Oxford Msc Mathematical and Computational Finance Interview

[amraj]

Hello everyone,
I have been invited for an interview and I was wondering if there is anybody on here who has either had an interview or been invited to one, or even somebody with an offer for entry this year?
I would like to know what types of questions they will ask/have asked since I only been given four days notice. Thanks for your help in advance.

 

[Klade]

Hello, I know this is an old thread but I was just invited for an interview as well. Can you share your experience to me and those after me?

 

[Zakel]

Hey Klade, did you have your interview yet?

 

[Marchi]

Any comments on the interview process?

 

[Klade]

Interview was largely technical. I was first asked to "Tell me about yourself." After a short introduction and no follow-up questions I was told that "We would get straight into it." I was asked whether I felt more comfortable in Probability or Analysis. When I said Analysis, the first question asked was to elaborate on "Different ways a series of functions can converge." After this I was asked whether I had experience in Partial Differential Equations. When I said only Ordinary Differential Equations my interviewer said "Ok let's attempt to solve a partial differential equation" This took the remainder of the interview with the exception of "Do you have any questions for me." When I would get stuck I would be prompted with hints but I fear I got stuck a little too often and didn't make great progress with the hints I was given.

 

[Marchi]

Thank you for your response! Have you heard back from them already? I have my interview on Thursday and am a little nervous.. did they ask any questions that were more related to finance/work experience? Or was that all of it?

 

[Klade]

That was it for me. No finance/work related questions though I imagine you could highlight that in your answer to "Tell me about yourself." The interview was very relaxed and informal so I doubt you will have the same structure. I didn't make the cut at Oxford. Off to Columbia next year.

 

[Marchi]

Jokes on them, I would choose the Columbia program over the Oxford one any day! Enjoy

 

[Daniel Duffy]

After this I was asked whether I had experience in Partial Differential Equations. When I said only Ordinary Differential Equations my interviewer said "Ok let's attempt to solve a partial differential equation" This took the remainder of the interview

How did you get on moving from ODE to PDE? An ODE has 1 independent variable and a PDE has more than one, yes?

Did the interviewer give any hints?

 

[Marchi]

How did you get on moving from ODE to PDE? An ODE has 1 independent variable and a PDE has more than one, yes?

Yes, that's the basis of it. ODEs are a subset of PDEs given that their solutions are one-dimensional. In general, PDEs are much more difficult to understand/solve given that a large number of the theorems learnt with regards to ODEs are not applicable to PDEs.

 

[DavidHilbert]

Yes, that's the basis of it. ODEs are a subset of PDEs given that their solutions are one-dimensional. In general, PDEs are much more difficult to understand/solve given that a large number of the theorems learnt with regards to ODEs are not applicable to PDEs.

Heh, I am sure @Daniel didn't know this...

Technically what you are saying is ok, but to me ODE theory and PDE theory are two different worlds. One big misconception among young students is that ODE and PDE theory is all about finding closed form solutions to textbook examples and that ODE's are pretty much just subset of PDE's. This is, generally speaking, very far away from reality. Once you get beyond the abc stuff they teach in most math programs, PDE theory has little overlap with ODE theory.

 

[Marchi]

Once you get beyond the abc stuff they teach in most math programs, PDE theory has little overlap with ODE theory.

I entirely agree. I personally struggled with ODE theory, and expected the same difficulties from PDEs but was pleasantly surprised!

 

[Daniel Duffy]

It's not so much about learning lots of theorems, but maybe more about insight into a problem.
The latter would impress an interviewer more than rote learning. I'm second guessing here. My feeling is that Oxford would be quite rigorous.

//
If you consider PDEs and ODEs as Venn diagram then you are probably correct :D But they are intimately connected in many ways.

Example: The vertical and horizontal (Rothe) method of lines (MOL) reduce a PDE and ODE. In the former can you discretize in space to get a system of ODEs.

http://people.math.gatech.edu/~meyer/MOL-notes/Chap1.pdf

Linienmethode – Wikipedia

Clever mathematicians convert a PDE to an ODE, an they solve the latter, thereby solving the former.

