Is it right to say that calculus is advanced algebra?

[Collisionman]

I was having a discussion with a friend and I wanted to know if the following statement is true:

"calculus is advanced algebra and deals with curves (changing numbers), group theory is another branch of advanced algebra. The point is they are all algebra."

 

[mathman]

Definitions are neither true or false. If your friend wants to define calculus as a branch of algebra, he is welcome to. Most mathematicians probably would not agree. The main difference is that the subject of algebra (as ordinarily defined) does not involve limits, while analysis (calculus being a part) does.

 

[czelaya]

I wouldn't agree with that statement. Calculus is the mathematics of change and integration of volumes. While calculus uses algebra in its analysis, it doesn't make it algebra. Algebra is concerned with the study of the rules of operations and relations, and how it constructs structures (Wiki).

For instance, if you have the following equation; f(x)=y=Ax^2.
Algebra is concerned with what the value of y is when x is equal to a particular value.

Calculus on the other hand, is concerned with how the same function changes with respect to a particular variable. In this case, dy/dx would be how y changes with respect to x (y'=2Ax).

Then again, I'm not a mathematician so I could be wrong.

 

[disregardthat]

The fundamental difference between calculus and algebra is not surprisingly the fundamental axiom of analysis.

 

[mikeph]

The statement you quote seems to come from someone with a high-school type view that algebra is just replacing numbers with letters, and that therefore most advanced maths is advanced algebra.

I think algebra is its own subject area, but it is easy to end up discussing semantics and not mathematics when talking about names of subjects.

 

[mrbohn1]

One very obvious distinction between algebra and calculus: the former deals withs discrete quantities, the latter continuity.