148,525 reputation
593245
bio website math.ubc.ca/~israel
location Richmond, Canada
age
visits member for 3 years, 10 months
seen 5 hours ago

I'm an Emeritus Associate Professor of Mathematics at University of British Columbia and an Optimization Algorithms Researcher at D-Wave Systems in Burnaby BC


Jan
20
answered Convexity of a subset is convex?
Jan
20
answered Find expectation of conditional probability
Jan
20
answered A complex Analysis proof
Jan
20
answered Find Planar Graph fromVertices and Faces
Jan
20
awarded  Nice Answer
Jan
20
answered Write$\frac{\sin(nx)}{\sin(x)}$ as polynomial in $\sin^2(x)$
Jan
20
comment Why do transcendental numbers exist?
Why does anything exist?
Jan
19
answered complete DAGs extends every non-complete DAG over the same vertex set
Jan
19
comment Elementary Proof that $x^x \geq x!$
It's not true for real numbers (where you interpret $x!$ as $\Gamma(x+1)$). For $0 < x < 1$, $x^x < \Gamma(x+1)$.
Jan
19
comment Explicit form for $\left(e^{-x^2}\left(\frac{d^n}{dx^n}e^{x^2}\right)\right)^2$
If $P_n(x) = \sum_{i=0}^n a_i x^i$, then $P_n(x)^2 = \sum_{i=0}^{2n} b_i x^i$ where $b_i = \sum_{j= \max(0,i-n)}^{\min{n,i}} a_j a_{i-j}$. Is that what you're looking for?
Jan
19
answered Explicit form for $\left(e^{-x^2}\left(\frac{d^n}{dx^n}e^{x^2}\right)\right)^2$
Jan
19
revised Integers Positioned Around a Circle
added 841 characters in body
Jan
19
answered Integers Positioned Around a Circle
Jan
19
answered Determining at what points multiple variable functions are continuous
Jan
19
comment Series does not converge
... where $\mathbb H$ and $\Lambda$ are ...?
Jan
19
answered Is it possible to prove dot product by the law of cosines?
Jan
19
comment How does a geometric distribution converge to an exponential distribution?
Since $0 \le x/p - \lfloor x/p \rfloor \le 1$, $(1-p)^{\lfloor x/p \rfloor - x/p} \to 1$, while $\ln \left((1-p)^{x/p}\right) = x \dfrac{\ln(1-p)}{p} \to -x$ by definition of derivative of $\ln(x)$ at $x=1$.
Jan
19
revised How does a geometric distribution converge to an exponential distribution?
edited body
Jan
19
comment Deterministic seeded shuffle
Depending on interpretation, that criterion is either too subjective or impossible.
Jan
19
comment Prove $\int_{-\pi}^{\pi}\sin \sin x \,dx=0$ without using the fact that $\sin(x)$ is odd.
Why? It's a perfectly good substitution.