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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.


Dec
18
answered How to visualize $f(x) = (-2)^x$
Dec
17
comment Every projection of the square of the middle thirds Cantor set contains an interval
@Behaviour How can you tell, if the question is misstated? Here is a statement that definitely is true: If we project the point $(x_0,y_0)$ along a line of slope one, we hit the $x$-axis at the point $x_0-y_0$. Now, it's well known that $C-C=[-1,1]$; this can be proven using the triadic expansion representation of $C$. As a result, the projection along this direction certainly contains an interval.
Dec
17
comment Proving that plane - cantor - set contains an interval
Something seems not quite right. The dimension of your set $C_{\lambda}$ is $\log(2)/\log(1/\lambda)$, provided that $\lambda<1/2$ - correct? If $\lambda\geq 1/2$, then $\dim(C_{\lambda})=1$. In any case, $\dim(E)=2\dim(C_{\lambda})$, not $\dim(C_{\lambda})$, as you have written. I'm guessing that your interesting situation is $1/4<\lambda<1/2$, where $E$ is a totally disconnected set with dimension greater than $1$.
Dec
17
comment How many cube roots does 1 have modulo 162?
@MRK I didn't say that you need to upvote, I said you should simply because the answerer did put some effort into answering your question. Now, I don't tell my students to run straight to the computer for "every simple problem" (any more than I tell them to come here for such a problem), but I do tell them that it is often valuable to think about a problem from multiple perspectives - including computational.
Dec
17
comment How many cube roots does 1 have modulo 162?
@MRK You needn't accept the answer but you should certainly upvote any answer that gives you a reasonable approach to think about the problem.
Dec
17
answered Slightly Chunky Cantor Sets
Dec
16
awarded  Yearling
Dec
15
comment Why is it differential equations exist on an interval instead of a domain?
Because the domain happens to be an interval, according to the standard existence and uniqueness theorems.
Dec
11
revised Identifying Hamiltonian Systems with Phase Portrait
added 31 characters in body
Dec
10
revised Dynamical System , Series : can't find the general terms
deleted 1 character in body
Dec
10
comment Dynamical System , Series : can't find the general terms
@Boo - The book is a classic!
Dec
10
answered Dynamical System , Series : can't find the general terms
Dec
9
revised Let there be 9 fixed point on the circumference of a circle.
added 116 characters in body
Dec
8
comment Solving Kepler's second law
These notes aren't so bad.
Dec
8
comment Nature of Equilibrium Points
@Mitscaype If you find Nick's answer at all helpful, then you should upvote it. If it "really helps you out", then you might consider accepting it, particularly if another answer doesn't improve on it.
Dec
8
awarded  Caucus
Dec
8
revised Surface area of this helicoid?
added 14 characters in body
Dec
8
comment Surface area of this helicoid?
Looks good to me, so far! The integral can be done with a hyperbolic trig substitution $r=\cosh^{-1}(\theta)$ that ultimately leads to an answer like $\left(\sqrt{2}+\sinh^{-1}(1)\right)/2$.
Dec
7
answered Find the number of all 3 digit numbers $n$ such that $S(S(n))=2$
Dec
3
comment Does $\pi$ contain any zeroes?
This would have been a fabulous question in 1630!