3,440 reputation
1927
bio website
location Baltimore, MD
age 24
visits member for 3 years, 1 month
seen 12 hours ago

Graduate student at Johns Hopkins University. Interests include Mathematical Physics, Particle Theory, Geometry (combinatorial, differential, and algebraic), Representation Theory, and Algebraic Topology.

I haven't been very active here recently. I'm currently pretty busy with research and teaching responsibilities, so I don't intend to answer any questions here unless they are somehow related to what I'm studying. This is honestly not much of a loss at all, as there are many capable users here who provide answers far better than what I am capable of.


1d
awarded  Excavator
2d
revised How to prove $\cos \frac{2\pi }{5}=\frac{-1+\sqrt{5}}{4}$?
Corrected final expression
Mar
20
awarded  Yearling
Mar
5
comment Uncountable disjoint union of $\mathbb{R}$
I suspect you may be getting confused about the definition of a basis, which requires that for any pair of sets $B_1, B_2$ in $\mathcal B$, then each $x \in B_1 \cap B_2$ has a neighborhood $B_x \in \mathcal B$ contained in $B_1 \cap B_2$.
Mar
5
comment Uncountable disjoint union of $\mathbb{R}$
@DavidToth Sorry, I can't follow what you're saying. Anyway, my argument was just that for each $i \in I$, $\mathbb R \times \{ i \}$ is an open set in $\sqcup_I \mathbb R$. Hence, by definition, for any basis $\mathcal B$, $\mathbb R \times \{ i \}$ is a union of a collection of sets in $\mathcal B$ for each $i$. In particular, there exists a nonempty set $B_i \in \mathcal B$ which is contained in $\mathbb R \times \{ i \}$ for each $i$, and it's easy to see that these sets are pairwise disjoint. That defines an injection from $I$ to $\mathcal B$ which proves that the latter is uncountable.
Feb
9
comment Product of $n$ consecutive positive integer is not a $n$th power?
Sorry to be random, but was this question inspired by the anime Nisekoi? This problem was featured in episode 4 of that show, which aired a few days ago, and by chance I happened to spot this question here today. If not, it's probably still interesting to note.
Jan
11
comment Are the integers closed under addition… really?
I wrote a joke about using these sorts of arguments here.
Jan
3
awarded  Vox Populi
Jan
3
awarded  Talkative
Jan
3
awarded  Suffrage
Dec
21
reviewed No Action Needed Darboux's theorem of several variables
Dec
21
reviewed Close Matrix with orthogonal columns?
Dec
21
reviewed Approve suggested edit on Is Lyapunov equation always solvable with A as a negative definite matrix?
Dec
21
reviewed Close Evaluate the integral, $\int\sec^2x(\sec x+\tan x)^6\,\mathrm{d}x$
Dec
21
reviewed Approve suggested edit on Restrictions on universal specification (in first-order logic)?
Dec
21
reviewed Reject suggested edit on Is this true? $(1+1/n)^n=1+1/1!+1/2!+1/3!+1/4!+\cdots + 1/n!$
Dec
21
reviewed Approve suggested edit on Extended version of the boundedness theorem: $f$ attains its bounds $\inf$ and $\sup$ of $\{f(x) | x \in [a,b]\}$
Dec
21
reviewed Reviewed Infiniteness of non-twin primes.
Dec
21
reviewed Looks Good Let $x,y,z$ be integers and $11$ divides $7x+2y-5z$. Show that $11$ divides $3x-7y+12z$.
Dec
21
reviewed No Action Needed In a family with two children, what are the chances, if one of the children is a girl, that both children are girls?