Do I need Numerical Linear Algebra?

[Ethan Lim]

Hi.

I was wondering if taking a Numerical Linear Algebra course is unnecessary considering I have already taken
1. Econometrics
2. Introduction to Scientific Computing ( Text: Mathematical Principles for Scientific Computing and Visualization - Gerald Farin & Dianne Hansford)
3. Will be taking Numerical Analysis in fall.

I am not sure if taking a Numerical LA course would be wasting time and effort or not.
P.S. Not that it really matters but the course HW is done submitted in Fortran.

Thanks in advance for your advice

 

[quantstart]

NLA underpins many areas of numerical methods. Matrix decomposition methods (such as LU, QR and Cholesky) are generally used to solve the matrix equation Ax=b, with A (matrix) and b (vector) known. Matrix iterative methods (such as Jacobi, Gauss-Seidel and SOR) are also used substantially. NLA makes frequent appearances in finite difference methods, Monte Carlo methods and regression techniques.

NLA is extremely useful for understanding how many algorithms work. It will give you a good idea of how to optimise algorithms as well as their limitations.

These days it is highly unlikely you will ever need to code up a NLA algorithm directly (except for homework assignments!). Robust, well-tested and optimised libraries exist for these methods in all the major languages. You will be expected to know when each method can be applied, however, and for that reason I would suggest it is worth taking the course.

Have a look at the textbook "Matrix Computations" by Golub and Van Loan. It's extremely comprehensive.

 

[Ethan Lim]

Thanks for the insight. I guess I will(or should) be taking NLA course then!

 

[quantstart]

Numerical Analysis is also extremely useful, if only to help you understand how computers store numbers and thus the limitations on numerical algorithms. All good knowledge for a quant career!

 

[Ethan Lim]

What are your thoughts about econometrics?
How would you weigh importance or relevance with quant careers of the three courses Econometrics, Numerical Lin. Algebra, Numerical Analysis.
Sounds like it would be something like NLA>=NA>Econometrics.

 

[quantstart]

That question really needs to be answered in the context of the type of job you're applying for. Unfortunately, the derivatives pricing quant jobs have declined significantly in the last few years, and the word "quant" has become attached to any sort of task related to mathematical programming within finance.

If you wanted to go work in a hedge fund, perhaps eventually as a quant trader (i.e. a "trader/researcher"), who will still be coding in some form, then all three would be beneficial, but particularly econometrics (mostly time-series analysis).

I would strongly suggest doing as many time-series and statistics courses as you can, since this seems to be the way the industry is shifting. Also, any programming ability is going to be a big plus - particularly in C++.

If you are more interested in an academic career in numerical methods, then indeed NLA and NA would be extremely useful (if not prerequisites) for grad school in that area.