Math department seminar: Volterra's Function and Other Counterexamples: or, Why Hypotheses Are Important

Our next seminar will take place on Friday, March 12 at 4:00 p.m. over Zoom. Dr. Elizabeth Gillaspy of the University of Montana will speak about counterexamples in analysis. She will assume that the attendees have taken Calculus II but no additional math. The Zoom information and her title and abstract follow.


Title: Volterra's Function and Other Counterexamples: or, Why Hypotheses Are Important

Abstract: On the surface, Volterra’s function V(x) seems to violate the Fundamental Theorem of Calculus. V(x) is differentiable on the interval [0,1], but the integral of the derivative V′(x) on that interval does not equal V (1) - V (0)!

In this talk, I’ll explain what Volterra’s function is and why it does not, in fact, contradict the Fundamental Theorem of Calculus. (The answer has to do with hypotheses...) Along the way, we’ll see a number of other, seemingly contradictory, examples from Real Analysis: a function g(x) that is differentiable but g'(x) is not continuous; a subset of [0,1] that contains no intervals and yet has length 1/2; and perhaps the most contradictory example of all, the Cantor set. By the end of the talk, I hope to have convinced you that the hypotheses of a theorem are at least as important as its main result.
 
Please contact Dr. Johanna Franklin at johanna.n.franklin@hofstra.edu for the Zoom information.

Friday, March 12, 2021

Cost:

none

Categories:

Location:

Zoom
Zoom Link
Online, NY 00000


Contact:

Johanna Franklin

Phone: 516-463-5739

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