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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.


7h
comment What do Root[], #, & mean in Wolfram Alpha?
@NotNotLogical The question is about WolframAlpha and there's no reason to think that the OP knows Mathematica at all.
Apr
17
comment Help me integrate this function using Simpson's rule
The question is about Simpson's rule and Wolfram|Alpha can do computations with Simpson's rule directly.
Apr
16
comment Primitive $r/(1+r^2)$ without abs()
By default Mathematica and W|A work with complex functions. Now, $\log(z)$ is differentiable on the complex plane, except on the negative real axis where it has a branch cut. $\log(|z|)$, by contrast is nowhere differentiable as a complex plane. So, to assert that $\int(1/z)dz=\log(z)$ in this context is simply incorrect.
Apr
15
comment radius of convergence of half iterate of sinh(z)?
This is guaranteed to happen in the neighborhood of a neutral fixed point: see the Fatou petal theorem.
Mar
26
comment Should I use the ratio test to determine convergence for $\sum_{k = 1}^{\infty}{1 \over k\left[1 + \ln^{2}\left(k\right)\right]}$?
Give the integral test a try.
Mar
25
comment Intuition behind chain rule
math.stackexchange.com/questions/62614/chain-rule-intuition
Mar
23
comment parametrize surface region
Almost. The set is two dimensional and requires two input variables, specified by $u$ and $v$ by the OP.
Mar
21
comment Why does Fixed Point Iteration work?
Oh, I guess I misunderstood the word "requires". My bad!!
Mar
21
comment Why does Fixed Point Iteration work?
You said that the iterative technique for finding fixed points requires that the function be contractive. I'm saying that's not necessarily true. I only happen to know this since I've been studying the iteration of the Takagi function recently. It turns out, that for almost every initial seed, the orbit converges to the fixed point 2/3. So, in this case, we might say that the technique works in the absence of a contraction condition. On the other hand, your comment is certainly apropos in the differentiable case. +1!
Mar
21
comment Why does Fixed Point Iteration work?
Is this really true? If your contraction condition is satisfied, then we can expect convergence to a fixed point. What if the function mapping a closed interval to itself is nowhere continuous but differentiable? We certainly expect a fixed point.
Mar
13
comment How can I use math to fill out my NCAA tournament bracket?
@Arkamis Thanks for the input but, again, the question is not at all about the NCAA ranking system. It's about the mathematics of such systems in general. Most importantly, it's just for fun. Interestingly, though, the scheme I describe below, and which is certainly opinion free, has Duke ranked above Virginia. :)
Mar
13
comment How can I use math to fill out my NCAA tournament bracket?
@Arkamis The system? Or all such systems?
Mar
13
comment How can I use math to fill out my NCAA tournament bracket?
@Arkamis You are very wrong! :)
Mar
13
comment How can I use math to fill out my NCAA tournament bracket?
@vadim123 Of course, that's close since the committee that seeds the tournament considers exactly the things that a ranking system would consider. Thus, a winning bracket is exceedingly unlikely, given the well known phenomenon of upsets. Ultimately, the question concerns the mathematics behind such a ranking system.
Mar
13
comment Why do we want the Periodic Points to be dense for a Chaotic Map?
I think your interpretation of my comment is correct, at least in part. It's definitely multifaceted, though. A major "discovery" of chaos is that seemingly random phenomena can have a relatively simple origin and have hidden patterns. In this case, the "hidden patterns" are the periodic orbits. They tend to be mostly repulsive so they're hard to find and, in that sense, hidden.
Mar
13
comment Why do we want the Periodic Points to be dense for a Chaotic Map?
Denseness of the periodic points implies an underlying structure. If, in addition, there's a dense orbit (topological mixing) we can say that every open set of the space contains points with very different behavior.
Mar
11
comment I don't like Wolfram Alpha's evaluation of an integral
FWIW, Your answer can be derived in Mathematica using Simplify[Integrate[Abs[Sin[t]], {t,0,x}], Assumptions -> x>0], but this takes more time than WA typically allows. The actual Alpha result in a slightly different form can be derived via Integrate[Abs[Sin[t]], t, Assumptions -> Element[t,Reals]].
Mar
10
comment Newton's method for roots of multiplicity
Well, in this case $g(x)=x$ and the corresponding Newton's method iteration function is $n(x)=0$ - i.e., you get to the exact root in one step from any starting value. :)
Mar
10
comment Newton's method for roots of multiplicity
Just write down the formula $n(x)=x-f(x)/f'(x)$ in the case $f(x)=g(x)^2$ and compare to what you get when you write down $x-g(x)/g'(x)$ directly. You should find that you are adjusting your approximation in the former case by only half the amount that you do in the latter.
Mar
10
comment Why does $\dfrac{1}{1+x^2}=1-x^2+x^4-x^6+x^8\dots$?
Look up the geometric series and substitute $x \rightarrow -x^2$.