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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37 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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24 votes

Proving facts about groups with representation theory.

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

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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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14 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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13 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

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

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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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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 the derivative of a vector orthogonal to the vector itself?

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

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Upper Bound vs. Least Upper Bound

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Why is zero the only infinitesimal real number?

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

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

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

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

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

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Do row operations change the column space of a matrix?

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Determine if the following is surjective

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Must all Lebesgue integrable functions really be invertible?

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Teaching the History of Mathematics in High School

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

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

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

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

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Convolution and multiplication of polynomials is the same?

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Intuition about the semidirect product of groups

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Is multiplication by zero clear for and understood by K-3 students?

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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?

Proving facts about groups with representation theory.

Why study operator spaces?

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

The spectrum of a product of operators

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

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

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

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