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The Oxford maths interview, shaking up admissions

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Re: The Oxford maths interview, shaking up admissions

#31
post #26
post #19

Earlier quoted context omitted.

They recently (a few years ago) introduced A* grades for 90+/100 scores, where A was 80/100 before and so, as you note, not very discriminating. I'm not totally sure, but I think a standard offer for one of the elite universities is A*AA these days. I'm not sure I like the idea. Only having to hit 80 reduces stress quite a bit, and it gave me time to do extracurricular things like programming, and way more maths modu…

[At least when I took them a few years ago] the admissions offices get your raw results anyway - so even if it was just 'A', they could still have their own internal A* for 90+. Surprised nobody's mentioned STEP, three exams at least two of which are required for the mathematics tripos (and I think engineering at some colleges) and is significantly more likely to require preparation. I don't think any applicant would…

>the admissions offices get your raw results anyway - so even if it was just 'A', they could still have their own internal A* for 90+.

But as I understand it, they can't make an offer based on that, so they're already obliged to accept you by the time they get those results.

Re: The Oxford maths interview, shaking up admissions

#32

I was curious to see the plot of log(log x). It's weird. Fortunately we have Wolfram Alpha so it was trivial to quickly see it: http://www.wolframalpha.com/input/?i=plot+log(log+x)

So I would argue the easiest way to plot log log x is to parameterize the x domain.

For f x = log x where log has base b, we know that f b^0 = 0, f b^1 = 1, etc. what does g x = log log x look like? Well, we know log x is undefined for x < 0, which implies g is undefined for x < b^0 = 1, or b^b^0. More generally, you can say when f x = y, g b^x = y. So we know that g intercepts 0 at b^b^0 = b. You could do this for several more points for y = 1, y = 2, and so on, or you could draw a graph of log x and just relabel the x-axis to be 1) shifted by 1 with the x-intercept at b and 2) scaled logarithmically.

Re: The Oxford maths interview, shaking up admissions

#33

I was curious to see the plot of log(log x). It's weird. Fortunately we have Wolfram Alpha so it was trivial to quickly see it: http://www.wolframalpha.com/input/?i=plot+log(log+x)

I was going to comment that Google search does plots too, but in this case it seems to get it wrong:

https://www.google.ca/search?q=plot%20ln(ln(x))

Re: The Oxford maths interview, shaking up admissions

#34
post #4

I wonder to what extent there is anyone who could cope with the Oxford course but who could not breeze through A-level Further Maths. I entirely understand that the converse is false: there are people who are extremely good at exams but who simply couldn't cope with the Oxford course. Almost all of those on the Cambridge maths course (which I'm taking to be similar) found A-level maths/further maths very easy. Of cou…

My experience is that there are three levels of maths ability among people who breezed A-level, or at least passed it well enough to do university maths: - fundamentally does not grok University-level maths at all; - gets "ordinary" university maths (ie redbrick and "below"), but would not be able to cope with Oxbridge level; - Oxbridge level There are stark step-jumps between these three, and exam results are not a…

Liked the tone of your post. Did not detect any bitterness. Does your mathematical background serve a use in your current career, which I assume is as a dev of some sort since you are on Hacker News?

Re: The Oxford maths interview, shaking up admissions

#35
post #4

I wonder to what extent there is anyone who could cope with the Oxford course but who could not breeze through A-level Further Maths. I entirely understand that the converse is false: there are people who are extremely good at exams but who simply couldn't cope with the Oxford course. Almost all of those on the Cambridge maths course (which I'm taking to be similar) found A-level maths/further maths very easy. Of cou…

My experience is that there are three levels of maths ability among people who breezed A-level, or at least passed it well enough to do university maths: - fundamentally does not grok University-level maths at all; - gets "ordinary" university maths (ie redbrick and "below"), but would not be able to cope with Oxbridge level; - Oxbridge level There are stark step-jumps between these three, and exam results are not a…

What does "redbrick" mean in this context?

Re: The Oxford maths interview, shaking up admissions

#36

I was curious to see the plot of log(log x). It's weird. Fortunately we have Wolfram Alpha so it was trivial to quickly see it: http://www.wolframalpha.com/input/?i=plot+log(log+x)

I was going to comment that Google search does plots too, but in this case it seems to get it wrong: https://www.google.ca/search?q=plot%20ln(ln(x) )

How so?

The important parts to include on a sketch are that the function is monotonically increasing, has an asymptote at x=1 [0], intercepts the x-axis at x=e (approx 2.7) and quickly becomes almost flat. Both graphs agree on these points.

Wolfram Alpha is using the complex logarithm (https://en.wikipedia.org/wiki/Complex_logarithm) to extend to x [0]: For values of x < 1, ln(x) < 0, so ln(ln(x)) is not a real number.

Re: The Oxford maths interview, shaking up admissions

#37
post #36

Earlier quoted context omitted.

I was going to comment that Google search does plots too, but in this case it seems to get it wrong: https://www.google.ca/search?q=plot%20ln(ln(x) )

How so? The important parts to include on a sketch are that the function is monotonically increasing, has an asymptote at x=1 [0], intercepts the x-axis at x=e (approx 2.7) and quickly becomes almost flat. Both graphs agree on these points. Wolfram Alpha is using the complex logarithm ( https://en.wikipedia.org/wiki/Complex_logarithm ) to extend to x [0]: For values of x < 1, ln(x) < 0, so ln(ln(x)) is not a real num…

You're right, the plot is correct. I didn't look closely and thought the vertical asymptote was at x=0, but actually it is at x=1 as you mentioned.

Re: The Oxford maths interview, shaking up admissions

#38
post #35

Earlier quoted context omitted.

My experience is that there are three levels of maths ability among people who breezed A-level, or at least passed it well enough to do university maths: - fundamentally does not grok University-level maths at all; - gets "ordinary" university maths (ie redbrick and "below"), but would not be able to cope with Oxbridge level; - Oxbridge level There are stark step-jumps between these three, and exam results are not a…

What does "redbrick" mean in this context?

Mea culpa, UK cultural assumption: https://en.wikipedia.org/wiki/Red_brick_university

Re: The Oxford maths interview, shaking up admissions

#39

Earlier quoted context omitted.

My experience is that there are three levels of maths ability among people who breezed A-level, or at least passed it well enough to do university maths: - fundamentally does not grok University-level maths at all; - gets "ordinary" university maths (ie redbrick and "below"), but would not be able to cope with Oxbridge level; - Oxbridge level There are stark step-jumps between these three, and exam results are not a…

Liked the tone of your post. Did not detect any bitterness. Does your mathematical background serve a use in your current career, which I assume is as a dev of some sort since you are on Hacker News?

Thanks. Dev: yes; maths useful: not so much, except I guess in the broader "mental training" sense.
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