# Gerald Edgar

people.math.osu.edu/edgar.2

 8h comment Why do we call a linear mapping "linear mapping"?I think "seems to be" answers need references. 17h comment Hints on solving $y''-\frac{x}{x-1}y'+\frac{1}{x-1}y=0$Laplace has formulas for multiplying by the independent variable. They involve derivatives, but sometimes the new differential equation is easier than the original one. 17h comment Gamma function still hard for meIt seems your evaluation involves $(x+1)!$ where $x$ may not be an integer. That is where the gamma function is hiding. 1d awarded nt.number-theory 1d comment What conditions imply that a function over $\mathbb{Z}$ is a polynomial?Only defined on the positive integers? Take Anthony's suggestion, and convert to this: take the difference finitely many times, and get identically zero. The difference $\Delta F$ of $F$ is: $\Delta F(n) = F(n+1)-F(n)$. 1d comment Solve integrals using residue theorem?If $z = e^{i\theta}$, then $f(z)dz = d\theta/(2+\cos\theta)$, maybe with a factor $i$ in there. 1d comment Source for Hilbert's famous quote "Mathematics in Göttingen? There really is none anymore"References can be valid, even if they are not "free online". 1d comment Should I appear in a test, if I have not completely prepared for it?You should at least inform (and possibly also get advice from) the instructor before you merely fail to show up. 1d comment What action is appropriate when co-authors admit that the first author committed plagiarism?It seems the plagiarism was the "introduction and discussion" ... But maybe the bulk of the paper describes clinical trials carried out or something. So maybe merely adding appropriate references will be enough. 1d comment Hotkeys (COMMAND-V ....) don't honor Dvorak layoutThis is the way the basic short-cuts were originally designed. They are not ZXCV, but instead they are the first 4 keys from the left on the bottom row. This "first four keys" rule is still the default for other keyboard layouts. This also explains the strange choice of V for paste and Z for undo. 1d comment $L_{\infty}$ normAnother way to sort out the question would be to find a simple case where your two candidates are different, and do the computation in that case. Say $n=2$ and the functions are constants. 1d comment Is this operator $A = \pmatrix{1&1\\0&1}$ self-adjoint?I think it is safe to say that "self-adjoint" with no mention of a quadratic form means the usual quadratic form. And when we ask something about an "operator" but it is shown as a matrix, we assume it is asked about the linear transformation associated to that matrix in the usual way. And when it is not specified what field the entries are in, we assume the reals. And so on. 1d comment If $a+b+c+d=1$ then why is the maximum value of $(a+1)(b+1)(c+1)(d+1)$ is ${\left(\frac{5}{4}\right)}^4$?"Symmetry suggests that..." But of course you need more computation, as you have given. Note that also "symmetry suggests that" the minimum occurs when $u=v=w=x$. 2d comment Why is $\sum_{k=1}^{\infty}\mathbb{E}[\mathbb{1}(T=k)]=\sum_{k=0}^{\infty} k \mathbb{P}[T=k]$user should reveal the secret source of this misinformation! 2d comment Did clergymen contribute more to science than scientists in the 19th century?Can we really say that Thomas Bayes was not a mathematician? He published a number of pamphlets on mathematics (as well as pamphlets on religious topics). True, he was as a Presbyterian pastor, but in the early 1700s there were very few "professional" mathematicians. .... so maybe instead of saying "clergymen contributed more than scientists" we should say "most scientists were clergymen". 2d comment Was the world life expectancy only 30 years at 1900?There is another recent thread here, claiming half of all children in rural Africa die before age 10, mostly from malaria. 2d comment Not understanding the results of standard deviationMy guess: A1 is not a single measurement; but instead A1 was done by making lots of measurements (a "random sample"), and then these measurements were used to estimate that 15.4 was the mean and 1.91 was the standard deviation for A1. Jun 28 comment Is it prohibited to marry more than one woman in US?I guess we are talking about polygamy, here is a map. womanstats.org/substatics/… Jun 28 comment Is it natural for self-learners to forget most proofs of the theorems they learn?Some self-learners get impatient, and don't go back and review (because it's "boring"). Learners in courses, which have homework and tests, usually do go back and review. For some people, this repeated review helps in remembering. Who knows: maybe you are one of those who needs this external encouragement to do the boring parts of learning. Jun 28 comment Universal instantiation another question why couldn't?I think you misunderstand "universal instantiation". For that, you need one $\forall$ applying to the whole thing.