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	<title>Math ∩ Programming</title>
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	<description>A place for elegant solutions</description>
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		<title>Math ∩ Programming</title>
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		<item>
		<title>Properties of Morphisms</title>
		<link>http://jeremykun.com/2013/05/15/properties-of-morphisms/</link>
		<comments>http://jeremykun.com/2013/05/15/properties-of-morphisms/#comments</comments>
		<pubDate>Wed, 15 May 2013 17:43:42 +0000</pubDate>
		<dc:creator>j2kun</dc:creator>
				<category><![CDATA[Category Theory]]></category>
		<category><![CDATA[categories]]></category>
		<category><![CDATA[epimorphism]]></category>
		<category><![CDATA[mathematics]]></category>
		<category><![CDATA[monomorphism]]></category>
		<category><![CDATA[morphisms]]></category>

		<guid isPermaLink="false">http://jeremykun.com/?p=3376</guid>
		<description><![CDATA[This post is mainly mathematical. We left it out of our introduction to categories for brevity, but we should lay these definitions down and some examples before continuing on to universal properties and doing more computation. The reader should feel &#8230; <a href="http://jeremykun.com/2013/05/15/properties-of-morphisms/">Continue reading <span class="meta-nav">&#8594;</span></a><img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=jeremykun.com&#038;blog=23934684&#038;post=3376&#038;subd=jeremykun&#038;ref=&#038;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>2</slash:comments>
	
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		<item>
		<title>&#8220;Dog&#8221; Print Available for Sale</title>
		<link>http://jeremykun.com/2013/05/13/dog-print-available-for-sale/</link>
		<comments>http://jeremykun.com/2013/05/13/dog-print-available-for-sale/#comments</comments>
		<pubDate>Mon, 13 May 2013 17:58:03 +0000</pubDate>
		<dc:creator>j2kun</dc:creator>
				<category><![CDATA[General]]></category>
		<category><![CDATA[art]]></category>
		<category><![CDATA[bezier curves]]></category>
		<category><![CDATA[low-complexity art]]></category>
		<category><![CDATA[merchandise]]></category>
		<category><![CDATA[picasso]]></category>

		<guid isPermaLink="false">http://jeremykun.com/?p=3518</guid>
		<description><![CDATA[My girlfriend and I decided we want a print of my recent artistic creation from the post Bezier Curves and Picasso. I set up an account at Society6, which does professional art printing (framed or unframed).  I can&#8217;t imagine anyone &#8230; <a href="http://jeremykun.com/2013/05/13/dog-print-available-for-sale/">Continue reading <span class="meta-nav">&#8594;</span></a><img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=jeremykun.com&#038;blog=23934684&#038;post=3518&#038;subd=jeremykun&#038;ref=&#038;feed=1" width="1" height="1" />]]></description>
		<wfw:commentRss>http://jeremykun.com/2013/05/13/dog-print-available-for-sale/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
	
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			<media:title type="html">bezier-dog-for-web</media:title>
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			<media:title type="html">Dog Framed</media:title>
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		<item>
		<title>Bezier Curves and Picasso</title>
		<link>http://jeremykun.com/2013/05/11/bezier-curves-and-picasso/</link>
		<comments>http://jeremykun.com/2013/05/11/bezier-curves-and-picasso/#comments</comments>
		<pubDate>Sat, 11 May 2013 05:32:05 +0000</pubDate>
		<dc:creator>j2kun</dc:creator>
				<category><![CDATA[Algorithms]]></category>
		<category><![CDATA[Design]]></category>
		<category><![CDATA[art]]></category>
		<category><![CDATA[bezier curves]]></category>
		<category><![CDATA[de Casteljau]]></category>
		<category><![CDATA[graphics]]></category>
		<category><![CDATA[javascript]]></category>
		<category><![CDATA[low-complexity art]]></category>
		<category><![CDATA[math]]></category>
		<category><![CDATA[picasso]]></category>
		<category><![CDATA[programming]]></category>
		<category><![CDATA[svg]]></category>

