ESP Biography
MADELEINE UDELL, ESP Teacher
Major: Applied Math (iCME) College/Employer: Stanford Year of Graduation: G 

Brief Biographical Sketch:
Not Available. Past Classes(Clicking a class title will bring you to the course's section of the corresponding course catalog)M1117: Music to my ears: why harmony sounds good in Splash! Fall 2010 (Nov. 13  14, 2010)
Why do certain harmonies sound better than others? In this class, we'll explore the basic math that underlies most systems of harmony, and learn how to use that knowledge to harmonize your favorite melodies. For the math, we'll derive the basic equation for how a wave moves down a string (or your eardrum) and a beautiful mathematical theory that explains the notes you hear in terms of the shape you make when you pluck a string. We'll move from the fundamental mathematics and physics of how instruments make sounds and how your ears detect them, to the practical knowledge of how to make a simple and pleasant harmony for a tune.
As for strings to pluck harmonically, we'll have a piano and a harp (!) for you to try out.
M1120: Introduction to Proofs: Why Algebra Works in Splash! Fall 2010 (Nov. 13  14, 2010)
What does it mean to prove that a statement is true? This class will have two components. In the first, I'll introduce an abstract logical system within which we can prove some of the basic formulas you learned in middle school so that we can understand what a very high standard of proof looks like. In the second half, we'll discuss the limitations of that kind of proof: how can you prove that the abstraction you've constructed has anything to do with the world you live in?
