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bio website bu.edu/sed/about-us/faculty/…
location Boston University, SED
age 28
visits member for 2 years, 8 months
seen 4 hours ago

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

Postdoctoral Fellow, Mathematics Education, Boston University SED.

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

Dissertation: Conceptions of Creativity in Elementary School Mathematical Problem Posing. (Relevant MESE post here.)

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; relevant MSE post here.)


Have you solved any of my puzzles? If so, send me an email!
Email: bdickman[at]bu。edu


Dec
16
comment Producing finite objects by forcing!
w.r.t. @AndreasBlass' comment ("As for making 'genuine' priority arguments look like forcing, I think there have been many attempts over the years, but I haven't really learned about any of them") I asked a related question about the priority method and forcing some time ago: mathoverflow.net/q/124011/22971
Dec
14
comment Good Pre-Calculus book?
As yet another alternative: matheducators.stackexchange.com is a stackexchange site specifically for questions about mathematics education.
Dec
2
comment Question about tetrahedron decomposition
@PerAlexandersson Agreed! And if you like questions about tetrahedra, then you might also like this one: mathoverflow.net/q/142983/22971 (Separately: I'm not sure why the simplicial-stuff tag was removed in the most recent edit -- the answer involves simplices...)
Nov
28
comment Do we know that 'most' finite groups are Galois groups of number fields?
See also mathoverflow.net/q/150603/22971 and the comments/answers.
Nov
16
awarded  Necromancer
Nov
16
comment number of divisors
It seems to me that providing some of the background (e.g., the Bourgain paper to which you refer in the comments) would be helpful in answering (or at least motivating) the question. I do not think anything is gained by obscuring what is already known (to be known)...
Nov
16
awarded  Notable Question
Nov
8
comment Randomly placing nonoverlapping unit cuboids
More generally, I believe what you want is the random sequential adsorption for a system of parallel cuboids. Here is a brief paper that refutes the $d=2$ (Palasti) conjecture (as do several other numerical works) and provides some citations/terminology that you may find of interest: journals.aps.org/pra/pdf/10.1103/PhysRevA.43.631
Nov
8
comment Randomly placing nonoverlapping unit cuboids
Is it possible that you are asking a question equivalent to an extension of the parking problem? Cf. mathworld.wolfram.com/RenyisParkingConstants.html
Oct
25
comment What arrangement of unit cubes minimizes surface area?
A polycube that can be written as length x width x height; among Joseph O'Rourke's pictures, only the middle one is a rectangular prism. So it would be finding the ℓ,w,h such that the polycube of dimensions ℓ×w×h has minimal surface area. (Meaning you can't, e.g., for n=9 assemble a 2×2×2 polycube and stick the ninth unit cube to one of the faces as is done in JO'R's rightmost picture.)
Oct
13
comment Does $\binom{2n}{n} \equiv 2 \pmod p$ ever hold?
Observing that $n(n-1)$ is always even (an interesting fact on its own! cf. mathoverflow.net/a/152300/22971), you have a prime of the form $p = 4k+1$. In this light, an earlier answer and link from Lucia (mathoverflow.net/a/165441/22971) may be relevant to your question. My hunch is that the information there can be pushed through to answer your question in the negative, but I don't see how to do it. Maybe someone else (or you) will!
Oct
3
comment Why do roots of polynomials tend to have absolute value close to 1?
"The zeros of random polynomials cluster uniformly near the unit circle" www-old.newton.ac.uk/preprints/NI04017.pdf
Sep
21
comment same paper was published in the same journal twice
Sun Xiaotao's page lists only the pp. 303-343 version: math.ac.cn/index_E/Personal_Web/Sunxiaotao_E.htm
Sep
8
awarded  Popular Question
Sep
8
comment What arrangement of unit cubes minimizes surface area?
It will take me some time to try and make sense of your last paragraph (I had not seen Young diagrams before, and "isoperimetric arguments" are not presently in my arsenal!). (1) Do you have any suggestions for what I might read to be able to grasp the last paragraph? (2) Do you see any way to modify your response to Question A so as to make sense of Question B? (Or perhaps B should be tackled using a more number theoretical approach instead of a geometric one?)
Sep
3
comment What arrangement of unit cubes minimizes surface area?
(If you are up for making another image: It would be great to see an example worked out using the approach described by Ian Agol...!)
Sep
3
comment What arrangement of unit cubes minimizes surface area?
For my own clarification (paragraph after the diagram): Given an $n$, is there an obvious way to compute $k$? I will write out my understanding so that you can tell me where I've gone wrong! In your example, $n = 8$, so the $\max$ formula for $P(2k)$ suggests making $\frac{k}{2} = 3$ will be a good idea, i.e., so that $n = 8 \leq 9$. Indeed, this value of $k=6$ satisfies the given inequality, and (since $n=8$ is even) we make a $6/2 \times (6/2 - 1) = 3 \times 2$ rectangle with a row of $8 - 6(6-2)/4 = 2$ squares added on, for the (non-unique but optimal) Young sequence $3,3,2$.
Aug
31
revised What arrangement of unit cubes minimizes surface area?
Added a note at the start to indicate that the arrangements can be assumed polycubes, and added the number-theory tag as suggested by a comment.
Aug
30
awarded  Announcer
Aug
29
comment What arrangement of unit cubes minimizes surface area?
@Michael That's a good question; certainly I mean as much in the case of Question B. For A, let us say the same (i.e., that both questions concern polycubes). I will try to clarify (along with adding a number theory tag) in my next edit.