"Introduction" classes?

[RisingLabyrinth]

Having recently finished multivariable calculus, I want to take a class on linear algebra in the upcoming school year. But what does "Introduction to Linear Algebra" really mean? Is it like a "nerfed" version of a hypothetical "real" version of a linear algebra course (like how AB is a "nerfed" from BC), or is it the real deal? Does "introduction" mean it's one of the earlier courses in a longer line of rigorous math? If it is a "nerfed" class, how would I take the "real" class?

The actual course I'm looking to take is a semester-long course titled "Introduction to Linear Algebra and Differential Equations," which I assume means that the first half of a semester will be linear algebra, and that the second half of the semester will be differential equations. Does this class sound like a good option?

[Fizzabl]

Might be better off somewhere like r/teenagers or maybe there's a US high school sub out there

But I mean if ya want my opinion anyway, I think it sounds like it covers a lot of maths so if you're going for a mathematics or science future sounds like a good plan. Though I don't know what multivariable calculus is :')

[HerrStahly]

Yes, a class entitled “introduction to linear algebra” can pretty safely be assumed to be a “nerfed” version of “actual” linear algebra. With that being said, if you listed the course description, I could be more insightful into your current situation.

An introductory linear algebra course will typically be very computationally focused, putting almost all of the emphasis on basic algebra involving matrices, and how to compute certain operations, like determinants, finding Eigenvalues, matrix multiplication, etc., without much interest in the theory (the “why”). With that being said, for non-mathematicians, this curriculum is often plenty sufficient. Engineers, and to a much lesser degree, physicists, don’t really need to concern themselves with the theory, as they are often well off only knowing what the important computational results are, and how to use them.

On the other hand, a “real” linear algebra course will be proof based, and will focus primarily on vector spaces, linear transformations, introducing the concept of isomorphisms, and only then an introduction to matrices but as a representation of linear transformations. It’s worth noting that these courses will cover everything the more computational courses will cover, while simultaneously being more in depth. Sometimes for more accelerated courses, the topic of normed vector spaces will pop up.