MappingsIn which I work through problems and write explorable explanations.
http://christosilvia.github.io/
Tue, 14 Jul 2015 13:37:20 -0400Tue, 14 Jul 2015 13:37:20 -0400Jekyll v2.4.0Grokking the Product Rule<p>This post is going to be about an integral identity called the
<a href="https://en.wikipedia.org/wiki/Product_rule">product rule</a>.
This identity is going to be central to an efficient
scheme for computing the energy-laplacian matrix
for the serpinski gasket.
It’s also cool.</p>
<p>In regular normal one-dimensional calculus, we define the derivative:</p>
<p><img src="/latex/latex-737d2eb6622e021220c63e14ddec64f1.png" /></p>
<p>Let’s explore some of the properties.
Some functions can be split into a product of two other functions.
For example, <img src="/latex/latex-2b1da92727ecca7e2e16c4c4616abbb8.png" />
can be split into two functions in the following way:
<img src="/latex/latex-985a4943240409d2e247d085a11f38ba.png" />.
If <img src="/latex/latex-4d00ad1f87ade895fb298a3b4c40ba99.png" /> is of this form,
then knowing a rule for determining <img src="/latex/latex-207ca5a8f7bb215499f1d4155e7449af.png" /> from <img src="/latex/latex-fc16282f28a71eb0355b8516f28eac31.png" /> and <img src="/latex/latex-e31b212e1c2877a7f9219586c973d541.png" />
might be valuable and save a good deal of effort.
If you want to, you might want to stop reading and try to figure out
a way to do this yourself.
It will be rewarding even if you give up and keep reading.</p>
<p>Our first step in trying to figure out this rule is simply to use
the definition of a derivative.</p>
<p><img src="/latex/latex-02f9c7ff38b64cc6252ca125b928deb0.png" /></p>
<p>What would be a nice form for this to take?
If the right side would perhaps contain either </p>
<p><img src="/latex/latex-fa738825f7f36061c1593ecf545fa670.png" /> </p>
<p>or </p>
<p><img src="/latex/latex-391b35b64c3f8e2c5b3f6dbae7aed1a7.png" /></p>
<p>then the formula would be very nice: it would simply express the
derivative of <img src="/latex/latex-f5db0e392fb80e56fe541b91d7eb981d.png" />
in terms of the derivatives of its parts.</p>
<p>With that motivation in mind, I’m going to try to refactor the expression
for the derivative of <img src="/latex/latex-ef2c32d7fbbb61a8a99d016756552239.png" />.
We assume that the functions involved are contintuous.</p>
<p><img src="/latex/latex-5044aa767cf23fceade0da1eb44b2331.png" /></p>
<p>I learned this under the name of the <em>product rule</em>.</p>
<p>We can use this fact about derivatives to learn a fact about integrals.
We use newton’s Fundamental Theorem of Calculus:</p>
<p><img src="/latex/latex-2d1d936416bb816b3599f9d7260856af.png" /></p>
<p>On the function <img src="/latex/latex-eca6adc75f5d5952e1b2df28c2e5e0fe.png" />:</p>
<p><img src="/latex/latex-9940ae16c0e2750056a61e6af5d5dcb3.png" /></p>
<p>for <em>any two functions</em>.</p>
Mon, 06 Jul 2015 00:00:00 -0400
http://christosilvia.github.io/math/reu/grokking/2015/07/06/Cool-Integral-Identity-On-Laplacian.html
http://christosilvia.github.io/math/reu/grokking/2015/07/06/Cool-Integral-Identity-On-Laplacian.htmlmathreugrokkingComputing The Laplacian<p>This post is going to be somewhat longer, because I’m going
to cover something that I’ve been doing in my math program.
It may also have some background which I will link to and expand on.
The first section of this post presents work done by Bob Strichartz,
while the second part contains my work.</p>
<h3 id="theorem-carr-duchamps">Theorem (Carré-DuChamps)</h3>
<p>Suppose <img src="/latex/latex-1376255d5363f16f6d0bf4755bc3f684.png" /> is an energy measure defined
by harmonic functions <img src="/latex/latex-338b9a6e2dcea8115370a119b9d7dc9f.png" /> and
<img src="/latex/latex-94e3272fa69f39d4755779ac0021420c.png" />.
Then:</p>
<p><img src="/latex/latex-5c886e927847e7875fe787300e6e5855.png" /></p>
<p>First of all, this looks superficially similar to the definition of the
Christoffel Symbols in riemannian geometry.