Knowing some numerical analysis allows one to see the relationship.

Chapter 1. Boost.Numeric.Odeint - 1.63.0

//
I see a lot of ode and pde courses with focus on the 'pure' maths aspects. In general, PDE/ODE do not have closed solutions. In real life you need to solve them numerically. \

 

[Daniel Duffy]

Just remembered
There's a zillion transform to map a PDE to ODE

Laplace
Fourier
Mellin

Here's a nice example

http://web.math.ucsb.edu/~helena/teaching/math124b/heat.pdf

These are topics for 1st year undergrad, or if not they should be.

If you don't know the heat PDE at the very least then I would have grave doubts about your mathematical background.

Broaden the scope and the focus.

 

[Daniel Duffy]

Heh, I am sure @Daniel didn't know this...

.

Actually, I didn't now that :D thanks for pointing it out!

 

[Daniel Duffy]

Another link ..
First order PDEs can be solved as systems of ODEs

https://web.stanford.edu/class/math220a/handouts/firstorder.pdf

More in Courant and Hilbert's book

 

[Drew L]

Just remembered
There's a zillion transform to map a PDE to ODE

Laplace
Fourier
Mellin

Here's a nice example

http://web.math.ucsb.edu/~helena/teaching/math124b/heat.pdf

These are topics for 1st year undergrad, or if not they should be.

Excuse me but on what planet do they teach PDEs to first-year undergrads in any subject? I would not put forth PDEs to anyone who wouldn't had Cal 3, Linear Algebra, and tbh I've found Analysis incredibly helpful in my use of calculus.
Holy hell, who would do that.

 

[Daniel Duffy]

Excuse me but on what planet do they teach PDEs to first-year undergrads in any subject? I would not put forth PDEs to anyone who wouldn't had Cal 3, Linear Algebra, and tbh I've found Analysis incredibly helpful in my use of calculus.
Holy hell, who would do that.

I didn't exactly say that; I was referring to transforms but it is touching on PDE.

The interviewee do not know PDE but I assume he/she has > 4 years undergrad. Then you should know some PDE.

You can learn PDEs in 1st year as a methods course (we did) without too much analysis. Maths education has been dumbed down the last years so maybe PDEs are done later if at all.

This is a gem for 1st years
An Introduction to Linear Analysis by Donald L Kreider Robert G Kuller Donald R Ostberg and Fred W Perkins - AbeBooks

Here's one curriculum I know (things get serious by year 2)

Senior Freshman - Moderatorship in mathematics - Undergraduate : School of Mathematics : Trinity College Dublin, The University of Dublin, Ireland

 

[Delilah Peyton]

Does anyone know if they hold interviews for their part-time option MSc in Mathematical Finance?

 

[Quasar Chunawala]

I didn't exactly say that; I was referring to transforms but it is touching on PDE.

The interviewee do not know PDE but I assume he/she has > 4 years undergrad. Then you should know some PDE.

You can learn PDEs in 1st year as a methods course (we did) without too much analysis. Maths education has been dumbed down the last years so maybe PDEs are done later if at all.

This is a gem for 1st years
An Introduction to Linear Analysis by Donald L Kreider Robert G Kuller Donald R Ostberg and Fred W Perkins - AbeBooks

Here's one curriculum I know (things get serious by year 2)

Senior Freshman - Moderatorship in mathematics - Undergraduate : School of Mathematics : Trinity College Dublin, The University of Dublin, Ireland

I downloaded the book on Linear Analysis. I found that it really builds upon many ideas I learnt in linear algebra, it all fits like the pieces of a jigsaw puzzle. Can I work through this text, with a background of Single variable calculus and Linear algebra?

Also, the book by David Bleecker, many say is an excellent, yet rigorous introduction to Partial differential equations - perhaps, better than Strauss.

http://mapmf.pmfst.unist.hr/~skresi...artial Differential Equations (Bleecker).pdf