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I received my Ph.D in mathematics from Ohio State in 1994 under the direction of Gerald Edgar and have been a professor of mathematics at The University of North Carolina - Asheville since 1997. In recent years, I've also worked as a part-time consultant to Wolfram Research focusing on development of mathematical content for WolframAlpha.


1d
answered What is the most important (outside of mathematics) results known to require the axiom of choice?
2d
comment Relating convergence theorem for Newton-Raphson method to Newton fractal
Thanks for this answer - I was unaware of such a simple bound. I wonder if there is a similar result for rational functions as well? In practice, I typically try to find a positive $\varepsilon$ such that $|N'(x)|<1$ for all $x$ within $\varepsilon$ of the root. This not too hard to code, but certainly must take much longer than using a simple bound like the one that you state here.
Nov
24
revised Is it possible to prove that some point belongs to Mandelbrot set? Is this an example of Gödel's theorem?
edited tags
Nov
24
answered Is it possible to prove that some point belongs to Mandelbrot set? Is this an example of Gödel's theorem?
Nov
23
comment Prove that if $\,\lvert\, f(\,f(z))\rvert>r,\,$ then $f$ is constant
But $e^{e^z}$ is entire as well so, by Picard's theorem again, it must assume all values with one possible exception - correct? In fact, $e^{e^z} = 1$ at $z=2\pi \, i +\log (2 \pi \, i )$.
Nov
23
comment Inflection point of $\,f(t) = \frac{1}{1+e^{(-t)}}$
@YvesDaoust Edited. The main point that I was trying to get across, though, was that we have an inflection point because $f'$ has an isolated local extreme at zero - not because $f''$ is zero at zero, which is a different thing.
Nov
23
revised Inflection point of $\,f(t) = \frac{1}{1+e^{(-t)}}$
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Nov
22
comment Vertical tangent line at edge of domain
So, the answer to the question is?
Nov
22
answered Upper step function of the Cantor set.
Nov
22
revised Inflection point of $\,f(t) = \frac{1}{1+e^{(-t)}}$
added 106 characters in body
Nov
22
answered Inflection point of $\,f(t) = \frac{1}{1+e^{(-t)}}$
Nov
21
comment Evaluating a decimal exponent
Here is a WolframAlpha blog post that describes a bit about how non-integer roots are dealt with by WolframAlpha. The post deals with rational roots which is related but a bit different from decimal roots, I suppose.
Nov
20
comment Solving over-identified model in Mathematica
As far as I can tell, $a,b,c$, and $d$ can all be completely arbitrary. $m,n,o,p,q$, and $r$ then depend functionally upon them. What kind of output are you expecting?
Nov
20
revised Solving over-identified model in Mathematica
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Nov
20
answered Open source lecture notes and textbooks
Nov
19
revised What do polynomials look like in the complex plane?
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Nov
19
answered What do polynomials look like in the complex plane?
Nov
19
revised Finding the area of a implicit relation
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Nov
18
revised Finding the area of a implicit relation
edited title
Nov
18
answered Finding the area of a implicit relation