The only difference and difficulty is mastering “long division” using Gaussian Integers. This is actually not much different from long division of polynomials (which you are probably familiar with from some time in your math career). Here is a short worksheet with some interesting examples of the Euclidean algorithm using Gaussian Integers, in case you are interested.

]]>You got the main point I think: there are interesting, accessible, math problems out there that you could study or think about if you found yourself with extra time and interest. It is always nice to know what has been done and what people find interesting enough to talk about.

]]>I’m curious to see what you find out if you do this for your capstone. There will definitely be a lot of data for you next month. ]]>

Eventually, Saari gives a pretty good way to think about elections using linear algebra. I think you could follow up and use this pretty well. You could run a few “elections” with some friends or students here at school and see how you can use linear spaces to manipulate the “winner.”

If this is a way you choose to go, I am happy to discuss it with you further, but maybe you will continue with your interest in Diophantine Equations (coming up soon in Abstract…)

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