What is well written math?

The solutions to $(x-3)(x-4)=0$ are \[ x=3 \quad\textrm{and}\quad x = 4. \]

• It reads like how we think!
• It uses plain English to explain the math.
• It uses complete English sentence.
• It is properly spaced and easy to read.

We expect your homework to be written like this!

At the end of this tutorial, you will

• be familiar with \(\LaTeX\),
• know the right terminologies to ask for help efficiently,
• have created your very own LaTeX document for assignments.

Math 1200 requires your assignments to be submitted as a PDF produced by \(\LaTeX\). This is in the course outline.

To access just the slides, scan or click the following QR code on your mobile devices.

This tutorial is interative! You can try out code by going to https://ktychan.gitlab.io/teaching/1200-latex/

A typical workflow

Time saving tip: Solve problems on paper before typing them up.

Syntax consists of some special purpose symbols

• the % starts a comment that gets ignored

                    
                      This shows up in the output.  % gets ignored :(
                    
                  

• the \ starts a command that does special things

                    
                      \commandname[option]{argument}
                    
                  

Anatomy of a .tex file

              
                \documentclass{amsart}
                \begin{document}
                  hello!
                \end{document}
              
            

• lines 2 to 4 make up the document body
• anything above the document body is called preamble
• anything after the document body gets ignored

Packages

Many \(\LaTeX\) features come in packages. To activate them, put usepackage commands in the preamble.

              
                \usepackage[margin=1in]{geometry}
              
            

Note usepackage commands placed inside document body will result in errors.

Giving your document some structure

              
                \documentclass{amsart}

                \begin{document}
                \section{Introduction}
                This is Section 1
                \subsection{Definitions}
                This is Section 1.1.
                This will be in the same line as above.

                This is a new line!
                \end{document}
              
            

A blank line starts a new paragraph!

A really basic template.

              
\documentclass[12pt,letterpaper,reqno]{amsart}

\author{Your Name}
\title{title}
\date{\today}

\begin{document}
\maketitle

% start writing here!


% don't write past this line!

\end{document}
              
            

YOUR TURN! @ https://ktychan.gitlab.io/teaching/1200-latex/

Add to one of the above template

• in preamble
  • a command title with argument template
  • a command author argument as your name
  • a command date with argument \today
• in document body
  • a maketitle command with no argument immediately below \begin{document}

\(\LaTeX\) distinguishes math and text by special markers that start and end math modes.

              
                Inline math mode: $x = 3$.
                Display math mode: \[ x = 3. \] This is in a new line.
              
            

Inline math mode: $x = 3$. Display math mode: \[ x = 3. \] This is in a new line.

Compare the readibility of the following.

The absolute value function $|x|$ can be defined piecewisely by assigning $|x| = x$ when $x \ge 0$, and $|x|=-x$ when $x \lt 0$.

The absolute value function $|x|$ can be defined as \[ |x| = \begin{cases} x, &\textrm{if } x \ge 0, \\ -x, &\textrm{if } x \lt 0. \end{cases} \]

Which one do you prefer?

Warning! The following doesn't output what you think it does.

              
                \[
                  x=3
                  and
                  x=4.
                \]
              
            

The above code ouputs the following.

\[ x=3 and x = 4. \]

Commands for symbols

Some examples

• operations \times \div \ge \sqrt{n} \frac{a}{b}
• Greek letters \alpha \beta \gamma ...
• brackets (...) \{...\} [...]
• subscript and superscripts x_{1,2} x^{3} \alpha_{0}^{2^{2}}

Detexify (free!) is your friend to find the command for the symbol you want.

It works amazingly well on mobile.

YOUR TURN! @ https://ktychan.gitlab.io/teaching/1200-latex/

Add to your file the following

The solution to $ax^{2} + bx + c = 0$ is \[ x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}. \]

Syntax: \begin{blah} ... \end{blah}

You have already met some of them

• \begin{document} ... \end{document}
• $...$
• \[...\]

Equations with numbers (math mode)

              
                \begin{align}
                  (x+y)^{n+1} &= (x+y) (x+y)^{n}  \nonumber \\
                              &= (x+y) \sum_{k=1}^{n} \binom{n}{k} x^{k}.
                \end{align}
              
            

\[ \begin{align} (x+y)^{n+1} &= (x+y) (x+y)^{n} \nonumber \\ &= (x+y) \sum_{k=1}^{n} \binom{n}{k} x^{k}. \end{align} \]

Notice \\ is necessary to make a new line.

Equations without numbers (math mode)

              
                \begin{align*}
                  (x+y)^{n+1} &= (x+y) (x+y)^{n} \\
                              &= (x+y) \sum_{k=1}^{n} \binom{n}{k} x^{k}.
                \end{align*}
              
            

\[ \begin{align*} (x+y)^{n+1} &= (x+y) (x+y)^{n} \\ &= (x+y) \sum_{k=1}^{n} \binom{n}{k} x^{k}. \end{align*} \]

Notice the little * disables numbering.

