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You can have a lambda calculus, the calculus of the real numbers or a logical calculus but on the other hand you could also have an algebra of sets, a Lie algebra, or a linear algebra.

Is there any convention which dictates whether something is an algebra or a calculus?

From my understanding, a calculus seems to give you information about objects you might encounter within a space, while an algebra gives you information about the interactions and structure within the space as a whole. Is this correct?

Christian Chapman
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    Calculus is kind of a catch-all term and in days of old, calculus meant any procedure by which things were calculated (loosely speaking). Algebra is also a bit liberally used in mathematics, but when one comes across the word algebra, one should think about some sort of operations on sets, i.e. algebras of sets, algebras over fields, etc. – Cameron L. Williams Jun 23 '14 at 03:21
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    The question is about difference, rather than meaning. What I'm unclear about is: Under what viewpoints can one be seen as a sub-set of the other? What do these different things allow you to do that the other won't. e.g. if calculus is just a procedure, does expanding it to an algebra (implied super-set) then allow proofs about the calculation's applicability?, etc. – Philip Oakley Aug 09 '16 at 14:13

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A calculus is a system of rules for manipulating symbols and expressions. An algebra is a set with operations that can be preformed on its elements.

Rene Schipperus
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