Theorem/Definition/Lemma problem --- Numbering

Question

I am trying to work on the numbering of the theorems/definitions/lemmas etc., and I have some problems with the numbering.

I would like the theorems, propositions, corollarys, definitions, conjectures, examples to follow the same numbering, and to reduce the numbering. For example, in my code below, the stuff goes as follows:

Chapter 1

Addition

1.1 Basics (SECTION)

Definition 1.1.1.

Theorem 1.1.1.

Theorem 1.1.2.

Example 1.1.1.

1.1.1. Some tips (SUBSECTION)

Definition 1.1.2.

1.2 Advanced stuff (SECTION)

Definition 1.2.1.

But how would I get it to be like this below?:

Chapter 1

Addition

1.1 Basics (SECTION)

Definition 1.1

Theorem 1.2

Theorem 1.3

Example 1.4

1.1.1. Some tips (SUBSECTION)

Definition 1.5

1.2 Advanced stuff (SECTION)

Definition 1.6

And for each new chapter, how would I get the numbering to be resetted? Like it would be Definition 2.1, Theorem 2.2, Theorem 2.3 for chapter 2.

I like the layout of my table of contents, i.e. Part I is addition and subtraction, Part II is Multiplication and division, and I am happy with the way the sections and subsections are working, but I just want to definitions, theorems etc. to be corrected.

\documentclass[11pt,a4paper]{report}
\usepackage{amsmath,amsfonts,amssymb,amsthm,epsfig,epstopdf,titling,url,array}


\theoremstyle{plain}
\newtheorem{thm}{Theorem}[section]
\newtheorem{lem}[thm]{Lemma}
\newtheorem{prop}[thm]{Proposition}
\newtheorem*{cor}{Corollary}

\theoremstyle{definition}
\newtheorem{defn}{Definition}[section]
\newtheorem{conj}{Conjecture}[section]
\newtheorem{exmp}{Example}[section]

\theoremstyle{remark}
\newtheorem*{rem}{Remark}
\newtheorem*{note}{Note}





\begin{document}
\tableofcontents

\part{Addition and Subtraction}

\chapter{Addition}
\section{Basics}
\begin{defn}
Here is a new definition
\end{defn}
\begin{thm}
Here is a new theorem
\end{thm}
\begin{thm}
Here is a new theorem
\end{thm}
\begin{exmp}
Here is a good example.
\end{exmp}
\subsection{Some tips}
\begin{defn}
Here is a new definition
\end{defn}
\section{Advanced stuff}
\begin{defn}
Here is a new definition
\end{defn}
\subsection{Warnings}
\begin{defn}
Here is a new definition
\end{defn}

\chapter{Subtraction}
\section{Basics}
\subsection{Some tips}
\section{Advanced stuff}
\subsection{Warnings}

\part{Multiplication and Division}

\chapter{Multiplication}
\section{Basics}
\subsection{Some tips}
\section{Advanced stuff}
\subsection{Warnings}

\chapter{Division}
\section{Basics}
\subsection{Some tips}
\section{Advanced stuff}
\subsection{Warnings}



\end{document}

Answer 1

Similar to the solution at this question and section 3 of the amsthm documentation:

\documentclass[11pt,a4paper]{report}
\usepackage{amsthm}

\theoremstyle{plain}
\newtheorem{thm}{Theorem}[chapter] % reset theorem numbering for each chapter

\theoremstyle{definition}
\newtheorem{defn}[thm]{Definition} % definition numbers are dependent on theorem numbers
\newtheorem{exmp}[thm]{Example} % same for example numbers

\newcommand{\chaptercontent}{
\section{Basics}
\begin{defn}Here is a new definition.\end{defn}
\begin{thm}Here is a new theorem.\end{thm}
\begin{thm}Here is a new theorem.\end{thm}
\begin{exmp}Here is a good example.\end{exmp}
\subsection{Some tips}
\begin{defn}Here is a new definition.\end{defn}
\section{Advanced stuff}
\begin{defn}Here is a new definition.\end{defn}
\subsection{Warnings}
\begin{defn}Here is a new definition.\end{defn}
}

\begin{document}
\tableofcontents
\part{Addition and Subtraction}
\chapter{Addition} \chaptercontent
\chapter{Subtraction} \chaptercontent
\part{Multiplication and Division}
\chapter{Multiplication} \chaptercontent
\chapter{Division} \chaptercontent
\end{document}

Answer 2

You can do something like this

\newtheorem{theorem}{Theorem}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem*{observation}{Observation}
\newtheorem*{example}{Example}
\newtheorem*{remark}{Remark}