How to organise the mathematics subjects on the pages below this?

I would like to document and classify the mathematics and how it can be computed. Euclid made one of the first attempts to classify mathematics although we now know, through the theorems of Kirt Gödel, that there is no definitive so the organisation here has to be arbitrary in some ways and reflects my own interests.

There are a number of 'foundational' mathematics theories which provide a common approach to a large part of mathematics, these include:

However, for the organisation of this site, we will follow a 'universal algebra' approach where we divide the subject into:

- Theories
- Varieties of those theories
- Models of those theories.

So theories are things like:

- Set theory
- Graph Theory
- Group Theory
- .. and so on.

Different people like to think in different ways, a particular approach to a subject may fire one persons imagination but leave another person cold. I am hoping that the way that the topics are richly interconnected will allow someone who is following an approach that is not working to back off and approach the subject from a different direction. In that way, when you understand one topic it should help you understand other topics.

The general hierarchy of this part of the site follows a fairly conventional division of the subject into algebra, geometry, calculus, etc. but many subjects cut across this. For instance: vectors, we might prefer to look at vectors as purely geometric objects, something with magnitude and direction. Another person may like to think of vectors as objects containing an array of scalar values which are treated as a single element with operations defined on it which have algebraic rules. There are other ways of looking at vectors and the real power of the subject comes when we relate all these.

Many (most even) of the topics on this site are cross connected in this way.