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Visiting Assistant Professor of Mathematics at Swarthmore College


2d
answered Circle in the plane of complex numbers
Nov
25
answered To find Basis and kernel of matrix A
Nov
25
answered Summation of values with odd index in a sequence
Nov
24
comment Does a colouring of a graph on two colours always have certain kinda of circle
The question is "Does there exist a point set with the property", not "Do all point sets have the property".
Nov
24
comment How do you calculate how big a 20" circle will appear when it is 500 yards away?
Can you measure the angle the circle takes in your field of vision at a given distance?
Nov
24
comment proof of a property of modular arithmetic
They aren't necessarily equal, but $n^\prime | k$ and $n | k^\prime$. So $a - b = mnn^\prime$, so what is $a - b \mod nn^\prime$?
Nov
24
answered proof of a property of modular arithmetic
Nov
23
comment Integral equation $f(x) - \int_0^x f(t)dt = 0$
Can you solve $\frac{d}{dx}F(x) - F(x) = 0$?
Nov
20
comment Connectivity of a Hamiltonian path
To see $\omega(G-S) \leq \omega(H-S)$, note that adding edges to a graph cannot increase the number of connected components. $G-S$ and $H-S$ share the same vertex set, and $G-S$ contains every edge in $H-S$...
Nov
20
comment Connectivity of a Hamiltonian path
Take a path and remove $0$ vertices, and it remains in $1$ piece. Take a path and remove $1$ vertex, and it falls into $2$ pieces. Take a path and remove $2$ vertices, and it falls into at most $3$ pieces, etc...
Nov
20
answered Connectivity of a Hamiltonian path
Nov
16
comment Locating a paper in Euler's complete works
eulerarchive.maa.org -> Date -> Date Published -> 1741 yields 10 papers E046-E056, listed in order of page number...
Nov
16
answered Locating a paper in Euler's complete works
Nov
16
comment Disquisitiones Arithmaticae art. 49
+1. I was worried that I was the only one who couldn't come up with anything better that "it takes mathematical maturity" or "that's why he's Gauss"...
Nov
16
answered Disquisitiones Arithmaticae art. 49
Nov
16
answered Discrete math counting.
Nov
16
answered What is an elementary yet important application of matrix in finance?
Nov
16
answered Why does an improper integral turn into an answer with factorial?
Nov
16
comment what's the summation of this finite sequence?
I'm not sure it has a name. It is identity #8 on the Wikipedia page for binomial coefficients.
Nov
16
comment what's the summation of this finite sequence?
Think of the ways of choosing $k+1$ objects out of $n+1$. In one way of counting it is simply $\binom{n+1}{k+1}$, and in another you fix $j$, and count the ways to choose the objects so that the $m+1$st object is the $j+1$st chosen.