\documentclass[letterpaper, twoside, 12pt]{book}
\usepackage{amsmath,amsfonts,amsthm}
\usepackage{notes}
\usepackage{hyperref}
\title{MATH 3142 Notes | Spring 2016}
\date{Updated: \today}
\author{Your Name Here\\ UNC Charlotte}
\begin{document}
\maketitle
\setcounter{chapter}{9}
\chapter{The Euclidean Space \texorpdfstring{\(\mathbb R^n\)}{Rn}}
\section{The Linear Structure of \texorpdfstring{\(\mathbb R^n\)}{Rn}
and the Scalar Product}
\begin{proposition}[10.2]
Let \(\mathbf u,\mathbf v,\mathbf w\in\mathbb R^n\)
and \(\alpha,\beta\in\mathbb R\). Then both of the following hold:
\[
\langle \mathbf u,\mathbf v\rangle=\langle \mathbf v,\mathbf u\rangle
\]
\[
\langle \alpha\mathbf u+\beta\mathbf w,v\rangle
=
\alpha\langle \mathbf u,\mathbf v\rangle+\beta\langle \mathbf w,\mathbf v\rangle
\]
\end{proposition}
\begin{proof}
\end{proof}
\begin{lemma}[10.4]
For \(\mathbf u,\mathbf v\in\mathbb R^n\), \(\mathbf u,\mathbf v\) are
orthogonal if and only if
\(\|\mathbf u+\mathbf v\|=\|\mathbf u\|^2+\|\mathbf v\|^2\).
\end{lemma}
\begin{proof}
\end{proof}
\begin{lemma}[10.5]
For \(\mathbf u,\mathbf v\in\mathbb R^n\) where \(\mathbf v\not=\mathbf 0\),
define \(\lambda=\frac{\langle \mathbf u,\mathbf v\rangle}{\langle \mathbf v,\mathbf v\rangle}\)
and \(\mathbf w=\mathbf u-\lambda\mathbf v\). Then \(\mathbf v,\mathbf w\)
are orthogonal and \(\mathbf u=\mathbf w+\lambda\mathbf v\).
\end{lemma}
\begin{proof}
\end{proof}
\begin{theorem}[10.6, The Cauchy-Schwarz Inequality]
For any two vectors \(\mathbf u,\mathbf v\in\mathbb R^n\),
\[
|\langle \mathbf u,\mathbf v\rangle|
\leq
\|\mathbf u\|\|\mathbf v\|
.\]
\end{theorem}
\begin{proof}
\end{proof}
\begin{theorem}[10.7, The Triangle Inequality]
For any two vectors \(\mathbf u,\mathbf v\in\mathbb R^n\),
\[
\|\mathbf u+\mathbf v\|
\leq
\|\mathbf u\|+\|\mathbf v\|
.\]
\end{theorem}
\begin{exercise}[3]
Show that for \(\mathbf u\in\mathbb R^n\), \(\alpha\in\mathbb R\):
\begin{enumerate}[(a)]
\item \(\|\mathbf u\|=0\) if and only if \(\mathbf u=\mathbf 0\).
\item \(\|\alpha\mathbf u\|=|\alpha|\|\mathbf u\|\).
\end{enumerate}
\end{exercise}
\begin{proof}
\end{proof}
\begin{exercise}[4]
For \(\mathbf u,\mathbf v\in\mathbb R^n\) verify the identity
\[
\|\mathbf u-\mathbf v\|^2
=
\|\mathbf u\|^2+\|\mathbf v\|^2-2\langle \mathbf u,\mathbf v\rangle
.\]
\end{exercise}
\begin{proof}
\end{proof}
\begin{exercise}[9]
Let \(\mathbf u\in\mathbb R^n\) and suppose \(\|\mathbf u\|<1\).
Show that for \(\mathbf v\in\mathbb R^n\),
\(\|\mathbf v-\mathbf u\|<1-\|\mathbf u\|\) implies
\(\|\mathbf v\|<1\).
\end{exercise}
\begin{proof}
\end{proof}
\begin{exercise}[10]
Let \(\mathbf u\in\mathbb R^n\) and \(r>0\). Suppose \(\mathbf v,\mathbf w\in\mathbb R^n\)
are at a distance less than \(r\) from \(\mathbf u\). Prove that if
\(0\leq t\leq 1\), then the point \(t\mathbf v+(1-t)]\mathbf w\) is also
at a distance less than \(r\) from \(\mathbf u\).
\end{exercise}
\begin{proof}
\end{proof}
\end{document}
The above markup is causing the strange error from the title: LATEX ERROR: BAD MATH ENVIRONMENT DELIMITER.
Errors:
./foo.tex:121: LATEX ERROR: BAD MATH ENVIRONMENT DELIMITER. [\end{document}]
./foo.tex:121: Extra }, or forgotten $. [\end{document}]
./foo.tex:121: Extra }, or forgotten $. [\end{document}]
./foo.tex:121: Missing $ inserted. [\end{document}]
./foo.tex:121: Missing } inserted. [\end{document}]
./foo.tex:121: Missing } inserted. [\end{document}]
Note that it's completely capitalized, unlike the error that I can get by adding an extra $ in the document. Actually, adding any sort of environment seems to be causing the error. To make matters more bizarre, this error does not seem to occur when compiling on, say, Overleaf.
Since it's system-specific I'm not sure a solution will be found. For what it's worth I'm using Ubuntu 14.04 LTS. At the least, does anyone know why I'm getting the error in all uppercase?
Best Answer
Although
\(and\)are robust commands, it is safer to use$in moving arguments like chapter and section titles. This seems to be a case in which these commands were insufficiently robust.