Here’s one of the things about category theory that takes a while to get used to. Mathematical objects are usually defined internally. For example, the Cartesian product P of two sets A and B is defined to be the set of all ordered pairs (a, b) where a comes from A and b comes from B. The definition of P depends on the elements […]

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Academics / Mathematics : Programming Praxis

Today’s exercise is a simple little interview question: Generate the pairs of cartesian coordinates within a square bounded by (1,1) and (n,n) ordered by their product in ascending order. For instance, when n is 3, the coordinates a...

Academics : The Endeavour

Joseph Goguen gave seven dogmas in his paper A Categorical Manifesto. To each species of mathematical structure, there corresponds a category whose objects have that structure, and whose morphisms preserve it. To any natural constru...

Academics / Mathematics : Terence Tao's Blog

Given a function between two sets, we can form the graph which is a subset of the Cartesian product. There are a number of “closed graph theorems” in mathematics which relate the regularity properties of the function with the closur...

Humor : Boing Boing

Last week, I wrote a piece for BoingBoing about fundamentalist Christian objections to the mathematical idea of set theory. Those objections are, apparently, real—sourced to math textbooks produced by publisher A Beka. And, if you u...

Academics / Mathematics : Good Math, Bad Math

Category theory is really all about building math using composition. Everything we do, we do it by defining things completely in terms of composition. We've seen a lot of that. For example, we defined subclasses (and other sub-thing...

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