Most difficult course/topic covered in MFE/MQF-type programs?

[mathemagician]

I'm currently in my undergrad for mathematics, enrolled in a graduate-level mathematics introductory theory of PDEs course. It is an entirely new experience for me and the course moves extremely fast - we covered the entirety of ODE and beyond in less than a week, Green's function (with special guest, the Delta Dirac function) the next week. We just finished Second-0rder linear PDEs using change of variables to determine their conic section type (hyperbolic, parabolic, elliptic) and canonical forms, and the Cauchy-Kowalewskaya theorem. We started Homogeneous Wave Equations in 1-dimension last week (D'Alembert's Formula, now delving into infinite and semi-infinite strings)

I'm subjecting myself to this struggle to prepare for a MFE/MQF program - but this PDE course has me doubting my confidence in pursuing a degree in mathematical finance. I am having difficulty keeping up with the workload as it is something I am not used to as an undergraduate.

So, I'm asking anyone currently enrolled in a MFE/MQF or similar program (or, if you have earned your degree) - what has been the most difficult material/course you have encountered? If PDE is the "gatekeeper" then I think I'll survive.

 

[IntoDarkness]

unless taking very theoretical phd level courses, mfe level stuff r more applied. source: i checked some of their final exams before

 

[Daniel Duffy]

I suspect that much of this PDE stuff is not relevant to computational finance. Applied and numerical PDE is what is needed IMO. In particular, finite difference method.

Long story short; convection-diffusion-reaction PDE is what quants use.

infinite and semi-infinite strings
wha?

 

[bigbadwolf]

I'm currently in my undergrad for mathematics, enrolled in a graduate-level mathematics introductory theory of PDEs course

Wrong course. In addition, the speed of the course means a superficial treatment, with little comprehension and little sticking to the minds of students after the final.

 

[mathemagician]

I suspect that much of this PDE stuff is not relevant to computational finance. Applied and numerical PDE is what is needed IMO. In particular, finite difference method.

Long story short; convection-diffusion-reaction PDE is what quants use.

infinite and semi-infinite strings
wha?

Haha, long story short:

For the infinite string, its a string that is not held/fixed at either end but remains taught throughout so that we can "pluck" it like a string on a string instrument. a function u(x,t) measures the vertical displacement of a point x at time t. If we fix t = t0, we get the profile of the string @ t0 - if we fix x = x0, we get the motion of x0 in time. let p be the linear density and T be the tension constant of the string. Let c^2 = T/p, then, let u_tt = the first and second partial derivatives of u wr.t. t, and similar for x (If only I could LATEX...) and we get

u_tt - (c^2)u_xx = 0
called the vibrating string equation

EDIT:
AND THANK YOU VERY MUCH for the classification of PDEs that quants use - I can now ask my professor about what will be covered in these areas so that he can point me in the right direction with my studies. This is exactly what I was hoping for.

 

[mathemagician]

Wrong course. In addition, the speed of the course means a superficial treatment, with little comprehension and little sticking to the minds of students after the final.

The graduate students seem to be receptive - I'm seeing this course as an intense review of ODE and Calc III that introduces us to introductory methods for solving PDEs and the various forms PDEs can take. But you are right - a lot of this won't stick in my mind for long after the final, its a lot to absorb, but I'd rather be exposed to it so that I am somewhat familiar with the material.

 

[Daniel Duffy]

Haha, long story short:

For the infinite string, its a string that is not held/fixed at either end but remains taught throughout so that we can "pluck" it like a string on a string instrument. a function u(x,t) measures the vertical displacement of a point x at time t. If we fix t = t0, we get the profile of the string @ t0 - if we fix x = x0, we get the motion of x0 in time. let p be the linear density and T be the tension constant of the string. Let c^2 = T/p, then, let u_tt = the first and second partial derivatives of u wr.t. t, and similar for x (If only I could LATEX...) and we get

u_tt - (c^2)u_xx = 0
called the vibrating string equation

EDIT:
AND THANK YOU VERY MUCH for the classification of PDEs that quants use - I can now ask my professor about what will be covered in these areas so that he can point me in the right direction with my studies. This is exactly what I was hoping for.

Ah, got it, I had thought it was that new fangled hype called string theory. All's well.

You're welcome. And PDE is a great area. Do as much as you can.