Points to anybody who figures out if there’s a real connection there.</p>
<h3 id="our-energy-measures">Our Energy Measures</h3>
<p>For our purposes, we consider energy measures of the form:</p>
<p><img src="/latex/latex-c755520b313851e51f432732e2b7aaf3.png" /></p>
<p>The integral of a function <img src="/latex/latex-d5be9597b9b93a8c5e585a9c98b2f5bc.png" /> with respect to
this energy measure will be:</p>
<p><img src="/latex/latex-d18119dbab7ca845054f8a4b8c1ddabe.png" /></p>
<p>The level m approximation <img src="/latex/latex-62f52c13774b65d87d756b582fbb64cb.png" /> to the energy
measure laplacian is:</p>
<p><img src="/latex/latex-58b3bac9253815a1d1673eec3232ca46.png" /></p>
<p>It turns out that we can use what we know about the serpinski gasket to compute
the above expression exactly.
The function <img src="/latex/latex-c242e19318d0d08fbe6ad11dc61bb5a6.png" /> is piecewise harmonic
on level m, being 1 at <img src="/latex/latex-cfd3d63d29992771e390aaceb5f22d34.png" />
and zero everywhere else.
Therefore, we can express the energy in a finite way:</p>
<p><img src="/latex/latex-f699bc8cea1e6a7312c48d960f4fe846.png" /></p>
<p>We notice that almost every term in the sum of the energy is zero;
the only nonzero contributions come from the vertices
which are adjacent to <img src="/latex/latex-cfd3d63d29992771e390aaceb5f22d34.png" />.
If we let <img src="/latex/latex-a81b2190a510d31d944587e453fbfb77.png" /> are the
neighboring vertices to <img src="/latex/latex-cfd3d63d29992771e390aaceb5f22d34.png" />
at level m:</p>
<p><img src="/latex/latex-0f9f6d0fb8e982c0e27778ba66db43d8.png" /></p>
<p>Which we can condense into a formula for the integral in question:</p>
<p><img src="/latex/latex-65335946569a8c50c72f0b046b3f160b.png" /></p>
<p>Therefore, the denominator of the energy measure now looks like this:</p>
<p><img src="/latex/latex-d9285a0c687ed5729af57f3d63e19aca.png" /></p>
<p>Using our new notation for the vertices, we can now write the energy
laplacian with a nice pointwise formulation.
Note that the normalization factors nicely cancel each other out.</p>
<p><img src="/latex/latex-93d56774b83c52cf6e33d607ed30a524.png" /></p>
<p>With a formula like this, we can reasonable start to go around looking for
a way to compute the laplaian matrix, and find out some of its
properties including its eigenvalues and eigenvectors.</p>
<h3 id="computing-the-energy-laplacian">Computing the Energy Laplacian</h3>
<p>Once we begin to start considering computing the energy laplacian matrix,
we are presented with the problem of representing functions on
the serpinski gasket.</p>
<p>The graph representations at level 0 of the serpinski gasket is just
a triangle:</p>
<p><img src="https://raw.githubusercontent.com/ChristoSilvia/mappings/master/_assets/vertices_level_0.png" alt="level-0" /></p>
<p>Add one more level:</p>
<p><img src="https://raw.githubusercontent.com/ChristoSilvia/mappings/master/_assets/vertices_level_1.png" alt="level-0" /></p>
<p>And so on.
If we’re working with an mth level approximation, we’re going to represent
a function by storing an array of its values on the mth level
graph approximation to the serpinski gasket.
The formula we need to use includes differences between a vertex and its
neighbors.
Therefore, for every element of a function’s array representaiton,
we need a way of efficiently figuring out which elements are adjacent
to it.</p>
<p>We accomplish this by indexing the serpinski gasket with a space-filling path.
We will store an additional path in memory.
We will use these two paths to find all adjacent vertices.</p>
<p>We will create a path which touches every point in the mth-level serpinski gasket
exactly once (note that this path is a spanning tree).
We will refer to this path as the “spiked path”.
The path will start at one endpoint and finish at the other.
We will then construct another path which starts and ends at the same points
as the first path, does not touch the third boundary point at all,
touches all of the vertices, and does not use any of the edges
that the first path used.
We will refer to this path as the “flat path”.
We can inductively construct these paths.
