Thursday, March 28, 2013

definite articles - Why is the word "the" used before different categories of calculus?

I've noticed that, when referring to certain branches of calculus, mathematicians sometimes precede the name of those branches with the word "the". For example, "the lambda calculus" or "the predicate calculus".



To be fair, a Google search turns up plenty of references to "lambda calculus" (without "the" as a prefix). But it also turns up an equally large number of references to the phrase with the prefix included. Further, I haven't noticed this with other branches of math. For example, I haven't heard anyone use the phrase "the linear algebra" or "the Euclidean geometry". They just say "linear algebra" or "Euclidean geometry".




My question is, why the difference?



EDIT:



As requested by @Lawrence in the comments, here are some examples of full sentences where "the" is used before "calculus":



1) "The λ-calculus can be called the smallest universal programming language in the world. The λ-calculus consists of a single transformation rule (variable substitution, also called β-conversion) and a single function definition scheme. It was introduced in the 1930s by Alonzo Church as a way of formalizing the concept of effective computability."
Source- https://arxiv.org/pdf/1503.09060.pdf



2) "Church (1936) invented a formal system called the lambda calculus and

defined the notion of computable function via this system." Source- http://www.cse.chalmers.se/research/group/logic/TypesSS05/Extra/geuvers.pdf



3) "The Lambda calculus is an abstract mathematical theory of computation, involving functions. The lambda calculus can be thought of as the theoretical foundation of functional programming." Source- https://brilliant.org/wiki/lambda-calculus/



In response to @Trevor's comment, we can replace "Euclidean geometry" with "boolean algebra", meaning we're now comparing two types of algebra (linear and boolean). I haven't heard either of these genres of algebra used with "the" as a prefix, yet they're both 2 sub-branches of the same branch of mathematics.



I'm able to find the phrase "the linear algebra" as part of a broader phrase (i.e. "The Linear Algebra Survival Guide" or "The Linear Algebra Behind Search Engines"), but the usage of the phrase in these examples is different from the usage in the examples I mentioned in response to Lawrence's comment.

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