
Cambridge Interview Advice (Maths)
Hi,
I just finished my AS levels and I'm about to head into Year 13. My teachers have said that it's very likely that I would be having an interview for the university of Cambridge (mathematics G100) in November, but I am very worried about it. Does anyone here know anything that might be useful for preparing for it? For example, one person I heard got a question asking him to derive an expression for e^{A} where A is a matrix. The solution was to use Taylor series, but it never occurred to me to do that until after half an hour of thought (is there any other way of getting there, by the way?). In an interview it's expected that you'd get that answer quite quickly. How can I prepare for this sort of thing? Any advice would be much appreciated, as I do not have a lot of time left.
Thanks.
Re: Cambridge Interview Advice (Maths)
Hi zetafunc.
I know a guy who goes to Cambridge and had the interview, but I would have to see if he would like telling you about it.
On a different note, you could also derive an expression for e^A from the spectral decomposition of the matrix A.
The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 bobbym
 Administrator
Re: Cambridge Interview Advice (Maths)
Hi;
but it never occurred to me to do that until after half an hour of thought
The time taken is related to your experience and what fields of math you prefer and major in. It only takes someone in computational mathematics 5 seconds to think of that since they use the Taylor's series every day and for darn near every problem.
In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 bob bundy
 Moderator
Re: Cambridge Interview Advice (Maths)
hi zetafunc,
They will already have your school reference so they'll know you are a good mathematician. But they want to find out how you respond to a new question. So trying to 'second guess' what they may ask defeats their objective.
And they won't necessarily expect a full, 'robust', and complete answer in such a short time. After all, Andrew Wiles took 7 years to prove Fermat's LT (at Cambridge of course!)
Just give them your ideas, showing you can think about a problem and apply maths to it. That should do it.
Good luck!
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Re: Cambridge Interview Advice (Maths)
anonimnystefy wrote:Hi zetafunc.
I know a guy who goes to Cambridge and had the interview, but I would have to see if he would like telling you about it.
On a different note, you could also derive an expression for e^A from the spectral decomposition of the matrix A.
Can you show me how to do this? Is this the same as matrix decomposition?
Re: Cambridge Interview Advice (Maths)
bobbym wrote:Hi;
The time taken is related to your experience and what fields of math you prefer and major in. It only takes someone in computational mathematics 5 seconds to think of that since they use the Taylor's series every day and for darn near every problem.
But at the moment I'm not supposed to have developed a preference yet  I'm still in the last year where there is pretty much a set syllabus everyone should be able to use. I am just worried because I was not able to get that solution...
Re: Cambridge Interview Advice (Maths)
bob bundy wrote:hi zetafunc,
They will already have your school reference so they'll know you are a good mathematician. But they want to find out how you respond to a new question. So trying to 'second guess' what they may ask defeats their objective.
And they won't necessarily expect a full, 'robust', and complete answer in such a short time. After all, Andrew Wiles took 7 years to prove Fermat's LT (at Cambridge of course!)
Just give them your ideas, showing you can think about a problem and apply maths to it. That should do it.
Good luck!
Bob
I forgot about the reference... although regarding secondguessing, I have noticed that they repeat some questions from time to time, and I just found the e^A where A is a matrix question in an old STEP paper. So, it might be useful... although I'm just worried about being thrown into a new environment! What if I get completely stuck and get nowhere at the interview?
Thanks everyone for your replies.
 bobbym
 Administrator
Re: Cambridge Interview Advice (Maths)
Hi;
Thinking on your feet is an attribute like having a high IQ. It pretty much comes built in, you do not train to get it. Some people are faster than others, some cleverer, some more dogged.
I am sure you will get in. Anyways, do not worry about it.
In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 bobbym
 Administrator
Re: Cambridge Interview Advice (Maths)
Hi zetafunc;
It seems that style of interview originated at M__icro$oft. Someone once said that If the zombies of Redmond developed it, it is sure to be of no value. You might like to read this fellow's comments:
http://www.bearcave.com/random_hacks/permute.html
In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
