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I am a PhD student in Physics that studies math as a hobby.

My current mathematical interests involve p-adic and adelic numbers and in particular their applications to alternative formulations of quantum mechanics that do not have a "preferred" number system.

My favorite mathematical proof is Euler's solution of the Basel problem using the infinite product representation of the sinc function.


1d
answered Find a matrix transformation mapping $\{(1,1,1),(0,1,0),(1,0,2)\}$ to $\{(1,1,1),(0,1,0),(1,0,1)\}$
2d
reviewed Approve suggested edit on Discrete Mathematics Helps
2d
reviewed Reject suggested edit on Normal distribution problem - “6 times the standard deviation”
Oct
27
comment When does sum to infinity starts getting negative?
The sum you are referring to has a very technical way of interpreting that sum via an "analytic continuation". When it comes to infinite sums there are different conventions for interpreting them which give different results. Your intuition isn't wrong you're just using a different convention for how to interpret the sum.
Oct
26
comment When is it insufficient to treat the Dirac delta as an evaluation map?
-mathematical discrepancy. If your interested in a rigorous treatment of the sequence definition then I can recommend M.J. Lighthill's book "An introduction to Fourier analysis and generalised functions"; its only 75 pages and very direct.
Oct
26
comment When is it insufficient to treat the Dirac delta as an evaluation map?
I'm not sure how far the theory of generalised functions has been developed. I know that in elementary situations like this one it is a good minimalist rigorous theory of delta functions. There may be contexts in which it hasn't even been developed since the theory of distributions is already there. The point I'm making here is that when they are equivalent there may be reasons of personal preference to use one over another since different formalisms can provide different insights. Obviously I can't make a sweeping statement that one is always better than another unless there is an objective-
Oct
26
comment When is it insufficient to treat the Dirac delta as an evaluation map?
I don't disagree that thinking of the delta function as an evaluation map is sufficient. I think that having multiple (rigorous) interpretations of the delta function can be helpful. I think this is similar to the idea of a tangent space in differential geometry, I know at least 4 equivalent definitions of the tangent space of a point $p$ in a manifold, but they all evoke completely different images of whats going on (for me at least).
Oct
26
revised When is it insufficient to treat the Dirac delta as an evaluation map?
added 768 characters in body
Oct
26
comment When is it insufficient to treat the Dirac delta as an evaluation map?
@MarianoSuárez-Alvarez, there is an elementary treatment of the delta function promoted by M.J.Lighthill. In this context the delta function is an example of a "generalised function" which are equivalence classes of sequences of "Good Functions".
Oct
26
answered When is it insufficient to treat the Dirac delta as an evaluation map?
Oct
26
comment Why is $e^{-x^2}$ such a big deal?
True, the second sentence was meant to refer to the importance of the Delta Function rather than the particular sequence. Bad writing on my part. I do maintain that many proofs of the Delta's properties are more easily executed using a sequence of Guassians than many other representations.
Oct
26
revised Why is $e^{-x^2}$ such a big deal?
added 1 character in body
Oct
26
answered Why is $e^{-x^2}$ such a big deal?
Oct
25
answered Can any of these polynomials be a square?
Oct
25
comment Finding $\sum \frac{1}{n^2+7n+9}$
There is an approach to summing rational series which uses the polygamma functions that is pretty cool. You can find it in Abromowitz and Stegun page 264. This is a link to an online version of the book nr.com/aands .
Oct
24
awarded  Quorum
Oct
24
comment For what values of $x$ is the assignment $y=1-\cos x$ problematic, and why?
@user3390252, for very small angles the numerical value of $\sin(\theta)$ and $\theta$ are very close to being the same. Similarly for $\cos(\theta)$ and $1-\theta^2/2$ (just try it on your calculator for angles of about a degree or less). These are called small angle identities and can be understood to come from the Taylor series of the sine and cosine functions. These identities can be very useful in cases such as your own because we can then see that $1-\cos(x) \approx 1-(1-x^2/2) = x^2/2$ if $x$ is close to $0$.
Oct
24
comment Radian, an arbitrary unit too?
I need to make a figure to properly explain whats going on. I'll update the answer Saturday.
Oct
24
answered Recommendation for free graph plotter that can produce beautiful graphs
Oct
23
answered eigenvectors, linear systems