6,492 reputation
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visits member for 2 years, 7 months
seen 9 hours ago

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.


Jun
30
accepted How can I use math to fill out my NCAA tournament bracket?
Jun
27
awarded  Good Answer
Jun
25
comment Entering “binned” values
There are file upload and data entry (like a spreadsheet) modes, if you subscribe to WolframAlpha Pro, but - you gotta get the data in there somehow, don't you?
Jun
25
answered Wolframalpha find Fourier series
Jun
25
comment Integrate $\dfrac{\tan{3x}}{\cos{3x}}\mathrm{d}x$
No, the integrand simplifies to $\sin(3x)/\cos^2(3x)$. Now use $u$-subs.
Jun
18
reviewed Approve suggested edit on Application of Weierstrass theorem
Jun
18
revised Does $\sum_{j = 1}^{\infty} \sqrt{\frac{j!}{j^j}}$ converge?
added 122 characters in body
Jun
17
comment If a function has a inverse that is well defined is it a bijection
Your function is certainly a bijection between $X$ and $\text{range}(f)$. It will be a bijection between $X$ and $Y$ only if $f$ is surjective, i.e. $\text{range}(f)=Y$.
Jun
16
comment Spectral radius and Dominant Eigenvalue
@Ranade Correct - such a matrix does not have a dominant eigenvalue.
Jun
16
comment Spectral radius and Dominant Eigenvalue
@user1551 Maybe - Every time I've seen the term 'dominant eigenvalue', it's uniqueness is essential. The power method is a classic example. More to the point, the uniqueness is an essential part of the answer as stated.
Jun
16
comment Spectral radius and Dominant Eigenvalue
@lavkush No problem! I was typing up an answer when yours came through. You hit the crux so I just added some context.
Jun
16
revised Spectral radius and Dominant Eigenvalue
added 803 characters in body
Jun
16
comment Spectral radius and Dominant Eigenvalue
@user1551 False
Jun
15
comment What level of rigour is expected in Real Analysis?
@DanielFischer Thanks!
Jun
15
answered What level of rigour is expected in Real Analysis?
Jun
15
comment What level of rigour is expected in Real Analysis?
I would expect an undergraduate student in first semester real analysis to state precisely why $-A$ is bounded above.
Jun
13
comment Strange things on WolframAlpha: derivation, modulo and doubling result
@EricTowers Like all discrete functions in Mathematica, there is no symbolic derivative for Mod. When asked to compute a numerical value of derivative for such a function, Mathematica falls back to numerical estimates. The "galloping values" arise from a finer discretization used for increased precision.
Jun
9
comment Sturm-Louiville Problem
If you found eigenvalues, then you probably found eigenfunctions at the same time. With that information, you can simply check to see if your eigenvalue/eigenfunction pairs work. If not, you can remove the word "apparently" from your question. :)
Jun
9
answered Is there a reason that sine substitution is preferred to cosine substitution?
Jun
9
comment Solve an equation for a particular variable using Wolfram Alpha
This is not a particularly good question but it is certainly not off topic, as claimed by the close voters. In fact, the use of mathematical software tools is explicitly listed as on topic in the faq and there is a wolfram-alpha tag. Use of the WolframAlpha website is explicitly off-topic on the Mathematica SE, however.