Early advice!

[Gian]

Hi all!
I am a second year doing Maths at Oxford who got a first last year.
I am in the process of choosing options, at the moment I will probably go for: Stats, Topology, Probability, Integration and Numerical Analysis.
For the future I have got 2 ideas: either get a job straight after my 4 years degree or do the last year in Cambridge and then do a PhD in something related to Stochastic Equations- Functional Analysis (if I am good enough to get in a top uni)

Now, I am also interested in Mathematical Finance but I want do to it seriously. Hence I asked my tutor about it and he told me to stay away from it until I have solid basis in topology, measure theory, functional analysis and probability.

What do you think of this?

Also, at the present stage, I am applying to Spring weeks in Investment Banks and to research projects this summer, do you think these kind of thing can be beneficial? What else could I do?

Thank you very much!

 

[bigbadwolf]

Now, I am also interested in Mathematical Finance but I want do to it seriously. Hence I asked my tutor about it and he told me to stay away from it until I have solid basis in topology, measure theory, functional analysis and probability.

That´s overkill.

 

[Gian]

That´s overkill.

well, mathematical finance employs quite a lot of the mathematics I mentioned...
I don't want to have an approach as the one of an engineer...

 

[Andy Nguyen]

On the job, you would need all the skill of an engineer. There is little advanced math being done at most quant jobs.

 

[Shantanu Kumar]

Aren't courses like Topology, Measure Theory/Probability compulsory for a Maths grad?

 

[Gian]

On the job, you would need all the skill of an engineer. There is little advanced math being done at most quant jobs.

well, the top quants tend to have a good mathematical background.

I am interested in quant research roles mostly, at the moment.

 

[Gian]

Aren't courses like Topology, Measure Theory/Probability compulsory for a Maths grad?

not in my university, I have done Probability last year, but i would call that an introduction.

 

[Shantanu Kumar]

Its good to plan but I would say keep your options open. As it has been discussed so many times here the kind of Quant research roles you are planning for aren't many. So build a background which can give you many options. Hence a good background in Mathematics and Programming/CS would help you in long term. I would say choose a course in Topology (its fun ) and Probabilistic Measure Theory (it isn't so much of fun ). Functional Analysis is completely your choice whether you enjoy(ed) Analysis or not.Also develop your programming skills if you haven't yet.
Good Luck!

 

[Gian]

Its good to plan but I would say keep your options open. As it has been discussed so many times here the kind of Quant research roles you are planning for aren't many. So build a background which can give you many options. Hence a good background in Mathematics and Programming/CS would help you in long term. I would say choose a course in Topology (its fun ) and Probabilistic Measure Theory (it isn't so much of fun ). Functional Analysis is completely your choice whether you enjoy(ed) Analysis or not.Also develop your programming skills if you haven't yet.
Good Luck!

thank you very much!
I really like analysis and I think it is the subject at which I am best
I used to play with C++ when I was younger, I made a Dos-graphic Ping Pong once which took me ages, I should probably get back on that language even if at the moment I'm using mostly R and Matlab :D

 

[Daniel Duffy]

well, mathematical finance employs quite a lot of the mathematics I mentioned...
I don't want to have an approach as the one of an engineer...

You need to reconsider your assumptions. As a pure mathematician, effort will be needed to move to engineering mindset. Industry is not academia!!

I would say become the best mathemagician you can be and avoid 'falling between 2 chairs' (not sure if that is the correct phrase).

I would say focus on Numerical and Functional Analysis.

 

[Gian]

You need to reconsider your assumptions. As a pure mathematician, effort will be needed to move to engineering mindset.

that would be a huge effort... I have never liked using stuff I do not understand fully.

So do you think there is no place for pure mathematicians (or at least non-engineers) in finance?

 

[Daniel Duffy]

not in my university, I have done Probability last year, but i would call that an introduction.

How can you be a mathematician without topology?

 

[Gian]

How can you be a mathematician without topology?

I know, it's quite stupid that it is not a compulsory course... It is true that we do the basic of metric spaces in the Analysis and Complex analysis, but the only big result we prove is the Heine-Borel thm...

 

[bigbadwolf]

So do you think there is no place for pure mathematicians (or at least non-engineers) in finance?

Applied mathematicians and engineers make up heuristic arguments for the conceptual tools that they use, rather than insist on strict proofs and definition-lemma-theorem-corollary structures. Making up heuristic and ad hoc arguments and arriving at heuristic and ad hoc insights is key in quant finance. It´s nice to have a rigorous and structured understanding but it´s not indispensable and often the thought patterns engendered by pure math can be a hindrance to the kind of thinking needed in applied areas (such as engineering and quant finance).

 

[Daniel Duffy]

that would be a huge effort... I have never liked using stuff I do not understand fully.

So do you think there is no place for pure mathematicians (or at least non-engineers) in finance?

I think bigbadwolf has summed it up well.

 

[Daniel Duffy]

Here is the senior freshman maths curriculum at TCD, Dublin. It is a healthy mix of pure, applied and physics.
Just proving theorems leaves things one-sided IMHO. Applications are good. In the past you could also do fluid dynamics and FEM/FDM in years 3 and 4.

http://www.maths.tcd.ie/undergraduate/mod-mathematics/sf.php

 

[Gian]

Here is the senior freshman maths curriculum at TCD, Dublin. It is a healthy mix of pure, applied and physics.
Just proving theorems leaves things one-sided IMHO. Applications are good. In the past you could also do fluid dynamics and FEM/FDM in years 3 and 4.

http://www.maths.tcd.ie/undergraduate/mod-mathematics/sf.php

I appreciate that you can't do functional analysis is you are a quant...what I say is that i think is better to have a solid mathematical background...wrong assumptions can lead to big mistakes and if you don't understand the assumption you make then everything is harder.

anyway, this is the maths curriculum at my uni:
http://www.maths.ox.ac.uk/courses/material

 

[Daniel Duffy]

Functional Analysis is _hugely_ important for numerical analysis, PDE, FEM etc. And it's fun.

http://personal.lse.ac.uk/Sasane/ma412.pdf