Oct 3rd, 2022

Things to do

The theorem environment; we will cover the bibliography and itemize environments, and the includegraphicx command soon.

LaTeX Theorem Environment

Note

For a detailed and complete explanation, refer to the Overleaf document https://www.overleaf.com/learn/latex/Theorems_and_proofs.

Also, check out our thesis template, https://www.overleaf.com/read/prmnfsqfxmzr.

Naive approach

When writing mathematical documents such as your thesis, we often need to use definitions, theorems, etc. When there are more than a handful, it is customary to put labels on them. The LaTeX theorem environment provides a way to handle this efficiently.

Here is an example without using the theorem environment.

Theorem 1. We have \(\begin{pmatrix} 1&0 \\ 0 &1 \end{pmatrix} \begin{pmatrix} 2&0 \\ 0&0 \end{pmatrix} = \begin{pmatrix} 2&0 \\ 0&0 \end{pmatrix}\).

Proposition 2. Another good theorem.

Theorems, naive approach

\noindent \textbf{Theorem 1.} We have
$\begin{pmatrix}
1&0 \\
0 &1
\end{pmatrix}
\begin{pmatrix}
2&0 \\
0&0
\end{pmatrix}
= \begin{pmatrix}
2&0 \\
0&0  \end{pmatrix}$.\\

\noindent \textbf{Proposition 2.} Another good theorem.

If these are all you need in your writing, one does not need to use the theorem environment. However, if you change a proposition into a corollary or add a definition between statements, you need to redo the numbering. Imagine, that you do it for 20 statements and 10 times….

Theorem environment approach

The theorem environment is often defined in the preamble.

theorem environment example

\newtheorem{theorem}{Theorem}
%           theorem is used in a begin and end pair to call Theorem
%                    Theorem N. will be displayed

Once we have this we can write our theorems in the \begin{theorem} and \end{theroem} pair. Be careful there are theorem and Theorem. That is, with this setting, we may type Theorem 1 as follows.

theorem environment example

\begin{theorem}
We have an amazing matrix multiplication example.
\end{theorem}

The theorem in \newtheorem{theorem}{Theorem} can be anything you want. The following two codes will produce the same result

theorem environment example

\newtheorem{thm}{Theorem}
...
...

\begin{thm}
We have an amazing matrix multiplication example.
\end{thm}

theorem environment example

\newtheorem{IamNotSureIfThisIsaTheorem}{Theorem}
...
...

\begin{IamNotSureIfThisIsaTheorem}
We have an amazing matrix multiplication example.
\end{IamNotSureIfThisIsaTheorem}

Additional types

You will most likely use the following types of statements.

definitions;
questions/conjectures;
examples;
remarks;
theorems;
propositions;
corollaries;
lemmas.

Though you need to define them manually, often you want to combine the their numbering systems. Here is an example to have both definitions and theorems to share the same numbering.

theorem environment example

\newtheorem{theorem}{Theorem}
\newtheroem{definition}[theorem]{Definition}
...
...

\begin{theorem}
We have an amazing matrix multiplication example.
\end{theorem}

\begin{definition}
My grade is an "A".
\end{definition}

Numbering options

Subtle differences

\newtheorem{theorem}{Theorem}
\newtheroem{definition}[theorem]{Definition}
\newtheroem{lemma}{Lemma}[theorem]

There are differences when putting [theorem] before or after the theorem name. Let’s assume that the last theorem was Theorem N. Then \newtheroem{definition}[theorem]{Definition} will produce Definition (N+1), whereas \newtheroem{lemma}{Lemma}[theorem] will do Lemma N.1.

In your article, you may have multiple chpaters (e.g. your thesis), sections, and subsections. You may number your theorems following these document structures by appending the option [<chapter>|<section>|<subsections>].

theorem numbering following section numbers

\newtheorem{theorem}{Theorem}[section]
                             % with this setting the numbering
                             % is of the form:
                             % Statement {sec. num}.{N}.

A named theorem

There are theorems with special names such as the Pythagorean theorem.

Theorem 1 (The Pythagorean Theorem). ……

To add such a theorem name, use the following option.

add a theorem name

\newtheorem{theorem}{Theorem}
...
...
...

\begin{theorem}[{The Pythagorean Theorem}] .......
...
\end{theorem}

This will be helpful when you quote statements from books and papers or even within your article. We will touch upon this when covering the bibliography and references section.

Theorem styles; amsthm

Sometimes, people follow the convention of highlighting key words. In the following example, the theorems, definitions, and lemmas will be in itatic.

all in italic

\newtheorem{theorem}{Theorem}
\newtheroem{definition}[theorem]{Definition}
\newtheroem{lemma}[theorem]{Lemma}

Using both bold and italic may be too much. To avoid this, the amsthm package provides theorem styles. Here is a suggestion.

theorem style

\usepackage{amsthm}

\newtheorem{theorem}{Theorem}
\newtheroem{lemma}[theorem]{Lemma}

\theoremstyle{definition}
\newtheroem{definition}[theorem]{Definition}
\newtheroem{example}[theorem]{Example}

\theoremstyle{remark}
\newtheroem{remark}[theorem]{Remark}
% \newtheroem*{remark}{Remark} % use this if you prefer unnumbered remarks

Checkout our thesis template preamble, https://www.overleaf.com/read/prmnfsqfxmzr.