| Yeah, probably should be a different area. I'll break it off after I post.
Math is not a linear subject. That's something that surprises a lot of people. Once you get the basics down, a whole world opens up that you can choose from. Usually there are 3 primary areas considered for mathematics: algebra, analysis, and stats. Calculus falls in the analysis area, for example. Now, in each of those, there is definitely overlap, but those are generally considered to be the specialties. You'll hear, for example, people say that they are analysts or algebraists or statisticians.
OK. That said, let's take a look at what the future holds for your mathematical career:
After finishing Calc III, you can take the analysis courses such as advanced calculus, ODEs, PDEs, real analysis, complex analysis, numerical analysis, ...
After finishing college algebra and getting a background in calculus (remember, there's overlap), you can then take linear algebra, abstract algebra, combinatorics (overlapping begins here with stats), number theory, ...
I won't go into stats as that's fairly obvious and really just applications of algebra and analysis into the purview of stats, but due to its general perception stats gets assigned its own little world.
All that said, you'd do better to think of mathematics as a tree of knowledge. You've been climbing the trunk and are now ready to explore the branches. Choose your favorite. I lean much more heavily towards algebra.
Now, all that said -- linear algebra IS NOT EASY. It is usually your first smack in the face with proofs and proofs are generally challenging to grasp. If you're not already, work with your peers to get assistance on proofs and consult with those in upper mathematics classes as they can give you some great tips. |