If we have constructed these paths according to plan, a point’s four
neighbors will be its neighbors on the spiked path and flat path.</p>
<h3 id="base-case">Base Case</h3>
<p>Consider the paths:</p>
<p><img src="https://raw.githubusercontent.com/ChristoSilvia/mappings/master/_assets/spiked_0.png" alt="base-spike" /></p>
<p>and</p>
<p><img src="https://raw.githubusercontent.com/ChristoSilvia/mappings/master/_assets/flat_0.png" alt="base-flat" /></p>
<p>Note that the spiked path touches every point once.
That path touches two corners once and one corner twice.
Next, note that the flat path starts and ends at the same place as the
spiked path, and doesn’t touch the one other vertex.
It (trivially) touches every other point.
Therefore, for the 0th level serpinski gasket, we have constructed
paths which satisfy our conditions.</p>
<h3 id="inductive-step">Inductive Step</h3>
<p>We want to construct a pair of spiked path and flat path for the m+1-th
level serpinski gasket, if the m-th level serpinski gasket has
such a path.
Note that if the m-th level serpinski gasket has a pair of spiked path
and flat path, then we can put those paths into one of the three
subtriangles of the serpinski gasket.</p>
<p>To construct a m+1-th spiked path, we join the lower left and upper vertices
of the triangle with the m-th spiked path, so that the intersetion
between the lower-left and lower-right triangles is covered by this path.
Next, the upper triangle is traversed from left to right by a spiked path.
Finally, the lower-left triangle is traversed from top to bottom-right by a flat path.
This path joins the lower left with the lower right, and touches the top vertex,
and is a spanning tree.
Therefore, this path is an m+1-th spiked path.</p>
<p>To construct an m+1-th flat path, we replace the spiked paths with flat paths in
the previous construction.
Note that since the m-th flat path is a flat path, when superimposed with the m-th
spiked path they do not overlap, and together use all of the edges on
the serpinski gasket.
The m+1-th flat path does not include the top vertex because the m-th flat path
doesn’t.
This satisfies all of the properties that an m+1-th flat path needs to satisfy.</p>
<p>Below, we feature some of these paths.</p>
<h4 id="st-spiked-path">1st spiked path</h4>
<p><img src="https://raw.githubusercontent.com/ChristoSilvia/mappings/master/_assets/spiked_1.png" alt="spiked-1" /></p>
<h4 id="st-flat-path">1st flat path</h4>
<p><img src="https://raw.githubusercontent.com/ChristoSilvia/mappings/master/_assets/flat_1.png" alt="flat-1" /></p>
<h4 id="nd-spiked-path">2nd spiked path</h4>
<p><img src="https://raw.githubusercontent.com/ChristoSilvia/mappings/master/_assets/spiked_2.png" alt="spiked-2" /></p>
<h4 id="nd-flat-path">2nd flat path</h4>
<p><img src="https://raw.githubusercontent.com/ChristoSilvia/mappings/master/_assets/flat_2.png" alt="flat-2" /></p>
<h4 id="rd-spiked-path">3rd spiked path</h4>
<p><img src="https://raw.githubusercontent.com/ChristoSilvia/mappings/master/_assets/spiked_3.png" alt="spiked-3" /></p>
<h4 id="rd-flat-path">3rd flat path</h4>
<p><img src="https://raw.githubusercontent.com/ChristoSilvia/mappings/master/_assets/flat_3.png" alt="flat-3" /></p>
<p>Using this layout scheme, we can extract some of the invariants which
we care about.
Let’s start with the eigenvalues:</p>
<p>When <img src="/latex/latex-955ae08980c23f6c65642f83a1ab6cd3.png" />,
<img src="/latex/latex-587cabdc7d34267c6f6a0a47b4909e56.png" />, and
<img src="/latex/latex-301bdb48ceb578382926cd20961e187a.png" /></p>
Mon, 06 Jul 2015 00:00:00 -0400
http://christosilvia.github.io/math/2015/07/06/Computing-The-Laplacian.html
http://christosilvia.github.io/math/2015/07/06/Computing-The-Laplacian.htmlmathA Talk About Math Grad School<p>As some of you know, I’m working on
<a href="http://www.math.cornell.edu/~reu/">Cornell’s Summer Math Research Program for Undergrads</a>
this summer.
The program directors held a workshop/talk about what us undergrads should
expect when applying to math grad school.
Most of us are rising juniors, with a smattering of rising seniors and sophomores.
