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Windows Nerd
December 30th, 2010, 04:13 AM
Hey all,

So my math teacher recently assigned us a math project to do about a month before the Winter Break. It can be on any topic we want as long as it is math related. I am still unsure what my topic for the project is, asking this.

I am interested in computers (well, obviously, being on this forum :D) and I want to incorporate my love of computers with the project. I am at a grade 11 Math level, and the project is worth approximately one Unit test. I have until the middle of January to do it.

I am interested in "hacking" - in both senses. Not that I do anything malicious, I just find that stuff interesting. Cryptography may be a good area related to this, but I think it is a little too big for a project. I know some Python (still learning), tried (and failed) to learn Java and C++ as far as programming goes. Even given how interested I am with computers and how much I know, I still can't really think up of something I can do for the project. Some of the other things my teacher suggested was GPS, or proofs of the Pythagorean theorem for the really lazy. Some other things he suggested were Fibonacci numbers and the golden ratio; the history of zero; code breaking; and imaginary numbers/complex numbers.

Could anyone help me out? I want to do well with the project, but I have been too unsure on what I want to do for too long.

Scott

matthew.ball
December 30th, 2010, 04:38 AM
First of all, is this mainly a written report type project? Or more to talk about some particular mathematics?

If it's mainly about writing, and you're looking for a topic you might feel passionate about, you could have a look at something related to graph theory. Perhaps you could write something about the "4 colour theorem" (http://en.wikipedia.org/wiki/Four_color_theorem), or you could write about "the seven bridges of Königsberg" (http://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg).

In the latter case - if it's mainly to talk about the mathematics - you could probably cover asymptotic notation (http://en.wikipedia.org/wiki/Big_O_notation) for algorithms. I can help you out with some basic number theory and a "naive" RSA-scheme if you want to go the cryptography route, but it is quite involved (I don't want to assume much about your mathematical background).

Sorry if these are too advanced (specifically the asymptotic notation, the graph theory problems should be fairly intuitive). If you want more ideas, just ask. :)

Windows Nerd
December 30th, 2010, 05:02 AM
It can be a written report, or a "show the class" type thing. Like I said, I am in (Canadian) grade 11 math, or 16-17 years of age. My mathematical knowledge does not extend much beyond that. However, it's mainly to talk about mathematics. It was assigned by a math teacher, and in grade 11 it is still some basic stuff, not so much applied math (like physics or chem). I am interested in cryptography, but like you probably think it may be a topic that is too advanced. The project should be about some particular mathematics, so it will be the "latter" route you said.

Idefix82
December 30th, 2010, 05:06 AM
I don't think that RSA is too advanced. You just have to know some modular arithmetic, and if you don't know it yet then you can learn it. To be honest, I don't even know what you mean by "interested in cryptography", since I doubt that you know any cryptography. Most of it is rather involved mathematics, but RSA is one of the mathematically easiest widespread crypto-systems. So if you want to find out whether you are actually interested in cryptography, I think that that's a good place to start.

matthew.ball
December 30th, 2010, 05:20 AM
Well, the mathematics of graph theory is deeply related to computer science (algorithms and complexity!), so I thought you might find something there interesting (this is not the "graph of a function" stuff you might have seen).

I'm sorry, I don't remember what I covered in year 11 mathematics; it was a while ago. So I could have a bit of a bias, but nothing's really too deep - certainly not "analysis" deep. If you can do division (well modular arithmetic) and know some basic results in number theory (Euler's totient function and Euclid's greatest-common-divisor algorithm) then you could do the naive RSA. With small enough primes you can write out a full instantiation on a couple of a4 pages (and that would be enough I think).

Edit: Beaten by Idefix82 :)

Spr0k3t
December 30th, 2010, 05:52 AM
How about discussing the possibility of a non-planar existence of division-by-zero. It does exist, and can be proven over and over. Several scientists have recorded the phenomena and have recreated it.

Oh wait, 11th grade, right. Fibbinocci and other scales would be good to look into. Write a python program that finds the largest prime number against the user input (would be really handy in some of those math tests I'm sure).

Windows Nerd
December 30th, 2010, 06:09 AM
Hey, so thanks for the suggestions, RSA seems like a really good idea. If you have anything more to add (like resources, those are always good) please do!

Scott

Legendary_Bibo
December 30th, 2010, 06:17 AM
Boolean Algebra, 'nuff said.