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<!DOCTYPE html>
<!--**************************************-->
<!--* Generated from MathBook XML source *-->
<!--* on 2016-03-05T09:10:50-05:00 *-->
<!--* *-->
<!--* http://mathbook.pugetsound.edu *-->
<!--* *-->
<!--**************************************-->
<html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>UML-MBX LaTeX</title><meta name="Keywords" content="Authored in MathBook XML"></meta><meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=0, minimum-scale=1.0, maximum-scale=1.0"></meta><script xmlns:b64="https://github.com/ilyakharlamov/xslt_base64" type="text/x-mathjax-config">
MathJax.Hub.Config({
tex2jax: {
inlineMath: [['\\(','\\)']],
},
TeX: {
extensions: ["AMSmath.js", "AMSsymbols.js", "extpfeil.js", "autobold.js", "https://aimath.org/mathbook/mathjaxknowl.js", ],
equationNumbers: { autoNumber: "none",
useLabelIds: true,
// JS comment, XML CDATA protect XHTML quality of file
// if removed in XSL, use entities
//<![CDATA[
formatID: function (n) {return String(n).replace(/[:'"<>&]/g,"")},
//]]>
},
TagSide: "right",
TagIndent: ".8em",
},
"HTML-CSS": {
scale: 88,
},
});
</script><script xmlns:b64="https://github.com/ilyakharlamov/xslt_base64" type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML-full"></script><script xmlns:b64="https://github.com/ilyakharlamov/xslt_base64" type="text/javascript" src="https://sagecell.sagemath.org/static/jquery.min.js"></script><script xmlns:b64="https://github.com/ilyakharlamov/xslt_base64" type="text/javascript" src="https://sagecell.sagemath.org/embedded_sagecell.js"></script><script xmlns:b64="https://github.com/ilyakharlamov/xslt_base64">
$(function () {
// Make *any* div with class 'sage-compute' an executable Sage cell
sagecell.makeSagecell({inputLocation: 'div.sage-compute',
linked: true,
evalButtonText: 'Evaluate'});
});
$(function () {
// Make *any* div with class 'sage-display' a visible, uneditable Sage cell
sagecell.makeSagecell({inputLocation: 'div.sage-display',
editor: 'codemirror-readonly',
hide: ['evalButton', 'editorToggle', 'language']});
});
</script><script xmlns:b64="https://github.com/ilyakharlamov/xslt_base64" type="text/javascript" src="https://code.jquery.com/jquery-latest.min.js"></script><link xmlns:b64="https://github.com/ilyakharlamov/xslt_base64" href="https://aimath.org/knowlstyle.css" rel="stylesheet" type="text/css"></link><script xmlns:b64="https://github.com/ilyakharlamov/xslt_base64" type="text/javascript" src="https://aimath.org/knowl.js"></script><script xmlns:b64="https://github.com/ilyakharlamov/xslt_base64" src="https://aimath.org/mathbook/js/lib/jquery.sticky.js"></script><script xmlns:b64="https://github.com/ilyakharlamov/xslt_base64" src="https://aimath.org/mathbook/js/lib/jquery.espy.min.js"></script><script xmlns:b64="https://github.com/ilyakharlamov/xslt_base64" src="https://aimath.org/mathbook/js/Mathbook.js"></script><link xmlns:b64="https://github.com/ilyakharlamov/xslt_base64" href="https://fonts.googleapis.com/css?family=Open+Sans:400,400italic,600,600italic|Source+Code+Pro:400" rel="stylesheet" type="text/css"></link><link xmlns:b64="https://github.com/ilyakharlamov/xslt_base64" href="https://aimath.org/mathbook/stylesheets/mathbook-3.css" rel="stylesheet" type="text/css"></link><link xmlns:b64="https://github.com/ilyakharlamov/xslt_base64" href="https://aimath.org/mathbook/mathbook-add-on.css" rel="stylesheet" type="text/css"></link></head><body class="mathbook-book has-toc has-sidebar-left"><div xmlns:b64="https://github.com/ilyakharlamov/xslt_base64" style="display:none;">\(\newcommand{\identity}{\mathrm{id}}
