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location Albany, CA
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visits member for 2 years, 5 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.


9h
answered Finding all solutions to the equation $|||||x|-1|-1|-1|-1|=0$
1d
comment If $p(z)$ is an injective polynomial $\Longrightarrow$ $p(z)=az+b$
:-)! ${}{}{}{}{}$
1d
comment If $p(z)$ is an injective polynomial $\Longrightarrow$ $p(z)=az+b$
+1: Very nice! ${}{}$
1d
answered If $p(z)$ is an injective polynomial $\Longrightarrow$ $p(z)=az+b$
1d
comment Show A and B have a common eigenvalue
If $Cv \neq 0$ for all $v$ then there would be a much simpler proof.
1d
comment In how many ways can we multiply three numbers?
You have to do at least some work. How hard is it to list the permutations of $a,b,c$????
1d
comment In how many ways can we multiply three numbers?
Is this a serious question?
1d
comment The unit vector in the direction of u
What is the length of $u$ and what is the length of $\lambda u$, where $\lambda$ is a scalar? What value(s) must $\lambda$ have so that $\lambda u$ has unit length?
1d
comment How to find the number of revolutions?
The circumference of the wheel is $2 \pi 50$ cm.
1d
comment Elements in a convex set, regarding distance
Let $\phi(t) = y+t(x-y)$, with $t \in (0,1)$. Then $|x-y|=|x-\phi(t)|+|\phi(t)-y|$.
1d
comment Check correct delta in eps-delta proof
I would be more inclined to write $\epsilon { 5 \over 5+ \epsilon} < \epsilon$ as it seems more clear to me. The above is correct, as long as you have established $|x+2| < 5$.
1d
answered Find $\lim\limits_{x \to \infty} \left(\sqrt{x^2+x+1} - \sqrt{x^2-x} \right)$
1d
answered Check correct delta in eps-delta proof
2d
revised Why $\sin(n\pi) = 0$ and $\cos(n\pi)=(-1^n)$?
mathjax
2d
comment Why $\sin(n\pi) = 0$ and $\cos(n\pi)=(-1^n)$?
The point on the unit circle at an anti-clockwise angle $\theta$ from the positive $x$-axis is $(\cos \theta, \sin \theta)$. Since $2 \pi $ corresponds to a complete rotation, half a rotation will correspond to switching sign of both $\cos$ and $\sin$ (since it corresponds to a reflection through the origin). Since $\theta=0$ corresponds to $(1,0)$ the result you desire follows...
2d
comment Partial derivatives of a piecewise defined function
It doesn't say that is is not defined. Set $x=y=0$ in the formula above and get 10. Now evaluate the other formula for $x=y=0$. It is also 10. Hence the first formula (which defines a smooth function) defines $f$ everywhere.
2d
comment Partial derivatives of a piecewise defined function
Well, from my previous comment, you have ${\partial f(x,y) \over \partial x} = 2x +2 $ and ${\partial f(x,y) \over \partial y} = 5$ everywhere. Can you finish from here?
2d
comment Determine stability of the fixed points of $\dot x=x-x^3$
Draw a picture! The state space is $\mathbb{R}$ so you can guess by drawing the function $f(x) = x-x^3$ and noting where it is zero, positive and negative...
2d
comment Partial derivatives of a piecewise defined function
Note that $f(x,y) = x^2+2x+5y+10$ everywhere not just for $(x,y) \neq 0$. I think this problem is testing if you are reading the question carefully...
2d
revised Common subdifferentials of convex function
edited tags