Should I take Elementary Linear Algebra before Analysis?

[andyroo]

I have yet to take Elementary Linear Algebra MATH 341, but I am currently signed up for Intro to Analysis MATH 413. I'm about to complete Elementary Analysis MATH 315. I could take MATH 341 and MATH 413 at the same time, but I'm already signed up for two other economics classes that I feel I should probably take this fall term. I'd take all 4 classes at the same time, but I have a job that's about 15 hours a week as well, so I'm not sure if taking all 4 would be a good idea. Overall, I'm asking if anyone thinks I should take linear algebra before this analysis course? Thanks.

-Andy

 

[Dr. Seafood]

I found that being comfortable with the abstract setting of a vector space helped when I was introduced to other general algebraic structures. We must be used to generalization when thinking about analysis. That said, linear algebra deals a lot with discrete (separate) objects like matrices and ℝⁿ (positive integer n), while analysis explicitly formalizes the continuous (complete) nature of the reals.

I think a real analysis course will use properties of ℝⁿ a lot. There is a lot of stuff in linear algebra you probably won't even need to know about to discuss analysis, but I personally think you should take linear algebra first. It's not terrible if you can't, though, you'll be fine.

 

[eumyang]

In a number of schools, a course like Intro to Analysis has Linear Algebra as a prerequisite. If this is Oregon we're talking about, I find it curious that MATH 413 does not require MATH 341 as a prerequisite. I'm with Dr. Seafood -- you should take MATH 341 first.

 

[Curtis1000]

Andyroo:

There is a wonderful book called "Linear Algebra Done Wrong" by Professor Sergei Treil.
(The title is a play on the title of Axler's popular book "Linear Algebra Done Right")
Professor Treil's book is used by Caltech for Intro Linear Algebra as well as at Brown Where Treil teaches) for Honors Linear Algebra. The book is free and can be downloaded at the following link: http://www.math.brown.edu/~treil/papers/LADW/LADW.pdf