66,652 reputation
23084
bio website
location Albany, CA
age
visits member for 2 years, 10 months
seen 5 hours ago

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 is the smallest number composed of the first two primes that would allow me to have watch on RTÉ the slightly contradictory small step for man and giant leap for mankind.

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.


6h
comment Little o(h) limit about h=0
I don't know what you mean, the definition only involves $h \to 0$? It is exactly equivalent to $f(0) =0$ and $f'(0) = 0$.
6h
comment Little o(h) limit about h=0
I understand. I don't understand what you are asking.
6h
comment Absolute square in deriving Fourier transform variance
I'm not really sure what you are trying to do.
6h
comment Little o(h) limit about h=0
It is a definition - I don't understand what you mean by explanation? You could interpret it as saying $f(0) = 0$ and $f'(0) = 0$.
6h
comment Is the Law of Large Numbers empirically proven?
I presume you are referring to the Diaconis, Holmes & Montgomery result. Even if you follow their line of argument (which is amusing) you need to be careful about their conclusion which is that 'Any coin that is tossed vigorously and high, and caught in midair has about a 51 % chance of landing with the same face up that it started with.' It does not conclude that tails are more probable, in fact their analysis doesn't distinguish either side (other than labeling).
7h
comment Absolute square in deriving Fourier transform variance
I am guessing you are looking for Parseval's theorem? You went from the product of two integrals to a single integral above without any justification, the $(x,y)$ variables in each integral are different.
10h
comment What is the mathematically operation referred to where you put a matrix of lower dimension into a matrix of higher dimension
Embedding seems good to me. You might want to wait for some other comments that might have other suggestions.
10h
comment What is the mathematically operation referred to where you put a matrix of lower dimension into a matrix of higher dimension
Its called putting a smaller matrix into a larger one. Seriously, I don't think there is a specific name for this operation.
20h
comment Partial fractions and trig functions
I think the 'all' is a bit too broad. The above works because $\cos^2 x + \sin^2 x = 1$, so for a general approach you would probably need more constraints.
20h
comment Partial fractions and trig functions
'All' is a bit broad. What class of issues are you trying to solve?
20h
comment Partial fractions and trig functions
Try ${\sin x \over \cos x} + {\cos x \over \sin x}$.
20h
comment How to use matlab for plotting functions that contain summations?
@A.Donda: Thanks!
20h
comment How to use matlab for plotting functions that contain summations?
@A.Donda: Thanks. I think it is a little harder to read for a toy example. How did you highlight the code in your comment?
20h
comment Is the Law of Large Numbers empirically proven?
@afuna: You wrote that 'It would be better stated as...', I was just pointing out that this is a weaker statement that the statement than the Wiki statement that preceded it.
20h
comment Is the Law of Large Numbers empirically proven?
When you make any binary valued observation, if the underlying process is iid. (or a reasonable approximation thereof) then the law of large numbers & central limit theorem apply. So, your question is, why do many measurements of aspects of the universe seem to iid? I don't know the answer, but would suppose that independence arises out of a lack of apparent 'communication' (for example, the coin has no state which it carries from one toss to the next) and identical arises from symmetry (why would a head be preferred over a tail?), or similar dynamics.
1d
comment Is the Law of Large Numbers empirically proven?
This is the weak law. The Wikipedia describes the strong law.
1d
comment Determine the set of points that satisfy $Re\left(\frac{z-z_1}{z-z_2}\right) =0$ for $z_1,z_2$ are fixed
If you treat $a,b$ in my comment above as pairs then the condition is equivalent to $\operatorname{re}a \operatorname{re}b +\operatorname{im}a \operatorname{im}b =0$ which shows them as orthogonal in $\mathbb{R}^2$. Draw a picture and use Thales' theorem.
1d
comment Is it possible to have simultaneously $\int_I(f(x)-\text{sin} x)^2 dx\leq \frac{4}{9}$ and $\int_I(f(x)-\text{cos} x)^2 dx\leq \frac{1}{9}$?
I am truly curious as to why this was downvoted?
1d
comment How to use matlab for plotting functions that contain summations?
@A.Donda: I am only familiar with using sum for adding the elements of an array, what were you thinking? (Aside: How did you highlight sum?)
1d
comment Closed vector space and a subspace of a vector space
I don't understand the question. How do you define closed, open and $\oplus$?