Maths beyond A Level without doing a degree

Also, send me a PM with your email address and I will send you a PDF version of Stroud's excellent Engineering Mathematics and Advanced Engineering Mathematics textbooks.

Shamika's suggestions would seem helpful. In principle there's no reason why you couldn't learn some university maths, in a self-taught way.

On the pure side:
(1) "Transition" from A-level to degree level: The number systems, N, Q, R and C, proof by induction
(2) Sets, functions and relations; the fundamentals of pure mathematics
(3) Sequences and series, followed by an introduction to real analysis
(4) An introduction to abstract algebra; groups, rings and fields (probably slightly focusing on groups), isomorphisms and homomorphisms (of groups rings and fields), isomorphisms and homomorphisms generally
(5) Linear algebra

Those aren't actual names of courses as such, rather a very brief description of courses that might, and do, exist.

But that would be the basics that you would cover in the first two years at a normal uni. Or in Fresher's week at Cambridge.

I wasn't sure quite where to put this, since it didn't really belong in the A Level Maths forum.

I love Maths. I can sit around and work my way through problems all day long and just genuinely enjoy it - I've done all the A Level Maths I possibly can (Regular, Further and Additional, although additional isn't aggregated past AS since I missed an exam).

I enjoyed Pure the most, followed closely by Mechanics. Statistics could be interesting at S3/S4 level, but Decision was pretty nonsensical outside of topics like Game Theory.

The problem is, I didn't like the idea of the end result of having done a degree in Maths (usually the result is either go into Banking, Economics etc or Teaching - there are very few actual 'academic' positions AFAIK), so I chose a different field to do at undergraduate (along with other reasons).

I was wondering if there was anything I could do beyond A Level that would keep my interest in Maths alive; any books or websites etc to use and problems to do that sort of build on A Level maths and go from there - i.e, they introduce a topic and explain it and give you some problems to solve (I know the dynamic of Maths changes once you get to university in that it isn't particularly about "Here's X - integrate it") - I've done STEP papers in my spare time, but the reality is that they are firmly grounded in A Level Maths - the questions are just a lot more difficult.

I'm not looking to get any qualification in it, or to not focus on my degree and I'm not trying to pretend I would be doing it at / understanding it at the level of someone actually doing a Maths degree, but I would just like to make sure that I have the same passion for Maths in 10 years time, rather than just slowly forgetting it all because it isn't being used.

Thanks for reading.