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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.


3h
comment Assertions about measures with computers
I guess you could say the same thing about written human language. We have finitely many symbols we work with in written language and there's only countably many strings with such symbols. Yet, we talk about about measures on $[0,1]$.
1d
comment Is there a name for this kind of “Pascal's Triangle”?
@DavidRicherby Well, the question asks us to place the triangle in some broader context, which the answer certainly does. Sounds like your problem is not at all with this answer but with the "sledgehammer" of cellular automata or, possibly, Mathematica - I don't know which.
1d
answered Is there a name for this kind of “Pascal's Triangle”?
1d
comment Periodic Points and One Dimensional Maps Homework Help
Which also, of course, leads to the very important topic of symbolic dynamics - making this an excellent answer. Looking at this question (and some of jerry2144's other questions), I suspect that a more direct, geometric, and intuitive response might be appropriate - which is what motivated my answer.
1d
revised Supremum of all y-coordinates of the Mandelbrot set
edited tags
1d
comment Fixed Points Homwork Help
I've answered a few of your questions by providing and analyzing a graph. I strongly recommend that you graph this function, together with the line $y=x$ and see if you can figure out what's going on. It's trivial to generate a graph these days using a tool like WolframAlpha or Desmos. Also keep in mind that a fixed point is attracting precisely when the derivative is less than one in absolute value there. Geometrically, the graph crosses the line with a relatively shallow slope.
1d
comment Periodic Points and One Dimensional Maps Homework Help
The questions you've been asking definitely fall under the topic of dynamical systems and should be tagged as such. Another possibility is Chaos Theory, but that tag seems to be used less frequently.
1d
revised Periodic Points and One Dimensional Maps Homework Help
edited tags
1d
answered Periodic Points and One Dimensional Maps Homework Help
2d
comment One-Dimensional Maps
The approach here is exactly the same as the approach outlined for your other question, which I answered. Hopefully, you'll be able to work this out after looking at that.
2d
revised Periodic Points Homework Help
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2d
comment Periodic Points Homework Help
Well, you've got $3^4-2^4=81-16=65$ points fixed by $f^4$ and you've got $3^2-2^2=5$ points fixed by $f^2$, so how many of the points fixed by $f^4$ must be genuine points of period 2?
2d
revised One-Dimensional Maps
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2d
revised Fixed Points and Graphical Analysis
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2d
answered Fixed Points and Graphical Analysis
2d
answered How to determine the orbits of points under the tripling map $f(x)=3x\bmod 1$?
Sep
16
answered Name of this fractal
Sep
15
comment Why such iteration leads to fractal?
@Mr.Wizard Not planning to - I think it should be closed.
Sep
15
comment Is there a way to rewrite integrals in Mathematica using u substitution?
Perhaps you should ask over on mathematica.stackexchange.com? If you do, be sure to a specific example you'd like to see worked and some code indicating some effort on your part.
Sep
15
comment Why such iteration leads to fractal?
It might be worth mentioning that the code is not particularly good. I have a package that generates the image, with all 100000 points and colors, in well under half a second.