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How to use LATEX

Christopher A. Wong

University of California, Berkeley

13 September 2012

C. Wong (UC Berkeley) How to use LATEX 13 September 2012 1 / 29

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Outline

1 General structure of LATEX

2 Writing mathematics - AMS LATEX

3 Environments

4 Bibliographies


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What is TEX?

Pronunciation: ‘Tek’

Developed by Donald Knuth.

A low-level typesetting program.Provides precise formatting control over basic features such asspacing, justification, and fonts.

The availability of macros.


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What is LATEX?

Pronunciation: ‘Lay-tek’

A higher-level system running on top of TEX for end-users.

Advantages: Document styles, bibliographies, equation and figurereferencing, and more.

Platform-independent and can be edited through a text editor.

LATEX is the standard for professional academic paper writing.

An example:

(1)


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Settings up LATEX

LATEX package: Look up TeX Live.

There are a variety of TeX editors out there, but we will not usethem today. Windows: TeXnicCenter. For Mac: TeX Shop.

The download can be large and possibly annoying. Pay attentionto the instructions.

For today we will use a web compiler:http://sciencesoft.at/latex/?lang=en

http://www.artofproblemsolving.com/Resources/texer.php

Please type everything in a text editor, then paste into the website.


http://sciencesoft.at/latex/?lang=en



http://sciencesoft.at/latex/?lang=en

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Obligatory First Document

We need to specify a document type, and then create the document.

\documentclass{article}

\begin{document}

Hello world!!!

\end{document}

One of the most important things to note is that LaTeX treats yoursymbols as commands, not directly typed text. So you can addarbitrary spaces between words.Try testing the text when you skip lines.


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Special charactersMany characters on the keyboard are now reserved for LaTeX codeinstead of being printed directly on the screen. This includes :

1 $ - mark the beginning and end of math.2 % - for comments (try this!)

3 & - mark separation between columns in a table

4 _ - denote subscript

5 - at the beginning of every LaTeX command6 { } - used to enclosed arguments of LaTeX commands.

To actually reproduce these symbols, we use

\$

\%\&

\_

$\backslash$

\{ \}


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Some basic mathematics

We can now try doing some math. We must begin and end any math

symbols with $. Arithmetic:$ 1+1 = 2$ \\

$ 3-2 = 1$ \\

$ \sqrt{9} = 3, 9^{1/2} = 3$. \\

$ 4^2 = 16, 3^{2 + 1} = 27$.

If you are using any math variables, also use dollar signs:

Let $x$ be an unknown. If $x = 1$ then $x + 1 = 2$.

I can also do nested super and sub scripts:

A googol is equal to $10^{10^2}$.

A sequence $\{a_n\}$ has a subsequence $\{a_{n_k} \}$.


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AMS Packages - the preamble

The American Mathematical Society has provided several packages thatexpand on the math functionality of LaTeX. We have to place thefollowing commands before we begin our document, in the preamble :

\usepackage{amsmath}\usepackage{amssymb}

\usepackage{amsthm}

From now on, include these packages in your preamble.


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Basic mathematics, continued

Many of the most important symbols used in math mode can be found

here:http://www.artofproblemsolving.com/Wiki/index.php/LaTeX:

Symbols On that same website, you can find a tutorial similar to thisone. Binary relations:

$5 < 6, x \le y, 9 > 4, z \ge x, q = r, q \neq x$.

Set notation, blackboard font, the symbol:

Let $A = \{ f(x) \in C^{\infty}(\mathbb{R}): f(0) = \pm 1 \}$.

Fractions:

\frac{x^2 + x + 1}{2x + 5}


http://www.artofproblemsolving.com/Wiki/index.php/LaTeX:Symbols




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Exercise!

Try writing the quadratic formula:

If , then .


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Exercise!

Try writing the quadratic formula:

If , then .

Notice that our fractions so far have been a little bit squished. If we use

\dfrac{}{}

we get

.


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Other valuable commands

$F(b) - F(a) = \int_a^b f(x) \, dx$. \\

$\lim_{n \rightarrow \infty} \sin(1/n) = 0$.\\$\sum_{n = 1}^{\infty} \dfrac{1}{n^2} = \dfrac{\pi^2}{6}$.

.

.

.

Notice that the summation and integral symbols are too small. We canuse

\displaystyle

beforehand (inside math mode) to improve their appearances. Basicallyevery command you can imagine is written very similarly to whatwould be natural.


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Greek letters

Very simple; it’s just plus the name of the greek letter. If you use acapital first letter then you get the upper-case version (warning: thisdoes not work if the upper-case letter is actually just a regular Romanletter).

$\alpha, \beta, \gamma, \delta, \pi$ \\

$\Gamma, \Delta, \Pi$.

.


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Exercise

Try writing the following:


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Exercise

Try writing the following:

$\displaystyle \sum_{j=0}^{\infty} \epsilon \pi^{1 - j} =

\frac{\epsilon \pi}{1 - \frac{1}{\pi}} $

If I use displaystyle, I don’t have to use dfrac or dint.


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Displaymath Environment

Notice that in the previous frame, my series was centered and on a lineof its own, unlike your own recreation. This was done using thedisplaymath environment.

An example of display math:

\begin{displaymath}

A = \pi r^2

\end{displaymath}

Try recreating the previous series, but using the displaymath

environment. You will not need displaystyle or dollar signs.


