Research Methods: Typesetting with LaTeX Ian Morris (based on - - PowerPoint PPT Presentation

Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Research Methods: Typesetting with LaTeX

Ian Morris (based on earlier notes by Shu Sasaki) October 1, 2020

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Today’s topic:

This lecture introduces the basics of LaTeX typesetting.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Today’s topic:

This lecture introduces the basics of LaTeX typesetting. No knowledge of computer programming is assumed.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Today’s topic:

This lecture introduces the basics of LaTeX typesetting. No knowledge of computer programming is assumed. The aim of this lecture is just to get you started: you can learn all sorts of tricks as you start using LaTeX yourself.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Today’s topic:

This lecture introduces the basics of LaTeX typesetting. No knowledge of computer programming is assumed. The aim of this lecture is just to get you started: you can learn all sorts of tricks as you start using LaTeX yourself. The course materials for this week include an example document, example.tex, which contains examples of how to write various mathematical expressions. You can copy and adapt these in your

• wn work, if you like.

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Some fundamentals

LaTeX is not a “WYSIWYG” document format like Microsoft Word, where the final document looks exactly the same as what is typed into the computer.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Some fundamentals

LaTeX is not a “WYSIWYG” document format like Microsoft Word, where the final document looks exactly the same as what is typed into the computer. Rather, it is a markup language (like HTML): you create a source code file which instructs the computer about what the final document will contain. The source code has a .tex file extension.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Some fundamentals

LaTeX is not a “WYSIWYG” document format like Microsoft Word, where the final document looks exactly the same as what is typed into the computer. Rather, it is a markup language (like HTML): you create a source code file which instructs the computer about what the final document will contain. The source code has a .tex file extension. This is then compiled to make a PDF or Postscript document.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Some fundamentals

LaTeX is not a “WYSIWYG” document format like Microsoft Word, where the final document looks exactly the same as what is typed into the computer. Rather, it is a markup language (like HTML): you create a source code file which instructs the computer about what the final document will contain. The source code has a .tex file extension. This is then compiled to make a PDF or Postscript document. These days the editing and compiling are usually both done using a single piece of software, e.g. Overleaf (which runs in a web browser), TeXShop (Mac), TeXWorks (Windows).

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Some fundamentals

LaTeX is not a “WYSIWYG” document format like Microsoft Word, where the final document looks exactly the same as what is typed into the computer. Rather, it is a markup language (like HTML): you create a source code file which instructs the computer about what the final document will contain. The source code has a .tex file extension. This is then compiled to make a PDF or Postscript document. These days the editing and compiling are usually both done using a single piece of software, e.g. Overleaf (which runs in a web browser), TeXShop (Mac), TeXWorks (Windows). In the live session this week we will be using Overleaf.

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Some strengths of LaTeX:

It can make very complicated mathematical expressions appear very neatly and with little effort!

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Some strengths of LaTeX:

It can make very complicated mathematical expressions appear very neatly and with little effort! Internal and external references can be taken care of automatically: each equation can be given an internal label, and you can refer back to the equation using a LaTeX command. This means you don’t have to keep track of equation numbers yourself.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Some strengths of LaTeX:

It can make very complicated mathematical expressions appear very neatly and with little effort! Internal and external references can be taken care of automatically: each equation can be given an internal label, and you can refer back to the equation using a LaTeX command. This means you don’t have to keep track of equation numbers yourself. Similarly bibliography references can be handled automatically.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Some strengths of LaTeX:

It can make very complicated mathematical expressions appear very neatly and with little effort! Internal and external references can be taken care of automatically: each equation can be given an internal label, and you can refer back to the equation using a LaTeX command. This means you don’t have to keep track of equation numbers yourself. Similarly bibliography references can be handled automatically. LaTeX makes its own decisions on page layout. Usually they are good decisions (but placement of large tables and diagrams can be problematic)

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Source File

The source code file must contain at least these commands (in blue):

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Source File

The source code file must contain at least these commands (in blue): \documentclass[11pt]{article} (Preamble) \begin{document} (Text) \end{document}

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Source File

The source code file must contain at least these commands (in blue): \documentclass[11pt]{article} (Preamble) \begin{document} (Text) \end{document} Anything which follows \end{document} is ignored!

