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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.


18h
comment How many digits are there in 100!?
@YvesDaoust I just think it's neat that discrete sums can be estimated using integrals. So often, it's the other way around.
23h
comment How many digits are there in 100!?
Yes, probably so. But, then, I didn't learn Stirling's formula until well after I had learned about Riemann sums. And, as your answer nicely illustrates, it's nice to think about it from a relatively elementary perspective. I think I'll go upvote it! :)
1d
comment How many digits are there in 100!?
+1 Though, if you're going use a computer program, then why not just Length[IntegerDigits[100!]] in Mathematica or WolframAlpha? My answer is similar in that it uses the same sum but then estimates that sum with an integral.
2d
comment How we can drow a Blaschke $3$ ellipse?
@Nilan I rather like Stan Wagon's Mathematica in Action. The reason is that the book focuses on mathematics first, thus, there's always an objective. I find it difficult to learn to program without an objective or project in mind. At some point, you'll want a more general introduction, I think that Mathematica Programming is good (and free). Then, you need a good reference so definitely make use of the internal documentation. Finally, this question on mathematica.se has plenty more references.
2d
comment software for drawing sequence in metric space
When you say that a "textbook can show it", it sounds like you have some particular type of picture in mind. Do you have a pointer?
2d
comment How to visualize $f(x) = (-2)^x$
@aes Glad you like them!
2d
comment Solving 2D Laplace eigenfunction equation
What's the region? And boundary conditions? The problem is not fully specified without that information.
2d
comment Calculating Triple Integral
@slmkarta Looks like you figured out the general idea while I was typing. My answer has some more details, but not all.
2d
comment How did Sir Isaac Newton develop and formulate the famous binomial theorem?
To expand on Yves' comment, the basic binomial theorem for positive, integer powers is typically attributed to Pascal and Yves himself provides a nice answer for that. Newton generalized this to rational exponents. The easiest way to do so is to apply Taylor's theorem the function $(1+x)^p$, where $p\in\mathbb Q$ or even in $\mathbb R$. I'm not sure that this is how Newton approached the problem, though.
2d
comment Differential Equations and Newtons method
To answer your second equation, you first need the correct equation for $k$, namely $k^3+3k^2-1=0$ - i.e. exponents, rather than subscripts. You're asked to find the smallest positive root and then write down the solution. Your solution should look like $Ae^{1.23t}$, though $1.23$ isn't the correct number.
2d
comment Differential Equations and Newtons method
You've really got two fairly different questions so I would recommend that you ask separate questions on the site.
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
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
10
comment Dynamical System , Series : can't find the general terms
@Boo - The book is a classic!
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
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 $\left(\sqrt{2}+\sinh^{-1}(1)\right)/2$.