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BoundariesIf we just write

\begin{displaymath} ( 1 + \frac{1}{n})^2 \end{displaymath}

I get

These parentheses are too small. The way to fix this is by using

LaTeX’s automatic boundary sizes. A boundary means things likebrackets, parentheses, curly braces, etc. The commands are:

\begin{displaymath}

\left( 1 + \frac{1}{n} \right)^2

\end{displaymath}

which produces


E

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Exercise

Produce the following limit definition of :


E i

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Exercise

Produce the following limit definition of :

\begin{displaymath}

e = \lim_{n \rightarrow \infty} \left(1+\frac{1}{n} \right)^n

\end{displaymath}


B d i ti d

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Boundaries, continued

We can nest boundaries in one another; this will typically make theoutside boundary larger:


B d i ti d

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\[ e^x = \left[ \lim_{n \rightarrow \infty}

\left(1+\frac{1}{n} \right)^n \right]^x \]


B d i ti d

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\[ e^x = \left[ \lim_{n \rightarrow \infty}

\left(1+\frac{1}{n} \right)^n \right]^x \]

Notice that instead of using begin{displaymath}, etc, I was able to use[. This is a shortcut for displaymath.


Try things out!

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Try things out!


Also, we can use lots of common functions like

\sin{x}, \cos{x}, \tan{x}, \dim{V}, \hom(G),

\max, \sup, \min, \inf, \det, \gcd, \exp, \binom{n}{k}


Try things out!



http://detexify.kirelabs.org/



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Try things out!


Also, we can use lots of common functions like

\sin{x}, \cos{x}, \tan{x}, \dim{V}, \hom(G),

\max, \sup, \min, \inf, \det, \gcd, \exp, \binom{n}{k}

We can choose between

$\sin{x}$ and $\sin(x)$

depending on whether we want parentheses or not. To find moresymbols, use Detexify: http://detexify.kirelabs.org


Equation Environment







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Equation Environment

Like displaymath, the equation environment centers and full-sizes the

math in its contents. However, the equation environment hasreferencing capabilities, thus making it valuable for papers.

\begin{equation}

i\hbar \frac{\partial}{\partial t} \Psi(x, t) =

- \frac{\hbar^2}{2m} \frac{\partial^2}{\partial x^2} \Psi(x,t)

+ V(x) \Psi(x,t)

\label{schrodinger}

\end{equation}

(2)


Equation Environment continued

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Equation Environment, continued

Notice that my equation is labeled (2). I wrote the above sentence bydoing:

Notice that my equation is labeled (\ref{schrodinger}).

The number indicated will update for all references if you decide to addan equation before that one.


Align Environment

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Align Environment

For a series of equations, we can do the following

\begin{align}

x + 2y + z & = 0 \\

2x + y - z & = 2 \\

- 3 x - y - z & = 1

\end{align}

(3)

(4)

(5)

The & symbol makes all the equations line up according to thepositions of that symbol.


Align Environment continued

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Align Environment, continued

To label each equation in the align environment, I use the labelcommand before the line break:

\begin{align}

x + 2y + z & = 0 \label{eqn1} \\

2x + y - z & = 2 \label{eqn2} \\

-3x - y - z & = 1 \label{eqn3}

\end{align}

If we want some of the equations in our align to be unlabeled (nonumber on the right side), use nonumber where you would normallyput

label. If we want to suppress labels altogether, use

\begin{align*} \end{align*}

\begin{equation*} \end{equation*}


Macros

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MacrosOften, we use the same things over and over. Or worse, somecommands just simply take a lot of typing.

irrationals \[ \text{irrationals} = \mathbb{R} \setminus \mathbb{Q} \]

Instead, we can put in our preamble:

\newcommand{\RQ}{ \mathbb{R} \setminus \mathbb{Q} }

Then I can write

\[ \text{irrationals} = \RQ \]


Macros

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MacrosOften, we use the same things over and over. Or worse, somecommands just simply take a lot of typing.

irrationals \[ \text{irrationals} = \mathbb{R} \setminus \mathbb{Q} \]

Instead, we can put in our preamble:

\newcommand{\RQ}{ \mathbb{R} \setminus \mathbb{Q} }

Then I can write

\[ \text{irrationals} = \RQ \]

Similarly, if I was writing about the University of California, Berkeley,a lot, I could define

\newcommand{\UCB}{\text{University of California, Berkeley}}


The Theorem Environment

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The Theorem Environment

The AMS package provides us with a standard template to state a

theorem.Theorem (Dov Jarden)

There exist irrational numbers such that is rational.

\begin{theorem}[Dov Jarden]There exist irrational numbers $\alpha, \beta$ such

that $\alpha^\beta$ is rational.

\label{thm1}

\end{theorem}

Notice that I can label this theorem just like I can label anything else. Ihave turned off theorem numbering in my document, however.


The Proof Environment

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e oo v o e t

Proof.

Pick

. If is rational, then we are done. Otherwise, isirrational. But then

is rational.

\begin{proof}

Pick $\alpha = \beta = \sqrt{2}$. If $\alpha^\beta$

is rational, then we are done. Otherwise, $\alpha^\beta$

is irrational. But then $(\alpha^{\beta})^{\sqrt{2}} =

(2^{\sqrt{2}/2})^{\sqrt{2}} = 2$ is rational.

\end{proof}

The proof environment even makes the little QED tombstone for you!


Setting up a bibliography

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g p g p y

First we have to create a bibliography file, which is just a plain textdocument with the extension .bib. Let’s say that the file is called “ref.bib”. Make sure it is in the same folder as our .tex file. Then,before the end of our LaTeX document, do the following:

\bibliography{ref}

This will generate a bibliography with entries that are given in the .bibfile.


Creating the .bib file

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g

We simply go to our online article, find the exported citation in bibtex,

and then copy it into our .bib file.


The End!

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LATEX is an incredibly powerful tool for developing high-qualitydocuments.

There are still many features I have not even touched upon, suchas graphics, more advanced macros, and more powerful formattingfeatures.

There are also many templates online that you can look at tofamiliarize yourself with other features.

Don’t forget Detexify!


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