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Source File

The source code file must contain at least these commands (in blue): \documentclass[11pt]{article} (Preamble) \begin{document} (Text) \end{document} Anything which follows \end{document} is ignored! Of course, you could vary the font size (10pt, 12pt et cetera) and

• ther document classes may be useful, e.g.: beamer, amsart, thesis.

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The preamble

The title, author and date which appear at the front of the article go in the preamble:

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

The preamble

The title, author and date which appear at the front of the article go in the preamble: \title{Modular elliptic curves and Fermat’s Last Theorem} \author{Andrew Wiles} \date{\today}.

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The preamble

The title, author and date which appear at the front of the article go in the preamble: \title{Modular elliptic curves and Fermat’s Last Theorem} \author{Andrew Wiles} \date{\today}. You will also need to put \maketitle immediately after \begin{document} in order to make the title actually appear.

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Types of content

There are two basic kinds of content in a LaTeX document: text, and mathematical symbols. These are written in between \begin{document} and \end{document}.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Types of content

There are two basic kinds of content in a LaTeX document: text, and mathematical symbols. These are written in between \begin{document} and \end{document}. By default, material in the source code is turned into text in the final document. To write mathematics instead we must use $· · · $: anything occuring in between the two symbols will be interpreted as mathematics.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Types of content

There are two basic kinds of content in a LaTeX document: text, and mathematical symbols. These are written in between \begin{document} and \end{document}. By default, material in the source code is turned into text in the final document. To write mathematics instead we must use $· · · $: anything occuring in between the two symbols will be interpreted as mathematics. For example, if part of the source code reads:

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Types of content

There are two basic kinds of content in a LaTeX document: text, and mathematical symbols. These are written in between \begin{document} and \end{document}. By default, material in the source code is turned into text in the final document. To write mathematics instead we must use $· · · $: anything occuring in between the two symbols will be interpreted as mathematics. For example, if part of the source code reads: The equation $x^n+y^n= z^n$ has no non-trivial integer solutions when $n\geq 3$,

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Types of content

There are two basic kinds of content in a LaTeX document: text, and mathematical symbols. These are written in between \begin{document} and \end{document}. By default, material in the source code is turned into text in the final document. To write mathematics instead we must use $· · · $: anything occuring in between the two symbols will be interpreted as mathematics. For example, if part of the source code reads: The equation $x^n+y^n= z^n$ has no non-trivial integer solutions when $n\geq 3$, then this produces: The equation xn + yn = zn has no non-trivial integer solutions when n ≥ 3.

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Text structure

You can create section, subsection, subsubsection, by writing \section{Whatever the title of the section is}, \subsection{ }, etc.

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Text structure

You can create section, subsection, subsubsection, by writing \section{Whatever the title of the section is}, \subsection{ }, etc.

• Exercise. Try:

\section{ }, \subsection{ }, \section{ } \section{ }, \section{ }, \subsection{ } and observe the difference.

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Text fonts

Use \textbf{x}, \textit{x}, \textrm{x}, \textsf{x} etc. to create texts in different fonts.

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Text fonts

Use \textbf{x}, \textit{x}, \textrm{x}, \textsf{x} etc. to create texts in different fonts. Use {\tiny x}, {\scriptsize x}, {\footnotesize x}, {\small x}, {\normalsize x}, {\large x}, {\Large x}, {\LARGE x}, {\huge x} and {\Huge x} to change size of texts.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Text fonts

Use \textbf{x}, \textit{x}, \textrm{x}, \textsf{x} etc. to create texts in different fonts. Use {\tiny x}, {\scriptsize x}, {\footnotesize x}, {\small x}, {\normalsize x}, {\large x}, {\Large x}, {\LARGE x}, {\huge x} and {\Huge x} to change size of texts. Use \emph{ · · · } to emphasise some text. Usually this will make the text between the brackets appear in italic, like this.

