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[popsofctown]

Apparently, due to deadlines I've been not paying attention to and juggling stuff around the wrong way, I need to give a 20 minute presentation for my Introduction to Elementary Number Theory class tomorrow.  I haven't even picked a topic.  If I don't come up with something I'll fail.  It's for a research paper, based on any advanced number theory concept (he suggested cryptography, but most things are ok).

Preferably I can include proofs or theorems in the presentation, to add value and burn time.

I'm supposed to use multiple legitimate sources.  I might have access to some online through my university somehow.

I am in dire straits and not sure where to start with this.  I was supposed to meet with my instructor a few days ago to discuss what topic I should do, but he wasn't there.  I knocked on his office door about 500 times. When I emailed he insisted that he was there, or "around" at least, all day.  Man you told me to come to your office to meet you and you weren't there anytime during a twenty minute window, <removed> me right?

Some of the topics we covered during the course is Peano's axioms, group theory, greatest common factors, least common divisors, cyclic groups, equivalence classes, well ordered principle, induction and some other things.  Those are not good topics themselves but they could give some idea of what the class was like.

I am by no means asking anyone here to do research on my behalf, I'm just having "writer's block" as far as selecting a topic.  It can't be too basic so that my audience (a graduate student and a senior) is already incredibly familiar, but not too complex to work with.  I need to be able to find multiple sources talking about it.  It needs to last 20 minutes (I'm an excellent public speaker, so that will help a bit)

[popsofctown]

He sent me a pretty rough email regarding the missed appointment and a recent class absence, so I'm a little emotional right now

[popsofctown]

This doesn't belong here at all, but I have a really crappy social/support network

[Watno]

Symmetry groups of polyhedra?

[Kirian]

Obviously you need to apply one of those things to Dominion!

Seriously though, good luck man.  Is game theory and statistics too basic?

[Watno]

Or just go with what he suggested and talk about RSA (http://en.wikipedia.org/wiki/RSA_%28algorithm%29)

[popsofctown]

Game theory is too basic.  Statistics is uninteresting to him (too practical, the class is much "purer" than that)

[SirPeebles]

Lagrange's four square theorem?

Something about the discrete log problem? (used in cryptography)

[popsofctown]

Or just go with what he suggested and talk about RSA (http://en.wikipedia.org/wiki/RSA_%28algorithm%29)

Is this so supercommon to talk that one of the other 2 students might be doing it?  I just emailed them, which I should have done way earlier.

I have yo-yo depression, which means that sometimes I don't give a damn and then other times I'm more motivated.  I'm basically cleaning up Hyde's mess right now

[popsofctown]

Lagrange's four square theorem?

Something about the discrete log problem? (used in cryptography)

My instructor wants to marry Lagrange.  Let me look into that.

[Kirian]

Fermat's Last?  Ulam spiral?

Does voting theory fall under number theory?

[Watno]

Or just go with what he suggested and talk about RSA (http://en.wikipedia.org/wiki/RSA_%28algorithm%29)

Is this so supercommon to talk that one of the other 2 students might be doing it?  I just emailed them, which I should have done way earlier.

It probably is.

[popsofctown]

Fermat's last is probably too much of an open and shut case kind of thing. 
An important aspect is that he wanted me to use multiple sources in a meaningful way.  Which is kinda hard in math when two authors are essentially repeat themselves saying "Yes.  The theorem is true".  But there could be various authors saying, "Well this consequential claim seems likely, and I can't prove it, but I think with time we can probably prove it", and maybe another author disagrees or is more interested in other consequences.

Voting theory works if it is a super pure thing and not too applied.  If it's a form of game theory than it's no good.  The fact that he never even touched on game theory makes me feel like he is probably not really a fan of game theory.

[popsofctown]

Yknow, an unsolved problem that has been proved for several special cases seems like it might be a really good thing to work with.  Because various authors will have various proofs for various special cases in various wild journal articles I will need to hunt down.
And I could reproduce the proofs for some special cases.

[Watno]

I guess it's rather that game theory isn't really connected to number theory?

Also wanting multiple sources in a mathematical talk is really strange I think.

[Kirian]

Fermat's last is probably too much of an open and shut case kind of thing. 
An important aspect is that he wanted me to use multiple sources in a meaningful way.  Which is kinda hard in math when two authors are essentially repeat themselves saying "Yes.  The theorem is true".  But there could be various authors saying, "Well this consequential claim seems likely, and I can't prove it, but I think with time we can probably prove it", and maybe another author disagrees or is more interested in other consequences.

Voting theory works if it is a super pure thing and not too applied.  If it's a form of game theory than it's no good.  The fact that he never even touched on game theory makes me feel like he is probably not really a fan of game theory.

Given that voting theory is mainly studied by political scientists, it might be too practical.

There must be some unsolved prime problems, right?

[popsofctown]

I guess it's rather that game theory isn't really connected to number theory?

Also wanting multiple sources in a mathematical talk is really strange I think.

Yeah, I'm inclined to agree.    Little need for it, if one man can make a legitimate proof for his theorem, he does not need corroboration from his peers to be right about it.

[popsofctown]

Fermat's last is probably too much of an open and shut case kind of thing. 
An important aspect is that he wanted me to use multiple sources in a meaningful way.  Which is kinda hard in math when two authors are essentially repeat themselves saying "Yes.  The theorem is true".  But there could be various authors saying, "Well this consequential claim seems likely, and I can't prove it, but I think with time we can probably prove it", and maybe another author disagrees or is more interested in other consequences.

Voting theory works if it is a super pure thing and not too applied.  If it's a form of game theory than it's no good.  The fact that he never even touched on game theory makes me feel like he is probably not really a fan of game theory.

Given that voting theory is mainly studied by political scientists, it might be too practical.

There must be some unsolved prime problems, right?

"Every number can be represented as the sum of two primes" is unsolved.  But I think all the special cases for that are just empirical.

[spiritbears]

What about the familiar/philo stone bane problem?

[Watno]

Classification of finite groups is unsolved, but some subsets of finite groups have been classified. That would kinda burst a 20 minute talk though^^

[SirPeebles]

The shortest vector problem is another cute problem in cryptography.  If you're interested in group theory or quantum algorithms/computation, you could look into the hidden subgroup problem.  I gave a talk on that several years ago and found it to be interesting.

[popsofctown]

Wikipedia claims classification of finite groups has a thousands-of-pages proof.  Is that proof not universally accepted?

[popsofctown]

The Lagrange four square thing looks really manageable.  Does it have unproven generalizations to talk about?

[SirPeebles]

"Every number can be represented as the sum of two primes" is unsolved.  But I think all the special cases for that are just empirical.

Every even.

Classification of finite groups is unsolved, but some subsets of finite groups have been classified. That would kinda burst a 20 minute talk though^^

In particular the finite simple groups.  There are some really nice connections between the sporadic finite simple groups and certain error correcting codes (Golay code)

[heron]

Goldbach's conjecture is indeed unsolved, but it has been proven that every number is the sum of at most 6 (or is it 5?) primes.

But I think the best advice at this point is pick a topic (the Lagrange thing sounded good, but I know nothing), and go go go go go!
I think you can do this; pulling an all-nighter gives you 8-ish hours; just enough time if you are constantly working!