Proofs (text mode)

              
                \begin{proof}
                Let $\epsilon \gt 0$. Choose $\delta = \sqrt{\epsilon}$.
                Then...
                \end{proof}
              
            

Let $\epsilon \gt 0$. Choose $\delta = \sqrt{\epsilon}$. Then...

Lists (numbered) (text mode)

Use enumerate environment for numbered lists. Each item must be prefixed with \item command.

              
                \begin{enumerate}
                \item Look there's a number to my left!
                \item Another one!
                \end{enumerate}
              
            

Output:

1. Look there's a number to my left!
2. Another one!

Lists (bullets) (text mode)

Use itemize environment for unnumbered lists. Each item must be prefixed with \item command.

              
                \begin{itemize}
                \item This item has no number.
                \item Just a lonely bullet.
                \end{itemize}
              
            

Output:

• This item has no number.
• Just a lonely bullet.

Typical assignment

              
                \begin{question}
                  You are on an island and there are three crates of fruit that
                  have washed up in front of you. ...
                \end{question}
                \begin{proof}
                  we claim ...
                \end{proof}

                \begin{question}
                  Determine whether the following statements are true or false ...
                \end{question}
                \begin{proof}
                  Part (1) is ...
                \end{proof}
              
            

Questions (optional)(text mode)

Add to your preamble

              
                \newtheorem{question}{Question}
              
            

Then just use it in your assignments to type up the question.

              
                \begin{question}
                  You are on an island and there are three crates of fruit that
                  have washed up in front of you. ...
                \end{question}
              
            

YOUR TURN! @ https://ktychan.gitlab.io/teaching/1200-latex/

Add to your file a proof environment with a factorization of this polynomial.

\begin{align*} x^{3} + 2 x^{2} - x &= \cdots \\ &= \cdots. \end{align*}

Be sure to write out all details and use the align or align* to put each step in its own line.

\(\LaTeX\) has its own spacing rule and most likely will ignore spaces in your .tex file. The precise rules are hard to describe. But here is the gist.

Spacing (text mode)

• only one space is preserved between characters
• new line counts as a single space
• a blank line or starts a new paragraph
• \\ forces a line break

Spacing (math mode)

• blank lines sometime give you error
• all white spaces between non-commands are ignored

              
                \[
                  x=3
                  \textrm{ and }
                  x=4.
                \]
              
            

\[ x=3 \textrm{ and } x = 4. \]

Styling

              
                % text mode
                normal:  \textrm{very normal}.
                bold:    \textbf{look at me!}.
                italic:  \textit{something that stands out}.

                % math mode
                normal:   $\mathrm{very normal}$.
                bold:     $\mathbf{look at me!}$.
                italic:   $\mathit{something that stands out important}$.

                % fonts
                blackboard:  $\mathbb{R}$
                caligraphy:  $\mathcal{S}$
              
            

Cross-referencing

              
                \begin{align}
                  (x+y)^{n+1} &= (x+y) (x+y)^{n} \label{eq:1}
                \end{align}

                The above is Equation~\eqref{eq:1}.
              
            

\begin{align} (x+y)^{n+1} &= (x+y) (x+y)^{n} \label{eq:1} \end{align}

The above is Equation \eqref{eq:1}.

Table

They are notorisely complicated.

Use tablesgenerator.com (free!) instead.

Graphics

Put \usepackage{graphicx,float} in the preamble which provides includegraphics command.

              
                % inside document body
                \begin{figure}[H]
                \centering
                \includegraphics{path/to/your_image.png}  % must be valid path
                \caption{Your caption}
                \label{fig:your_figure}
                \end{figure}
              
            

Warning: This feature is disabled on my webiste.

Try out Overleaf for typesetting your own homework.

To learn more, check out

• latex-project.org
• learnlatex.org
• overleaf.com/learn

An assignment template

              
\documentclass[12pt,letterpaper,reqno]{amsart}

\usepackage{microtype,bm,enumitem,amssymb}
\usepackage{graphicx,float,tikz}
\usepackage[margin=1in]{geometry}
\newtheorem{question}{Question}

\title{Math 1200 - Assignment X}
\author{Your Name}
\date{\today}

\begin{document}
\maketitle                      % do not remove

%\begin{question}
%  Optionally uncomment and put the question here.
%\end{question}

\begin{proof}[Solution for Question 1]
  Your solution goes here.
\end{proof}

%\begin{question}
%  Optionally uncomment and put the question here.
%\end{question}

\begin{proof}[Solution for Question 2]
  Your solution goes here.
\end{proof}

\end{document}