I’m going to briefly lay out a schedule of what an aspiring math grad student
should look forward to.</p>
<p>The first thing to do is the GRE, typically in the applicant’s junior year.
In 2014-2015, the tests were held on September 27th, October 25th, and April 18th.
There are also subject tests.
It seems like the Math subject test is the only one that matters for Math grad school.
The presenter didn’t linger on this topic.
It seems like GRE scores won’t help you, but can hurt you if they are low.
The presenter told a story of a promising Cornell math undergrad who didn’t study
at all for the GRE.
He had impressive coursework and some research, and seemed on track to get into one
of the “big six” grad schools.
However, he completely bombed the GRE, and went to a second tier school as a result.
Apparently, we shouldn’t worry too much or to little about the GRE.</p>
<p>In our junior and senior years, we should work on developing a mix of general background (undergrad courses),
expertise on specific topics (grad courses), and research experience (published papers).
Published papers are not necessary: the typical accepted applicant has published no papers.
They are tremendously helpful, however.
The most important thing is developing good relationships with professors, to write letters of recommendation.
Also, make sure that the trends on grades are good.
Good grades in sophomore and junior year are crucial; a few C’s in freshman year can be overlooked.
That’s really it for junior year, next comes the beginning of the application process.</p>
<p>The next part is choosing which schools to apply to.
By the fall of senior year, the applicant should have at least a vague idea of their specialty.
This is not meant to be a final idea, and it should not be constricting.
The big six graduate schools are:</p>
<ul>
<li><a href="http://www.math.harvard.edu/graduate/">Harvard</a></li>
<li><a href="http://math.mit.edu/academics/grad/index.php">MIT</a></li>
<li><a href="https://www.math.princeton.edu/graduate">Princeton</a></li>
<li><a href="https://math.berkeley.edu/programs/graduate">Berkeley</a></li>
<li><a href="http://mathematics.stanford.edu/academics/graduate/">Stanford</a></li>
<li><a href="https://math.uchicago.edu/graduate/">U Chicago</a></li>
</ul>
<p>The second tier (given by the presenter) are:</p>
<ul>
<li><a href="https://www.math.cornell.edu/m/Graduate/graduate">Cornell</a></li>
<li><a href="https://www.lsa.umich.edu/math/graduate">Michigan</a></li>
<li><a href="https://www.math.ucla.edu/grad">UCLA</a></li>
</ul>
<p>This is not meant to be an exhaustive list.
One word of caution: don’t <em>just</em> apply for the big six.
If you don’t get into any, then you might be left high and dry.
Apply to a mix of stretch, standard, and safety schools, like with college.</p>
<p>At this point, the applicant should be writing the essays for their schools.
The essays, like the GRE scores, can disqualify you, but cannot help much.
DO NOT start your essay with :</p>
<p><img src="/latex/latex-b47ca5589a43f8c716e4e15b8a588dd6.png" /></p>
<p>The essay should be a statement of interest, similar to the college admissions essay.
Talk about why you like math, and why you want to go to grad school.
If you can’t write about this, you should reconsider your motivations for going to grad school.</p>
<p>Your applications will be submitted in early January.
Cornell returns decisions by February 1st.
The presenter told us that we should tell every college we have yet to hear
from when we are accepted into another grad school.
This is good for the applicant, because the admissions officers will be thinking more about the strength
of applicants than their yield rate, according to the presenter.
This is the time when it’s good to apply to a mix of stretch, normal, and safety options, because
you don’t want to suddenly have to start interviewing for jobs
with no warning if no graduate school accepts you.
To give an idea of the statistics, in 2015 Cornell had 250 applicants.
They admitted 30 of them, and 10 accepted.</p>
<p>Every grad school will have an official vising weekend, and will give the accepted students a small travel budget.
You can meet and talk with professors and especially current grad students.
They’re a good bellweather.
They are most often honest about the struggles that they face, and will tell you the strengths
and weaknesses of that program honestly.</p>
<p>Once you’ve decided which program you want to accept (if any), that’s it!
Have fun in graduate school!</p>
Sun, 28 Jun 2015 00:00:00 -0400
http://christosilvia.github.io/math/grad/college/2015/06/28/Math-Grad-School.html
http://christosilvia.github.io/math/grad/college/2015/06/28/Math-Grad-School.htmlmathgradcollegeMath Notation with MathJax and Jekyll<p>I am configuring Latex preprocessors for math blogging.
