Without math, very little science would be possible.

Science relies on math both to describe predictions about the relationships between real-world phenomena and to test those predictions. Even fields like ethics rely heavily on mathematics (ethics draws on game theory specifically the Prisoner's Dilemma.

The beauty of mathematics, however, is that it does not have to work only within the confines of the known real world. In the broadest sense, if scientists attempt to explain our universe, then mathematicians try to explain the workings of every possible universe. Clearly, mathematics has much more to offer than the algebra, geometry, and functions courses you've had in school!

In Radical Math, we'll explore a wide array of subjects, including (but not limited to!):

• Logic and the foundations of mathematical thought
• Methods of proof (and what can go wrong!)
• Probability, Game Theory, and why life's choices are not simple
• Graph Theory
• Geometry and life in non-Euclidean space

The final direction for Radical Math is open to the interests of the students, so student curiosity will determine which topics we cover in more depth (and what other topics we may wish to explore).

We'll spend much of the second week of ASRA working on research projects individually or in small groups. Students will design their own projects, and will get to show off their nifty findings to peers and parents at the closing day colloquium.

Instructors:
Jay Schamel is a graduate student in mathematics at the University of Alaska Fairbanks.