I'm an undergraduate student at the University of Minnesota, and I'm wondering about how necessary abstract algebra is for future careers in computational industry work or statistics graduate school. I have figured out that I will need advanced linear algebra, real analysis, and some basic probability theory to give myself flexibility, but I am unsure about abstract algebra. From what I have heard, I could get by without it, but graduates schools may be suspicious of a math student who did not take abstract algebra.

Right now I have three options: pursue a computer science minor, do the computational specialization for the math major, or pursue a statistics minor.

A computer science minor would give me enough room to study abstract algebra, but the other groupings are a bit more limiting. The computational math specialization essentially swaps abstract algebra out for numerical analysis while the statistics minor would focus more on statistical computing, though I doubt the usefulness of this path since it seems most statistics-related careers require grad school so I would learn this anyways.

So given the paths I want to take, would abstract algebra be a good idea?

Any advice is appreciated, and an extremely special thank you to those who are willing to offer some career guidance as well.

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    $\begingroup$ You don't need it. It's helpful, though. Gives you a new way of thinking about abstract structures. $\endgroup$ – Don Thousand Nov 15 '19 at 19:05
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    $\begingroup$ How necessary is complex analysis for computational/statistical careers? I think these are not the right questions. Any field will show you something which you still have to learn and which is useful for a scientific career in any field (well, of mathematics, say). Do you have a special problem with abstract algebra? $\endgroup$ – Dietrich Burde Nov 15 '19 at 19:09
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    $\begingroup$ @DietrichBurde I don't have a problem with the subject itself and if I had more free slots in my schedule, I would take it. However, I will have to choose between abstract algebra and numerical analysis. From what I can see, numerical analysis will help me get an industry career, but might shoot me in the foot for graduate statistics study if I take it over abstract algebra. I'm wondering if the opposite is true for abstract algebra, or if I'm worrying over a whole lot of nothing. $\endgroup$ – mrkevomeli Nov 15 '19 at 20:53

I'm writing this as an answer as it is too long for a comment. Knowledge of abstract algebra can be useful, especially if you'll be looking into computational/stats careers in science and engineering.

In particular, polynomials, polynomial rings, varieties and the theory of Gröbner bases are used througout science and engineering.

To quote Bernd Sturmfels (What is... a Gröbner basis):

Gröbner bases have been used by researchers in optimization, coding, robotics, control theory, statistics, molecular biology, and many other fields.

I would encourage you to take a look at

Cox, Little, O'Shea - Ideals, Varieties, and Algorithms. An Introduction to Algebraic Geometry and Commutative Algebra

to get an idea about what kind of topics appear in computational abstract algebra, how the algorithms look like, and how they are used (e.g. Forward and Inverse robotic kinematic problem, Chapter 6 of the book above).


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