16,541 reputation
13480
bio website sites.google.com/a/unca.edu/…
location Asheville, NC
age
visits member for 2 years, 3 months
seen 2 hours ago

I've been a professor of mathematics at The University of North Carolina - Asheville since 1997. I've been using Mathematica since I started graduate school in mathematics at Ohio State in 1989. At that time, we used version 1.1 (as I recall) to teach calculus in our Calculus and Mathematica classes. I've used it pretty much continuously in my teaching and research since then.

In addition to my posts on SE, you can find some of my papers, teaching notebooks and other Mathematica based oddities strewn throughout my website.

In recent years, I've also worked as a part-time consultant to Wolfram Research focusing on development of mathematical content for WolframAlpha.


May
6
comment solving a cubic equation
I agree that it should probably be a comment but I couldn't help upvoting, as I think it's an interesting point. For specific irreducible cubics, you can often (always??) express the roots in this form using ComplexExpand. For example: ComplexExpand[Re[z /. Solve[z^3 - 3 z - 1 == 0, z]]]. In this case, the Re simply removes the imaginary parts, which we know to be zero anyway.
May
5
comment Confused about Unevaluated
I agree with this analysis. I guess this behavior of Unevaluated is exactly why we use it in a case like Length[Unevaluated[1+2+3]]. An even simpler example would be f[x_]=x^2; f[Unevaluated[2]].
May
5
comment Confused about Unevaluated
Now, I'm not claiming to fully understand the whole deal here (which is why I wrote a comment, rather than an answer). I'm simply stating that Table and Map have different evaluation procedures and that's what leads to this behavior. Also, functions like Unevaluated and attributes like HoldAll are intimately connected with these issues.
May
5
comment Confused about Unevaluated
Yes. Try your "two kinds of evaluate" with Unevaluated[1+1] as input vs Evaluate[Unevaluated[1+1]] as the input.
May
5
comment Confused about Unevaluated
I'm just saying that Table evaluates it's arguments in a non-standard way and (by implication) that Map does not. Thus, when the documentation says that Map "constructs a complete new expression and then evaluates it", it does so in the standard way. Thus, Map[Unevaluated,{1,2}] produces the same output as {Unevaluated[1],Unevaluated[2]}.
May
5
comment Confused about Unevaluated
It's just that Table evaluates it's arguments in a non-standard way. In particular, it Holds it's arguments, explicitly evaluates the second argument (the iterator), substitutes values obtained from the iterator into the first argument and then (importantly!) explicitly evaluates the first argument at those values.
Apr
30
comment Nest for large value of n
@SimonWoods I believe he's interested in a specific sequence of such k, the ratios of consecutive differences of which converges to Feigenbaum's constant.
Apr
29
comment Nest for large value of n
@thewanderer I assume that you mean when n>5, but note that for n=5, your polynomial has degree 2^2^5. and it's simply not feasible to solve this using simple techniques. You should look into some of the papers of Keith Briggs to learn his extrapolation techniques: keithbriggs.info
Apr
29
comment Nest for large value of n
@belisarius No, I don't think you can analytically find the attractive orbit in terms of k in a simple way. What I think J.M. is suggesting is extrapolate from when the bifurcations occur. In fact, the existence of the Feigenbaum constant is really an assertion that such an extrapolation works.
Apr
29
comment Nest for large value of n
@J.M. 3.8 - ish.
Apr
29
comment Nest for large value of n
@belisarius Try k=2.9 or 3.1 or 3.4. You happen to be choosing a value of k right at a bifurcation, where the convergence to the fixed point is absurdly slow. But, of course, the iteration need not always converge to a periodic orbit; that's the point behind chaos.
Apr
27
comment Mathematica does not understand (R^3)^(1/3) is the same as R
One other thing - Is Power discontinuous? Root definitely is, as you can tell by examining Plot[Root[a-12 #1+#1^5&,1],{a,-20,0}] but I think that Power is continuous. If I investigate things like Limit[x^(1/3),x->0,Direction->1], I get 0. You might be interested in this: goo.gl/IhDcm That deals with x^x, but x^(1/n) can be treated in a similar way.
Apr
27
comment Mathematica does not understand (R^3)^(1/3) is the same as R
@JacobAkkerboom No biggie - I probably deserve downvotes somewhere. Your vote is locked until the question is edited, at which point you can change it. But, honestly, I'm a bit confused about your objection. Doesn't the R=i example make it clear that this is a complex/real issue? Of course, your right about the definition thing; ultimately, this is just a choice of branch cut. At any rate, it hardly seems worth worrying about over a question that's been closed anyway!
Apr
27
comment How can this image (optical illusion) be created with Mathematica?
If that's the best you can do, then I guess I'll just have to vote for that. :)
Apr
27
comment Mathematica does not understand (R^3)^(1/3) is the same as R
@JacobAkkerboom Yes, Mathematica generally assumes that unspecified symbols represent complex quantities. However, certain mathematical functions work only with a proper subset of the complexes. Many number theoretic functions, such as EulerPhi work only with the integers, for example. The point behind my answer is that the new CubeRoot function assumes the input is real.
Apr
26
comment Mathematica does not understand (R^3)^(1/3) is the same as R
Ahh... that too.
Apr
26
comment Mathematica does not understand (R^3)^(1/3) is the same as R
And while I was typing my answer.
Apr
23
comment How to speed up the plot of NIntegrate?
@luyuwuli It should work whenever NDSolve works. My guess is that it is not quite a broadly applicable as the integrate technique, but it should be nearly so.
Apr
22
comment Solving Intervals
Here's a very similar question: mathematica.stackexchange.com/questions/11345/…
Apr
22
comment Why the difference?
Pretty much exactly the opposite of what I did - very cool!