it's not like i think the HSC is the be all and end all of any educational endeavour, hell if the HSC has done anything for me, it's frustrated me and annoyed me in more ways then I can describe. However, I do apologise if i seem snappy, there is a very obvious reason for this. Guess what it is. But i am sorry. Anyways, I do see your point in the whoe "you'll appreiciate it more as you learn about it", there is certainly no doubt about that. But the question then becomes, does it become necessary to make such distinct groups especially considering the audience is mostly well face it HSC students. Thus by introducing a *large* amount of stuff that people have never heard of, or only know of, let's use partial differential equations for arguments sake. All those that do 4U maths will have a fairly good idea what a DE is, I am no exception. Some will know what partial derivatives are, some won't. But importantly, a lot will *never* know, mainly due to the fault of a shitty syllabus, but we shall not delve into that.
Point is, by introducing so many different topics, it defeats the point of my thread. My thread was aimed to *try and be general as possible*. Of course I could've chosen the easier path and jsut said, "Pure Maths" and "Applied Maths". Hell both of those would require the use of ODEs and even PDEs as one progresses, but Pure Maths and Applied Maths is a well recognised system of classification. Is it broad? Hell Yeh. Is it wrong? No. So what's the matter with broadness? I was hoping that the 4 or 5 things I did list could encompass the things which Buchanan has mentioned. There is no doubt there is a BIG difference between Calculus of single variables (where ODEs are), and Calculus of Several Variables (PDEs), well not that much, but the theory is slighty different. And I do not claim that the HSC is any good reference point, it introduces some *very* elementary theory in single variable calculus, but does that really change the broad catergories I have set out? No not really. Point is, if I wanted to classify *all* of maths specifically, I would definately agree, what I have set out is nowhere *near* close to what maths has to offer. *But* by the same token, the catergories I set out seems to encompass most (if not all) the different sections. As I have said, I believe quite strongly that Real and Complex Analysis could fit neatly under "Analysis".
And one other thing has just dawned to me. No i am not saying that because i am trying to be broad i am trying to find one word to encompass all of maths. There already exists such a word, but I am trying to break it down into what can be considered main classifications. Of course this becomes very subjective, which is kinda why I have this rather long post. Hell this post is probably longer than all the other 50 odd I have posted before.
And yes it was tempting to put it *all* in binary, but nah, people wouldn't read it that way. Not that many will read it now, it's a *big* slab of text, I know for the most part I skim big slabs of text, so i don't mind. But eh? Beats studying for English.