How important is Calculus for Pure Maths?

[ECmathstudent]

Haha I hope this doesn't come off as one of those, "has this B ruined my chances at grad school?" kind of posts.
I've kind of taken an odd path through my first three years of undergrad, and just finished my school's second year calculus portion, but I've also gone through group and ring theory, and a basic real analysis course. I've more or less come to the conclusion that Algebra will be my main focus, preferably algebraic number theory since it seems really interesting. And I'll probably do as much analysis and topology as I'm able to through undergrad.

I've just found that I don't really enjoy calculus, I don't have any particular trouble understanding it, but I have not been able to make myself put the work into mastering it that I should have. I'm alright, I think for the year I'd have an 80 average between the two intermediate calculus courses, an 85 and 75-80.

I'm guessing the lack of interest in calculus could hold me back in analysis when it comes time to prove Stoke's theorem and what-not, but is there any chance it'll hold me back in any other way?

 

[gb7nash]

Calculus is the foundation for a lot of math. Saying you're a math major and not being able to understand calculus will put you at a disadvantage (and make people wonder). I suppose you could try to avoid anything that has to do with calculus, but you'd probably end up doing something you wouldn't like.

 

[ECmathstudent]

Well, part of the reason is I've taken 3 or 4 math courses each semester, and I just ended up finding the upper level courses like abstract algebra and real analysis more interesting, and let calculus slip to the A-/B+ range.

 

[Leptos]

Well, part of the reason is I've taken 3 or 4 math courses each semester, and I just ended up finding the upper level courses like abstract algebra and real analysis more interesting, and let calculus slip to the A-/B+ range.

What I'm wondering is how the heck are you even allowed to take those courses without completing the basic calculus sequence(single variable and multivariate)?

 

[ECmathstudent]

Well I screwed the pooch first year, took my third semester off semester off basically, then went through discrete math, proof-writing/logic and intro stats. Since I had the proof-writing/logic course they let me into the third and fourth year pure math courses where I've been doing way better. But I still need to get through the intermediate calculus courses to catch up.

 

[gb7nash]

What I'm wondering is how the heck are you even allowed to take those courses without completing the basic calculus sequence(single variable and multivariate)?

I was wondering the same thing! Most places won't even let you touch that stuff until you've got the basics out of the way.

 

[ECmathstudent]

Well, we have two years of calculus, first year is the single variable, two classes, f and the second is multivariate, two classes.

 

[Rasalhague]

I'm guessing wildly here, but could your dislike be something more to do with the way calculus was presented in these classes than with the subject matter itself - which after all is a part of analysis, a thing you say you find more interesting? For example, could it be that you prefer the from-the-ground-up axiomatic approach of analysis and abstract algebra courses to more technique-oriented styles of basic calculus courses?

 

[ECmathstudent]

I think that might be it. If I stick to the pure math side of things, I should be able to avoid that, right?

 

[mathwonk]

differential calculus shows us that many very difficult non linear computations can be approximated locally by linear ones. Linear computations are the easiest ones in all of mathematics so calculus tells us that even the most difficult of all calculations can be locally approximated by easy ones. Thus there are two essential subjects in mathematics: 1) linear algebra, and 2) differential calculus, which reduces other more difficult subjects locally to linear algebra.

integral calculus is also crucial but is harder.

 

[ECmathstudent]

Ah. I'm actually doing research in linear algebra this summer. Would you recommend taking something along the lines of a mathematical physics course to get more familiar with Greene and Stoke's theorems?