Formerly known as C-RAM.

Bachelor's degree in pure mathematics from the University of Waterloo.

I enjoy working on problems in analytic number theory and combinatorics, as well as evaluating interesting integrals and series.

Some of my more interesting answers so far:

• On the function $Q(x)=\sum_{n=1}^\infty \frac{P_n(x)}{n(2n+1)}$ where $P_n(x)$ are polynomials defined by the binary expansion of $n$.

• Does there exist an injective function $f:\mathbb{R}^2\rightarrow\mathbb{R}^2$ that maps circles to $n$-gons?

• An odd proof of an astounding identity: $\int_0^{\pi/2}\ln\lvert\sin(mx)\rvert\cdot \ln\lvert\sin(nx)\rvert\, dx$

• A short proof of a theorem of Kronecker on the roots of monic polynomials in $\mathbb{Z}[x]$.

• Evaluating a multidimentional integral: $\int_0^1\int_0^1\cdots\int_0^1\frac{n\max\{x_1,x_2,\cdots,x_n\}}{x_1+x_2+\cdots+x_n}dx_1dx_2\cdots dx_n$

Other answers of note:

• An unexpected alternate form for a power series: $\sum_{n=1}^\infty \zeta'(2n)y^{2n}$

• On the Galois group $\text{Gal}(\mathbb{Q}(\alpha)/\mathbb{Q})$ where $\alpha=\sum_\pm \sqrt{2\pm\sqrt{2\pm\sqrt{2}}}$ .

• An identity of the sum $\sum_{k=0}^n16^k[6\tan^4(2^kx)+8\tan^2(2^kx)+2]$ and higher order generalizations.

• A quick derivation: On the number of Schröder trees with $n$ leaves.

A question I would like more answers to:

• Alternate proofs of a combinatorial generating function identity $G(x)=\overline{G}(-x)^{-1}$ related to counting strings.

Profile picture: The Topology of Images
Artist: Me