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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.


11h
comment Mathematica Output Meaning ({{}})
Probably, that there were no solutions.
Aug
23
comment Deciding if sets are bounded and/or closed
I'm pretty sure that edits are solely intended to improve posts! :) Of course, a comment wouldn't hurt but it seemed pretty clear in this case.
Aug
23
revised Deciding if sets are bounded and/or closed
deleted 3 characters in body
Aug
23
revised Integral over filled Julia sets
edited tags
Aug
23
answered Integral over filled Julia sets
Aug
10
comment My first partial differential equation attempt
@Dmoreno I'm glad you liked it. I generate the image with Mathematica. I generated a list of images and then exported that to an animated GIF. The command to generate the list of images was something like so: Table[Plot[Exp[-Pi^2 t] Sin[Pi*x], {x, 0, 1}, PlotRange -> {0, 1}], {t, 0, 0.7, 0.01}].
Aug
7
revised Can the graph of $x^x$ have a real-valued plot below zero?
edited body
Aug
6
reviewed Approve suggested edit on Get position of a point with known distance between other points
Aug
6
comment Get position of a point with known distance between other points
Well, there's a fairly obvious system of equations to write down. Do you have a specific example?
Aug
6
answered My first partial differential equation attempt
Aug
6
comment Non-Trivial Self-Inverse Analytic Function In The Complex Plane
This is a well studied problem on the Riemann sphere - namely the complex plane plus infinity. In that context, the only holomorphic, self-inverse functions are the Mobius functions, $z\rightarrow (az+b)/(cz+d)$. In the everywhere analytic case, $c\neq 0$ and you're left with your two examples.
Aug
6
comment Analytic Function In The Complex Plane Which Always Gives Real Values
You can use the Cauchy-Riemann equations to prove fairly easily that, if $f$ is defined and analytic for all $z$ in the complex plane, then $f'=0$ on the complex plane. It follows that $f$ must be constant.
Aug
6
comment Optimization Software
You need to ask a much more precise question. If you're using Mathematica, you might consider asking on mathematica.se but, again, you must reference a specific example. Is there any chance you're using the Minimize command command when NMinimize would be more appropriate?
Aug
2
comment interpreting triple integrals
You could make the question more clear with a specific example.
Aug
1
comment Limit of a Discrete Dynamical System
@user54738 Many software packages provide the ability to do numerical computations to much higher precision that just the 16 decimal digits provided by the CPU. I used Mathematica which provides significance tracking so that you can actually measure how precise your computations are. As a result, you can have confidence of your results. To see the need for this sort of thing, try iterating $f(x)=4x(1-x)$ from $x_0=(2+\sqrt{3})/4$ at machine precision. It will appear to converge to $0.75$ (correctly) but, after around 40 iterates, it moves away from $0.75$, even though $3/4$ is fixed.
Jul
31
revised Can you uniquely define a tangent line at a point for a 3D csurve?
added 285 characters in body
Jul
31
answered Can you uniquely define a tangent line at a point for a 3D csurve?
Jul
31
answered Limit of a Discrete Dynamical System
Jul
23
awarded  Revival
Jul
20
answered Triple Integral exercise