I'm taking a class right now that requires me to give a talk on some topic from any branch of mathematics. The talk has to be an hour long, but that is the only requirement placed on it.
I've taken differential, integral and multivariable calc, linear algebra, ODE, introductory complex analysis, and am currently taking my first Real Analysis course as well as a class on set theory. I was wondering if anyone might have suggestions about something interesting I could discuss. It can be an open problem or a closed one with an interesting solution  anything, really, as long as I can make an interesting presentation out of it to fill an hour. I just don't want to bite off more than I can chew and give a talk that I myself can't understand, so whatever math is involved will need to be stuff I can come within [imath]\epsilon[/imath] of understanding. I have several weeks to write the presentation/learn the material, but I also have a heavy courseload, so I don't want to (eg) teach myself abstract algebra for the sake of the lecture.
If anyone has any suggestions  even insofar as a good place to look, I appreciate it.
An interesting topic for a math talk
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 agelessdrifter
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Re: An interesting topic for a math talk
Who is your audience? What should we assume about their math background?
Re: An interesting topic for a math talk
I think you should present a proof that e is transcendental.
wee free kings
Re: An interesting topic for a math talk
There's no lack of interesting applications of elementary linear algebra. You could talk about the fundamental results of Von Neumann game theory or fairly ranking a roundrobin tournament.
Re: An interesting topic for a math talk
If your audience has the same background as you do, how about: analytic continuation, the Riemann Zeta function, and an introduction to the Riemann hypothesis.
Re: An interesting topic for a math talk
Since you're taking real analysis, what about discrete analysis? There are some nice analogues.
 RogerMurdock
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Re: An interesting topic for a math talk
Talk about foundational set theory and how it was formulated. Hilberts problems, big picture stuff.

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Re: An interesting topic for a math talk
Plan your presentation to last for 35 minutes with three breaks for questions and making sure everyone is following, one after 10 minutes, one after 20 minutes, and one at the end. Practice giving your presentation at least once. These two steps will improve your talk more than selecting a good topic rather than a mediocre topic.
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Re: An interesting topic for a math talk
If you are presenting in front of your classmates, then pick anything you all did in previous semesters or classes. Make sure you subdivide your topic in three sections, at least which are introduction, body and conclusion and subdivide your one hour as 10  40 10 for three respectively. Pick a topic you think you are most comfortable with and you can answer the questions if any questions arises from the audience.
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