How do I convert an existing system into a mathematical model?

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Question description

I'm talking about a software system, involving users interactions such as answering to a question, where each question has a difficulty, which is tuned after each answer based on the user's level on the specific topic. 

Each user's level is updated after each answer as well. The real complexity is that each piece of content is eventually labelled with more than one topic and topics are organized in a hierarchical structure.  Let's say that I can generate an unbalanced tree of scores for each user, where non-leaf nodes are computed as weighted averages of their underlying branches.

My goal would be creating a model in order to study its stability and critical parameters.

Tutor Answer

(Top Tutor) Daniel C.
School: University of Maryland
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