 

[CasanovaJ]

I'm half way through the second semester of an MFE... during undergrad I did three semesters of calc, two linear algebra, one ODE, and three probability/stats-- no PDE. I was a bit worried about starting MFE without PDE, but at least so far I've gotten through most things fine, and the hardest course for me so far was actually time series, not either of the semesters of stocal... and my trouble with time series wasn't because of not taking PDE, it was because of never taking real analysis-- Hilbert spaces, spectral densities, Fourier, etc. Stochastic has been tough, but not because of PDE

 

[bigbadwolf]

The graduate students seem to be receptive - I'm seeing this course as an intense review of ODE and Calc III that introduces us to introductory methods for solving PDEs and the various forms PDEs can take. But you are right - a lot of this won't stick in my mind for long after the final, its a lot to absorb, but I'd rather be exposed to it so that I am somewhat familiar with the material.

What text are you using?

 

[mathemagician]

What text are you using?

Linear Partial Differential Equations for Scientists and Engineers, 4th Ed. by
Tyn Myint-U and Lokenath Debnath

a link to an available pdf (security certificate not verified)
https://www.pmfst.hr/~skresic/PDJ/L...ns_for_Scientists_and_Engineers (Debnath).pdf

 

[Daniel Duffy]

good practical books

Charles R. MacCluer Boundary Value Problems and ... Dover

Kreider, Kuller, Ostberg and Perkins .. an inrtroduction to linear analysis.

 

[bigbadwolf]

good practical books

Charles R. MacCluer Boundary Value Problems and ... Dover

Kreider, Kuller, Ostberg and Perkins .. an inrtroduction to linear analysis.

The one he's using is also a good one.

 

[Daniel Duffy]

Consulting other books as well does no harm.

 

[ExSan]

I'm currently in my undergrad for mathematics, enrolled in a graduate-level mathematics introductory theory of PDEs course....

what are the textbooks you are using ??
sorry dbl question

 

[tfors]

I think you are missing prerequisites, they were merely revisiting those in the first weeks of the course, that's why it seemed to go so fast for you.

 

[mathemagician]

I think you are missing prerequisites, they were merely revisiting those in the first weeks of the course, that's why it seemed to go so fast for you.

I had taken ODE so I was familiar with everything up to Green's function, though the ODE course did not cover initial boundary problems. I think the problem is lack of exposure to what the graduate students have been exposed to and the fact that I have not taken Real Analysis and some more in-depth calculus courses. Pre-requisite was Advanced Linear Algebra (bases, spans, gram-schmidt method - really a more in-depth, proof-based extension of regular Linear Algebra, which is structured for non-mathematics majors)

what are the textbooks you are using ??
sorry dbl question

I posted the link above:
Linear Partial Differential Equations for Scientists and Engineers, 4th Ed. by
Tyn Myint-U and Lokenath Debnath

https://www.pmfst.hr/~skresic/PDJ/L...ns_for_Scientists_and_Engineers (Debnath).pdf

I'm half way through the second semester of an MFE... during undergrad I did three semesters of calc, two linear algebra, one ODE, and three probability/stats-- no PDE. I was a bit worried about starting MFE without PDE, but at least so far I've gotten through most things fine, and the hardest course for me so far was actually time series, not either of the semesters of stocal... and my trouble with time series wasn't because of not taking PDE, it was because of never taking real analysis-- Hilbert spaces, spectral densities, Fourier, etc. Stochastic has been tough, but not because of PDE

We JUST began the chapter about Fourier series in Hilbert spaces and I agree 100% about the Real Analysis. I guess this is the course where Cauchy sequences are talked about.

good practical books

Charles R. MacCluer Boundary Value Problems and ... Dover

Kreider, Kuller, Ostberg and Perkins .. an inrtroduction to linear analysis.

Thank you for the suggestions, if I can find free copies of them I will look them over. I am liking PDE - its challenging because of how much it demands, but also very rewarding - it feels as if my spatial memory has grown exponentially since the beginning of the semester.

TheBigBadWolf is right about the textbook - I like it, but I haven't seen enough REAL mathematics textbooks to offer a credible opinion. When I need further explanation or a different view on a topic in the book, I've been able to get by with Google searches.

 

[Daniel Duffy]

Schaum "Partial Differential Equations" has lots of worked examples.

And even FDM + FEM.

 

[Quant4Life]

I'm currently enrolled in a top MFE. Stochastic Calculus is definitely the hardest series in my program. C++ and stats are a lot easier...

 

[CasanovaJ]

What time series book do you guys use?

 

[Quant4Life]

What time series book do you guys use?

We haven't taken Time Series Analysis yet. It will come in the next quarter. The syllabus says Brockwell & Davis, Introduction to Time Series and Forecasting, 2nd edition, Springer (2002) and N.H. Chan, Time Series: Applications to Finance, Wiley (2002)

However, neither of the books are required. All our classes are highly customized to address the specific important issues relevant in the industry from a more practical perspective.