		<guid isPermaLink="false">http://jeremykun.com/?p=3383</guid>
		<description><![CDATA[Simplicity and the Artist Some of my favorite of Pablo Picasso&#8217;s works are his line drawings. He did a number of them about animals: an owl, a camel, a butterfly, etc. This piece called &#8220;Dog&#8221; is on my wall: These &#8230; <a href="http://jeremykun.com/2013/05/11/bezier-curves-and-picasso/">Continue reading <span class="meta-nav">&#8594;</span></a><img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=jeremykun.com&#038;blog=23934684&#038;post=3383&#038;subd=jeremykun&#038;ref=&#038;feed=1" width="1" height="1" />]]></description>
		<wfw:commentRss>http://jeremykun.com/2013/05/11/bezier-curves-and-picasso/feed/</wfw:commentRss>
		<slash:comments>15</slash:comments>
	
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			<media:title type="html">Dachshund-Picasso-Sketch</media:title>
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			<media:title type="html">the bull</media:title>
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			<media:title type="html">example-curve</media:title>
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			<media:title type="html">Screen Shot 2013-05-07 at 9.38.42 PM</media:title>
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		<media:content url="http://jeremykun.files.wordpress.com/2013/05/beziercurve.gif" medium="image">
			<media:title type="html">BezierCurve</media:title>
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		<media:content url="http://jeremykun.files.wordpress.com/2013/05/subdivision.png" medium="image">
			<media:title type="html">subdivision</media:title>
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		<media:content url="http://jeremykun.files.wordpress.com/2013/05/bezier-dog-image.png" medium="image">
			<media:title type="html">Picasso&#039;s &#34;Dog,&#34; redesigned as a sequence of eight bezier curves.</media:title>
		</media:content>

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			<media:title type="html">bezier-dog-for-web</media:title>
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		<item>
		<title>Facebook Page, Google+ Community, and Whispers of Guest Posts</title>
		<link>http://jeremykun.com/2013/05/04/facebook-page-google-community-and-whispers-of-guest-posts/</link>
		<comments>http://jeremykun.com/2013/05/04/facebook-page-google-community-and-whispers-of-guest-posts/#comments</comments>
		<pubDate>Sun, 05 May 2013 01:01:42 +0000</pubDate>
		<dc:creator>j2kun</dc:creator>
				<category><![CDATA[General]]></category>
		<category><![CDATA[facebook]]></category>
		<category><![CDATA[google]]></category>
		<category><![CDATA[guest-post]]></category>
		<category><![CDATA[twitter]]></category>

		<guid isPermaLink="false">http://jeremykun.com/?p=3425</guid>
		<description><![CDATA[I recently decided to add a few new ways for readers to keep up with what&#8217;s going on at Math ∩ Programming. These come in the form of a Google+ community and a Facebook group. I also have a seasoned Twitter &#8230; <a href="http://jeremykun.com/2013/05/04/facebook-page-google-community-and-whispers-of-guest-posts/">Continue reading <span class="meta-nav">&#8594;</span></a><img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=jeremykun.com&#038;blog=23934684&#038;post=3425&#038;subd=jeremykun&#038;ref=&#038;feed=1" width="1" height="1" />]]></description>
		<wfw:commentRss>http://jeremykun.com/2013/05/04/facebook-page-google-community-and-whispers-of-guest-posts/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
	
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			<media:title type="html">jeremykun</media:title>
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			<media:title type="html">gplus-community</media:title>
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			<media:title type="html">fbpage</media:title>
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	</item>
		<item>
		<title>Categories as Types</title>
		<link>http://jeremykun.com/2013/05/04/categories-as-types/</link>
		<comments>http://jeremykun.com/2013/05/04/categories-as-types/#comments</comments>
		<pubDate>Sun, 05 May 2013 00:30:35 +0000</pubDate>
		<dc:creator>j2kun</dc:creator>
				<category><![CDATA[Category Theory]]></category>
		<category><![CDATA[Data Structures]]></category>
		<category><![CDATA[categories]]></category>
		<category><![CDATA[mathematics]]></category>
		<category><![CDATA[ML]]></category>
		<category><![CDATA[programming]]></category>

