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Visiting Assistant Professor of Mathematics at Swarthmore College


3h
comment Evaluating $\lim_{x\rightarrow\pi}\frac{\sin x}{x^2-\pi ^2}$ without L'Hopital
$x^2 - \pi^2 = (x+\pi)(x-\pi)$
Jan
23
comment Why Do The Axioms of Euclidean Geometry Not Need To Include the Definition of Space?
Hilbert didn't define space or coordinates either, and that was a bit more recent.
Jan
23
comment Why Do The Axioms of Euclidean Geometry Not Need To Include the Definition of Space?
You are equating points with coordinates. Geometry doesn't need coordinates, so its basic axioms don't use them...
Jan
21
reviewed Approve Is the hyperbola isomorphic to the circle?
Jan
6
comment The number of e-even connected components of a graph
How many edges does a tree with $|V|$ vertices have? What is $|V|\mod 2$ and what is $eh(T)$?
Jan
6
answered The number of e-even connected components of a graph
Jan
1
comment Polygons with coincident area and perimeter centroids
You should be able to take any two polygons (rotated so their four centroid points are all collinear) and glue appropriately scaled versions together with a thin corridor so that the resulting polygon has centroids that are coincident.
Dec
29
answered Prove no odd number can be abundant.
Dec
17
comment Calculate the variance of $Y=2X+7$
$E[X^2] \neq E[X]^2$
Dec
16
comment Prove ${x:d(x,p) < d(x,q)}$ is open in metric space $X$
I edited. You should also look at your definition of $N_r(x)$. I think it should be $N_r(x) = \{y:d(x,y) < r\}$.
Dec
16
revised Prove ${x:d(x,p) < d(x,q)}$ is open in metric space $X$
added 746 characters in body
Dec
16
answered Prove ${x:d(x,p) < d(x,q)}$ is open in metric space $X$
Dec
15
comment Projection of vectors
How are you calculating that $0$?
Dec
15
reviewed Approve How to find out whether a group is Abelian
Dec
15
comment Is the series $\sum_{n=1}^\infty\frac{n-1}{n+\ln n}$ convergent?
Yes, one condition that is necessary for a series $\sum a_n$ to converge is that $\lim_{n \to \infty} a_n = 0$.
Dec
15
answered How to integrate using known distributions
Dec
15
comment How to integrate using known distributions
You could also substitute $u = x^2$ and then do integration by parts...
Dec
15
comment Is the series $\sum_{n=1}^\infty\frac{n-1}{n+\ln n}$ convergent?
That is a very good question. What happens when I try to take an infinite sum of numbers that approach $1$?
Dec
15
comment Some questions about the Eigenvalues of this $4\times 4$ matrix
Win some, lose some, I guess. :)
Dec
15
answered Some questions about the Eigenvalues of this $4\times 4$ matrix