trying to be a mile wide AND a mile deep
Happy Boxing Day, everyone. We went through a phase in graduate school of writing poems and songs, usually based off existing ones. I think they’re worth preserving, though I do shake my head a bit when I read some of them. I’ve given credit (blame?) below, though I did leave them in their original first-name-only […]
Mathematical recreation is to be distinguished from recreational mathematics. I am just not entirely certain how. Astonishingly, the links below – labeled “unchecked since 2004” – all still work as of this writing. I had them in a section headed “math entertainment.” The Mathematical Quotation Server is perhaps not “entertainment” per se, and is definitely […]
Which of the following are vector spaces over the scalar field R of real numbers? A) U = (R x R, +U, *U) where (a1, a2) +U (b1, b2) = (a1 + 2b1, a2 + 3b2) and *U is the usual scalar multiplication B) V = (R x R, +V, *V) where (a1, a2) +V […]
In my third year of graduate school, after getting some positive response to my advice for prospective graduate students, I decided to write a second essay, advising current graduate students on staying happy and self-confident in grad school. As with the other, I don’t dare edit it at this remove, so here it is in […]
Parametrization is applied when an object is “really” of lower dimension than the space it lives in. Curves, whether they live in 2D or 3D, are really only one-dimensional. A surface, which might live in 3D (such as a sphere), is really only two-dimensional. The “really” is made rigorous by our ability to represent such […]
While I was a graduate student, no later than my third year of studies, I decided to write an essay of advice to prospective graduate students about choosing a program and mentally preparing themselves for graduate study. I’d been through it myself, of course, and also was closely involved in the prospective student visits at […]