I've just come to the end of the second section of study: Group Theory! It was great to get back to this. Since my introduction to it a few modules ago I had been really curious as to what the next steps were with it all, and it's really fun!
Though now I'm back in the same situation as I was when I was introduced to it: I just want to learn more! Group theory will now be shelved until about March I think (like analysis, there are two group theory sections).
Something I noticed though, even group theory at this level is starting to reflect what Alcock was saying in her book about analysis and the building of theorems to prove another further theorem. As such, I may have benefitted from creating that spider diagram I was such a big fan of before. Next up is linear algebra, but after that is the first section of analysis. I'll have to go into that with the view to actually making that spider diagram to get an overview of how all the concepts build on each other.
or 
. When I read those symbols I see them both so often, I frequently gloss over them without properly considering their usage. Again, pretty basic stuff.
. This can be rearranged in terms of 
as 
. So substituting y, in the symmetrical 
results in: 
. Of course, at this point, proving that what's inside the brackets is an integer is pretty difficult. But that's where I left it. A bit more play would've shown that I could easily have arranged the first equation in terms of 
instead which would've resulted in 
, which is rather obviously an integer given the initial variables. More exploration required in future...