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Accents, Greek letters, special characters

Accents: Example In text In mathematics â \^a \hat a ˇ a \v{a} \check a ã \ ∼a \tilde a á \ ´ a \acute a à \ ` a \grave a

• a

\vec a

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Accents, Greek letters, special characters

Accents: Example In text In mathematics â \^a \hat a ˇ a \v{a} \check a ã \ ∼a \tilde a á \ ´ a \acute a à \ ` a \grave a

• a

\vec a Greek letters: \alpha, \beta, \gamma, . . . ; \Gamma, \Delta, . . .

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Accents, Greek letters, special characters

Accents: Example In text In mathematics â \^a \hat a ˇ a \v{a} \check a ã \ ∼a \tilde a á \ ´ a \acute a à \ ` a \grave a

• a

\vec a Greek letters: \alpha, \beta, \gamma, . . . ; \Gamma, \Delta, . . . Special characters: \ss, \ae, \flat, \sharp, . . .

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Making lists:

\begin{itemize} \item . . . \end{itemize} produces a list with bullet points.

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Making lists:

\begin{itemize} \item . . . \end{itemize} produces a list with bullet points. On the other hand, \begin{enumerate} \item . . . \end{enumerate} produces a list where each item is marked with a number.

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Tables containing text

\begin{tabular}{ccc} stuff & goes & here\\ stuff & goes & here\\ stuff & goes & here \end{tabular} creates a (non-mathematical) 3-by-3 table.

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Tables containing text

\begin{tabular}{ccc} stuff & goes & here\\ stuff & goes & here\\ stuff & goes & here \end{tabular} creates a (non-mathematical) 3-by-3 table. The special symbol & tells the computer when a column has ended; the special symbol \\ tells it when a row has ended. (Note that the last row ends automatically.)

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Tables containing text

\begin{tabular}{ccc} stuff & goes & here\\ stuff & goes & here\\ stuff & goes & here \end{tabular} creates a (non-mathematical) 3-by-3 table. The special symbol & tells the computer when a column has ended; the special symbol \\ tells it when a row has ended. (Note that the last row ends automatically.) Here {ccc} tells the computer to expect three columns, each with the text positioned in the centre of the column. We could have chosen centre, left, or right.

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Packages

LaTeX has a large inventory of commands, but new ones are being created all the time.

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Packages

LaTeX has a large inventory of commands, but new ones are being created all the time. To add more commands to LaTeX you will need to add a package in the preamble, e.g.:

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Packages

LaTeX has a large inventory of commands, but new ones are being created all the time. To add more commands to LaTeX you will need to add a package in the preamble, e.g.: \usepackage{amsmath}

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Packages

LaTeX has a large inventory of commands, but new ones are being created all the time. To add more commands to LaTeX you will need to add a package in the preamble, e.g.: \usepackage{amsmath} Example: if you want to use non-Roman letters (Chinese, Cyrillic, Japanese etc) then you should expect to need a package which enables the relevant commands.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Packages

LaTeX has a large inventory of commands, but new ones are being created all the time. To add more commands to LaTeX you will need to add a package in the preamble, e.g.: \usepackage{amsmath} Example: if you want to use non-Roman letters (Chinese, Cyrillic, Japanese etc) then you should expect to need a package which enables the relevant commands. Some particularly useful packages: amsmath, amsfonts, amsthm, enumerate, graphicx. I will assume for the rest of the presentation that the first three of these packages are being used.

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Macros

To reduce the amount of incessant typing, you can define your own shorter commands.

