I don’t have a strong background in Math. All I got from my undergraduate study is standard calculus, linear algebra and some prob and stat. I did learn a lot about probability(calculus based), statistical inference and econometrics in my MS study in Economics. I’m working full time now and trying to get myself more math. I have taken a PDE course (Seperation of Variables, Laplace, Fourier Series, Fourier Transform and etc) and a course in numerical method (focusing on using FDM to solve PDE: explicit, Crank Nicholsom, ADI and etc). For next semester, I’m looking at two courses:(1) Numerical Linear Algebra: not really sure what it is about. I do want to take the chance to refresh my Linear Algebra and learn more about it.(2) Calculus of Variations and Control Theory: This course covers: Optimization with constraints, Functionals, Euler's equation, Weiserstrass-Erdmann corner conditions, integral constraints and isoperimetric problem, fields of extremals and Hilbert's invariant integral, sufficiency conditions, conjugate points and Jacobi equation, introduction to optimal control, Pontryagin maximum principle, optimal control to target curves, time-optimal and fuel-optimal control of linear systems, singular control, and the calculus of variations revisited. Computational methods as well as applications to engineering areas will also be discussed.Which one is more helpful in terms of quantitative finance? Given that I can only take one course each semester. (BTW, i will not worry about not having sufficient background for a course. I can pick up things fast and I'm willing to devote time to study. Professors have always been helpful.)Thanks a lot for your help.Wondering

I do not think either one; but if you have to select between these two...Control theory is much, much interetingM

Thanks, Maelo. Is a course in Real Analysis helpful? Or one just need Mathematical Analysis.Wondering

Also look at Probability/Stochastic processes courses. I dont think real analysis would help you a lot. But again that is my own .02 cQuoteOriginally posted by: wonderingThanks, Maelo. Is a course in Real Analysis helpful? Or one just need Mathematical Analysis.Wondering

Numerical linear algebra will be a waste.It's inverting matrices numerically and the like.Control theory can be useful. For example, the early exercise of American options can be thought of as a stochastic control problem.

Chaos theoryDynamical systemsCoupled map lattices

Try to take some courses covering Stochastic processes and SDEs (the Springer book by Oksendal on SDEs is good, also for self-study)A course in Measure and Integration theory (i.e. Lebesgue integral etc.) could also be useful

QuoteOriginally posted by: ppauperNumerical linear algebra will be a waste.It's inverting matrices numerically and the like.Control theory can be useful. For example, the early exercise of American options can be thought of as a stochastic control problem.Pliska's text have some chapters on optimal control applications.

QuoteOriginally posted by: MaeloI do not think either one; but if you have to select between these two...Control theory is much, much interetingMWhat the heck? Are you suggesting Quants never need Numerical Linear Algebra! I guess if you're getting paid to wax lyrical about market price of risk and complete markets but if you want to get something done you'll be throwing some matrices around.My NLA was one of my most useful courses, definitely take that one. On the other hand I can't remember using my Control Theory course once.

QuoteOriginally posted by: crowlogicChaos theoryDynamical systemsCoupled map latticesall useful, but the question seemed to be "I can only take course (a) or course (b); which should I choose"

I definately agree. Linear algebra is the foundation of damn near anything useful you'll need to do. You don't need to code the algorithms yourself, but you need to know how to use them, what they do, their properties, etc.QuoteOriginally posted by: westwood23QuoteOriginally posted by: MaeloI do not think either one; but if you have to select between these two...Control theory is much, much interetingMWhat the heck? Are you suggesting Quants never need Numerical Linear Algebra! I guess if you're getting paid to wax lyrical about market price of risk and complete markets but if you want to get something done you'll be throwing some matrices around.My NLA was one of my most useful courses, definitely take that one. On the other hand I can't remember using my Control Theory course once.Ahh, well I was just throwing stuff out. I've never took courses on any of this stuff and taught myself by reading journals and books.QuoteOriginally posted by: ppauperQuoteOriginally posted by: crowlogicChaos theoryDynamical systemsCoupled map latticesall useful, but the question seemed to be "I can only take course (a) or course (b); which should I choose"

You need to both at some point. Linear algebra and calculus of variations. It's not an either or thing.

QuoteOriginally posted by: westwood23QuoteOriginally posted by: MaeloI do not think either one; but if you have to select between these two...Control theory is much, much interetingMWhat the heck? Are you suggesting Quants never need Numerical Linear Algebra! I guess if you're getting paid to wax lyrical about market price of risk and complete markets but if you want to get something done you'll be throwing some matrices around.My NLA was one of my most useful courses, definitely take that one. On the other hand I can't remember using my Control Theory course once.No, it seems that the fact I have taught Conytrol System Theory to EE Undergrads (course that is tipycally at the adv. undegrad or beg gard studies for EE's) only can be used to wax lyrical. Now, ignoring the clowns, if you alreday have a good courese in Linear Algebra you already have the basic knowledge needed to cope with adv. finance. Optimal Control systems deals with trajectories or path dependent integrals. Useful stuff to know for certain path dependent exotics options.Unless you plan to make research I would not take neither. BUT IF you have to make your choice between them..agian Control Theory is much more beautiful and elegant math.M