@BalarkaSen Here is a bit tougher one, probably not within your interests. Find all the roots of $\cos(\cos(\cos(\cos(x))))=\sin(\sin(\sin(\sin(x))))$.
Yesterday I computed all subgroups of $S_4$, and it turns out this group has the special property that it has a subgroup of order $d$ for every divisor of $4!=24$. =)
Now I'm looking at the Unitriangular group, or the Heisenberg group over a field.
@BalarkaSen You want to have Fourier series for modforms, so $X$ itself is mostly out of the picture. Although... I recall Zagier listing Taylor series of modforms e.g. series in $w=\frac{\tau-\mathrm{i}}{\tau+\mathrm{i}}$ as an interesting object of study.
Using this answer here I have been able to draw smooth curves using tikz
Easy curves in TikZ
but I also wanted arrows along my curves, after a bit of fiddling I came up with
the following
\documentclass[a4paper,12pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows}
\input{arrowsnew}
\useti...
Same, but usually the procedure goes like this: 1) Hate tikz. 2) Then I search the web and 90% of the time someone has encountered the same problem before me. This time I am stuck at 1)
tikz is way better than any previous TeX drawing package I know of. That said, I am more experienced with asymptote, but images of some fundamental domains can be easily made directly in tikz. Let's see whether I can post an example...
@AlexanderGruber A document about all the various things I know about integrals. I have just started working on the complex part, drawing all the contours and paths is killing me >.< ugh. Hopefully someone can come up with a nice solution for the paths.
Consider a random $m$ by $m$ circulant matrix $M$ whose entries are from $\{0,1\}$. Let $M'$ be the $n$ by $m$ matrix which is simply the first $n \leq m$ rows of $M$. What is the probability that $M'$ has two identical columns?
We know that for $n=m$, it can only have two identical columns if...
@felix: If $M$ has first row $(1,0,1,0,\ldots)$, then $M$ has only two different columns, so the claim about all-$0$ or all-$1$ does not hold. Am I missing something?
can someone help me ? I don't know how the generalized second mean value theorem for integrals works .. can someone give me a few links as to where I can study it ?
@AlexanderGruber pastebin.com/mAFRr568 far from perfect, but you just have to juggle a bit with the text to make sure the textheight is the same as the figure.
I do admitt that it does not look as nice as wrapfig - I think I would use wrapfig if I really wanted to wrap things. But it offers perhaps a different way to look at things. I also am not particularly fond of the text spacing before and after the minipages
@felix: It's a combinatorial problem. In fact, I'd propose to remove the linear-algebra tag and add something along combinatorics unless you expect linear algebra constructs to play a role here.
Using this answer here I have been able to draw smooth curves using tikz
Easy curves in TikZ
but I also wanted arrows along my curves, after a bit of fiddling I came up with
the following
\documentclass[a4paper,12pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows}
\input{arrowsnew}
\useti...
Consider a random $m$ by $m$ circulant matrix $M$ whose entries are from $\{0,1\}$. Let $M'$ be the $n$ by $m$ matrix which is simply the first $n \leq m$ rows of $M$. What is the probability that $M'$ has two identical columns?
We know that for $n=m$, it can only have two identical columns if...
