Splash Biography

“I saw that at some stage in my life the whole structure would have to be utterly demolished, and that I should have to begin again from the bottom up if I wished to construct something lasting and unshakeable in the sciences.” –Descartes Have you ever wondered what “7” is, or whether addition actually works? How do we know that numbers exist? What if I told you that you didn’t have to take your 1st grade teacher’s word for it when she said that 2+2=4? In this course, we will start with nothing (quite literally) and construct basic arithmetic from the ground up, developing the natural, rational, and real numbers and proving that addition, subtraction, multiplication, and division exist and work like everyone says they do. Be prepared for some pretty rigorous proof along the way.

You've probably heard of chaos theory: a butterfly flaps it's wings and creates a hurricane on the other side of the world. This course explores the real mathematical principles behind chaos. We'll look at how chaos arises in simple physical systems, and look at different ways of modeling chaotic systems: bifurcation diagrams, state-space orbits, and Poincaré sections.