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<title>You don't need to prove this</title>
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<a href="https://newptcai.github.io/tiling-chessboard-with-l-shaped-tiles.html"><img src="" style="width: 100%;"></img></a>
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<h1><a href="https://newptcai.github.io/tiling-chessboard-with-l-shaped-tiles.html">Tiling chessboard with L-shaped tiles</a></h1>
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<div class="w3-opacity w3-margin-right w3-margin-bottom" style="flex-grow: 1;">
<span> Posted on Wed 22 May 2019 in <a href="https://newptcai.github.io/category/math.html" style="font-style: italic">math</a>
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<a href="https://newptcai.github.io/tag/combinatorics.html" title=" All posts about Combinatorics
">#combinatorics</a>
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<div class="entry-content"><p>I created a <a href="https://github.com/newptcai/math-note/blob/v0.1.1/2019-05-22-chessboard.ipynb">Jupyter notebook</a> for teaching induction in combinatorics to demonstrate that you can
always tile a <span class="math">\(2^n …</span></p><script type='text/javascript'>if (!document.getElementById('mathjaxscript_pelican_#%@#$@#')) {
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<h1><a href="https://newptcai.github.io/randomtreejl-simulation-on-large-random-trees-with-julia.html">RandomTree.jl -- Simulation on large random trees with Julia</a></h1>
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<div class="w3-opacity w3-margin-right w3-margin-bottom" style="flex-grow: 1;">
<span> Posted on Mon 13 May 2019 in <a href="https://newptcai.github.io/category/math.html" style="font-style: italic">math</a>
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<a href="https://newptcai.github.io/tag/probability.html" title=" All posts about Probability
">#probability</a>
</span>
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<div class="entry-content"><p>I have been working on a software package
<a href="https://github.com/newptcai/RandomTree.jl"><code>RandomTree.jl</code></a> that could effectively generate pretty
large (<span class="math">\(10^8\)</span> nodes) random …</p><script type='text/javascript'>if (!document.getElementById('mathjaxscript_pelican_#%@#$@#')) {
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<h1><a href="https://newptcai.github.io/combinatorics-1ma020-spring-2019-archive.html">Combinatorics 1MA020, Spring 2019 (Archive)</a></h1>
<div class="post-info">
<div class="w3-opacity w3-margin-right w3-margin-bottom" style="flex-grow: 1;">
<span> Posted on Sat 12 January 2019 in <a href="https://newptcai.github.io/category/math.html" style="font-style: italic">math</a>
</span>
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<a href="https://newptcai.github.io/tag/combinatorics.html" title=" All posts about Combinatorics
">#combinatorics</a>
</span>
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<a href="https://newptcai.github.io/tag/teaching.html" title=" All posts about Teaching
">#teaching</a>
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<div class="entry-content"><p>I just finished teaching the course Combinatorics 1MA020 (Spring 2019) at Uppsala University. Here are the
materials that I prepared …</p></div>
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<h1><a href="https://newptcai.github.io/the-joy-of-experimental-mathematics.html">The joy of experimental mathematics</a></h1>
<div class="post-info">
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<span> Posted on Sat 12 January 2019 in <a href="https://newptcai.github.io/category/math.html" style="font-style: italic">math</a>
</span>
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<a href="https://newptcai.github.io/tag/analysis.html" title=" All posts about Analysis
">#analysis</a>
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">#Mathematica</a>
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">#CAS</a>
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">#experimental-math</a>
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<div class="entry-content"><p>I came across <a href="https://math.stackexchange.com/q/3070440/1618">an interesting identity</a> on math.stackexchange.com.
</p></div>
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<h1><a href="https://newptcai.github.io/the-sum-of-n-uniform-01-random-variables.html">The sum of n uniform [0,1] random variables</a></h1>
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<span> Posted on Wed 09 January 2019 in <a href="https://newptcai.github.io/category/math.html" style="font-style: italic">math</a>
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<div class="entry-content"><p>Update: Svante Janson told me yesterday that the integral I had at the end of this post is
known as …</p></div>
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<h1><a href="https://newptcai.github.io/an-example-of-proving-summation-identities-with-computer.html">An example of proving summation identities with computer</a></h1>
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<span> Posted on Fri 21 December 2018 in <a href="https://newptcai.github.io/category/math.html" style="font-style: italic">math</a>
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<div class="entry-content"><p>I am trying to learn how to use computers to prove identities like this one
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<h1><a href="https://newptcai.github.io/the-strahler-horton-number-on-random-trees.html">The Strahler-Horton number on random trees</a></h1>
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<span> Posted on Mon 17 December 2018 in <a href="https://newptcai.github.io/category/math.html" style="font-style: italic">math</a>
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<div class="entry-content"><p>We list some open problems regarding the Strahler-Horton number on random trees <span class="math">\(T_n\)</span>.</p>
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<h1><a href="https://newptcai.github.io/the-moment-of-truncated-random-variables.html">The moment of truncated random variables</a></h1>
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<span> Posted on Sat 08 December 2018 in <a href="https://newptcai.github.io/category/math.html" style="font-style: italic">math</a>
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<div class="entry-content"><p>Given a random variable <span class="math">\(Y\)</span>, sometimes we want to compute the expectation of <span class="math">\(Y[Y\le a]\)</span>, where
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<h1><a href="https://newptcai.github.io/the-convexity-property-related-to-beta-densities-in-sage.html">The Convexity Property Related to Beta Densities -- In sage</a></h1>
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<span> Posted on Fri 07 December 2018 in <a href="https://newptcai.github.io/category/math.html" style="font-style: italic">math</a>
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<div class="entry-content"><p>This is a continuation of <a href="https://newptcai.github.io/the-convexity-property-related-to-beta-densities.html">my previous post on beta distribution</a>.</p>
<p>My colleague Tilo wants me to use Sagemath instead …</p></div>
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<h1><a href="https://newptcai.github.io/another-version-of-chernoffs-bound-and-a-mathematica-package-for-it.html">Another version of Chernoff's bound and a Mathematica package for it</a></h1>
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<span> Posted on Sun 02 December 2018 in <a href="https://newptcai.github.io/category/math.html" style="font-style: italic">math</a>
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<div class="entry-content"><p><a href="">Chernoff's bound</a> is a group of quite well-known concentration-inequalities. I though I know it
but last week my collage <a href="http://katalog.uu.se/empinfo/?id=N18-1440">Gabriel …</a></p></div>
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