Is calculus advanced algebra?

Michaelrsh

Is the following statement 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."

Fremen

It depends what you mean by "true". There's no absolute definition of the concept of "algebra", so it's kind of a matter of opinion.

But most mathematicians would agree that no, calculus is not algebra.

A huge number of branches of maths can be classified as one of two categories: Algebra and Analysis.

Calculus is the cornerstone of analysis. Other branches of analysis generalise the single variable calculus to multple variables, complex variables, abstract metric spaces and (possibly infinite-dimensional) vector spaces. Algebra takes structures like groups, rings and fields, and talks about relations between these objects.

Of course, there are areas of mathematics with flavours of both algebra and analysis. The study of Lie groups and Algebraic topology both have strong analytic and algebraic elements.

Linkage:
http://annoyingpi.wordpress.com/2010/04/04/algebra-vs-analysis/

To fill out Fremen's excellent answer, which overlooked (unintentionally I'm sure) group theory, Group theory isn't really "advanced algebra" but is more abstract algebra.

Mellor

Short answer.
no

A Primal Nut

Its really a pointless question. Ultimately all Mathematics is supposed to be tied in together, with many people aiming towards 'one equation that explains everything.' Terms like algebra and calculus are handy terms for textbooks to seperate certain sections and make them easier to study and specialise. But obviously calculus uses plenty of algebra as well as bits of other sections of mathematics. Algebra is used probably in almost every kind of mathematics, as well as a use in itself. But I find that as you study Maths more and more, you are using the same simpler sections over and over, they just get more complex because you are using many different subsections and so on. By the time I was in 4th year Engineering Maths I was using loads of different kinds of mathematics interchangeably, I wasn't really thinking; this part is calculus, this part is algebra, this part is area & volume, etc.

A Primal Nut

A Primal Nut wrote: »

Its really a pointless question. Ultimately all Mathematics is supposed to be tied in together, with many people aiming towards 'one equation that explains everything.' Terms like algebra and calculus are handy terms for textbooks to seperate certain sections and make them easier to study and specialise. But obviously calculus uses plenty of algebra as well as bits of other sections of mathematics. Algebra is used probably in almost every kind of mathematics, as well as a use in itself. But I find that as you study Maths more and more, you are using the same simpler sections over and over, they just get more complex because you are using many different subsections and so on. By the time I was in 4th year Engineering Maths I was using loads of different kinds of mathematics interchangeably, I wasn't really thinking; this part is calculus, this part is algebra, this part is area & volume, etc.

True, apart from the bit about many people trying to find one equation for everything. I think mathematicians would all agree, that doesn't exist.

mikhail

Deleted User wrote: »

True, apart from the bit about many people trying to find one equation for everything. I think mathematicians would all agree, that doesn't exist.

Google "Godel".