It turns out that wrapping up a permanent job and starting a new one takes an enormous amount of time. Throw a holiday or two into the middle of it and you suddenly completely lack any spare time whatsoever.
Glad to say I'm back now though. Ready to tackle the final assignment of my intro module, and close things off for a Summer (of Analysis study).
Speaking of Analysis, I've spent a few more lunch hours running through the exercises of the end of Chapter 1 on the real number system and even after ALL the reading I've done I'm only able to complete about 50% of the questions. I feel my knowledge is lacking enormously. What makes things more frustrating is that David Brannan's book doesn't contain any solutions for the exercises at the end of each chapter. So I'm completely unable to unstick myself (or check to see if I've answered the question in the correct way).
As a consequence I feel like I'm slightly wasting my time with this book. Just banging my head against another dead-ender of a question. This is extremely unfortunate, as I was looking forward to finally working through as much as possible before September. Hoping it would give me an edge for my next module. But today, I tried to think about the situation logically: It feels as if I'm lacking knowledge. Knowledge and experience. There haven't been nearly enough examples in this book for me to get a feeling for the kinds of things I should be proving. So maybe that's what I need... more examples... more simple questions to attempt.
There was only one source I could think of that may deliver this... On the maths forum, I was given a link to proof exercises as supplied to kids studying pure mathematics at a-level. This might just give me a leg up...