Nearly there... and at number five, I'm going slightly quirky and choosing an old textbook that probably came out in the early 80's if not before: "Algebra and Number Systems" by Monk et al. Ah, memories! This is a book that was used back in the original days of CSYS, for the "Pure" paper, which was Paper I, though in the revised CSYS it became Paper II, and now of course in the days of Advanced Higher it... er, doesn't exist. Oh sure, the new AH contains a bit of complex numbers and a smidgeon of proof by induction etc, but back in the day we had one helluva Pure paper, and this was the book that came with it.
A fiendishly difficult book, I might add. When I was teaching it, there were quite a few questions I spent many a happy hour over.
To think that at one point, we offered - in school, mark you - a paper that dealt with group theory, rings and fields (topics now covered typically in 2nd year university mathematics)... gosh, it makes me (a) proud (b) nostalgic (c) sad (d) all of the above.
So here's to you, Professor Monk (I think) and yours: solid, undiluted, pure mathematics, just for the hell of it. The joy of sets indeed.