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visits | member for | 2 years, 8 months |
seen | 11 hours ago | |
stats | profile views | 613 |
Oct 14 |
awarded | Good Question |
Oct 14 |
accepted | What did Rolle prove when he proved Rolle's theorem? |
Oct 14 |
awarded | Popular Question |
Oct 14 |
awarded | Nice Question |
Oct 14 |
revised |
What did Rolle prove when he proved Rolle's theorem?
deleted 7 characters in body |
Oct 14 |
asked | What did Rolle prove when he proved Rolle's theorem? |
Oct 6 |
comment |
The distribution of the shortest path through $n$ points
Maybe I'm just dense, but I don't understand what you mean by the shortest path through a set of points. |
Oct 4 |
awarded | Popular Question |
Oct 3 |
comment |
Why do roots of polynomials tend to have absolute value close to 1?
Here's a different way of stating the heuristic. Say the coefficients $a_i$ are IID with mean 1 and variance $\sigma^2$. Then for fixed $z$, $P(z)$ has a (complex) variance given by a geometric sum. For large $n$ and $|z|\gtrsim1$ this variance has real and imaginary parts that grow approximately like $|z|^{2n}$, and therefore the distribution gets too wide, and the probability of $|P|<\epsilon$ falls like $|z|^{-2n}$. This drops off so fast that the prob. of having $|z|$ significantly greater than 1 is small. But the problem is isomorphic under circle inversion, so the same holds for $|z|<1$. |
Oct 2 |
comment |
Why have mathematicians used differential equations to model nature instead of difference equations
I want to know what units the $10^{-10}$ is expressed in. |
Oct 1 |
comment |
Has philosophy ever clarified mathematics?
It's hard to imagine why ultrafinitism would exist except that its originators were philosophically allergic to infinities. Similar deal for nonaristotelian logic. |
Sep 30 |
comment |
Why have mathematicians used differential equations to model nature instead of difference equations
Furthermore, difference equations don't require complicated epsilon-delta definitions. Nor do differential equations require epsilon-delta definitions. Newton and Leibniz solved differential equations about 150 years before epsilontics came along. |
Sep 22 |
awarded | Good Question |
Sep 22 |
awarded | Popular Question |
Sep 21 |
accepted | Did Leibniz really get the Leibniz rule wrong? |
Sep 21 |
comment |
Did Leibniz really get the Leibniz rule wrong?
KConrad's comment says that on Nov 11, 1675, "He asked himself if (uv)′=u′v′ and quickly dismissed it by the example you gave: u=v=x." Is that correct? Your answer makes it sound like the dates are all much fuzzier, perhaps by years, and we have no way of knowing whether it took Leibniz five minutes or a year to discard the hypothesis. Am I correct in understanding that this was all material from an unpublished personal notebook? |
Sep 21 |
awarded | Nice Question |
Sep 21 |
asked | Did Leibniz really get the Leibniz rule wrong? |
Sep 21 |
comment |
Did differential geometry undergo a notation change?
related: mathoverflow.net/a/175956/21349 |
Sep 6 |
awarded | Curious |