Undergraduate Mathematics Seminar
Everywhere Continuous, Nowhere Differentiable Functions, by Michael McLaughlin (Ohio University, Mathematics)
What 


When 
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 realvalued 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 nowfamous “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.