The first one I’ve tried is MathJax, which does client-side rendering.
It seems slow on my laptop, but it is extremely simple.
I got it working in under a half an hour.</p>
<p>I found out about <a href="http://www.flx.cat/jekyll/2013/11/10/liquid-latex-jekyll-plugin.html">liquid latex</a>
from googling, but that website is very difficult to read.
Fortunately, they link to the <a href="https://github.com/fgalindo/jekyll-liquid-latex-plugin">github repo</a>.
The repo is <a href="https://en.wikipedia.org/wiki/MIT_License">MIT Licensed</a>, and the installation
instructions direct me to copy <code>liquid_latex.rb</code> to my <code>_plugins</code> directory.</p>
<div class="highlight"><pre><code class="language-bash" data-lang="bash"><span class="nv">$ </span>wget https://raw.githubusercontent.com/fgalindo/jekyll-liquid-latex-plugin/master/liquid_latex.rb</code></pre></div>
<p>One minor point of confusion is that nobody told me that I would have to create my own <code>_plugins</code>
directory.
From there, the configuration instructions direct me to update my <code>_config.yml</code>.
I copied the config information verbatum into my <code>_config.yml</code>.
Unfortunately, it didn’t work when I copied in the defaults, but it worked with not config. Strange.</p>
<p>Next, I tried it out:</p>
<p><img src="/latex/latex-1256d332106687c0b609ae4da2a5e3fb.png" /></p>
<p>Hooray!</p>
Tue, 23 Jun 2015 12:00:00 -0400
http://christosilvia.github.io/jekyll/math/mathjax/latex/notation/2015/06/23/Writing-Math.html
http://christosilvia.github.io/jekyll/math/mathjax/latex/notation/2015/06/23/Writing-Math.htmljekyllmathmathjaxlatexnotationMath Research<p>This summer I’m going to be doing math research with <a href="https://www.math.cornell.edu/m/People/Faculty/strichartz">Bob Strichartz</a> this summer. We’re going to be trying to develop a theory of analysis on fractals and other rough spaces.</p>
<p>This was the only summer program I applied to.
The previous summer, my mom got me a job working as a research assistant at
catholic university’s vitreous state lab.
I wasn’t particularly productive there.
The one good thing that came of that was that I began reading textbooks independently.
I started out reading David Griffiths excellent Introduction to Quantum Mechanics textbook.
I might do a fuller review later, here’s a wonderful <a href="http://www.physicspages.com/index-physics-quantum-mechanics/griffiths-introduction-to-quantum-mechanics-problems/">set of commentary and solutions</a>.</p>
<p>I’ve met many many other people who learned differential equations from griffiths.
It’s rather embarassing how common this is.
It could be that this is the first class in which solving differential equations is “expected” of us students.
Many of the people who I knew took differential equations (ex: Sascha) forgot everything about it,
but everybody who’s used differential equations in quantum knows a thing or two about actually
solving them.
The next best resource is definitely Farlow’s <a href="http://www.amazon.com/Differential-Equations-Scientists-Engineers-Mathematics/dp/048667620X">Partial Differential Equations for Scientists and Engineers</a>.</p>
<p>Anyways, at the beginning of spring semester, I knew that I needed to apply to some sort of summer program.
I didn’t particularly want to, it was much more of a push than a pull.
I was afraid of not having anything to do during the summer.
When I was told that I missed the deadline for Cornell’s summer math program, I was carrying Vivian’s
books at the time.
I dropped the books.
I then quickly talked to Bob and applied to his group, and I was fortunately accepted.</p>
<p>I had a tremendous amount of difficulty working through the background reading, and now here I am starting
the first real week of work after the background lectures.
