I am currently (and for the next year or two) bringing my maths skills back up to date, using Scottish school exam texts, then a pre university/first year maths book, along with a book on how to think like a mathematician.

Statistics, big data and related maths, Some Baysians maths, and some geometry and algebra online, aside, I haven’t really pursued maths since school (Scottish Higher level).

But I want a better grounding now, hence working through N4-Advanced Higher (gcse to A level), and hopefully onto first year Uni maths in due course.

My strategy is obviously revise the basics and build in old school maths, and it is going fine. I have a book coming on how to think like a mathematician covering stuff like proofs (my favourite part of my maths higher nearly 40 years ago) and logic, analysis etc.

Hence as I start on this journey I was wondering if any mathematicians here could offer any tips, words of wisdom, etc.

My aim is to be back at Advanced Higher/A level standard by this time next year. But I want a deeper understanding (as I have found maths to be everywhere) not to rote learn it. You can get formula etc easily enough so no need for someone at my stage in life to memorise them (but I will obviously be working my way through them).

So any tips on gaining a deeper, more conceptual understanding, as I work my way through the texts? I can already see the maths in pretty much everything, including my esoteric hobbies. Like a language that underpins everything.

I will never make a mathematician, but that isn’t my aim, I just want a better mathematical toolkit to explore with.

Thanks in advance.