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What do Algebra and Calculus mean?

I understand that there is calculus, as in math 101 integration and differentiation. Then there is lambda calculus, and there is logical calculus, propositional calculus, etc.

What does the general term "calculus" mean?

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you are mixing things up a bit. Calculus, from the point of view of mathematics, is a mathematical discipline. Lambda calculus is a concept found in programming languages. –  user20266 Aug 22 '12 at 20:02
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@Thomas: Lambda calculus is a formal system that appears both in mathematical logic and computability theory. More generally, theoretical computer science, like theoretical physics, has a great deal of overlap with mathematics. –  Rahul Aug 22 '12 at 20:17
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Ask a dentist and he'll tell you it's the gunky buildup on your teeth. –  Daniel R Hicks Aug 22 '12 at 21:27
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See also the prior question What do Algebra and Calculus mean? –  Bill Dubuque Aug 22 '12 at 21:30
    
System of calculations, that's why the word is frequently used in theoretical computer science: e.g. process calculus. –  user2468 Aug 22 '12 at 21:57
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marked as duplicate by Jennifer Dylan, M Turgeon, J. M., Pedro Tamaroff, Henning Makholm Aug 23 '12 at 17:52

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From Wikipedia:

More generally, calculus (plural calculi) refers to any method or system of calculation guided by the symbolic manipulation of expressions.

I think the key word here is "calculation" which is further explained to mean manipulating symbols, not just numbers as the lay-person might define it.

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I don't think there is really a most general sense; rather there are various different senses.

"Calculus" is Latin for "pebble". The "-ul-" suffix indicates that it refers to something small. In dentistry, "calculus" means mineral deposits in people's teeth. Among modern senses of the word, maybe that one is closest to the original meaning. The word "calculate" ultimately comes from the use of pebbles in abaci for calculating. Various modern senses come from that. When the word is used for the differential and integral calculus and also for the predicate calculus, they're two different meanings that evolved from the sense of calculating, not two instances of a general meaning. Some things like "vector calculus" and "calculus of finite differences" evolved from the sense in which the word is used when it refers to differential and integral calculus.

Addendum several minutes later:

See Calculus (disambiguation).

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Actually, the term is rather broadly used:

we start seeing a whole bunch of chemical weapons moving around or being utilized. That would change my calculus, that would change my equation

(Recent statement by President Obama)

Opinion: Milton Friedman and the calculus of common sense

Netanyahu’s calculus

In these senses the usage appears to match the definition "A particular method or system of calculation or reasoning." The mathematical definitions presumably derive from this, with each specific mathematical meaning being a separate "method or system".

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