# Abstract or Applied Linear Algebra?

I have room for one more class this semester, and i've narrowed it down to Abstract Algebra II or Applied Linear Algebra. I've taken a semester of abstract algebra and two semesters of linear algebra thus far.

I'm interested in going to graduate school for either mathematical physics or mathematics. Which course would be better to take if that's what i'm pursuing?

Also, i had the professor that is teaching applied linear algebra last semester and he is very good. i have heard nothing about the professor teaching abstract algebra.

djeitnstine
Gold Member
From what I know of pure Mathematically inclined degrees abstract algebra is an excellent tool. If you're leaning towards more physics (engineering perspective) Applied Linear Algebra is your best bet.

Jimmy, can you post the descriptions for both classes? I think you would get a more informed opinion this way, for we have no idea of knowing what's taught in both classes.

Jimmy, can you post the descriptions for both classes? I think you would get a more informed opinion this way, for we have no idea of knowing what's taught in both classes.
Course: MTH 411 Abstract Algebra II
Description: Continuation of MTH 310. Permutation groups, groups of transformations, normal subgroups, homomorphism theorems, modules. Principal ideal rings, unique factorization domains, noncommutative rings, rings of fractions, ideals.

Course: MTH 415 Applied Linear Algebra
Description: Matrices and linear algebra. General linear systems of equations. Least squares minimization techniques. Eigenvalues and eigenvectors, spectral decompositions, and exponentials.

thanks for the suggestion, djeitnstine. i think you're probably right. i'm concerned about mathematical physics, however. i don't know exactly what course would be better for it. i am more interested in doing something theoretical rather than something involving engineering or lab-work.

If you've already taken two semesters of linear algebra, I can't imagine there's a whole lot of new material in the applied linear algebra course. If you plan on going to grad school in math, you should probably finish up on abstract algebra, if you ever take a functional analysis course you might end up covering a lot of the applied linear algebra topics

Abstract Algebra II for the most part should be covered in the first Algebra upper division course. If you do not know most of those topics I would suggest taking MTH 411, not to mention Abstract Algebra's were some of my favorite courses in College ^_^. (Read the latter statement as admittance to bias)

From what I know of pure Mathematically inclined degrees abstract algebra is an excellent tool. If you're leaning towards more physics (engineering perspective) Applied Linear Algebra is your best bet.
Strongly agree. Linear Algebra is very useful in Physics, Statistics, Engineering, and Computer Science. You'll see it everywhere. Take as much as you can. I'm kind of curious about your Abstract Algebra I class - we did most of the stuff you listed in Abstract Algebra I.