Undergraduate Mathematics Seminar
Everywhere Continuous, Nowhere Differentiable Functions, by Michael McLaughlin (Ohio University, Mathematics)
Mar 13, 2013
from 04:10 PM to 04:55 PM
|Where||226 Morton Hall|
|Contact Name||Martin Mohlenkamp|
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Abstract: In a standard calculus course, one learns that the properties of continuity and differentiability are inherently related, i.e. a differentiable real-valued function is continuous. It is also understood that the converse is not necessarily true. This property begs the question, “Can a function be continuous everywhere, but differentiable nowhere?” In fact, the answer to this question is positive, which can be surprising. Nevertheless, Karl Weierstrass constructed his now-famous “Weierstrass function” which exhibits this property. In this seminar, I will discuss the properties of everywhere continuous, nowhere differentiable functions and I will prove the nowhere differentiability of the Weierstrass function. If time remains, continuity will also be discussed.