In terms of self learning mathematics, what are some good pathways to follow up on, especially beyond the specialist curriculum? (I know this is hard to put into words haha).

What I think is good to learn that directly follows specialist so far includes:

- Calculus (In American terms, Calc 2 and 3, as well as Multivariate Calculus and Applied Calculus)

- Differential Equations (applications as well?)

- Analysis 1 and 2, Real and Complex

- Linear Algebra

- some of the 'theories', Set Theory, Number Theory, Category Theory, Group Theory

- Further math logic and proofs

(I've been using MIT courses as a basis for some of these)

Any other suggestions? The perfect resource for me would be a mathematical tree showing which subjects naturally lead to which and how they are all linked together in terms of some reasonable progression, but after scouring the internet nothing like that seems to be out there.

Whilst you don't need to go into depth with linear algebra (i.e. vector spaces, linear transformations, eigenvalues, ...) you should have a more refined understanding of vectors and matrices before jumping into multivariable calculus. I feel as though specialising into one direction so early on isn't the best idea - you should have foundations in a bit of everything, and then decide on what to specialise in.

I prefer a reasonable understanding of vector geometry as well as knowing the cross product and matrices before beginning multivariable calculus (calc III stuff). Differential equations should be taken concurrently with calc II and III content because the techniques overlap, because the easy techniques in DEs only require calc II material whilst the more complicated ones require calc III. After that, you can fill in the gaps with linear algebra.

(Alternatively, do all of linear algebra before continuing with calculus and analysis.)

Discrete math topics (set theory, number theory, logic, ...) can be studied stand-alone. Whilst in practice set theory should be something you should always know, it's also one of the easier things to learn and along with everything else in discrete math, can be learnt whenever you want to.

Technically speaking though, you really shouldn't just put a whole bunch of topics down and be like "what should I do". (I also have a bad feeling that MIT topics are designed in an order suitable for the extremely gfited.) Instead, you can just look up some first year unit outlines (surely UniMelb and Monash have these somewhere) and just follow the structures they outline on their sem 1 courses first.