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

 

[Matrix0]

I cannot make a specific recommendation for your individual situation. However, I can provide some general advice to help you make an informed decision.

Both Linear Algebra and Analysis are essential mathematical topics for any scientist, and it is beneficial to have a solid understanding of both. However, they are also distinct and require different skills and thought processes. Linear Algebra focuses on vector spaces, matrices, and linear transformations, while Analysis deals with limits, continuity, derivatives, and integrals.

Based on the courses you have already completed, it seems like you have a good foundation in mathematical concepts and are capable of handling multiple courses at once. However, it is essential to consider the workload of each course and your other commitments, such as your job and other classes.

If you feel confident in your ability to manage your time and workload effectively, taking both MATH 341 and MATH 413 at the same time could be a good option. However, if you are concerned about being overwhelmed, it may be better to focus on your economics classes and take Linear Algebra at a later time.

Ultimately, the decision should be based on your personal strengths, interests, and goals. I would recommend discussing your options with your academic advisor or a math professor who can provide more specific advice based on your academic background and goals. Good luck with your decision!