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# The Proof is Trivial! watch

1. (Original post by Jkn)

Spoiler:
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Hahaha Are you referring to the infamous solution that launched the massive argument with LOTF on the STEP problem-solving thread? Hahahaha wasn't ​quite that bad!
It's surprising how often maths starts arguments. I had a whole argument about the distinction between Maclaurin and Taylor with my FM class.
2. (Original post by henpen)
What do you mean? Closer to real mathematics? I would have thought that the solutions to hard problems would help me learn more maths, and am grateful for that, although am new here so haven't had time to look at much or work on any.
I'm not here to argue what and what isn't "real mathematics" with those willing, I'm here to state my opinion, I feel that, with A-level knowledge ready for my mathematics degree next year, that some of these questions are wrongly titled and that principles that have been called "A-level knowledge" on here are not and are in fact "STEP and higher" and hence the titles are misleading.
3. Consider the following story as an analogy:

Two pupils in a Home Economics class (let's call one "Ukd" and the other "LotF", entirely random names of course) are both given a butter knife by the teacher and shown how to cut butter with it. They practice on thousands of blocks of butter until they could do it with their eyes shut. However one day the teacher decided to give them a block of margarine and a piece of steak and asked them to slice both. Ukd and LotF both found the maragarine easy, by deducing it has similar properties to butter, but Ukd struggles on the steak. LotF on the other hand, being the clever-clogs he is, went and grabbed two more butter knives and held all of them in one hand. By cutting with three knives simultaneously, LotF found he could exert much more power and manages to slice the steak. Of course the task could have been completed much more easily with a steak knife, but neither pupil knows what that is.

The point under debate here shouldn't be whether cutting a steak is correctly labelled as a suitable task for a class who has only learned how to use butter knives, but rather whether the clever technique LotF figured out (which still only uses what the class has been taught to use) counts as within the remit of only using the "knowledge" which the class imparted.
4. (Original post by bananarama2)
I had a whole argument about the distinction between Maclaurin and Taylor with my FM class.
WHAT! HAHAHAHAHAHA

Actually, in that problem a and b weren't distinct positive constants, they were assumed to be variables independent of x and y that were adjusted in such a way as to ensure continuity. The so-called contradiction was non-existent because a ended up being equal to b -.-

...but that argument has been and gone -.-
5. (Original post by bananarama2)
The solution has been posted. But think Maclaurin (or however you spell it, that never was my strong point )
Do you know what problem number it is by any chance?
6. (Original post by ukdragon37)
Consider the following story as an analogy:

Two pupils in a Home Economics class (let's call one "Ukd" and the other "LotF", entirely random names of course) are both given a butter knife by the teacher and shown how to cut butter with it. They practice on thousands of blocks of butter until they could do it with their eyes shut. However one day the teacher decided to give them a block of margarine and a piece of steak and asked them to slice both. Ukd and LotF both found the maragarine easy, by deducing it has similar properties to butter, but Ukd struggles on the steak. LotF on the other hand, being the clever-clogs he is, went and grabbed two more butter knives and held all of them in one hand. By cutting with three knives simultaneously, LotF found he could exert much more power and manages to slice the steak. Of course the task could have been completed much more easily with a steak knife, but neither pupil knows what that is.

The point under debate here shouldn't be whether cutting a steak is correctly labelled as a suitable task for a class who has only learned how to use butter knives, but rather whether the clever technique LotF figured out counts as within the remit of only using the "knowledge" which the class imparted.
Surely using more knives decreases the force applied by just one knife making it harder to cut. Then again LOTF can't do mechanics.?
7. (Original post by miketree)
Do you know what problem number it is by any chance?
216 http://www.thestudentroom.co.uk/show...1#post43045141
8. (Original post by ukdragon37)
...
I understand this, and would like to ask if going into a mathematics degree for a student such as Ukd is actually the right idea then?

This thread is pretty worrying if I'm going off to university next year and am struggling with "A-level knowledge"..
9. (Original post by miketree)
I understand this, and would like to ask if going into a mathematics degree for a student such as Ukd is actually the right idea then?

This thread is pretty worrying if I'm going off to university next year and am struggling with "A-level knowledge"..
Which university do you plan to go to next year exactly?
10. (Original post by bananarama2)
Surely using more knives decreases the force applied by just on knife?
I mean holding a more solid implement makes it easier to exert more force from your hand/arm/body to that implement.

(Original post by miketree)
I understand this, and would like to ask if going into a mathematics degree for a student such as Ukd is actually the right idea then?

This thread is pretty worrying if I'm going off to university next year and am struggling with "A-level knowledge"..
That depends on the specific course. Of course being better at applying will very likely make your time in the degree easier wherever you go, but that's not to say you specifically don't have the necessary skills such that you are going to struggle, since most maths degree courses are supposed to be accessible from the "A-level knowledge" you refer to.
11. (Original post by miketree)
Quoted from OP:

* = requires only​ A-level knowledge.

This is not A-level knowledge.
It uses no more than geometric series and basic complex numbers (if you know about the polar forms of complex numbers you know enough).
12. (Original post by ukdragon37)
I mean holding a more solid implement makes it easier to exert more force from your hand/arm/body to that implement.
Ahh right. I personally would opt for a light saber or one of the those knives in Hitch Hikers' Guide to the Galaxy.

