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I am going to be presenting a 2hr math lecture to a few students and I am supposed to make the lecture so interesting that they are left utterly fascinated about the topic that I choose. The students have a good foundation of calculus, algebra and geometry. I have been thinking of which topic to talk about and have come up with game theory, fractals as well as graph theory.

Any other suggestions for a good topic?

Thank you.

anonymous
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  • http://math.stackexchange.com/questions/71985/a-request-for-a-suggestion-for-a-mathematics-talk-aimed-at-first-year-and-second?rq=1 –  Oct 03 '15 at 12:12
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    Enter "lecture topic" into the search field, and you'll find a number of similar questions. – Blue Oct 03 '15 at 13:31
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    +1 for graph theory. You could also dazzle them with a taste of number theory and RSA, using RSA with, say, 3-digit numbers. But graph theory is more certain to fascinate; you can even grab Junior High students' attention with it. And, combinatorics, with example questions that are extremely easy to understand and ferociously difficult to solve without knowledge of combinatorics. Basically any discrete mathematics, because the foundations you mention (calc, algebra, geometry) don't even touch on the wonders of discrete maths. – Wildcard Oct 04 '15 at 23:13

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The conjecture of Birch and Swinnerton-Dyer? Ok, this is very advanced, but it can (almost) be presented in a very elementary way, and being a millennium prize problem, it can be appealing for them. You can define elliptic curves in an intuitive way and/or giving their equations, both ways are simple (you are in characteristic 0). You can justify the interest of their rational points with a diophantine equation whose solutions give rise to an elliptic curve in an easy way. You can define the group structure drawing some lines through points in the elliptic curve. Are you willing to sacrifice even more rigour to define L-functions? Do your students handle complex analysis? If so, you can present an "intuitive" BSD conjecture.

SlavaM
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