Numbering a theorem by section number

Question

I'm creating some lecture notes for my class using the book class, it is structured by chapters and sections. In some of my sections I want to add homework (and in some, I don't). I've been accomplishing this with the amsthm package:

\newtheorem{homew}{Homework} 
\begin{homew} Solve for $x$
\begin{enumerate}
\item $1=x+2$
\item $1=x-2$
\end{homew}

However, I want this homework to be numbered by the section it is in, so I can call back to it. So for example I want my document to look like this:

Chapter 1

Section 1

Homework 1

Section 2

Section 3

Section 4

Homework 4

And so on.

My question is two-fold:

1. How to accomplish this? The counter options when creating a newtheorem don't do it. I don't want the Homework to be numbered as Homework 4.1 (there's no Homework 4.2, so what's the point?), and giving it its own counter doesn't work since then I get Homework 2 in Section 4, which I don't want either.
2. Is there a more elegant way of doing this? I'm really new to LaTeX so I appreciate any help.

Answer 1

Here's a tcolorbox solution for a nicer output and using \thesection as counter:

\documentclass{article}

\usepackage{mathtools}
\usepackage{amsthm}

\usepackage[most]{tcolorbox}


\newtcbtheorem{homew}{Homework}{title={\tcbtitle \thesection},enhanced jigsaw,boxrule=0pt,coltitle=black,
  sharp corners,colback=white,colbacktitle=white!40!yellow}{homew}

\begin{document}

\section{First}

\begin{homew}{Solve for $x$}{first}
\begin{enumerate}
\item $1=x+2$
\item $1=x-2$
\end{enumerate}
\end{homew}

\section{Second}
\begin{homew}{Solve for $x$ and $y$}{second}
\begin{align}
  1 &= x+y \\
  1 &= x-y
\end{align}
\end{homew}

\section{Another section}    

\begin{homew}{Solve for $x$ and $y$ and $z$}{third}
\begin{align}
  1 &= x+y-z \\
  1 &= x-y-z \\
  1 &= x+y+z
\end{align}
\end{homew}



\end{document}

Answer 2

This is probably the easiest way:

\documentclass{article}

\usepackage{amsmath, amsthm}

\newtheorem{homew}{Homework} 
\def\thehomew{\thesection}

\begin{document}
\section{Some Section}

\begin{homew} Solve for $x$
    \begin{enumerate}
        \item $1=x+2$
        \item $1=x-2$
    \end{enumerate}
\end{homew}

\section{Some Other Section}

\begin{homew} Solve for $y$
    \begin{enumerate}
        \item $1=y+2$
        \item $1=y-2$
    \end{enumerate}
\end{homew}

\section{New Section}

\section{Last Section}

\begin{homew} Solve for $z$
    \begin{enumerate}
        \item $1=z+2$
        \item $1=z-2$
    \end{enumerate}
\end{homew}

\setcounter{section}{99}
\section{Just Kidding}

\begin{homew} Solve for $w$
    \begin{enumerate}
        \item $1=w+2$
        \item $1=w-2$
    \end{enumerate}
\end{homew}

\end{document}

Answer 3

Here's a solution that uses the \AtBeginEnvironment macro of the etoolbox package to modify the counter variable that's associated with the hw environment.

\documentclass{article}
\usepackage{ntheorem}     % Or: \usepackage{amsthm}
\newtheorem{hw}{Homework} % Set up "Homework" environment

\usepackage{etoolbox}
\AtBeginEnvironment{hw}{% % Modify "hw" counter variable
   \setcounter{hw}{\value{section}}
   \addtocounter{hw}{-1}}

\begin{document}
\section{A}
\begin{hw} abc \end{hw}
\section{B}
\section{C}
\begin{hw} def \end{hw}
\section{D}
\begin{hw} ghi \end{hw}
\end{document}