Edit: BTW I hope you realise I've resorted to pictures of Emma more exam motivation
13. (Original post by ukdragon37)
I mean holding a more solid implement makes it easier to exert more force from your hand/arm/body to that implement.

That depends on the specific course. Of course being better at applying will very likely make your time in the degree easier wherever you go, but that's not to say you specifically don't have the necessary skills such that you are going to struggle, since most maths degree courses are supposed to be accessible from the "A-level knowledge" you refer to.
So how would you recommend getting a more problem-solving focused mathematical view? If that is a right way to put it.
14. (Original post by bananarama2)
Ahh right. I personally would opt for a light saber or one of the those knives in Hitch Hikers' Guide to the Galaxy.

Edit: BTW I hope you realise I've resorted to pictures of Emma more exam motivation
I wish I could do the same for where I'm going, but I find Cornell ugly compared to Cambridge. (In fact I don't think there is a university in the US that compares in that respect. I went to Yale too and it was still meh.)

(Original post by miketree)
So how would you recommend getting a more problem-solving focused mathematical view? If that is a right way to put it.
Free yourself from the curriculum and learning in order to pass exams. Read and practice outside of the subject as it is taught. For recreation you can try puzzle/problem books, and for more "serious" improvements you can practice the range of super-curricular exams there are from AEA and STEP right up to BMO and IMO.
15. (Original post by ukdragon37)
I wish I could do the same for where I'm going, but I find Cornell ugly compared to Cambridge. (In fact I don't think there is a university in the US that compares in that respect. I went to Yale too and it was still meh.)
Many places don't look as nice as Cambridge though It is a very pretty place. Just imagine all the lovely maths...
16. (Original post by bananarama2)
Many places don't look as nice as Cambridge though It is a very pretty place. Just imagine all the lovely maths...
But I'm not moving to those "many places". And if I fail I probably get to stay.
17. (Original post by ukdragon37)
Read and practice outside of the subject as it is taught. For recreation you can try puzzle/problem books, and for more "serious" improvements you can practice the range of super-curricular exams there are from AEA and STEP right up to BMO and IMO.
I self-studied my A-level maths and further maths.

But surely practicing for exams such as AEA, STEP, etc. are just learning for an exam again, just exams that are at a higher level?
18. (Original post by miketree)
I'm not here to argue what and what isn't "real mathematics" with those willing, I'm here to state my opinion, I feel that, with A-level knowledge ready for my mathematics degree next year, that some of these questions are wrongly titled and that principles that have been called "A-level knowledge" on here are not and are in fact "STEP and higher" and hence the titles are misleading.
No offence but, whilst I am sure you are as prepared as your university requires you to be, the skills-based preparation (STEP) required for Cambridge is about teaches students to find ways to use A-Level knowledge in more intelligent ways.

Difficulty is subjective and, whilst most universities will teach you how to do these kinds of questions in the first few years, many will be able to "figure out" how to do them from proceeding information.

For example, I found C4 rather boring because, after having learnt C3, I found that I was already able to do almost all of the questions before I started the course! Whilst a C3 student has not sat a C4 module, the way I see it, most C4 questions can be done with C3 knowledge (partial fractions, almost all of the integration, etc...) Just because the A-Level system takes you by the hand doesn't mean that is how mathematics is done! You are taught to memorise how to do certain integrals that you already can figure out from previous knowledge.

A lot of FP3 can be worked out from the other modules as well. I mean, do we really need an entire chapter in the book on differentiating inverse trigonometric functions? Such can be deduced as a trivial consequence of C3 and C4 methods!

The meat of it: assumed knowledge is defined as what knowledge you need to do a question. At the end of the day, it is, by definition, impossible to give such ratings to questions because all mathematics can be extrapolated from the axioms. Lets interpret a * question as one that can be done with A-Level knowledge without having to "invent a new piece of maths" as far as the problem-solver is concerned (as I said before). What constitutes this is entirely subjective. Whilst questions that require, for example, laplace transforms (or things of a greater level of sophistication) can be done simply by the concept occurring to you (in the same way it originally did to laplace), we can assume that those on this thread are not going to do this. This means, as you have hinted at, the concepts of difficulty and assumed-knowledge are not independent. As a rule-of-thumb, if a typical student who has (at this stage in their development) a strong enough mathematical ability to do things like STEP questions can extrapolate the knowledge required to do the question from the A-Level syllabus then the asterisk rating should be *.

I now consider the point laboured enough and, asides from you replying to this response and one or two posts, if we continue to debate this, the thread will be dominated by this discussion (which is not desirable especially since the questions are hard enough to find given the lack of updates in the OP :/ )
(Original post by ukdragon37)
Consider the following story as an analogy...
PRSOM
(Original post by miketree)
Do you know what problem number it is by any chance?
'Bout three/four pages back!
19. (Original post by ukdragon37)
But I'm not moving to those "many places". And if I fail I probably get to stay.
I don't follow...sorry If you go to Cornell surely you are going to one of those many places? Wow...I wish I could say that.
20. (Original post by miketree)
But surely practicing for exams such as AEA, STEP, etc. are just learning for an exam again, just exams that are at a higher level?
They are different style of question which require you to use your knowledge in more of a "mathematical" way.

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