Mathematics final year projects

Do you have to write a dissertation for Maths final year projects? If so, how are you supposed to write 10k words about a Maths topic?

If you asked a 3rd or 4th year mathematician to "Write all you know about the area of ...." and named a common topic, they'd probably not even know where to start because you'll end up learning a considerable amount in university.

Bear in mind lecture notes for a single course can be anywhere from 50 to 200 A4 pages long, you're then supposed to 'join the dots' a lot in your head (no more spoon feeding like in A Level!) and in the cases of disseratations you're expected to read around the material, using textbooks and even published papers.

Wrangler and I had to write essays for our 4th year and I don't know anyone who stayed around the 5,000 word 'suggested length', everyone going to abotu 7,000 words or more. One friend even had to cut it back from somewhere in the region of 12,000~15,000 because it was longer than needed. If I'd not had to revise for exams and I'd had the drive I could have probably expanded it to 4 or 5 times it's size without even having to read more material, just put back in the results I skimmed over.

Even at university undergraduate level, where you're exposed to 100 times the number of results you are at A Level (per term I'd say!) if you take any 'interesting result' from a 3rd or 4th year course and go to the textbooks on it, you'll find that what is only 1 or 2 pages in your lecture notes has entire chapters devoted to it, sometimes entire books or series of books!

Things like matrices seem somewhat boring at A Level and I'm sure more than a few A Level students have asked themselves "WTF is the point in these". You could write 100 books on the applications of matrices to quantum mechanics, general relativity, group theory, symmetries, and 100 other topics which were too complicated and scary for me to want to learn, and you'd still have only scratched the surface of what matrices can be involved in.

On another forum I once read someone post "How can you do a degree in maths? Surely after A Level there's hardly any maths left to learn." Boy was he wrong. I could resit my 4th year 5 times and not make it to every lecture course they lecture, and those courses are each a tip of an enormous iceberg of material.

another thing is that you can like plan your study yourself, so if there is something which you do not understand you can just skip it and go for some of the other stuff that you understand hopefully.

Most definitely you can write an essay on elliptic curves. Here is the list of essay topics Wrangler and I had to pick a topic from to write about (though you can suggest your own if it's of sufficent depth). Essay topic 20 is about elliptic curves, and 11 is about hyperelliptic curves.

Can't seem to find the one Wrangler did (did you suggest it?). I did 58.
You attend lecture courses you are interested in, so if you like say modular forms, you can go to a course on that and not bother with something quite different like quantum field theory (sorry, I'm using 3rd or 4th year courses as examples just because they are fresh in my mind). You can't really skip parts within a lecture course without the worry that it'll come up in the exams and you've ignored that section, not to mention that most courses build upon themselves so missing bits out causes problems later.

You're forced to take certain courses in your first and the range of choice is usually narrow in the second year but by 3rd and 4th year you've complete freedom to pick your courses.

Latex is pretty much the "Microsoft Word for Mathematicians". Some unis might give quick classes in how to do it, but it's much like learning computer code, you pick the basics up quite quickly and then slowly learn to make it look extra fancy. Latex is very intuitive too. For instance, if you want any of the greek alphabet symbols you just do "\symbolname", such as \alpha is $\alpha$ or \gamma is $\gamma$. If you want capital letters you just capitalise the symbol's first letter, so \Gamma is $\Gamma$. Eventually tex code becomes very readable to you and quick to type.

Which reports are you referring to?

A lot of unis put notes to lecture courses online, or students type them up and then put them online themselves (I've done that). The list of essay topics is online because our maths department puts most of it's information and things like example sheets and past exam papers online so they are easy to get.

By 'college boy' what age do you mean?

...just some stuff that is a bit extrodinary and which could impress the teacher.

I suspect you'll impress them much more by getting to grips with the stuff you're meant to be studying.