154 reputation
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location Amherst, MA
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visits member for 1 year, 10 months
seen Apr 8 at 15:28

I'm an about-to-retire mathematics professor who's used numerous programming languages over the years, including FORTRAN, Pascal, and APL. I've dabbled a bit with Java. My current programming interests are in Mathematica and J (the jsoftware.com free product).


Apr
8
comment How can I prove this trigonometric statement true?
The phrase "presumes one already knows the identity to be proved" means you have already an equality (which may or may not be true and whose proof is being requested); for that the method of multiplying both sides by the same quantity is perfectly legitimate. But it's mathematically more meaningful just to have the expression on one of the two sides -- NOT an equality -- and then to perform operations upon that expression so as to obtain the expression on the other side of the equation.
Apr
7
comment How can I prove this trigonometric statement true?
But this allegedly "simplest" solution presumes one already knows the identity to be proved. Whereas the solution by @lab bhattacharjee is a direct calculation that starts with the left-hand side and arrives at the right-hand side.
Mar
25
comment Solving a simple differential equation
Please show what you tried already. And it would probably help if you showed what $rho$ is.
Mar
22
comment Series expansion of a complex function
Not sure what you mean by "the general case": how expand around an arbitrary point for this one particular function, or how to treat any rational function's expansion, or something even more general? In any case, you need to know whether the region includes a singularity, especially a pole, which would make it like the situation of expanding around $z = 1$; if not, then you want a Taylor series around some point in the region. Any standard book about complex analysis will help with these things.
Mar
22
awarded  Teacher
Mar
21
comment Series expansion of a complex function
For $|z| < 1$, you'll need to expand around $z = 0$, not $z = 1$. And from the code I provided, I think you can see how to express that in Mathematica.
Mar
21
answered Series expansion of a complex function
Jan
4
comment Solving: How to find an inverse function for this function?
Was the question a Mathematica question or just a mathematics question? If the latter: rewrite equation as $ln(-1+\sqrt{x}) = y-2$, then take the exponential of both sides, etc. (If the function is intended to apply just to reals, as noted you must restrict x-domain and then correspondingly restrict the y-domain of the inverse function.) Whether that's what Mathematica does with InverseFunction is probably known only to the developers.
May
19
comment In Grassmann algebra a la Browne, why are vectors dependent if their wedge product vanishes?
Yeah, underdetermined seems to be the case.
May
19
comment In Grassmann algebra a la Browne, why are vectors dependent if their wedge product vanishes?
But that property of determinants is not part of Browne's axioms. Note that he doesn't use the more familiar approach of defining exterior powers in terms of tensor powers, etc., but instead is trying to lay down a set of axioms for wedge product.
May
19
comment In Grassmann algebra a la Browne, why are vectors dependent if their wedge product vanishes?
@TedShifrin: No, unfortunately, what you guess in included in the axioms in Browne's treatment is not in fact there. Unless there's something much more subtle, I think what's missing is one or another version of what's called Axiom 4 in William Schulz's document cefns.nau.edu/~schulz/grassmann.pdf (pages 50-51).
May
18
awarded  Student
May
18
asked In Grassmann algebra a la Browne, why are vectors dependent if their wedge product vanishes?
May
15
awarded  Commentator
May
15
comment Solve $(x^2 + 5)^2 - 15(x^2 + 5) + 54 = 0$
I wasn't objecting to the procedure, but to the manifest logic of its description. As I said, a write-up indicating that the answer you obtain consists of roots and only roots, you need "if and only if" connectives, not "if ... then" connectives. What you have (thrice) is the latter.
May
15
comment Solve $(x^2 + 5)^2 - 15(x^2 + 5) + 54 = 0$
This answer has one-way implications. Presumably they should be two-way implications, i.e., logical equivalences; otherwise, you could be obtaining extraneous roots or numbers that are not roots at all.
Mar
12
comment Evaluating $f(z)=\sqrt{z^2-1}$, given the branch I am on.
There's also the issue of what branch of log is being used in your symbolic evaluation.
Jan
9
comment Is the term true? $\frac{\theta}{\theta - 1 } = \frac{1} {\theta-1} + 1$
It's not true for theta = 1.
Oct
5
comment What might be meant by “closed form explicit analytical solution” to an ordinary differential equation?
Yes, "closed-form" generally implies only a finite number of operations, but the issue remains as to what the functions operated upon are. Thus "closed-form" is mathematically ambiguous; "elementary" is not.
Oct
4
comment What might be meant by “closed form explicit analytical solution” to an ordinary differential equation?
The never actually said "elementary", just "analytic", "closed form", and "useful".