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Macros

To reduce the amount of incessant typing, you can define your own shorter commands. For example, if I find it laborious to write \textbf{Q} every single time to produce Q, I’d write

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Macros

To reduce the amount of incessant typing, you can define your own shorter commands. For example, if I find it laborious to write \textbf{Q} every single time to produce Q, I’d write \newcommand{\tbQ}{\textbf{Q}} in the preamble, and simply write \tbQ to produce Q.

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Defining a new command can produce mathematical symbols. For example, I can define

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Defining a new command can produce mathematical symbols. For example, I can define \newcommand{\mbbQ}{$\mathbb{Q}$}

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Defining a new command can produce mathematical symbols. For example, I can define \newcommand{\mbbQ}{$\mathbb{Q}$} and write \mbbQ to produce Q. The advantage is that the command incorporates $· · · $ in itself.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Defining a new command can produce mathematical symbols. For example, I can define \newcommand{\mbbQ}{$\mathbb{Q}$} and write \mbbQ to produce Q. The advantage is that the command incorporates $· · · $ in itself. Note that to use the command \mathbb{Q} we need to load the amsfonts package.

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Mathematical expressions

Mathematical formulas are made by combining commands for individual mathematical symbols:

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Mathematical expressions

Mathematical formulas are made by combining commands for individual mathematical symbols: $ \zeta (s)=\sum_{n=1}^{\infty}\frac{1}{n^s} $

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Mathematical expressions

Mathematical formulas are made by combining commands for individual mathematical symbols: $ \zeta (s)=\sum_{n=1}^{\infty}\frac{1}{n^s} $ This produces:

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Mathematical expressions

Mathematical formulas are made by combining commands for individual mathematical symbols: $ \zeta (s)=\sum_{n=1}^{\infty}\frac{1}{n^s} $ This produces: ζ(s) =

∞

• n=1

1 ns .

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Mathematical expressions

Mathematical formulas are made by combining commands for individual mathematical symbols: $ \zeta (s)=\sum_{n=1}^{\infty}\frac{1}{n^s} $ This produces: ζ(s) =

∞

• n=1

1 ns . The curly brackets above tell the computer to treat something as a single object. So for example, the brackets in {n=1} above make sure that the whole expression n = 1 goes below the sum. If they are omitted we get a mess:

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Mathematical expressions

Mathematical formulas are made by combining commands for individual mathematical symbols: $ \zeta (s)=\sum_{n=1}^{\infty}\frac{1}{n^s} $ This produces: ζ(s) =

∞

• n=1

1 ns . The curly brackets above tell the computer to treat something as a single object. So for example, the brackets in {n=1} above make sure that the whole expression n = 1 goes below the sum. If they are omitted we get a mess: ζ(s) =

• n

= 1∞ 1 ns .

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To make a mathematical expression occur in the middle of some text, we use $ · · · $.

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To make a mathematical expression occur in the middle of some text, we use $ · · · $. To make it appear on its own line, use $$ · · · $$ or \begin{equation} · · · \end{equation}.

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To make a mathematical expression occur in the middle of some text, we use $ · · · $. To make it appear on its own line, use $$ · · · $$ or \begin{equation} · · · \end{equation}. Anything which appears inside the “equation” environment is treated by the computer as mathematics.

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To make a mathematical expression occur in the middle of some text, we use $ · · · $. To make it appear on its own line, use $$ · · · $$ or \begin{equation} · · · \end{equation}. Anything which appears inside the “equation” environment is treated by the computer as mathematics. More advanced option: \begin{align} · · · \end{align} to produce a list of equations.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

To make a mathematical expression occur in the middle of some text, we use $ · · · $. To make it appear on its own line, use $$ · · · $$ or \begin{equation} · · · \end{equation}. Anything which appears inside the “equation” environment is treated by the computer as mathematics. More advanced option: \begin{align} · · · \end{align} to produce a list of equations. Note that \begin{equation} and \begin{align} will produce an equation with an equation number at the end of each line. To supress this, use \begin{equation*} and \begin{align*} which produces numberless equations.

