2,700 reputation
11444
bio website tc.columbia.edu/academics/…
location Brookline, MA
age 28
visits member for 2 years, 3 months
seen 6 hours ago

Profile for Benjamin Dickman on Stack Exchange: MESE, MSE, and MO

Ph.D., Mathematics Education, Columbia University. 2014. NSFGRFP.

Dissertation: Conceptions of Creativity in Elementary School Mathematical Problem Posing.

M.Phil., Mathematics Education, Columbia University. 2014.

Fulbright Grant, Mathematics/Mathematics Education, Nanjing Normal University. 2008-2009.

Research Topic: High School Mathematics Teacher Training in China.

B.A., Mathematics, Amherst College. 2008. Honors Program.

Undergraduate Thesis: On a Theorem of Dwork. (p-adic proof of the rationality part of the Weil Conjectures.)


Have you solved any of my puzzles? If so, send me an email!
Email: bmd2118[at]colunbia.edu. (Change n to m.)


Jul
18
answered Negative impact of wrong or non-rigorous proofs
Jul
12
comment What is known about tiling a rectangle in an irreducible way by smaller rectangles?
You might check Klarner's Theorem (Thm. 5) and its corollary in: Klarner, D. A. (1969). Packing a rectangle with congruent $N$-ominoes. *Journal of Combinatorial Theory, 7*(2), 107-115.
Jul
10
awarded  Enlightened
Jul
2
awarded  Curious
Jul
1
comment Is every set class generic over a given inner model?
I expect you would find the last section, beginning on p. 80, of math.berkeley.edu/~steel/papers/steel1.pdf to be helpful.
Jun
30
awarded  Nice Answer
Jun
30
revised Colourings of $\mathbb Q\times \mathbb Q$ in three colours
Corrected misspelling of 'Monsky' and made final remark slightly more precise.
Jun
30
answered Colourings of $\mathbb Q\times \mathbb Q$ in three colours
Jun
20
comment What's your favorite equation, formula, identity or inequality?
You might be interested in this answer: math.stackexchange.com/a/779515/37122
Jun
17
comment Review of Tim Maudlin's New Foundations for Physical Geometry
@NikWeaver I'm not a mathematical physicist, so I don't think my conclusions would serve much for the purpose of the OP. That said, the very first section gives an argument that $(0,1]$ is not open (in the sense of the standard topology on $\mathbb{R}$) with a foot-note attributing the argument to the Wikipedia page on Topology from 2005. That about summarizes my own personal feelings on the book preview...
Jun
16
comment Review of Tim Maudlin's New Foundations for Physical Geometry
You can read a fair amount of it on Google Books; probably enough to draw your own conclusions: books.google.com/books?id=10XbAgAAQBAJ
Jun
15
revised Is $x \, \tan(x)$ integrable in elementary functions?
Added in a full Liouville argument that int xtanx dx is not elementary
Jun
14
comment Enumeration of a finite group
@KevinO'Bryant The OP writes s/he hasn't found any example when $n$ is odd. When $n$ is even, consider $\mathbb{Z}/4\mathbb{Z}$ where $g_1 = 0, g_2 = 1, g_3 = 2, g_4 = 3$. Then $a_1 = 0, a_2 = 1, a_3 = 3, a_4 = 2$.
Jun
12
answered Frechet differentiable implies reflexive?
Jun
12
comment Origin of the term “generic” in set theory
@AsafKaragila The reason I remarked about Cohen's thesis is that his dissertation was entitled Topics in the Theory of Uniqueness of Trigonometric Series. See also the citation for a different piece on trigonometric series by Zygmund at the end of Cohen's On a Conjecture of Littlewood and Idempotent Measures. I think it's a pretty safe bet that he would have read the paper I mentioned above, but insignificant in the sense that a single foot-note with the word "generic" (used colloquially) is unlikely to have left a deep impression. (And I didn't root out other uses Cohen might have seen.)
Jun
12
comment Origin of the term “generic” in set theory
I think it just entered by its colloquial usage. You can find an earlier use by Cohen in Asymptotic Decay of Solutions of Differential Inequalities (with M. Lees, 1961) applied to an interval; this is unimportant. His advisor, Zygmund, writes in Some Points in the Theory of Trigonometric and Power Series a footnote: "In the following we use $C$ as a generic notation for an absolute constant..." Surely read by Cohen (as his advisee, and also given Cohen's own thesis topic) but, though the paper is from ~1934, this is not significant for your purpose here. I vote "via natural language use."
Jun
12
comment A question on the product of element orders of a finite group
The sum of elements theorem was proved in 1991 - earlier than the 2009 paper cited here. Citation: Schmidt, F., Stong, R., & Lindsey, J. H. (1991). 6636. American Mathematical Monthly, 970-972.
Jun
11
revised Does this Banach manifold admit a Riemannian metric?
Re-focused question on admissibility of Riemannian metric
Jun
11
comment Examples of theorems misapplied to non-mathematical contexts
Assume average life expectancy and use Secretary Problem to "guess" the best moment (or day, or whatever) of one's life.
Jun
10
answered What recent discoveries have amateur mathematicians made?