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Saturday Workshop Class Descriptions
(The following are Math Circle 2009 class descriptions.)
Probability Theory
Deanna Needell
Did you know that if you leave two monkeys in a room with a typewriter and let them type forever, there is a 100% chance they will recreate the works of Shakespeare? That if a bird flies randomly in the sky, he has no chance of finding his way home, but a man walking randomly on the ground will always get there? That with extremely high probability while reading this sentence you have breathed a particle that was also breathed by John Hancock has he signed the Declaration of Independence? Probability is everywhere in our daily lives, and its applications are near endless. We will discuss basic probability and its role in everyday activities. We will begin by investigating probability in simple games and eventually be able to analyze the probability involved in more complicated scenarios.
Symmetry in Geometry
Gabe Amos
In 1872, Felix Klein proposed his ``Erlangen Programme'' for the systematic study of geometries. The key component to his program: that a central idea in studying any type of geometry is that of symmetry, i.e. the ways you can move your space around without changing the way things look. So understanding these symmetries will give a deeper understanding of the geometry and give you new types of geometries you wouldn't have known about otherwise.
In this course we'll look at different types of geometries (including non-Euclidean ones!), and see what types of interesting symmetries we can derive. Some of what we'll be talking about:
- What are some other types of geometry on surfaces, etc.
- Classification of crystals in 2 and 3 dimensions
- The deep connection between algebraic and geometric ideas
- What would these geometries look like if we lived in one?
- Some other topics as dictated by interest.
Mathematical Graphics
Matt Stamps
Have you ever wondered how the animators at Pixar are able to make to make their characters look so real? In this workshop, we will learn the basic tools for creating graphics and animations while exploring the mathematics that lie underneath. You will learn introductory computer programming, coordinate geometry, and perspective drawing which you will use to create your own animation projects. No knowledge beyond basic geometry is expected. I will be covering the basics of mathematical graphics and animation.