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Arrays

Analogous to tabular in text, \begin{array}{ccc} x&x&x\\ x&x&x\\ x&x&x \end{array} creates a mathematical 3-by-3 table.

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Arrays

Analogous to tabular in text, \begin{array}{ccc} x&x&x\\ x&x&x\\ x&x&x \end{array} creates a mathematical 3-by-3 table. Again, the symbol & tells the computer when a column has ended and the symbol \\ tells it when a row has ended.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Arrays

Analogous to tabular in text, \begin{array}{ccc} x&x&x\\ x&x&x\\ x&x&x \end{array} creates a mathematical 3-by-3 table. Again, the symbol & tells the computer when a column has ended and the symbol \\ tells it when a row has ended. The align environment behaves similarly: & marks the place where the equations are supposed to align with each other, and \\ marks the end of each line.

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Aligned equations

Sometimes we want to write an equation which extends across several lines, for example: a

• x + b

2a 2 − b2 4 + c = ax2 + bx + b2 4 − b2 4 + c = ax2 + bx + c.

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Aligned equations

The source code for the previous example was: \begin{align*} a \left(x+\frac{b}{2a}\right)ˆ2 - \frac{bˆ2}{4} + c & = axˆ2 + bx + \frac{bˆ2}{4} - \frac{bˆ2}{4} + c \\ & = axˆ2 + bx + c. \end{align*}

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Aligned equations

The source code for the previous example was: \begin{align*} a \left(x+\frac{b}{2a}\right)ˆ2 - \frac{bˆ2}{4} + c & = axˆ2 + bx + \frac{bˆ2}{4} - \frac{bˆ2}{4} + c \\ & = axˆ2 + bx + c. \end{align*} A more complicated expression. Some features:

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Aligned equations

The source code for the previous example was: \begin{align*} a \left(x+\frac{b}{2a}\right)ˆ2 - \frac{bˆ2}{4} + c & = axˆ2 + bx + \frac{bˆ2}{4} - \frac{bˆ2}{4} + c \\ & = axˆ2 + bx + c. \end{align*} A more complicated expression. Some features: \frac{b}{2a} produces the fraction

b 2a

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Aligned equations

The source code for the previous example was: \begin{align*} a \left(x+\frac{b}{2a}\right)ˆ2 - \frac{bˆ2}{4} + c & = axˆ2 + bx + \frac{bˆ2}{4} - \frac{bˆ2}{4} + c \\ & = axˆ2 + bx + c. \end{align*} A more complicated expression. Some features: \frac{b}{2a} produces the fraction

b 2a

\left( and \right) produce appropriate-sized brackets around whatever is in between them

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Aligned equations

The source code for the previous example was: \begin{align*} a \left(x+\frac{b}{2a}\right)ˆ2 - \frac{bˆ2}{4} + c & = axˆ2 + bx + \frac{bˆ2}{4} - \frac{bˆ2}{4} + c \\ & = axˆ2 + bx + c. \end{align*} A more complicated expression. Some features: \frac{b}{2a} produces the fraction

b 2a

\left( and \right) produce appropriate-sized brackets around whatever is in between them The & signs align vertically (i.e. they make the = signs align vertically). Move them, and the vertical alignment will be different.

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Matrices

Two basic ways to write matrices: using \array or using \pmatrix.

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Matrices

Two basic ways to write matrices: using \array or using \pmatrix. \left( \begin{array}{cc} 2 & 1 \\ 1 & 0 \end{array} \right)

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Matrices

Two basic ways to write matrices: using \array or using \pmatrix. \left( \begin{array}{cc} 2 & 1 \\ 1 & 0 \end{array} \right)

• r

\begin{pmatrix} 2 & 1 \\ 1 & 0 \end{pmatrix}

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Matrices

Two basic ways to write matrices: using \array or using \pmatrix. \left( \begin{array}{cc} 2 & 1 \\ 1 & 0 \end{array} \right)

• r

\begin{pmatrix} 2 & 1 \\ 1 & 0 \end{pmatrix} Note that \pmatrix creates left and right brackets itself, but \array needs to be told to do this using \left( and \right). The former needs the amsmath package.

