-- [link|mailto:greg@gregfolkert.net|greg], [link|http://www.iwethey.org/ed_curry|REMEMBER ED CURRY!] @ iwethey Freedom is not FREE. Yeah, but 10s of Trillions of US Dollars?
Map, Filter, and Reduce are morphisms arising from mathematics. Likely that if you want to find the first use in programming languages, you'd probably find them in Lisp. But then Smalltalk was heavily influenced by Lisp (and Algol), so that wouldn't be surprising.
Map applies a function over a collection. Filter applies a predicate to a collection and returns a subset where the predicate is true. Reduce is a fold of a collection.
Guess I should also reuse my explanation of [link|http://z.iwethey.org/forums/render/content/show?contentid=247589|Higher Order Functions] in an earlier thread.