatorics?. But, I just love functions and injections and bijections and proofs that use it. Sort of like counting arguments but when they have a purpose. Amazing.

Can't explain how amazing this is. It basically tells you why counting works which is pretty impressive. As from this lemma then its pretty easy to prove a ton of other stuff like pigeonhole priniciple and even how to count infinite sets as its not that hard to extend this lemma. But, so far this is probably my favourite theorem and proof I have seen in the limited experience of uni maths I have. But, still I could talk about this for days.
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v-zero
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#977
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#977
(Original post by Simplicity)
But, why I know how to prove it.

Lemma, if there exist an injection f:N_m \rightarrow N_n therefore m \leq n.

Base case n=1, if m>n, then there is atleast two elements in N_m that map to the single element in N_n. So, f(1)=f(2)=1, which isn't a injection, contradictions.

Inductive hypothesis, is that if there exist an injection f:N_m \rightarrow N_k then m \leq k.

Consider two cases, either f(i)<k+1 for all i in N_m. Then, considering m \leq k it must be true that m \leq k+1, as from f(i) everything injectively maps to N_k and so if m \leq k+1( if this was false than there must be an element mapped to k+1, which would mean a contradiction.)

Now consider the other case i.e. f(i_{0})=k+1 where i_0 is in N_(m). Consider a function g where g(i)=i if i&lt;i_0 and g(i)=i+1 if i_0 \geq i, where g:N_{m-1} \rightarrow N_m.

Lastly, consider the composite function
f \circ g:N_{m-1} \rightarrow N_k, this is an injection since its a composite of injection, since f is a injection and g is a injection(if, I wanted to be spammy I would prove this). So m-1 \leq k, therefore m \leq k+1.

In both cases, m \leq k+1 and since these are the only two cases, QED.

P.S. Yeah, pretty impressed that I can prove it. Even in both cases i.e. induction on co domain, which is a bit easier as all you defined is a flip function. But, yeah I know how counting works and I don't know if there is branch of maths that is as obessively good as this I might do a PhD in it, I thought this was combinatorics?. But, I just love functions and injections and bijections and proofs that use it. Sort of like counting arguments but when they have a purpose. Amazing.

Can't explain how amazing this is. It basically tells you why counting works which is pretty impressive. As from this lemma then its pretty easy to prove a ton of other stuff like pigeonhole priniciple and even how to count infinite sets as its not that hard to extend this lemma. But, so far this is probably my favourite theorem and proof I have seen in the limited experience of uni maths I have. But, still I could talk about this for days.
This is my favourite: http://en.wikipedia.org/wiki/Fundame..._of_arithmetic

I just like it. :rolleyes:
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v-zero
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#978
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#978
(Original post by My Alt)
What's the intersection of 2 planes? The world trade centre, of course.
I recently said this IRL to assmaster, as she was talking about the intersection of two planes. It was not well met... :o:
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SimonM
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#979
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#979
Could I see what 3d and 5d are?
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MikeyW09
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#980
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#980
Hello

I'm actually with the School of Electrical Engineering (Manchester), but I graduated here with an MMath&Phys and I am learning a lot of maths right now anyway so I thought I'd come by. Discrete Fourier transforms, Abel transforms, symmetry groups and some fun obscure maths like that...
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