Cameron Williams

United States

I am a postdoctoral fellow at the University of Houston studying analysis. My interests are coupled supersymmetry (https://arxiv.org/abs/1701.02767), abstract harmonic analysis, and integral transform theory.

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Fiancée has a position lined up, but none of the universities in the area are hiring. What else can I do to get an academic position in the area?

mathematics job-search two-body-problem asked Dec 28 '16 at 22:17

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32 votes

Is the “product rule” for the boundary of a Cartesian product of closed sets an accident?

general-topology soft-question asked Sep 21 '14 at 0:36

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21 votes

Why study operator spaces?

functional-analysis operator-algebras operator-spaces asked Sep 26 '13 at 17:38

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18 votes

Proving facts about groups with representation theory.

group-theory representation-theory asked Jan 31 '14 at 4:36

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12 votes

The spectrum of a product of operators

functional-analysis operator-theory spectral-theory asked Oct 14 '14 at 0:02

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12 votes

Extending the domains of densely defined bounded integral transforms on $L^2(\Bbb R)$

functional-analysis integral-transforms asked Sep 4 '15 at 3:31

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11 votes

What plays the role of the identity for the generalized convolution associated to the Fourier-Bessel transform?

functional-analysis distribution-theory convolution integral-transforms asked Jul 21 '15 at 20:00

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11 votes

Why do we first introduce the open set definition for continuity instead of the neighborhood definition?

general-topology math-history teaching philosophy asked Dec 16 '14 at 3:47

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11 votes

When is a binomial coefficient a factorial, i.e. when is $\binom{m}{j} = n!$ for some $n,m,j$?

number-theory binomial-coefficients factorial asked Jun 11 '15 at 20:58

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9 votes

$\exp(A+B)$ and Baker-Campbell-Hausdorff

operator-theory asked Jan 14 '14 at 21:50

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Top Answers

Am I just not smart enough?

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Why are mathematician so interested to find theory for solving partial differential equations but not for integral equation?

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Is it common for an undergraduate thesis in pure mathematics to prove something new?

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Why is it not true that $\int_0^{\pi} \sin(x)\; dx = 0$?

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How do I tell my supervisor his idea is incorrect?

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Is this solution mathematically “legal”?

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Why is zero the only infinitesimal real number?

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$\frac1a+\frac1b+\frac1c=0 \implies a^2+b^2+c^2=(a+b+c)^2$?

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Why is the derivative of a vector orthogonal to the vector itself?

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Upper Bound vs. Least Upper Bound

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How good do I actually have to be to get into a top graduate program from an average undergraduate program?

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What is the dot product and why do we need it?

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What is the relation between a Banach space and a Hilbert space?

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How to prove $\exp(x)/(\exp(x)+1)^2$ is even?

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Why formulate continuity in terms of pre-images instead of image?

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$A^{-1}$ has integer entries if and only if the ${\rm det}\ (A) =\pm 1$

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Determine if the following is surjective

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Find $\lim\frac{1}{\sqrt{n}}\left(\frac{1}{\sqrt{1}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+\ldots+\frac{1}{\sqrt{2n-1}+\sqrt{2n+1}}\right)$

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Why do you need to use the chain rule in differentiation of ln?

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Why it's true? $\arcsin(x) +\arccos(x) = \frac{\pi}{2}$

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Importance of groups $(\mathbb R,+)$ and $(\mathbb Z,+)$ for Fourier series

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Teaching the History of Mathematics in High School

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Solve $2^{x+5} - 2^{x+2} = 7$

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Intuition about the semidirect product of groups

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Must all Lebesgue integrable functions really be invertible?

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Integral $\int_0^1 \log \left(\Gamma\left(x+\alpha\right)\right)\,{\rm d}x=\frac{\log\left( 2 \pi\right)}{2}+\alpha \log\left(\alpha\right) -\alpha$

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Solve equation with $x$ in the exponents

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Show $\sum_{i=0}^\infty {k+i \choose k}a^i=\frac1{(1-a)^{k+1}}.$

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If $x>0$ and $x^a=x^b$ can one assume that $a=b$?

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25th derivation of $\cos{x^3}$

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Cameron Williams

Fiancée has a position lined up, but none of the universities in the area are hiring. What else can I do to get an academic position in the area?

Is the “product rule” for the boundary of a Cartesian product of closed sets an accident?

Why study operator spaces?

Proving facts about groups with representation theory.

The spectrum of a product of operators

Extending the domains of densely defined bounded integral transforms on $L^2(\Bbb R)$

What plays the role of the identity for the generalized convolution associated to the Fourier-Bessel transform?

Why do we first introduce the open set definition for continuity instead of the neighborhood definition?

When is a binomial coefficient a factorial, i.e. when is $\binom{m}{j} = n!$ for some $n,m,j$?

$\exp(A+B)$ and Baker-Campbell-Hausdorff