ESP Biography

For too long have we submitted to the tyranny of unifying themes. How many bears can you run away from forever? How can electrons prove inequalities for us? Why is traffic so bad on your favorite roads? Are there theorems that are true but can't be proven? How can physics prove the Pythagorean Theorem? And most importantly, how many of these kinds of things can I answer in under an hour?

In the standard Plurality voting system, whoever gets the most votes wins. When there are many candidates this can get silly - a candidate that the vast majority of voters _hate_ could win with just 10% of the vote as long as ten other generally agreeable candidates split the other 90%. If voters supply not just their top choice but a ranking of all the candidates, a whole world of other voting systems become possible. In this class we will come up with those other systems and discuss their pros and cons.

Same idea as Unrelated Math I (M4087) except the topics will be - you guessed it - totally unrelated! So sign up for either or both of these; there will be no overlap between the two.

When you do an experiment, you're taught to control as many variables as possible. For example, if you want to know whether playing music helps plants grow (please don't actually try this), then the presence or absence of music should be the only thing you change - you should grow everything in the same amount of sun, the same amount of water, etc. But what you aren't always taught is that it's a losing battle - no matter how perfectly you try to grow two plants the same way, they won't grow to exactly the same height! So when your results come in and the musical plants grew a tenth of a centimeter taller, have you discovered a new phenomenon, or did it just happen by chance? There is a powerful tool that we can use to answer this question - the statistical significance test. There are a bunch of such tests, actually, and computers are quite good at doing them for you, so we won't delve into the details of any single one but instead we'll focus on the intuition behind all of them. Taking this class should help you use and interpret any significance test and be a more discerning consumer of statistical information (and do much better in science fairs, if you're planning to do one of those)*. *according to purely anecdotal evidence

What questions can computers solve quickly? In fact, what questions can computers solve at all? We will cover models of computation (what's a computer anyway?), examples of undecidable problems, and what's up with the famous open "P vs NP" problem.

Enter a weird world where a puzzle can be a list of pictures, a gibberish sound file, or just six words. What are the rules? Figure them out!