Abstract or Applied Linear Algebra?

Click For Summary

Discussion Overview

The discussion revolves around the decision of whether to take Abstract Algebra II or Applied Linear Algebra as a course in preparation for graduate studies in mathematical physics or mathematics. Participants explore the relevance and utility of each course in relation to the intended academic path.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • One participant notes that Abstract Algebra is a valuable tool for pure mathematics, while Applied Linear Algebra may be more suitable for those leaning towards physics or engineering.
  • Another participant suggests that the course descriptions for both classes would provide better context for making a decision.
  • Course descriptions reveal that Abstract Algebra II covers topics such as permutation groups and homomorphism theorems, while Applied Linear Algebra focuses on matrices, linear systems, and eigenvalues.
  • A participant expresses concern that Applied Linear Algebra may not offer much new material after two semesters of linear algebra, suggesting that Abstract Algebra II might be more beneficial for graduate studies in mathematics.
  • Another participant mentions that if the topics in Abstract Algebra II are not already known, it would be advisable to take that course.
  • One participant emphasizes the broad applicability of Linear Algebra in various fields, including physics, statistics, and engineering, advocating for taking as much as possible.

Areas of Agreement / Disagreement

Participants express differing opinions on the suitability of each course based on their academic goals, with no consensus reached on which course is definitively better for pursuing mathematical physics or mathematics.

Contextual Notes

Participants' recommendations depend on individual academic backgrounds and future aspirations, highlighting the subjective nature of course selection in relation to personal interests in theoretical versus applied mathematics.

jimmypoopins
Messages
64
Reaction score
0
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.
 
Physics news on Phys.org
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.
 
JinM said:
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)
 
djeitnstine said:
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.
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 9 ·
Replies
9
Views
4K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 6 ·
Replies
6
Views
6K
  • · Replies 8 ·
Replies
8
Views
2K
Replies
3
Views
2K
Replies
41
Views
9K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K