1. ## "The Calculus"

For those who have read multiple math books you like me have probably encountered the term "the calculus" and you know what I'm talking about.
For example the derivative of something is being taken so the book will phrase it as:
"From the calculus we can take the derivative of x with respect to y in order to get its slope at point P....."
But when we talk about algebra the books only ever say something like:
"Using algebra we can transform the equation into the form Mf(x,y) + Ng(x,y) = 0"
"Using algebra" would be the term used and not "the algebra"
also same with geometry no one ever says "the geometry".

But why do they often say "the calculus"? Why is not just "calculus"?

2. ## Re: "The Calculus"

Probably it reflects how much older a study algebra is. The "al" in algebra means "the."

3. ## Re: "The Calculus"

This is directly related to the mystery of why people in California refer to highways as "the," as in "We took the 10 to the 405."

4. ## Re: "The Calculus"

The most popular theory I've heard is that rather than an appendation to the subject matter (adding the "the"), it is rather a truncation of "The Calculus of Infinitesimals".

Infinitesimals fell into disfavor, because it did not seem possibly to define them in a logical way. It wasn't until the 1960's (I think) that this began to change.

5. ## Re: "The Calculus"

Originally Posted by JeffM
Probably it reflects how much older a study algebra is. The "al" in algebra means "the."
That's interesting.. so every time we say algebra we are actually saying 'the gebra'. Guess maybe geometry was supposed to be called algeometry but it was too long so they just said geometry.

6. ## Re: "The Calculus"

No. Geometry derives from Greek words and makes sense as a compound word meaning originally measurement of land. Bur algebra derives from the second and third words in the long title of a book in Arabic, does not really make sense as a summary of that original title, and reflects ignorance of the meaning of the title by early European mathematicians.

7. ## Re: "The Calculus"

I always figured it was a way of placing importance on the subject, making it less general. Like in the case of the empty set instead of saying an empty set, there is only one empty set and there is only one calculus we use.

8. ## Re: "The Calculus"

Originally Posted by Jonroberts74
I always figured it was a way of placing importance on the subject, making it less general. Like in the case of the empty set instead of saying an empty set, there is only one empty set and there is only one calculus we use.
This is clearly not true. There is for example propositional calculus.

9. ## Re: "The Calculus"

Originally Posted by JeffM
This is clearly not true. There is for example propositional calculus.
yes you are correct, maybe my example was bad. I just meant thats how it seems to be used "the calculus" as if its the only calculus we use--or at least the more or most important calculus used.

10. ## Re: "The Calculus"

Although I have no historical evidence to support it, Deveno's explanation seems highly probable. "Calculus" is a Latin word simply meaning computation, and Latin had no articles. So computation involving infinitesimals is a good description of calculus, and that can be described using a definite article in modern languages.

11. ## Re: "The Calculus"

I did a yahoo search, and I saw a few other posts on the same topic, and then I also looked at wikipedia. In wikipedia it states:
Calculus has historically been called "the calculus of infinitesimals", or "infinitesimal calculus".
However throughout the entire article when it says calculus it does not use the term "the calculus". So I guess when you are saying "the calculus" you are only referring to what it used to be called, or in order to differentiate from other kinds of calculus, like say lambda calculus, the abovementioned propositional calculus, etc. So it seems that there is really no need to call it "the calculus" and the ones who say "the calculus" are just the ones who were aware of "the calculus of infinitesimals". Kind of like a homage

12. ## Re: "The Calculus"

Calculus is very important for studying, it is the branch of mathematics that is all about mapping change.

13. ## Re: "The Calculus"

Don't know the answer but I know a good thing when I hear it.

From now I am going to say "The Calculus" (pronouncing it with capital letters) because it sounds grand and makes me feel important. Honestly, "The Calculus", I mean what higher authority could one appeal too ... Officer, "The Calculus" informs us that given the speed limit and the length of yellow light it was impossible to stop before entering the intersection ... Officer, Officer ... ....handcuffs?

14. ## Re: "The Calculus"

The reason for referring to "the" Calculus is that "Calculus" itself can refer to many different forms of mathematics. There are, for example, the "Calculus of finite differences" and the "Calculus of Variations".