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A miscellany

TeX source code Result $\frac{a+b}{c+d}$

a+b c+d

$\sqrt{3+x}$ √3 + x $(a_{n_k})_{k=1}ˆ\infty$ (ank)∞

k=1

$\|A\|$ A $\det A$ det A $\sin\theta$ sin θ

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Exercises

Use \prod_{ }^{ } and \frac{ }{ } to produce ζ(s) =

• p

1 1 − p−s

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Exercises

Use \prod_{ }^{ } and \frac{ }{ } to produce ζ(s) =

• p

1 1 − p−s Use \leq and \int_{ }^{ } (and \infty) to write: for any ǫ > 0,

∞

• n=1

|n−s| ≤ 1 + ∞

1

x−(1+ǫ)dx < ∞ provided Re(s) ≥ 1 + ǫ.

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Exercises

Using $$\begin{array} · · · \end{array}$$, \xarrow where x∈{left, right, up, down}, draw 1 → 2 ↑ ↓ 4 ← 3

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Bibliographies: by hand

There is one direct way of creating the references:

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Bibliographies: by hand

There is one direct way of creating the references: add \begin{thebibliography}{99} . . . \bibitem{FLT} A. Wiles, \emph{Modular elliptic curves and Fermat’s Last Theorem}, ... . . . \end{thebibliography}

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Bibliographies: by hand

There is one direct way of creating the references: add \begin{thebibliography}{99} . . . \bibitem{FLT} A. Wiles, \emph{Modular elliptic curves and Fermat’s Last Theorem}, ... . . . \end{thebibliography} immediately before \end{document} but after everything else.

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Bibliographies: by hand

There is one direct way of creating the references: add \begin{thebibliography}{99} . . . \bibitem{FLT} A. Wiles, \emph{Modular elliptic curves and Fermat’s Last Theorem}, ... . . . \end{thebibliography} immediately before \end{document} but after everything else. Here ‘FLT’ is a name I have decided to call the paper. To cite it in the text, write \cite{FLT}. The number, e.g. [n], corresponding to the order (n-th) of the reference appears instead.

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Bibliographies: using BibTeX

Referencing can also be automated. This requires you to create a separate .bib file (e.g. reference.bib) which consists entirely of entries like this:

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Bibliographies: using BibTeX

Referencing can also be automated. This requires you to create a separate .bib file (e.g. reference.bib) which consists entirely of entries like this: @article {Da44, AUTHOR = {Dalzell, D. P.}, TITLE = {On {$22/7$}}, JOURNAL = {J. London Math. Soc.}, VOLUME = {19}, YEAR = {1944}, PAGES = {133–134}, }

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Advantage: you do not have to write these yourself! You can just download them from e.g. MathSciNet, MRLookUp, Zentralblatt Math.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Advantage: you do not have to write these yourself! You can just download them from e.g. MathSciNet, MRLookUp, Zentralblatt Math.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

To instruct the computer to use the BibTeX file, add in the main source file, just before \end{document}:

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

To instruct the computer to use the BibTeX file, add in the main source file, just before \end{document}: \bibliographystyle{plain} \bibliography{reference}

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

To instruct the computer to use the BibTeX file, add in the main source file, just before \end{document}: \bibliographystyle{plain} \bibliography{reference} instead of the commands which we mentioned three slides ago. Now you can use \cite{Da44} to cite the article. (This may require you to compile the document twice before it works correctly.)

