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<!doctype html>
<html lang=en>
<head>
<meta charset=utf-8>
<title>Boston Computation Club</title>
</head>
<link rel="stylesheet" href="https://unpkg.com/[email protected]/build/pure-min.css" integrity="sha384-cg6SkqEOCV1NbJoCu11+bm0NvBRc8IYLRGXkmNrqUBfTjmMYwNKPWBTIKyw9mHNJ" crossorigin="anonymous">
<link rel="stylesheet" type="text/css" href="index.css" media="screen"/>
<body>
<p>
<center>
<h1>Boston Computation Club - Math Café</h1>
<h2>(<a href="https://bstn.cc/">return to homepage</a>)</h2>
</center>
<br>
<div style="margin: 10px 40px 40px 40px; font-size: 1.5em">
<h2>Café #1 - January 20</h2>
<p>For "homework" read chapters 1 and 2 of <a href="https://www.math3ma.com/blog/topology-book">Topology: A Categorical Approach</a> and attempt the following:
<ul>
<li>1.1 draw examples</li>
<li>1.3 check Zariski Topology property</li>
<li>1.10 prove quotient topology characterized by given universal prop</li>
<li>2.2 prove or disprove a local consistency property</li>
<li>2.9 proof about locally compact Hausdorff spaces</li>
<li>2.15 prove or disprove a compactness property</li>
<li>Optionally, exercises: 1.11, 2.21</li>
</ul>
</p>
<h2>Café #2 - February 10th at 1:30-2:30pm EST</h2>
<p>We'll start to follow along with the Albin lectures (<a href="https://www.youtube.com/watch?v=XxFGokyYo6g&list=PLpRLWqLFLVTCL15U6N3o35g4uhMSBVA2b">found here</a>).
For the 10th, aim for listening to the first two lectures + whatever supplemental reading you think might be relevant / helpful from Hatcher (<a href="https://pi.math.cornell.edu/~hatcher/AT/AT.pdf">link</a>).
</p>
<p>Instead of assigning problems, look at Albin's homework #1 (<a href="https://faculty.math.illinois.edu/~palbin/Math525.Spring2018/HW1.pdf">link</a>) and choose one you think might be tractable to work on. As usual we can discuss on slack or via ad-hoc meetings in the upcoming weeks.
</p>
<h2>Café #3 - Selected Topics in Kleene Algebra</h2>
<p>Cheng hasn't assigned any homework.</p>
<h2>Café #4 - Prep for Jean-Eric Pin's Lecture</h2>
<p>In preperation for Dr. Jean-Eric Pin's lecture on the Generalized Star Height Problem, we will discuss the following concepts:
<ol>
<li>first order logic</li>
<li>words and languages</li>
<li>finite deterministic automata</li>
<li>regular expressions
<li>monoids</li>
<ul>
<li>free monoids</li>
<li>monoid morphism</li>
</ul>
</li>
<li>metric spaces
<ul><li>completion of a metric</li></ul>
</li>
</ol>
Dr. Pin has provided us with <a href="artifacts/jeanEricPin/prep.pdf">some hand-written nodes</a> which we can use as a resource.
</p>
<h2>Café #5 - The Collatz Conjecture, in Ivy</h2>
<p>No need to prep for this one. Max will use the Collatz Conjecture (which he surely will not resolve) as a motivating example for a tutorial on Ivy, and more generally, on formal methods and inductive invariants.</p>
<h2>Café #6 - Infinite Analysis & Nets</h2>
<p>Read chapter 2 through section 2.6 (Nets) of <a href="https://link.springer.com/book/10.1007/3-540-29587-9">Infinite Dimensional Analysis: A Hitchhiker's Guide</a>. We will discuss the covered topics.</p>
<h2>Café #7 & #8 - More Infinite Analysis</h2>
<p>Read through section 2.8 (Compactness) of <a href="https://link.springer.com/book/10.1007/3-540-29587-9">Infinite Dimensional Analysis: A Hitchhiker's Guide</a>. We will discuss the covered topics.</p>
</div>
</p>
</body>
</html>