		<guid isPermaLink="false">http://jeremykun.com/?p=3390</guid>
		<description><![CDATA[In this post we&#8217;ll get a quick look at two ways to define a category as a type in ML. The first way will be completely trivial: we&#8217;ll just write it as a tuple of functions. The second will involve &#8230; <a href="http://jeremykun.com/2013/05/04/categories-as-types/">Continue reading <span class="meta-nav">&#8594;</span></a><img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=jeremykun.com&#038;blog=23934684&#038;post=3390&#038;subd=jeremykun&#038;ref=&#038;feed=1" width="1" height="1" />]]></description>
		<wfw:commentRss>http://jeremykun.com/2013/05/04/categories-as-types/feed/</wfw:commentRss>
		<slash:comments>6</slash:comments>
	
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			<media:title type="html">jeremykun</media:title>
		</media:content>

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			<media:title type="html">vert-arrow</media:title>
		</media:content>

		<media:content url="http://jeremykun.files.wordpress.com/2013/02/diagram-morphism.png" medium="image">
			<media:title type="html">diagram-morphism</media:title>
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	</item>
		<item>
		<title>Rings — A Primer</title>
		<link>http://jeremykun.com/2013/04/30/rings-a-primer/</link>
		<comments>http://jeremykun.com/2013/04/30/rings-a-primer/#comments</comments>
		<pubDate>Tue, 30 Apr 2013 17:17:28 +0000</pubDate>
		<dc:creator>j2kun</dc:creator>
				<category><![CDATA[Primers]]></category>
		<category><![CDATA[Ring Theory]]></category>
		<category><![CDATA[abelian groups]]></category>
		<category><![CDATA[algebraic geometry]]></category>
		<category><![CDATA[division algorithm]]></category>
		<category><![CDATA[euclidean domain]]></category>
		<category><![CDATA[mathematics]]></category>
		<category><![CDATA[polynomial ring]]></category>
		<category><![CDATA[UFD]]></category>

		<guid isPermaLink="false">http://jeremykun.wordpress.com/?p=2509</guid>
		<description><![CDATA[Previously on this blog, we&#8217;ve covered two major kinds of algebraic objects: the vector space and the group. There are at least two more fundamental algebraic objects every mathematician should something know about. The first, and the focus of this &#8230; <a href="http://jeremykun.com/2013/04/30/rings-a-primer/">Continue reading <span class="meta-nav">&#8594;</span></a><img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=jeremykun.com&#038;blog=23934684&#038;post=2509&#038;subd=jeremykun&#038;ref=&#038;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>6</slash:comments>
	
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			<media:title type="html">jeremykun</media:title>
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			<media:title type="html">rings</media:title>
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		<item>
		<title>Persistent Homology Talk at UIC: Slides</title>
		<link>http://jeremykun.com/2013/04/27/persistent-homology-talk-at-uic-slides/</link>
		<comments>http://jeremykun.com/2013/04/27/persistent-homology-talk-at-uic-slides/#comments</comments>
		<pubDate>Sat, 27 Apr 2013 21:50:15 +0000</pubDate>
		<dc:creator>j2kun</dc:creator>
				<category><![CDATA[General]]></category>
		<category><![CDATA[persistent homology]]></category>
		<category><![CDATA[slides]]></category>

		<guid isPermaLink="false">http://jeremykun.com/?p=3380</guid>
		<description><![CDATA[Today I gave a twenty-minute talk at UI Chicago as part of the first annual Chicago Area Student SIAM Conference. My talk was titled &#8220;Recent Developments in Persistent Homology,&#8221; and it foreshadows the theoretical foundations and computational implementations we&#8217;ll be &#8230; <a href="http://jeremykun.com/2013/04/27/persistent-homology-talk-at-uic-slides/">Continue reading <span class="meta-nav">&#8594;</span></a><img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=jeremykun.com&#038;blog=23934684&#038;post=3380&#038;subd=jeremykun&#038;ref=&#038;feed=1" width="1" height="1" />]]></description>
		<wfw:commentRss>http://jeremykun.com/2013/04/27/persistent-homology-talk-at-uic-slides/feed/</wfw:commentRss>
		<slash:comments>1</slash:comments>
	
