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added author display, better homepage, minor improvements
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README.md

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# iiit-notebook
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iiit-notebook is a public repository of notes taken by students of IIIT Hyderabad.
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The website itself is completely static, generated using Jekyll, and made by Pratyaksh Gautam.
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The website itself is completely static, generated using Jekyll.
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## Features
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+ Syntax highlighting for code using Rouge,
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<pre>
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```language-name
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insert code here
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```c
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printf("Hello, world!\n");
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```
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</pre>
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+ Graphs written in mermaid-js, simply by writing the code in a `mermaid` code block.
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After that, you can add, commit and push your repo, and then make a PR to merge your changes.
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### Compatibility between `pandoc` and `jekyll`
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The website itself uses jekyll, but the PDF's rendered by `pandoc` generally look better and are more preferable, however not everything is perfectly compatible between the two, especially in math mode.
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When writing your notes keep the following things in mind:
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1. If you need to have pipe symbols (`\|`) or curly brackets (`\{`), not only should you escape them as shown here, but also nest them in a `div`. If you don't do this jekyll (the site) probably won't render it properly.
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For inline math: `<div>$S = \{a, b\}$</div>`
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For display math:
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```
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<div>
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$$f(x) = \|2 \times x + 1\|$$
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</div>
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```
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2. `pandoc` doesn't take kindly to spacing in between math mode delimiiters.
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This works:
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```
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$\frac{a}{b}$
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```
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This might not:
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```
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$ \frac{a}{b} $
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```
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### Courses
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Sometimes you might be the first person to write notes for a certain course, and as a result, the course itself will not exist as part of the website.

_layouts/post.html

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<p>
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{% assign course = site.courses | where: 'code', page.code | first%}
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{% if course %}
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<a href="{{ course.url }}"><h1>{{ course.code | upcase }} - {{ course.name }}</h1></a>
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<h1><a href="{{ course.url }}">{{ course.code | upcase }} - {{ course.name }}</a> | {{page.title}}</h1>
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with {{ course.lecturer }}
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{% endif %}
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<div class = "date">{{ page.date | date: "%b %d, %Y - %A" }}</div>
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<div>Written by: {{ page.author }}</div>
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</p>
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{{ content }}

_posts/2020-11-05-ds-lecture-22.md

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(i) Left-cancellativity $\Rightarrow$ unique solution
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Consider the function $f_{a}: S \rightarrow S$, defined as $f_{a}(x) = a \cdot x$. If it is invertible, then the equation would have a unique solution. Its range is:
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<div> $ S_{a_{L}} = \{a \cdot x | x \in S \} $ </div>
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<div>$S_{a_{L}} = \{a \cdot x | x \in S \}$</div>
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By closure, $S_{a_{L}} \subseteq S$. If $\|S_{a_{L}}\| < \|S\|$, then (by PHP), $a \cdot x_{1} = a \cdot x_{2}, x_{1} \neq x_{2}$ for some $x_{1},x_{2} \in S$ (*i.e.*, $f_{a}$ is many-one). However, $a$ is left-cancellative; hence $x_{1} = x_{2}$ and $f_{a}$ is one-one. This is a contradiction – hence $\|S_{a_{L}}\| = \|S\|$ and $S_{a_{L}} = S$.
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| --- | --- | --- | --- |
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| Quasigroup | Closure, Cancellativity | $\langle \mathbb{Z}, - \rangle$ | $\langle \mathbb{V}_ {2}, \times \rangle$[^1] |
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| --- | --- | --- | --- |
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| Group | Closure, Associativity, E. of Inverse, E. of Identity | $\langle \mathbb{Z_{n}}, \times_{n} \rangle$ | $\langle \mathbb{N}, \div \rangle$ |
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| Group | Closure, Associativity, E. of Inverse, E. of Identity | $\langle \mathbb{Z}_{n}, \times_{n} \rangle$ | $\langle \mathbb{N}, \div \rangle$ |
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[^1]: $\mathbb{V}_{2}$ = set of all vectors in the plane (non-standard notation); $\times$ = cross product
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[^1]:
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$\mathbb{V}_{2}$ = set of all vectors in the plane (non-standard notation); $\times$ = cross product
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Note that (i) all semigroups, monoids, quasigroups and groups are groupoids, (ii) all monoids and groups are semigroups, and (iii) all groups are groupoids, semigroups, quasigroups and monoids.
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A semigroup or monoid is said to be *cyclic* if all its elements can be obtained from one of its elements by repeated application of the operation. Formally, for a system $\langle S, \cdot \rangle$, $\exists s \in S$ such that S can be written as
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<div>
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$$
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S = \{s^{n} | n \in \mathbb{N}_{0}\}

index.html

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---
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title: Index
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---
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<h1>Latest Notes</h1>
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<h1>iiit-notebook</h1>
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<p>
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iiit-notebook is a public repository of notes taken by students of IIIT Hyderabad.
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Find the README at the <a href='https://github.com/iiit-notebook/iiit-notebook.github.io'>github repository (click here).</a>
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</p>
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<h2>Latest Notes</h2>
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<ul>
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{% for post in site.posts %}

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