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visits member for 2 years, 7 months
seen 13 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
awarded  Scholar
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?