What kind of article would TPU like: short ones, long ones, complex ones, simple ones, specific ones. I would like to write article I just don't know what about, so far the only ones this site has is intros but does TPU what articles different from intros?

Well, consider that anything in depth about a topic is best made available to everyone, regardless of age. The quick start guides seem appropriate for this site because we get a lot of people who just have no idea what to do next to get into some area of programming. There may not be human-written summaries out there that speak from experience in telling exactly what to do next to get started. If you have an idea for some other type of article that meshes with the purpose of this site, then please do share it with us!

I think a good article about data management would be neat. Datastructures, search methodes, file handling and such. Something that covers their basics, when to use which structure, Big O notation and maybe some basic reading and writting of files. Perhaps even a short intro to STL.

I think it's best to write simple texts, that cover a subject as complete as possible (or needed). If you can't explain something to a six-year-old, you don't really understand it yourself. I think it's best to avoid 20 letter words(not everyone is native English, and while a word is very clear to you, it might not be to someone born in France, for example. So avoid words that aren't common, read 'The Raven' by Edgard Allan Po to see what I mean, most of his words weren't in my dictonary) and too complex math. The people who read it might not yet have learned the higher math-stuff (or might not learn it in their courses).
Or give a clear-and-simple explanation about the math-thingies you can't avoid.

RedX

If you want to cover data structures and algorithms properly, then you should turn to an established textbook. This will, in turn, draw on what you would probably call "advanced math," which is more of a sign that you should wait to learn it until after you have the math than a sign that the authors introduced unnecessary complexity. Thus, explaining basic data structure fun could be good, but big O notation is not something to be used informally, unless one wants those people who do go into Computer Science to be confused when they learn what it really means. =)