What other definitions for the quadrivium are you finding? The set and description I've cited have seemed fairly standard, though I'm not an expert in the area.

I'm finding the content and descriptions mostly interesting in a retrospective sense -- I'm not ent

advocating that the mediaeval curriculum be implemented in its original form today. At the same time, I find the notion of input, processing, and output to be quite useful, and one which might be considered as part of a modern curriculum.

For the maths progression of the quadrivium, there are a few other possible clusters or progressions. We've made some advances in maths as well.

I see a general structure of: quantitative notations and operations (arithmetic), solving for unknowns (algebra), geometry and trigenometry, integrals and derivatives, matrixes, differential equations and approximations (FFT). There's also logic (informal, formal, programmatic), programming, and artificial intelligence / machine learning. Genetic engineering seems also to fall somewhere on this axis.

Collectively, all of this falls under inforamtion acquisition, processing, storage, and transmission.