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Linear algebra vs. Numerical linear algebra? Which one for grad application?


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Hello,

In preparation for applying to biostat graduate programs for Fall 2016, I will be taking linear algebra at my home institution this summer.

However, I am a bit confused by the fact that both linear algebra and numeric linear algebra are offered as separate courses, at least during the spring and fall.

Numerical L.A. is described as: Matrix algebra, Gauss elimination, iterative methods; overdetermined systems and least squares; eigenvalues, eigenvectors; numerical software. Computer implementation.

And L.A.: Matrix algebra, solution of linear systems; notions of vector space, independence, basis, dimension; linear transformations, change of basis; eigenvalues, eigenvectors, Hermitian matrices, diagonalization; Cayley-Hamilton theorem.

It seems as if one cannont receive credit for taking both classes.

I would appreciate any help -- realizing that this is an informal request. I just want to be sure I take the appropriate class with regard to my application.

Thanks

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It sounds to me like Numerical Linear Algebra is a computational course (specifically, getting computers to tell you the answers to linear algebra questions), whereas Linear Algebra is about the theory itself. I know zilch about biostat, so I can't say which is more relevant.

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To solve a problem in linear algebra, you usually need to apply an algorithm( Is the system Lineary independent? do A, then B, then C, then repeat C until X happens or Y happens... if X, it is lineary independent, if Y, it is not). It seems that the course you describe(numerical L.A.) is nothing but the application of concepts of L.A. to create code to solve the problems( by my experience, Matlab, mathematica or C++). By reading your description, L.A. contains the theoretical foundation and N.L.A. is a very applied course. I would take L.A., and with a basic course on programming or computer science, you can achieve what N.L.A. describes. That is way better than knowing how to code without understanding the deeper concept.

Edited by Mechanician2015
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I took both of these courses in my undergrad, with descriptions very similar to the ones you listed. As others said, the "Linear Algebra" course was all about theory and our problems were mostly proofs about various matrices. The "Numerical Linear Algebra" course had the "Linear Algebra" course as a pre-req and while we did not learn any more theory (each class was a review of what we learned in "Linear Algebra" and then we went on to learn how to implement efficient numerical routines to solve these problems). So, our problems were mostly implementing algorithms derived in class based on the theories we learned in "Linear Algebra".

 

From an astrophysics point of view, both of these classes were very helpful (although only "Linear Algebra" was required for the degree). I think having the theory as well as learning how to implement them as a computer program is essential for being a good researcher in the astrophysical sciences. I don't know what you will need for biostat though, but I would imagine that the class with the numerical approach is going to be more helpful. And especially if your numerical class does not require the theoretical class as a pre-req, you might just learn what theory you need along the way. (I learned way more linear algebra theory than I ever needed in my Linear Algebra class).

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Thanks for the quick feedback. It sounds as if L.A. is the class I should be taking. To make things more confusing, though, the summer version of the L.A. course lists calc III (multivariate) as a prerequisite, while the spring/fall version lists 'transition to advanced mathematics' as the prequriste, and calc III as the prerequisite for the numerical L.A. course. 

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You should be taking "classic" linear algebra. I would echo what others have said on here re: the numerical version, i.e., that it can be quite useful to have, but "classic" gives you the foundation for a much of graduate-level mathematical statistics.

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