Wish me luck!</p>
Sun, 14 Jun 2015 11:30:00 -0400
http://christosilvia.github.io/math/2015/06/14/Math-Research.html
http://christosilvia.github.io/math/2015/06/14/Math-Research.htmlmathWriting Jekyll blog posts with Vim and Git<p>I’m going to lie to you in this blog post. As you read this, I think that you’re assuming I sat down
to write this (after some inspiration of course!) and then wrote the whole thing in one go. At least, I
bet that you thought that I wrote the beginning before the end. Wrong. Here’s the completed paragraph:</p>
<p>As I sit down to write about <a href="www.bro.ken">making mathematica-style manipulate on the web</a>,
I come across a problem. That problem is apostrophes. Vim does some markdown syntax
highlighting. Right now vim is making the string “Writing Jekyll blog posts with Vim and Git”
appear red to me. Now, I want to take a screenshot. I am running ubuntu, with the (i3)[i3wm.org]
window manager installed. I google “screenshots ubuntu” (note that the text in quotes is red), and I get
an <a href="http://askubuntu.com/questions/6558/what-screenshot-tools-are-available">askubuntu post</a> (which just
taught me that <code>"+p</code> is the vim paste command), and the askubuntu post tells me that there is a tool called
<a href="shutter-project.org">shutter</a> which lets me take screenshots on ubuntu.</p>
<p>Now I know what to do:
<code>bash
$ sudo apt-get install shutter
...
After this operation, 32.3 MB of additional disk space will be used.
Do you want to continue? [Y/n] y
</code></p>
<p>Just to be clear, the original goal of this was to make the vim syntax highlighting be sane about apostrophes
in markdown, and not treat them like they’re quotes. To show you this problem, I’m installing a screenshot
tool. I originally encountered this problem when trying to write another blog post.</p>
<p>I type <code>$ shutter</code> and looks like it has a gui. Shit. Close that. Google “shutter
screenshots command line”. A nice helpul <a href="http://www.linuxstall.com/take-screenshot-in-linux-with-shutter/">tutorial</a>
(so glad i didn’t have to type that whole url, because of the neat handy <code>"+p</code> command).
It tells me that i need to execute <code>$ shutter --full</code> to take a screenshot. I do so, but a
notification pops up (that I can’t screenshot, sorry) telling me where it saved the screenshot.
The notification fades very fast. Time to go hunting around my filesystem to see where the screenshot went.</p>
<p><code>bash
$ ls ~
college dev Downloads Dropbox media res tmp work Workspace 2_001.png
</code>
In order to get the above image, I’m trying to toy around with xclip. I do <code>$ ls ~ | xclip -i</code> (the ‘-i’
is for in), and it works? Nope! Not sure what’s wrong! I won’t be, I’ve already wasted enough time
that I just typed it manually.</p>
<h3 id="lets-back-up-a-bit">Let’s back up a bit.</h3>
<p>As I sit down to write about (making mathematica-style manipulate on the web)[www.bro.ken],
I come across a problem. That problem is apostrophes. Vim does some markdown syntax
highlighting. Right now vim is making the string “Writing Jekyll blog posts with Vim and Git”
appear red to me. Now, I want to take a screenshot. I am running ubuntu, with the (i3)[i3wm.org]
window manager installed. I google “screenshots ubuntu” (note that the text in quotes is red), and I get
an <a href="http://askubuntu.com/questions/6558/what-screenshot-tools-are-available">askubuntu post</a> (which just
taught me that <code>"+p</code> is the vim paste command), and the askubuntu post tells me that there is a tool called
(shutter)[shutter-project.org] which lets me take screenshots on ubuntu.</p>
<p>I just pasted a paragraph from above, which means that I need to know how to copy and paste text in vim.
I know how to paste, not how to copy. Google gets me
<a href="http://www.tech-recipes.com/rx/219/copy-and-paste-text-with-vi-or-vim/">here</a> which might help.<br />
Nope, let’s do <a href="http://vim.wikia.com/wiki/Copy,_cut_and_paste">this</a> instead. The text is still interpreting
anything posessive as a quote, making this crazy red. But, I can embed pitures!</p>
<p>Oh, wait, I’m using Jekyll. I have to look up how to embed pictures. <a href="https://www.google.com/search?client=ubuntu&channel=fs&q=embed+pictures+in+Jekyll&ie=utf-8&oe=utf-8">Google</a>
then <a href="http://jekyllrb.com/docs/posts/">the official jekyll site</a> which says midway down that you can
add in an image asset in a post. I have to move the screenshot to assets (good get it out of my home
directory!)</p>
<p><code>bash
$ ls ~/dev/jekyll-blog
about.md _config.yml css _includes _layouts README.md _site
about.md~ _config.yml~ feed.xml index.html _posts _sass
</code></p>
<p>Is assets in <code>includes</code>? </p>
<p><code>bash
~/dev/jekyll-blog$ ls _includes
footer.html header.html head.html
</code></p>
<p>Assets is probably not in includes. Do I have to create it? Yes, back on the <a href="http://jekyllrb.com/docs/posts/">official jekyll site</a> it says that I need to make a directory called “something like <code>assets</code> or <code>downloads</code>, into which any images, downloads, or other resources are placed.” Okay.</p>
<p><code>~/dev/jekyll-blog$ mkdir assets</code></p>
<p><code>~/dev/jekyll-blog$ mv ~/Workspace\ 2_001.png assets</code></p>
<p><code>~/dev/jekyll-blog$ ls assets</code></p>
<p><code>Workspace 2_001.png</code></p>
<p><code>~/dev/jekyll-blog$ mv assets/Workspace\ 2_001.png assets/red.png</code></p>
<p>Yay, it’s here. It should appear below.
