Linear algebra and abstract algebra simultaneously?

[interloper]

Is this a good idea (provided the university will allow it)? I'll be going into my sophomore year at my university. But I'm unfamiliar with exactly how much linear algebra an intro course in abstract algebra would require. In hindsight I probably should have taken linear last semester, but scheduling issues meant that I would have had to sacrifice a lot to do it. I'm interested in doing a major in pure math and maybe going to grad school, and thus I want to get involved with research as early as possible. For this reason I want to start taking advanced courses soon, and abstract felt like a good place to start.

There are other math courses I could take instead, but most of them seem to require linear algebra, and the ones that don't either interfere with my schedule or are only offered spring semester. Since abstract algebra seems to build from fundamentals, it felt like a good option. Thoughts?

 

[Vanadium 50]

Um...why are you asking us?

I think you hit a key point with "provided the university will allow it". Why would you take the recommendations of a bunch of folks on the internet over those of the university?

Courses in Linear vary from "a bag of computational tricks" all the way to "abstract lite". We can't tell how much rigor your particular university's version has, and we can't tell how much prior knowledge the abstract professor expects the students to walk in with. That's what prereqs and co-reqs are for. Taking them concurrently might work out, or you might get squashed like a bug.

 

[Mene]

I understand your desire to get involved in advanced courses and research as soon as possible. However, I would caution against taking linear algebra and abstract algebra simultaneously. While both are important branches of mathematics, they are quite different in terms of content and approach. Linear algebra is more focused on vector spaces and matrices, while abstract algebra deals with more abstract structures such as groups, rings, and fields.

Taking both courses at the same time could potentially be overwhelming and may not allow you to fully grasp the concepts in either course. It is important to have a solid foundation in linear algebra before delving into abstract algebra, as many concepts in abstract algebra build upon those in linear algebra.

Furthermore, universities typically have prerequisites in place for a reason – to ensure that students have the necessary background knowledge to succeed in a course. Taking linear algebra before abstract algebra will not only help you in understanding the material, but it will also show the university that you have taken the necessary steps to prepare for the course.

I would suggest speaking with your academic advisor or a math professor about your options for taking linear algebra and abstract algebra in a way that will not sacrifice your schedule or interfere with other courses. It may also be beneficial to consider taking a different advanced math course that does not require linear algebra, or taking linear algebra in the spring semester and abstract algebra in the fall semester.

In the end, it is important to prioritize your understanding and success in these courses over trying to take them all at once. Building a strong foundation in linear algebra will benefit you in your future studies in mathematics and research.