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Deciding whether or not to re-take Linear Algebra

  1. Mar 23, 2012 #1
    some relevant background: I intend to pursue a masters degree in math starting in the fall of next year, 2013. I attained a degree in economics back in 2004, but a couple years ago I started taking some undergrad courses part-time (one or two courses per semester) to prep me for a masters in math. I've taken diff calc, integral calc, multivariable calc, a course in reading and writing proofs with an emphasis on set theory, and linear algebra.

    Although the head of the department at Stony Brook seems to think I'd be able to complete the requirements for the masters degree with the background I have, I would feel more comfortable entering the program with some more background. In the fall then spring I intend to take 2 courses in Analysis (Introduction to Analysis then Analysis in Several Dimensions), an Abstract Algebra course, and a course labeled Topology and Geometry.

    I really didn't get too much out of the linear algebra course that I took. I don't want to blame too much on the professor, but he made us buy his book (which was this terrible paperback from 1980) and it was mainly a course in "matrix algebra". I learned many operations, we spent tons of time using gauss jordan etc, but very little time on theory or proofs. He never even taught us WHY gauss jordan elimination works, I had to figure that out on my own, i.e. how each step can be represented by an elimination matrix which when all multiplied together form the inverse matrix.

    I have the chance now to take a more sophisticated linear algebra course and I'm trying to decide if it would be worth it. I know that is very subjective, but that's why I'm here... for advice based on personal experience.

    Will it help me in my future studies (focusing on pure math)to have a deeper understanding of linear algebra or is it something one can pick up as they go along.

    opinions welcome.

    thank you.
  2. jcsd
  3. Mar 24, 2012 #2
    I´m doing undergrad economics now as well, and intend to do graduate maths too!
    I took two graduate courses in math so far: smooth manifolds and currently lie theory. From this I can tell that linear algebra really is crucial, and cannot be done half-assedly.

    I recommned getting Maclanes texbook Algebra (here) and reading thoroughly all linear algebra up to chapter X. From this book you can see he had it thought out really well and he´s good writer too!
  4. Mar 24, 2012 #3
    You should definitely take it again. If you can you might want to just audit the class, but if you can't you should take it anyways since you need to know things like span, linear independence, eigenvectors, eigenvalues, inner products, subspaces, projections, and SVD's. Many of these topics are very important to many different areas of mathematics. If you can, you should even take a intermediate linear algebra course after the one you are talking about. After the second one, you should know all the linear algebra you need for most graduate courses in math.
  5. Mar 24, 2012 #4
    It's not really re-taking the course, is it?? You want to take a more advanced course, rather than take the course you passed, right?

    Taking the advanced linear algebra course is a very good idea. I recommend this completely.
    If your talking about retaking the course you passed, then it's better not to. The course you mentioned sounds silly. So you'd be better of learning some advanced material.
  6. Mar 25, 2012 #5
    I have to preface this with saying: since I'm not sure what area of math you intend to focus on with your masters, nor where you want to go (and what quals you have to pass for your masters), but I'll ASSUME since you specifically said masters (rather than PhD), you're intending to do a terminal masters in some sort of applied math, then return to industry (possibly relating to what you did your undergrad in: finance / econ) ... you may want to consider:

    -this summer, watch Strang's LA lectures on MIT's OCW to give you a better understanding of the subject instead of just knowing the mechanical algorithms.

    -take what you planned to in the fall: analysis 1 + algebra 1

    -in the spring, take analysis 2 + some graduate course in LA (taught from something like Roman's Advanced LA, or at least LA Done Right by Axler).

    Chances are, you'll only have to take 1-2 quals as a masters student (probably analysis and/or algebra). In that case taking an intro topology course would (IMO) be less of a benefit than taking an advanced LA course after your first algebra class. It would get you more comfortable with concepts needed to pass an eventual exam in algebra, rather than just getting a tiny bit of exposure to topology (which you probably won't take more of if you're doing anything applied with your masters).
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