<img src="http://christosilvia.github.io/assets/red.png" alt="If it's not broken this should be an image" />.</p>
<p>Of course, I go to look and it’s not there. Wtf. </p>
<p>Maybe the directory needs to be named <code>_assets</code> and not <code>assets</code>? That doesn’t fix it.</p>
<h3 id="lets-start-over">Let’s start over</h3>
<p>As I sit down to write about (making mathematica-style manipulate on the web)[www.bro.ken],
I come across a problem. That problem is apostrophes. Vim does some markdown syntax
highlighting. Right now vim is making the string “Writing Jekyll blog posts with Vim and Git”
appear red to me.</p>
<p><img src="http://christosilvia.github.io/assets/red.png" alt="Ahaha sucker" /></p>
<p>I give up.</p>
Sun, 15 Mar 2015 14:31:00 -0400
http://christosilvia.github.io/vim/git/meta/2015/03/15/Writing-Posts-With-Vim.html
http://christosilvia.github.io/vim/git/meta/2015/03/15/Writing-Posts-With-Vim.htmlvimgitmetaManiuplating Graphs with mpld3<p>Have you seen mathematica?</p>
Sun, 15 Mar 2015 14:27:15 -0400
http://christosilvia.github.io/mpld3/d3/graphs/explorable-explanations/2015/03/15/manipulating-graphs-on-the-web.html
http://christosilvia.github.io/mpld3/d3/graphs/explorable-explanations/2015/03/15/manipulating-graphs-on-the-web.htmlmpld3d3graphsexplorable-explanationsWelcome to Jekyll!<p>You’ll find this post in your <code>_posts</code> directory. Go ahead and edit it and re-build the site to see your changes. You can rebuild the site in many different ways, but the most common way is to run <code>jekyll serve --watch</code>, which launches a web server and auto-regenerates your site when a file is updated.</p>
<p>To add new posts, simply add a file in the <code>_posts</code> directory that follows the convention <code>YYYY-MM-DD-name-of-post.ext</code> and includes the necessary front matter. Take a look at the source for this post to get an idea about how it works.</p>
<p>Jekyll also offers powerful support for code snippets:</p>
<div class="highlight"><pre><code class="language-ruby" data-lang="ruby"><span class="k">def</span> <span class="nf">print_hi</span><span class="p">(</span><span class="nb">name</span><span class="p">)</span>
<span class="nb">puts</span> <span class="s2">"Hi, </span><span class="si">#{</span><span class="nb">name</span><span class="si">}</span><span class="s2">"</span>
<span class="k">end</span>
<span class="n">print_hi</span><span class="p">(</span><span class="s1">'Tom'</span><span class="p">)</span>
<span class="c1">#=> prints 'Hi, Tom' to STDOUT.</span></code></pre></div>
<p>Check out the <a href="http://jekyllrb.com">Jekyll docs</a> for more info on how to get the most out of Jekyll. File all bugs/feature requests at <a href="https://github.com/jekyll/jekyll">Jekyll’s GitHub repo</a>. If you have questions, you can ask them on <a href="https://github.com/jekyll/jekyll-help">Jekyll’s dedicated Help repository</a>.</p>
Sun, 08 Mar 2015 14:10:14 -0400
http://christosilvia.github.io/jekyll/update/2015/03/08/welcome-to-jekyll.html
http://christosilvia.github.io/jekyll/update/2015/03/08/welcome-to-jekyll.htmljekyllupdateDoing Research<p>This summer, I will be working with Bob Strichartz doing analysis on fractals, I hope.</p>
Sun, 08 Mar 2015 00:00:00 -0500
http://christosilvia.github.io/2015/03/08/Doing-Research.html
http://christosilvia.github.io/2015/03/08/Doing-Research.html