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location Albany, CA
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visits member for 2 years, 3 months
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If I see further than most, it is because I have stood on the toes of giants and they kicked me high into the air...

However, there is nothing to suggest that I see further than most.

I am (inasmuch as one 'is' an occupation) an engineer. My mathematical skills are rather pedestrian, with a rare insight every now and then. I have been lucky enough to sit in the same room with some famous mathematicians & engineers. My Erdős number is 5, which undoubtedly makes me as unique as an Irishman in a pub. And I have been spotted in The Pub from time to time.

In professional circumstances, my value add has usually been the injection of common sense and completion of grunt work when perspectives and energies are unfocused.

My current age divides the current year.

My real name is Joe Higgins. Apparently, my last name means 'of the Viking' in Irish.

My alma mater is University College, Cork in Ireland, and I had the additional privilege of obtaining my Phd. from the University of California at Berkeley under the enlightened tutelage of Lucien Polak.

I can be reached at joe dot higgins at gmail dot com.


1h
comment How to find the polar dual of $\{(x,y):y\geqslant x^2\}$ in $\Bbb R^2$?
If $b<0$, then if $y\ge x^2$, we have $by \le b x^2$. So, if we have $ax+bx^2 \le 1$, we automatically have $ax+by \le 1$ (as long as $y \ge x^2$).
3h
revised Local minimum and gradient
added 227 characters in body
3h
answered Local minimum and gradient
4h
comment Probability of 2 teams winning
The answer is a half...
4h
answered Probability of 2 teams winning
6h
comment Probability of 2 teams winning
You need to quantify the probabilities in some way. Are you assuming that all teams are equally good in some sense?
6h
comment Probability of 2 teams winning
It depends. If both teams have a very low probability of making it through the semis, then the chances of winning the final are very low.
7h
answered How do I know if I have imaginary numbers when using Newton Raphson Method?
8h
comment How do I know if I have imaginary numbers when using Newton Raphson Method?
Your question/concern is unclear. You need to elaborate what your issue is. Are you asking if you can apply Newton's method to complex equations (yes, you can) or are you asking if complex numbers can ever arise when solving real systems using Newton's method (no, you can't, for reasons that have been pointed out twice above)?
8h
comment How do I know if I have imaginary numbers when using Newton Raphson Method?
How is this different from math.stackexchange.com/q/861105/27978?
8h
comment How do I know if I have imaginary numbers when using Newton Raphson Method?
Give an example of what you are talking about.
8h
comment How do I know if I have imaginary numbers when using Newton Raphson Method?
How could you possibly 'face an imaginary number'? The update is of the form $x_{n+1} = x_n -\alpha_n d_n$ where $d_n$ is obtained from solving a linear system of equations.
9h
comment How to prove law of tangent using vector method
en.wikipedia.org/wiki/Law_of_tangents
9h
comment Convexity of trace for the product of two matrices
Nothing immediately obvious to me (other than restricting $X$ or $Y$ to b constant :-)).
9h
comment Dimensions of Singular Value Decomposition Matrices
They are equivalent in some sense, I prefer to use the version in which $D$ has the same dimensions as $A$.
9h
answered Find the value of the Logarithmic Expression
9h
answered Convexity of trace for the product of two matrices
18h
comment integral with pdf of a gaussian
Surely $\phi'(x) = -x \phi(x)$? Then $\int_a^b x \phi(x)dx = \phi(a)-\phi(b)$?
18h
comment Help with Borel sets
This had been answered before, but I am unable to find a link.
18h
answered Help with Borel sets