Complex Analysis

[Sanket Patel]

I've got the entire summer to kill before grad school starts. Instead of just sitting around all day,I want to take some courses. I've already taken a Real Analysis course and what about a Complex Analysis course? How relevant, if at all, would Complex Analysis be for FE/Math Fin/QF? Any input?

 

[bigbadwolf]

I've got the entire summer to kill before grad school starts. Instead of just sitting around all day,I want to take some courses. I've already taken a Real Analysis course and what about a Complex Analysis course? How relevant, if at all, would Complex Analysis be for FE/Math Fin/QF? Any input?

I don't know about its relevance but complex analysis is great fun (much more than real analysis) and you might like to take it just because of its elegance. Real analysis is a rigorous theory of the calculus, built on careful definitions revolving around epsilons and deltas (unless you couch it in the even more abstract language if open sets and other notions from general topology). We do the same in complex analysuis but we have more powerful results and a more satisfying theory (thus, for example, holomorphic means it has a power series expansion: something that doesn't necessarily hold in the real case).

 

[Yuriy]

Can you, for example, take Differential Equations? Ordinary or Partial or maybe even Stochastic.

 

[Sanket Patel]

Can you, for example, take Differential Equations? Ordinary or Partial or maybe even Stochastic.

I've already taken both Differential Eqns. and Partial Differential Eqns. I would love to take a Stochastic Calc. or Stochastic Diff. Eq. course but unfortunately both courses are only offered in the Fall. During the summer, FSU generally don't offer the "higher" level courses. I bought a couple stochastic calc. textbooks and I'm trying to work through them over the summer. I suppose it won't hurt to take the complex analysis - at the least, I'll learn something new.

 

[Yuriy]

What else is being offered in the summer? Of course, taking complex analysis won't hurt (it won't help either )

 

[Andy Nguyen]

Complex analysis has little to no use in FE program. You would better off spend the summer working on your C++.

 

[Sanket Patel]

My other options are Abstract Algebra and Graph Theory. Everything else is below the Calc 3 level. I think I'll take the Complex Analysis course and use the other time to teach myself stochastic calc and continue working on my C++ skills.

 

[bigbadwolf]

My other options are Abstract Algebra and Graph Theory. Everything else is below the Calc 3 level. I think I'll take the Complex Analysis course and use the other time to teach myself stochastic calc and continue working on my C++ skills.

Abstract algebra is also great fun. But also, alas, of little or no applicability to finance. Incidentally, what books are going to be used for complex analysis and algebra? If it's the book by Churchill and Brown for complex, it won't be very exciting.

 

[Vic_Siqiao]

complex analysis has no direct use in FE, but it helps sometimes do calculations invloving complex variables. and i think some topics such as residual theorem are important, which i was asked in a fin math program interview.

 

[bigbadwolf]

complex analysis has no direct use in FE, but it helps sometimes do calculations invloving complex variables. and i think some topics such as residual theorem are important, which i was asked in a fin math program interview.

Many real phenomena can only be understood by recourse to the complex. For example, take the power series expansion of the function 1/(1-x). The series expanion will not equal the function for x >= 1, because there's a singularity at x =1. Straightforward so far. But now take the function 1/(1+x^2). The power series expansion also breaks down for x >= 1. But why when's there's no singularity at x =1? It's because there's a singularity at x = i, so the series expansion = function only within the radius of convergence.

The residue theorem is a generalisation of Cauchy's theorem. In my humble opinion, everyone having anything to do with math should have gone through at least one course in complex but I'm biased in this regard, and budding financial engineers have more pressing concerns.

 

[Sanket Patel]

Thanks everyone for the input - I appreciate it

 

[Andriy]

I would suggest you instead of Complex analysis class to take a good rest before studies start. Graduate study it is not so much fun as it was during undergraduate. You will have enough time to learn all these stuff when you will be sure what you really want to do.

 

[Andy Nguyen]

Definitely take a good vacation before school starts. I wish I took a week or two off then. It's a non stop cycle when the refreshers start, HW, internship, job, etc...

 

[VladimirBunicu]

I don't know about its relevance but complex analysis is great fun (much more than real analysis) and you might like to take it just because of its elegance.

It is fun indeed, and has elegant applications in mechanics, like Cauchy-Riemann equalities were used to come up with the first theory of air flow around a wing, and served (on par with PDE) as foundation for later aerodynamics. The same equations can be used to model electric and magnetic fields and heat flows along solid surface... If time allows, I would like to review complex analysis too.
So the class is worth to be taken even if there are no applications in financial math (and maybe there are :smt102)

 

[Sanket Patel]

@Andy
@Andriy

Taking a break/vacation sounds like a great idea

 

[kelcy]

for f(z) = (z^2-2)e^-x(cosy- isiny) can you apply Cauchy Riemann equations

 

[Daniel Duffy]

for f(z) = (z^2-2)e^-x(cosy- isiny) can you apply Cauchy Riemann equations

LATEX

 

[bootstrap]

Funny...I took both real and complex analysis many years ago. While I remember most of the key concepts from real analysis (it's very applicable if you study probability and statistics), I have practically forgotten everything I have learned in complex analysis. Well, except that there was a theorem in complex analysis cutely named the Picard's theorem. But the only reason I remember it is because I am a Star Trek fan.

On a serious note, I think you will be much better of taking real analysis instead of complex analysis if you are heading into a MFE program, if you haven't done so yet. Especially a more advanced real analysis course that deals with measure theory and all those convergence theorems for integrals. Those are essential for probability theory.

 

[Paul Lopez]

Funny...I took both real and complex analysis many years ago. While I remember most of the key concepts from real analysis (it's very applicable if you study probability and statistics), I have practically forgotten everything I have learned in complex analysis. Well, except that there was a theorem in complex analysis cutely named the Picard's theorem. But the only reason I remember it is because I am a Star Trek fan.

On a serious note, I think you will be much better of taking real analysis instead of complex analysis if you are heading into a MFE program, if you haven't done so yet. Especially a more advanced real analysis course that deals with measure theory and all those convergence theorems for integrals. Those are essential for probability theory.

Just excellently said bootstrap sir! Picard theorem gave me a good, hearty chuckle!