20,381 reputation
24497
bio website sites.google.com/a/unca.edu/…
location Asheville, NC
age
visits member for 2 years, 8 months
seen 43 mins ago

I've been a professor of mathematics at The University of North Carolina - Asheville since 1997. I've been using Mathematica since I started graduate school in mathematics at Ohio State in 1989. At that time, we used version 1.1 (as I recall) to teach calculus in our Calculus and Mathematica classes. I've used it pretty much continuously in my teaching and research since then.

In addition to my posts on SE, you can find some of my papers, teaching notebooks and other Mathematica based oddities strewn throughout my website.

In recent years, I've also worked as a part-time consultant to Wolfram Research focusing on development of mathematical content for WolframAlpha.


Mar
20
comment Why is this Mandelbrot set's implementation infeasible: takes a massive amount of time to do?
+1 I swear I didn't even know that ArrayPlot accepted complex values!
Mar
20
comment Why is this Mandelbrot set's implementation infeasible: takes a massive amount of time to do?
After seeing the chat you referred to, +1 for patience.
Mar
15
comment Showing steps Mathematica uses for Resolve[ForAll[…]]
Are you genuinely interested in the mathematical details or are you looking for some additional reassurance of correctness? In the latter case, perhaps a plot would be useful.
Mar
15
comment How do I evaluate the terms in an expression, but not the expression itself?
Oftentimes, Evaluate is used for this sort of thing, e.g. Plot[Evaluate[list],___], where list might involve a Table or some such. In this problem, you can't wrap Evaluate around the f[n].
Mar
15
comment How do I evaluate the terms in an expression, but not the expression itself?
Everyone has their favorite approach, although, I note that Evaluate doesn't work here.
Mar
15
comment How do I evaluate the terms in an expression, but not the expression itself?
@userX See edit.
Mar
14
comment Defining a function to determine when convergence is guaranteed
I edited your title, as "rate of convergence" is really something else.
Mar
14
comment Why is EigenValues returning Root expressions?
And my first ever rollback!
Mar
14
comment Why is EigenValues returning Root expressions?
@Mr.Wizard Will do. Generally, though, if you want to close something as too localized, it really doesn't matter to me. I just had something typed up and figured I'd put it in there for the OP's sake.
Mar
14
comment Defining a function to determine when convergence is guaranteed
What is the nature of your function? Polynomial? Rational? Transcendental? Numerically defined? If you're just looking for fixed points, is there some reason you don't just try to solve the equation $f(x)=x$? If you know the fixed point and you're really just interested in the rate of convergence, as your question suggests, then that is governed by the value of the derivative at the fixed point. Are you really just interested in fixed points, or more general periodic behavior? All these questions, and more, can be answered with more details.
Mar
13
comment Plotting an array of data onto a sphere
Also, your use of nested Do loops to generate colorMat could certainly be much faster. If you could describe the mathematics behind, it might be easier to figure out how. It looks interesting, whatever it is.
Mar
13
comment Plotting an array of data onto a sphere
@ThomasJebbSturges Although this has been marked as a duplicate, your use of MatrixPlot to create the texture does throw a little kink into the process. Since I can't add my own answer, I've edited your question to illustrate the solution.
Mar
13
comment Check Google PageRank for a given URL
@Stefan Done! If it's good enough for Leonid, then it's certainly good enough for me. Incidentally, I used to have MSVS on Windows in a VirtualBox on my Mac, just so I could get my C code working on colleagues computers. I had forgotten what a pain working with preprocessor could be, even when working with very low level code - no GUI or system interface type stuff at all.
Mar
12
comment Plotting an array of data onto a sphere
@Szabolcs Will he see an "edit" button, as a new user?
Mar
12
comment Plotting an array of data onto a sphere
@ThomasJebbSturges Just indent the code 4 spaces.
Mar
12
comment Plotting an array of data onto a sphere
It appears that your image was generated with Mathematica. Do you have the code? Regardless, this type of thing has been discussed before. You might be able to adapt the techniques listed here: mathematica.stackexchange.com/questions/15047/…
Mar
12
comment Check Google PageRank for a given URL
@Stefan Thanks - Wish I could vote for you!
Mar
12
comment What is the confidence limit on this convergence?
@rcollyer I was on iPhone earlier and couldn't respond in detail. As has been pointed out, we definitely need the terms in the product to converge to 1 in order to get convergence. Alternatively, the sum of the logarithms of the product must converge, and an intuitive analysis is typically simpler in the context. I'll post an answer detailing that shortly.
Mar
12
comment What is the confidence limit on this convergence?
David's comment on mathoverflow is absolutely correct, there's no way this product can converge.
Mar
9
comment Numerically solving an inhomogeneous partial differential equation
@xzczd Exactly! I guess you can also see this in the images by reflecting them about the vertical axis.