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			<media:title type="html">jeremykun</media:title>
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		<item>
		<title>Introducing Categories</title>
		<link>http://jeremykun.com/2013/04/24/introducing-categories/</link>
		<comments>http://jeremykun.com/2013/04/24/introducing-categories/#comments</comments>
		<pubDate>Wed, 24 Apr 2013 11:48:01 +0000</pubDate>
		<dc:creator>j2kun</dc:creator>
				<category><![CDATA[Category Theory]]></category>
		<category><![CDATA[Primers]]></category>
		<category><![CDATA[categories]]></category>

		<guid isPermaLink="false">http://jeremykun.com/?p=2955</guid>
		<description><![CDATA[It is time for us to formally define what a category is, to see a wealth of examples. In our next post we&#8217;ll see how the definitions laid out here translate to programming constructs. As we&#8217;ve said in our soft &#8230; <a href="http://jeremykun.com/2013/04/24/introducing-categories/">Continue reading <span class="meta-nav">&#8594;</span></a><img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=jeremykun.com&#038;blog=23934684&#038;post=2955&#038;subd=jeremykun&#038;ref=&#038;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>1</slash:comments>
	
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			<media:title type="html">jeremykun</media:title>
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			<media:title type="html">first-diagram</media:title>
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			<media:title type="html">graph-commutative</media:title>
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			<media:title type="html">vert-arrow</media:title>
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		<media:content url="http://jeremykun.files.wordpress.com/2013/02/diagram-morphism.png" medium="image">
			<media:title type="html">diagram-morphism</media:title>
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			<media:title type="html">composing-diagram-morphisms</media:title>
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			<media:title type="html">pairs-category</media:title>
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		<item>
		<title>Categories, What&#8217;s the Point?</title>
		<link>http://jeremykun.com/2013/04/16/categories-whats-the-point/</link>
		<comments>http://jeremykun.com/2013/04/16/categories-whats-the-point/#comments</comments>
		<pubDate>Tue, 16 Apr 2013 23:00:09 +0000</pubDate>
		<dc:creator>j2kun</dc:creator>
				<category><![CDATA[Category Theory]]></category>
		<category><![CDATA[General]]></category>
		<category><![CDATA[categories]]></category>
		<category><![CDATA[mathematics]]></category>

		<guid isPermaLink="false">http://jeremykun.com/?p=3297</guid>
		<description><![CDATA[Perhaps primarily due to the prominence of monads in the Haskell programming language, programmers are often curious about category theory. Proponents of Haskell and other functional languages can put category-theoretic concepts on a pedestal or in a mexican restaurant, and their benefits &#8230; <a href="http://jeremykun.com/2013/04/16/categories-whats-the-point/">Continue reading <span class="meta-nav">&#8594;</span></a><img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=jeremykun.com&#038;blog=23934684&#038;post=3297&#038;subd=jeremykun&#038;ref=&#038;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>12</slash:comments>
	
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	</item>
		<item>
		<title>Probabilistic Bounds — A Primer</title>
		<link>http://jeremykun.com/2013/04/15/probabilistic-bounds-a-primer/</link>
		<comments>http://jeremykun.com/2013/04/15/probabilistic-bounds-a-primer/#comments</comments>
		<pubDate>Mon, 15 Apr 2013 16:14:32 +0000</pubDate>
		<dc:creator>j2kun</dc:creator>
				<category><![CDATA[Primers]]></category>
		<category><![CDATA[Probability Theory]]></category>
		<category><![CDATA[chebyshev]]></category>
		<category><![CDATA[chernoff]]></category>
		<category><![CDATA[markov]]></category>
		<category><![CDATA[mathematics]]></category>
		<category><![CDATA[probabilistic method]]></category>
		<category><![CDATA[random variables]]></category>
		<category><![CDATA[variance]]></category>

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		<description><![CDATA[Probabilistic arguments are a key tool for the analysis of algorithms in machine learning theory and probability theory. They also assume a prominent role in the analysis of randomized and streaming algorithms, where one imposes a restriction on the amount &#8230; <a href="http://jeremykun.com/2013/04/15/probabilistic-bounds-a-primer/">Continue reading <span class="meta-nav">&#8594;</span></a><img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=jeremykun.com&#038;blog=23934684&#038;post=3262&#038;subd=jeremykun&#038;ref=&#038;feed=1" width="1" height="1" />]]></description>
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