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

To instruct the computer to use the BibTeX file, add in the main source file, just before \end{document}: \bibliographystyle{plain} \bibliography{reference} instead of the commands which we mentioned three slides ago. Now you can use \cite{Da44} to cite the article. (This may require you to compile the document twice before it works correctly.) This saves effort versus writing all the bibliography entries by hand. You can change the appearance by using different bibliography styles: acm, siam, etc.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Theorem numbering, internal reference

In the preamble, if we write \newtheorem{prop}{Proposition}, this allows us to use the command \begin{prop} · · · \end{prop} to create a header titled “Proposition” which we can use to state propositions in our document.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Theorem numbering, internal reference

In the preamble, if we write \newtheorem{prop}{Proposition}, this allows us to use the command \begin{prop} · · · \end{prop} to create a header titled “Proposition” which we can use to state propositions in our document. Similarly we could write: \newtheorem{theorem}{Theorem}, for example and use it by the command \begin{theorem} · · · \end{theorem}.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

By default, theorems and propositions will use different numbers: we would get Proposition 1, Theorem 1, Theorem 2, Proposition

• 2. . .

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

By default, theorems and propositions will use different numbers: we would get Proposition 1, Theorem 1, Theorem 2, Proposition

• 2. . .

If we wanted them to share a numbering system (e.g. Proposition 1, Theorem 2, Theorem 3, Proposition 4) we could write:

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

By default, theorems and propositions will use different numbers: we would get Proposition 1, Theorem 1, Theorem 2, Proposition

• 2. . .

If we wanted them to share a numbering system (e.g. Proposition 1, Theorem 2, Theorem 3, Proposition 4) we could write: \newtheorem{prop}{Proposition}, \newtheorem{theorem}[proposition]{Theorem}, in the preamble instead.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Suppose we have Theorem All semi-stable elliptic curves over Q are modular.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Suppose we have Theorem All semi-stable elliptic curves over Q are modular. This is given by: \begin{theorem} All semi-stable elliptic curve over $\mathbb{Q}$ are modular. \end{theorem}

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

In case I have to refer to the theorem multiple times in the text, it is very useful to have a system that deals with changes I make.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

In case I have to refer to the theorem multiple times in the text, it is very useful to have a system that deals with changes I make. ‘label’ the theorem by \label{ } a name I find it easy to remember–write \label{ssST} for example.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

In case I have to refer to the theorem multiple times in the text, it is very useful to have a system that deals with changes I make. ‘label’ the theorem by \label{ } a name I find it easy to remember–write \label{ssST} for example. use the command \ref{ } to create the ‘number’, given to the theorem–for example, ‘It follows from Theorem ∼\ref{ssST} that Fermat’s Last Theorem holds!’.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

In case I have to refer to the theorem multiple times in the text, it is very useful to have a system that deals with changes I make. ‘label’ the theorem by \label{ } a name I find it easy to remember–write \label{ssST} for example. use the command \ref{ } to create the ‘number’, given to the theorem–for example, ‘It follows from Theorem ∼\ref{ssST} that Fermat’s Last Theorem holds!’. This can be done with displayed and aligned equations as well as theorems: see the example file.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Resources

Additional course materials:

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Resources

Additional course materials: examples.tex – contains source code for some examples of equations, aligned equations, diagrams, propositions, proofs, tables etc

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Resources

Additional course materials: examples.tex – contains source code for some examples of equations, aligned equations, diagrams, propositions, proofs, tables etc exercises.pdf – some mathematical expressions for you to attempt to write using LaTeX.

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Resources

Additional course materials: examples.tex – contains source code for some examples of equations, aligned equations, diagrams, propositions, proofs, tables etc exercises.pdf – some mathematical expressions for you to attempt to write using LaTeX. A very comprehensive and reputable free textbook: A (Not So) Short Introduction to LaTeX2ǫ

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Resources

Additional course materials: examples.tex – contains source code for some examples of equations, aligned equations, diagrams, propositions, proofs, tables etc exercises.pdf – some mathematical expressions for you to attempt to write using LaTeX. A very comprehensive and reputable free textbook: A (Not So) Short Introduction to LaTeX2ǫ A recommended internet forum: tex.stackexchange.com

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Introduction Fundamentals Environments, packages and macros Mathematical symbols References

Thanks for listening!

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