The Calculus

Math Is Hard

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Why is Calculus sometimes referred to as "The Calculus"? I mean, I never studied The Algebra or The Trigonometry?
What makes it such a fancy-pants branch of mathematics that it deserves it's own article?
 

Tom Mattson

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Ha Ha! Good question.

I think the answer is that there are several "calculi". A calculus is, as the name implies, a method for calculating something, and calculi for different "somethings" are not related to each other. A partial list...

1. Differential calculus (for calculating slopes of curves)
2. Integral calculus (for calculating areas under curves)
3. Propositional calculus (for 'calculating' conclusions from premises in symbolic logic)
4. Wick calculus (for calculating normal ordered products in quantum field theory)

There are others, but I think you get the idea. By far, the most famous of these is the material contained in #1 and #2. Given the preeminence of those particular calculi, they are typically called "The Calculus" (big "C"), or simply "Calculus".
 

Math Is Hard

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What a great answer - thanks so much for the clarification! I am going to share this with the other students in my Calc class. I am sure they've been curious about this, too!
 
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No - it's nothing to do with there being several forms of calculus. A 'calculus' was an ancient Roman calculating device (like an abacus) which used small stones ('calculus' is Latin for 'pebble'). So to say 'THE calculus is useful....' rather than 'Calculus is useful...' is much the same thing as saying 'THE computer is useful...' rather than 'Computer is useful...'. However, it's now an archaic form that almost no-one uses unless they are being pretentious.

Interestingly, the 'al' part of al-gebra is Arabic for 'the' so 'the algebra' would be doubling up on the 'the'.
 

Math Is Hard

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Hmmm... that's interesting, too.
From the way you have described it, it seems almost as if Calculus has an imaginary "method" after it.
For instance, if you said I am studying "the Calculus method" or "the
Calculus methods", it works better than saying I am studying "Calculus method".
But I still think the "The" lends it just a tiny bit of loftiness. I wonder if David Berlinski's book would have sold just as well if it were called A Tour Of Calculus?

Anyway, thanks for taking the time to respond to my question. I appreciate your thoughtful answer.
 

mathwonk

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this interesting discussion reminds me of the work by the great grandfather of calculus archimedes, called "the method".
 

AKG

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I believe Tom Mattson is right, and not rdt2. See here. Here you can see a little on the history of Algebra. It could be wrong, but it says nothing to the effect of "al" meaning "the" in this context. They say "al-jabr" means, "reunion" (not the reunion), etc.
 
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W(hy)tf is mathwonk dragging up these old threads...?

But anyway... http://www.m-w.com/cgi-bin/dictionary?book=Dictionary&va=algebra&x=0&y=0 [Broken]

Main Entry: al·ge·bra
...
Etymology: Medieval Latin, from Arabic al-jabr, literally, the reduction
I'm more inclined to trust Merriam-Webster than Wikipedia :P
 
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AKG

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Muzza, I'll agree to that. Of course, I can't be certain since I don't know any Arabic.
 

chroot

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"Al" most certainly means "the" in arabic. Many star names begin with "al," like Aldebaran, the eye of the bull.

- Warren
 

Tom Mattson

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And of course, the most famous one of recent times, Al Qaeda: "The Base".

My answer was just a reasoned guess, but it sounded good to me. :P
 

Jin314159

I've never heard of "The Calculus" before. That sounds a bit pretentious.
 

mathwonk

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Dear Muzza,

I just found out about this cool site and went through everything the first day on the job.

This is a rather fun site and presumably topics here will attract new interest from time to time.

best,

mathwonk (roy).
 

Math Is Hard

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Hey, Mathwonk - welcome to PF, by the way! :smile:
 

Math Is Hard

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Jin314159 said:
I've never heard of "The Calculus" before. That sounds a bit pretentious.
We could call it Al Calculus. Makes it sound more sinister. :devil: And its members definitely have Weapons of Math Instruction. :biggrin:
 
It was called "the infinitesimal calculus" for quite a while. When the nineteenth century proceeded the "infinitesimal" part began to be dropped, because noone believed anymore that infinitesimal quantities actually existed logically. So you might say the phrase meant "the calculus formerly called infinitesimal".
 

Math Is Hard

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quartodeciman said:
So you might say the phrase meant "the calculus formerly called infinitesimal".
Reminds me of "The Artist formally known as Prince". :biggrin:
 
There is also "The Former Yugoslav Republic of Macedonia". That's the legal name of this country. That is an attempt to assuage the neighboring Greeks who consider the name "Macedonia" to be an historically-Greek entity, even though slavs have been living there for many centuries.
 

mathwonk

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heehee! wonderful.

cosa nostra lives again.
 

mathwonk

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this whole thread seems to reveal some innocence of the features of other languages by many, not all, of us. it seems clear that al does mean the in arabic, and in french also nouns such as algebra are usually preceded by an article like le or l' or la. i believe newton also wrote in latin?
 
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matt grime

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There is, famously, a village in England whose name, when translated, means Hill Hill Hill: each group who settled (angles, romans, celts, saxons, whoever) added hill in their own language to the name not realizing it was already so named.

http://en.wikipedia.org/wiki/List_of_tautological_place_names
 

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