Given an arbitrary unit, what other numbers (lengths) can we construct using only the famous tools of the geometer: the compass and the straightedge? Can we construct every integer? Every rational number? Every real number? It turns out that the answer to that last question is “no,” but figuring out the set of numbers we can construct leads to some interesting problems. For roughly the first half of the time, we’ll attempt to develop construction algorithms for various classes of numbers, and in the process define a new subset of the reals called the constructible numbers. For the second half, we’ll take a look at some of the properties of this set, and show how it was used to solve three of the most famous unsolved problems in the history mathematics.

What moral duties or obligations do human beings have to the natural world? Even if we want to see ourselves as “environmentally friendly,” it is not always so obvious what that means, or how we should act consistently with those beliefs. For example, consider a conflict between an animal rights activist who opposes all hunting, and a conservation biologist who sponsors deer hunts to reduce predation on vulnerable native prairie grasses. Both believe themselves to be acting ethically; who, if either, is correct? In this course, we’ll first take a brief tour of the major traditions in American environmental thought. Then, we’ll split into small groups to explore case studies centered around ethical conflicts involving humans and the natural world. The goal is not to find “correct” answers, but to arrive at a deeper understanding of how these complex issues relate to our own values. Possible case study topics (depending on student and teacher interest) could include climate change and geoengineering, biofuels, conservation biology, animal rights, nuclear energy, GMOs, water rights, and land use policy.

Sure, slaying dragons while wearing quasi-Viking armor is fun, but the 2011 video game The Elder Scrolls V: Skyrim been acclaimed as much for its nuanced theme of civil war as for its fantasy storyline. We will explore how Skyrim deals with political topics such as imperialism, nationalism, racism, and political economy, and conclude with a role-played debate between the Imperial and Stormcloak factions.

In high school, you learned to do geometric constructions using the traditional compass and straightedge. But there's nothing really special about those tools; they just happened to be the ones Euclid described in his axioms. Let's try using a different tool: folding paper! In this class, we will develop a set of "axioms for origami," and then challenge ourselves to solve various construction problems using paper folding-- and some of their solutions might surprise you!

The Nash equilibrium says that everyone loses-- can you do better?? We will create teams and play a couple of games of Iterated Prisoner's Dilemma! No prior knowledge of game theory is required or expected, but if you want to read up, check out Wikipedia: (http://en.wikipedia.org/wiki/Prisoner's_dilemma)

Sure, slaying dragons while wearing quasi-Viking armor is fun, but the fifth entry in Bethesda's Elder Scrolls series has been acclaimed as much for its realistic and nuanced depiction of civil war as for its fantasy storyline. We will explore how Skyrim deals with topics such as imperialism, nationalism, racism, and political economy, and conclude with a mock debate between leaders of the Imperial and Stormcloak factions.