Oxford MAT 2013/2014

2.i is fine, but I'm not too sure about ii, iii and iv. Again, for 3, you're saying that they are symmetric about x=1 but that's not true.

Posted from TSR Mobile

fk and -f 2-k are symmetric about x=1

fk and -f 2-k are symmetric about x=1

I think I got the same results for 4 and 5.

Posted from TSR Mobile

I could do 1 and 2, I hope I didn't get them wrong. I didn't use open sets for 2, do I have to? :-/
And I think I've forgotten connectedness, so I had to skip 3. Thanks for sharing the problems, by the way. I feel a little less scared now (though I still don't want my first college interview to also be my first test on things that I've just looked at passively, haha).
Posted from TSR Mobile

I make two mistakes on part 1 so it is hard for me to get 85+. I think you can get 85+

Thank you~ I think I can get 32+13+10+13+13=81 or so.

Sorry, I missed this quote. If you don't use open sets it's just a result from real-analysis, it's just the same proof though using the fact that for $f: M \rightarrow N$ being a map between metric spaces, $f$ is continuous at $x$ if

$\forall \epsilon > 0 \ \exists \delta > 0 \ f(B_M(x, \delta)) \subseteq B_N(f(x), \epsilon)$

Feel free posting how you did the first and second question if you're unsure if you did it correctly or not.

I'm not too sure about my answers in the first part so it's hard for me to get more than 85
Though on the bright side the average score of candidates who were interviewed last year was 68-69 I think so I hope it's the same this year as well :P



Posted from TSR Mobile

That's nice. Are you completely sure about 2, though?




Posting properly with LaTeX will take me ages, but here are the outlines:
1. If x and x' aren't equal, then d(x,x')=d>0. Used the standard epsilon definition for both convergences with epsilon < d/2, say epsilon=d/4. So we get, for sufficiently large n, d(x_n,x) and d(x_n,x') are both less than d/4, but d(x,x')=d. This is a clear violation of the triangle inequality for metrics.
2. Yeah, exactly. The real analysis proof using metrics instead of absolute differences. For epsilon I get delta, for delta, I get delta2. (I was rigorous, but this was the idea.)

Are there mistakes in my understanding and approach?

My Part2 answer is same with revelry26. What is your answer?

One more thing. In my PS I probably mentioned that I started studying a bit of real analysis and learnt about things like metric spaces over the summer. They'll understand that I'm just talking about an introduction, right? If they expect me to know that stuff as if I've been taught at Oxford then I'm screwed.

Posted from TSR Mobile

Actually, the average score of candidates who were interviewed last year was about 63, as I recall. It's usually 61-63.

My Part2 answer is same with revelry26. What is your answer?

I think it was actually smart putting that stuff on. I'm a physics applicant, but I also mentioned in my PS that I knew some post-high school stuff about math (mostly PDEs/Fourier analysis) and physics (QM/Relativity)

I think it was actually smart putting that stuff on. I'm a physics applicant, but I also mentioned in my PS that I knew some post-high school stuff about math (mostly PDEs/Fourier analysis) and physics (QM/Relativity)

It is not smart to do that by any stretch of the imagination. All it does is invite the tutor, who knows more on those basic topics that most undergraduates will by the end of their degree, to test you on it and judge you on how well you can teach yourself the material (and self-teaching is more than required for undergrad. maths and physics) so unless you really do know your stuff when it comes to PDEs/Fourier, you're not likely to impress.

It is not smart to do that by any stretch of the imagination. All it does is invite the tutor, who knows more on those basic topics that most undergraduates will by the end of their degree, to test you on it and judge you on how well you can teach yourself the material (and self-teaching is more than required for undergrad. maths and physics) so unless you really do know your stuff when it comes to PDEs/Fourier, you're not likely to impress.

Hey, did you notice my previous quote? Here's the post:

"Posting properly with LaTeX will take me ages, but here are the outlines:

1. If x and x' aren't equal, then d(x,x')=d>0. Used the standard epsilon definition for both convergences with epsilon < d/2, say epsilon=d/4. So we get, for sufficiently large n, d(x_n,x) and d(x_n,x') are both less than d/4, but d(x,x')=d. This is a clear violation of the triangle inequality for metrics. 2. Yeah, exactly. The real analysis proof using metrics instead of absolute differences. For epsilon I get delta, for delta, I get delta2. (I was rigorous, but this was the idea.)

Are there mistakes in my understanding and approach?"