\newcommand{\notdivide}{{\not{\mid}}}
\newcommand{\notsubset}{\not\subset}
\newcommand{\lcm}{\operatorname{lcm}}
\newcommand{\gf}{\operatorname{GF}}
\newcommand{\inn}{\operatorname{Inn}}
\newcommand{\aut}{\operatorname{Aut}}
\newcommand{\Hom}{\operatorname{Hom}}
\newcommand{\cis}{\operatorname{cis}}
\newcommand{\chr}{\operatorname{char}}
\newcommand{\Null}{\operatorname{Null}}
\newcommand{\lt}{ < }
\newcommand{\gt}{ > }
\newcommand{\amp}{ & }\)</div><header id="masthead"><div class="banner"><div class="container"><a id="logo-link" href="http://faculty.uml.edu/klevasseur/uml-mbx/" target="_blank"><img src="http://faculty.uml.edu/klevasseur/images/small_umllogo.gif"></img></a><div class="title-container"><h1 class="heading"><span class="title">UMass Lowell Mathbook XML</span><span class="subtitle">a guide to creating open source STEM materials.</span></h1><p class="byline">Ken Levasseur</p></div></div></div><nav xmlns:b64="https://github.com/ilyakharlamov/xslt_base64" id="primary-navbar"><div class="container"><div class="navbar-top-buttons"><button class="sidebar-left-toggle-button button active">Contents</button><div class="tree-nav toolbar toolbar-divisor-3"><a class="previous-button toolbar-item button" href="chapter-2.html">Previous</a><a class="up-button button toolbar-item" href="chapter-2.html">Up</a><a class="next-button button toolbar-item" href="features.html">Next</a></div><button class="sidebar-right-toggle-button button active">Annotations</button></div><div class="navbar-bottom-buttons toolbar toolbar-divisor-4"><button class="sidebar-left-toggle-button button toolbar-item active">Contents</button><a class="previous-button toolbar-item button" href="chapter-2.html">Previous</a><a class="up-button button toolbar-item" href="chapter-2.html">Up</a><a class="next-button button toolbar-item" href="features.html">Next</a></div></div></nav></header><div class="page"><aside xmlns:b64="https://github.com/ilyakharlamov/xslt_base64" id="sidebar-left" class="sidebar"><div class="sidebar-content"><nav id="toc"><h2 class="link"><a href="index.html"><span class="title">Front Matter</span></a></h2><ul><li><a href="colophon-1.html">Colophon</a></li><li><a href="acknowledgement-1.html">Acknowledgements</a></li><li><a href="preface-1.html">Preface</a></li></ul><h2 class="link"><a href="overview.html"><span class="codenumber">1</span><span class="title">Overview</span></a></h2><ul><li><a href="mbx-structure.html">Structure of an MBX book</a></li><li><a href="html-conversion.html">The Conversion Process to html</a></li><li><a href="latex-conversion.html">The Conversion Process to LaTeX</a></li></ul><h2 class="link active"><a href="chapter-2.html"><span class="codenumber">2</span><span class="title">LaTeX</span></a></h2><ul><li><a href="latex.html" class="active">LaTeX</a></li></ul><h2 class="link"><a href="features.html"><span class="codenumber">3</span><span class="title">MBX Features</span></a></h2><ul><li><a href="definition-xref-exercise.html">Definitions, referencing, and exercises</a></li><li><a href="theorem.html">Theorems</a></li></ul><h2 class="link"><a