What can I expect from a course in Abstract Linear Algebra?

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Discussion Overview

The discussion revolves around expectations for a course titled Abstract Linear Algebra, particularly in contrast to previous computational linear algebra courses. Participants explore the nature of the course content, including the balance between abstract concepts and computational tasks.

Discussion Character

  • Exploratory, Debate/contested, Conceptual clarification

Main Points Raised

  • One participant expresses concern about the inclusion of computations in the Abstract Linear Algebra course, questioning how much computational work will be required, especially on assessments.
  • Another participant suggests that Abstract Linear Algebra might focus on vector spaces and linear maps, distinguishing it from what they refer to as concrete linear algebra, which involves matrices.
  • A later reply indicates that the midterm will require constructing matrix transformations, which the participant finds frustrating.
  • Another participant proposes that Abstract Linear Algebra will likely involve minimal use of matrices and determinants, emphasizing proofs and abstract linear transformations instead.
  • A recommendation is made to consult "Linear Algebra Done Right" by Sheldon Axler as a resource that aligns with a more abstract approach to the subject.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the expectations for computational work in the course. There are competing views on the extent to which computations will be involved versus a focus on abstract concepts.

Contextual Notes

Participants express varying definitions of what constitutes Abstract Linear Algebra, leading to uncertainty about the course's content and structure. There are also differing opinions on the role of matrices and computations in the course.

JasonRox
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What should I expect out of a course named Abstract Linear Algebra?

I have just taken two courses on Linear Algebra, and it was mainly computational.

I was hoping that this course would not involve any computations, but the professor says we will have some (how much?) on our next midterm.

I don't mind having them for assignments, and as for examples, but on the midterm?

After doing annoying computations for two terms, I certainly don't want to continue doing them. Is it expected to continue doing computations in Abstract Linear Algebra?

Note: We still have questions like find a basis for V (a vector space).
 
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look at my notes on my web page for linear algebra. that's probably considered abstract linear algebra by some people, although i myself just consider it linear algebra.

http://www.math.uga.edu/~roy/

i would guess people mean vector spaces and linear maps as abstract linear algebra, and matrices as concrete linear algebra (I was tempted to say stupid linear algebra, but i won't)..
 
mathwonk said:
look at my notes on my web page for linear algebra. that's probably considered abstract linear algebra by some people, although i myself just consider it linear algebra.

http://www.math.uga.edu/~roy/

i would guess people mean vector spaces and linear maps as abstract linear algebra, and matrices as concrete linear algebra (I was tempted to say stupid linear algebra, but i won't)..

Well, on our midterm we will be expected to construct matrix transformations for any given transformation.

I really hate doing that. I really really really do.
 
Abstract linear algebra probably means little or no use of matrices at all as well as not doing any determinants. everything will be proofs and instead of matrices you will be using the abstract version of a linear transformation much more. if you have a chance, look at Linear Algebra Done Right by Sheldon Axler (you can look at it on amazon). His book is pretty much just a pure abstract treatment of linear algebra.
 

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