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https://github.com/rafael-a-monteiro-math/short-notes

These are some notes I wrote for internal seminars (audience made up of mathematicians, physicists and other scientists). They are only for teaching purpose.
https://github.com/rafael-a-monteiro-math/short-notes

dynamical-systems numerical-linear-algebra svd svd-matrix-factorisation

Last synced: about 1 month ago
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These are some notes I wrote for internal seminars (audience made up of mathematicians, physicists and other scientists). They are only for teaching purpose.

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code{white-space: pre;}

pre:not([class]) {
background-color: white;
}

if (window.hljs) {
hljs.configure({languages: []});
hljs.initHighlightingOnLoad();
if (document.readyState && document.readyState === "complete") {
window.setTimeout(function() { hljs.initHighlighting(); }, 0);
}
}

h1 {
font-size: 34px;
}
h1.title {
font-size: 38px;
}
h2 {
font-size: 30px;
}
h3 {
font-size: 24px;
}
h4 {
font-size: 18px;
}
h5 {
font-size: 16px;
}
h6 {
font-size: 12px;
}
.table th:not([align]) {
text-align: left;
}

.main-container {
max-width: 940px;
margin-left: auto;
margin-right: auto;
}
code {
color: inherit;
background-color: rgba(0, 0, 0, 0.04);
}
img {
max-width:100%;
height: auto;
}
.tabbed-pane {
padding-top: 12px;
}
.html-widget {
margin-bottom: 20px;
}
button.code-folding-btn:focus {
outline: none;
}
summary {
display: list-item;
}

/* padding for bootstrap navbar */
body {
padding-top: 60px;
padding-bottom: 40px;
}
/* offset scroll position for anchor links (for fixed navbar) */
.section h1 {
padding-top: 65px;
margin-top: -65px;
}
.section h2 {
padding-top: 65px;
margin-top: -65px;
}
.section h3 {
padding-top: 65px;
margin-top: -65px;
}
.section h4 {
padding-top: 65px;
margin-top: -65px;
}
.section h5 {
padding-top: 65px;
margin-top: -65px;
}
.section h6 {
padding-top: 65px;
margin-top: -65px;
}
.dropdown-submenu {
position: relative;
}
.dropdown-submenu>.dropdown-menu {
top: 0;
left: 100%;
margin-top: -6px;
margin-left: -1px;
border-radius: 0 6px 6px 6px;
}
.dropdown-submenu:hover>.dropdown-menu {
display: block;
}
.dropdown-submenu>a:after {
display: block;
content: " ";
float: right;
width: 0;
height: 0;
border-color: transparent;
border-style: solid;
border-width: 5px 0 5px 5px;
border-left-color: #cccccc;
margin-top: 5px;
margin-right: -10px;
}
.dropdown-submenu:hover>a:after {
border-left-color: #ffffff;
}
.dropdown-submenu.pull-left {
float: none;
}
.dropdown-submenu.pull-left>.dropdown-menu {
left: -100%;
margin-left: 10px;
border-radius: 6px 0 6px 6px;
}

// manage active state of menu based on current page
$(document).ready(function () {
// active menu anchor
href = window.location.pathname
href = href.substr(href.lastIndexOf('/') + 1)
if (href === "")
href = "index.html";
var menuAnchor = $('a[href="' + href + '"]');

// mark it active
menuAnchor.parent().addClass('active');

// if it's got a parent navbar menu mark it active as well
menuAnchor.closest('li.dropdown').addClass('active');
});

.tabset-dropdown > .nav-tabs {
display: inline-table;
max-height: 500px;
min-height: 44px;
overflow-y: auto;
background: white;
border: 1px solid #ddd;
border-radius: 4px;
}

.tabset-dropdown > .nav-tabs > li.active:before {
content: "";
font-family: 'Glyphicons Halflings';
display: inline-block;
padding: 10px;
border-right: 1px solid #ddd;
}

.tabset-dropdown > .nav-tabs.nav-tabs-open > li.active:before {
content: "";
border: none;
}

.tabset-dropdown > .nav-tabs.nav-tabs-open:before {
content: "";
font-family: 'Glyphicons Halflings';
display: inline-block;
padding: 10px;
border-right: 1px solid #ddd;
}

.tabset-dropdown > .nav-tabs > li.active {
display: block;
}

.tabset-dropdown > .nav-tabs > li > a,
.tabset-dropdown > .nav-tabs > li > a:focus,
.tabset-dropdown > .nav-tabs > li > a:hover {
border: none;
display: inline-block;
border-radius: 4px;
}

.tabset-dropdown > .nav-tabs.nav-tabs-open > li {
display: block;
float: none;
}

.tabset-dropdown > .nav-tabs > li {
display: none;
}

$(document).ready(function () {
window.buildTabsets("TOC");
});

$(document).ready(function () {
$('.tabset-dropdown > .nav-tabs > li').click(function () {
$(this).parent().toggleClass('nav-tabs-open')
});
});


Stochastic-Simulations


A glimpse of some stochastic simulation methods.

I don’t claim originality for the results posted here: these are mostly some quick experiments I did while doing research.


// add bootstrap table styles to pandoc tables
function bootstrapStylePandocTables() {
$('tr.header').parent('thead').parent('table').addClass('table table-condensed');
}
$(document).ready(function () {
bootstrapStylePandocTables();
});

(function () {
var script = document.createElement("script");
script.type = "text/javascript";
script.src = "https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML";
document.getElementsByTagName("head")[0].appendChild(script);
})();