href="chapter-4.html"><span class="codenumber">4</span><span class="title">Sage</span></a></h2><ul><li><a href="sage_cell.html">Sage Cell Calculations</a></li><li><a href="sageplot.html">Using sageplot to create images</a></li></ul><h2 class="link"><a href="backmatter.html"><span class="title">Reference</span></a></h2><ul><li><a href="chapter-5.html">Hints and Solutions to Selected Exercises</a></li><li><a href="chapter-6.html">Notation</a></li><li><a href="chapter-7.html">Lists of Elements</a></li></ul></nav><div class="extras"><nav><a class="mathbook-link" href="https://mathbook.pugetsound.edu">Authored in MathBook XML</a><a href="https://www.mathjax.org"><img title="Powered by MathJax" src="https://cdn.mathjax.org/mathjax/badge/badge.gif" border="0" alt="Powered by MathJax"></img></a></nav></div></div></aside><main class="main"><div id="content" class="mathbook-content"><section xmlns:b64="https://github.com/ilyakharlamov/xslt_base64" class="section" id="latex"><header><h1 class="heading" alt="Section 2.1 LaTeX" title="Section 2.1 LaTeX"><span class="type">Section</span><span class="codenumber">2.1</span><span class="title">LaTeX</span><a href="latex.html" class="permalink">¶ permalink</a></h1></header><p>Mathematical content should be displayed using LaTeX. This is accomplished using either <tt class="code-inline"><m></m></tt> for inline expressions or <tt class="code-inline"><me></me></tt> for display expressions.</p><p>For those who are new to LaTeX, several types of expressions appear in this section. The source code for this document can be consulted to see the LaTeX code to realize them. </p><article class="theorem-like" id="binomial-coefficient-formula"><h5 class="heading"><span class="type">Theorem</span><span class="codenumber">2.1.1</span><span class="title">Binomial Coefficient Formula</span></h5>
If \(n\) and \(k\) are nonnegative integers with \(0 \leq k \leq n\), then the number \(k\)-element subsets of an \(n\) element set is equal to <span class="displaymath" id="me-1">\[\binom{n}{k} = \frac{n!}{(n-k)! \cdot k!} \]</span></article><p>A simple array of sets.</p><span class="displaymath" id="me-2">\[
\begin{array}{cc}
\{1,2\} & \{3,4\} \\
\{1,3\} & \{2,4\} \\
\{1,4\} & \{2,3\} \\
\{2,3\} & \{1,4\} \\
\{2,4\} & \{1,3\} \\
\{3,4\} & \{1,2\} \\
\end{array}
\]</span><span class="displaymath" id="me-3">\[\binom{5}{0} x^5+\binom{5}{1} x^4 y+\binom{5}{2} x^3 y^2+\binom{5}{3} x^2 y^3+\binom{5}{4} x
\binom{5}{5} y^4+y^5
\]</span><p>Here is a chain of equalities:</p><p><span class="displaymath" id="me-4">\[\begin{split}
\lvert A \rvert & = \lvert A_1 \cup A_2 \cup A_3 \rvert \\
& = \lvert A_1 \rvert + \lvert A_2 \rvert + \lvert A_3 \rvert - \textrm{repeats} \\
& = \lvert A_1 \rvert + \lvert A_2 \rvert + \lvert A_3 \rvert - \textrm{duplicates} + \textrm{triplicates} \\
& = \lvert A_1 \rvert + \lvert A_2 \rvert + \lvert A_3 \rvert - (\lvert A_1 \cap A_2 \rvert + \lvert A_1 \cap A_3 \rvert+ \lvert A_2 \cap A_3 \rvert) + \lvert A_1 \cap A_2 \cap A_3 \rvert \\
& = 75 + 60 + 55 - 25 - 12 - 15 + 10 = 148 \\
\end{split}
\]</span></p><p>Here's a truth table generated in LaTeX:
<span class="displaymath" id="me-5">\[
\begin{array}{cccc}
p & q & \neg (p\land q) & \neg p\lor \neg q \\
\hline
0 & 0 & 1 & 1 \\
0 & 1 & 1 & 1 \\
1 & 0 & 1 & 1 \\
1 & 1 & 0 & 0 \\
\end{array}
\]</span>
</p></section></div></main></div></body></html>