Notes on L A TEX. Jim Howie. October 14, 2013

Transcription

1 Notes on L A TEX Jim Howie October 14, 2013 Contents 1 Introduction Structure of a L A TEX file A simple L A TEX file Sections etc TEXWorks L A TEX Errors System Errors Mathematics Some useful Mathematics commands Theorems and Things 7 5 Citing and Cross-referencing Cross-referencing Citing Lists and tables Arrays and Matrices Graphics in L A TEX Documents 12 8 Presentations in L A TEX Colours Overlays

2 1 Introduction A L A TEX file is a text file that is processed by software to produce several output files. If the file has no errors then one of the output files will be a printable document such as a PDF. This can be thought of as analogous to a computer language such as Java or MATLAB. We are writing a programme to produce a mathematical document. The TEXWorks system on the University Desktop Service is a comprehensive L A TEX development system that takes care of the nuts and bolts of the compilation process, so that all we have to see are the L A TEX source file and the final PDF output. 1.1 Structure of a L A TEX file A L A TEX file contains various kinds of text. Plain text, which will appear in the final document in the form that we type it in except that L A TEX will take care of the spacing and line-breaks for us. To begin a new paragraph, simply insert an empty line (or the command \par) in the L A TEX file. If you wish to leave a bigger space before your new paragraph, this can be done by inserting \medskip or \bigskip at the start of the new paragraph (after the empty line). It is possible to force a new line without indentation using the double backslash command \\. Text can be put into bold or italic font by including it in braces with the L A TEX command \bf or \it, for example: {\bf bold font text} produces bold font text. Replacing \it by \em in the above which toggles between roman and italic text (ie gives italic text unless we are already in italic mode, when it gives roman text). L A TEX commands: these always begin with the backslash character \. Mathematics: we tell L A TEX to switch into math mode or from math mode back to text mode by the use of the dollar symbol $. Within the dollar signs we can create mathematical symbols using special mathematical L A TEX commands. For example, $ \sin(2\pi x)$ will produce the output sin(2πx). Note that text such as x in math mode is automatically output in italics. The command \sin in math mode overrides this rule and prints sin in roman font. Greek letters α, β,..., π,..., ω are produced using L A TEX commands in math mode. Comments can be included in a L A TEX file by using the percentage sign %. Everything from the percent sign to the end of that line will be ignored by the compiler and will not appear as output. 2

3 There are three essential L A TEX commands that must be contained in every L A TEX file. \documentclass{... } This must be the first line of your file. It tells L A TEX to load one of several class files containing formatting information for different kinds of documents. The system comes equipped several different different class files, called article, letter, book,.... It is also possible to create your own class files, but that is not a task for beginners! To begin with, let us stick to the most commonly used document class article. So our first line should be \documentclass{article} \begin{document} This comes at some point after the \documentclass command, and tells L A TEX to begin typesetting in earnest. The space between \documentclass and \begin{document} is called the preamble. Here we can put optional header material, but more of that later. Following \begin{document} we put in the material both text and mathematics that we actually want to see in the final output. \end{document} is self-explanatory. L A TEX will stop typesetting at this point. We can put lots more in our file after the \end{document} command, but it will be treated as one giant comment. 1.2 A simple L A TEX file We can now construct a simple L A TEX file: \documentclass{article} \begin{document} Here is what we say what we want to say. \end{document} The above four lines will not produce very exciting output. somewhere! But we have to start Note the \begin and \end statements. This is how L A TEX opens and closes an environment. A L A TEX file will in general contain many environments often nested within one another. Each \begin{environment} command must be matched by a corresponding 3

4 \end{environment} command. More on environments later. For now, each L A TEX file contains precisely one document environment. Note also the use of braces, or curly brackets { and }. L A TEX uses these to collect together a string of text and treat it as a single entity. So a L A TEX file will typically contain many braces. Each left brace must be matched to a corresponding right brace and vice versa. Braces do not show up in the output. If you specifically want to have braces in your output document (for example to describe a set), then use \{ and \}. For example $\{1, 2, 3, 4\}$ will appear in your output as {1, 2, 3, 4}. 1.3 Sections etc. If you are writing a longer document, you may want to subdivide it into sections, and possibly subsections (or even subsubsections). Even longer documents (using \documentclass{book}) may be subdivided into chapters. To start a new chapter, section, subsection etc., simply type in a line \chapter{heading} or \section{heading} or so on. L A TEX will output a suitably sized, bold face heading Heading together with an automatically generated number. For example the second subsection of the third section will be numbered 3.2. Automatic numbering is one of the many useful attributes of L A TEX: if you later decide to insert another section in the middle of your document, or to subdivide or delete a section, then L A TEX will automatically change the numbering of all later sections for you. The same applies to chapters, subsections, etc., and also to numbered environments such as Equations (see Section 3 below) or Theorems (Section 4). 2 TEXWorks The only way to learn L A TEX properly is by doing it. The most convenient way to do so is via a user interface such as TEXWorks, which is available on the University Desktop Service. Log in to the University Desktop Service and let s get started. Start TEXWorks by going to All Programs HW Programs MikTeX 2.9 TeXWorks This opens a window into which we can type L A TEX commands to create our own L A TEX file. However, it is always easier to start from an existing L A TEX file and edit it. So why not download some of the sample L A TEX files and use one of these. 4

5 Warning When downloading a file from the internet to the UDS, always choose the Save As option. If you choose Save, or if you open the file and then save from an application programme, the system is likely to save it as a weblink (so it will no longer be on the system when you look for it next time). So, having safely downloaded a L A TEX file and saved it as myfile.tex, we can open it in TEXWorks using File Open There is a green arrow in the top left of the TEXWorks window. Press this and a new window will open, displaying a PDF ouptput file created from the L A TEX file. Experiment by editing the text in the L A TEX file and pressing the green arrow again. 2.1 L A TEX Errors Like any computer language, L A TEX works only if it is fed input that follows its own syntax rules. If your file contains a L A TEX error (which will happen frequently as you learn to use L A TEX), then instead of producing PDF output, TEXWorks will display error messages in the console at the foot of the L A TEX window. You then need to edit the L A TEX file and try again, by hitting the red cross. Some of these error messages are self-explanatory (for example, if you try to type a mathematical symbol such as \alpha without first entering a $ sign to go into math mode, or if you have unmatched brackets or a missing \end{environment} command). Other error messages are less easy to follow, so you may have to do some investigation and/or ask for help to interpret them. If in doubt, here is one trick to help locate the L A TEX error(s). Insert a line \end{document} somewhere in the middle of the document, and hit the green arrow/red cross. If the L A TEX file compiles successfully, then any error must be below the point at which you inserted the new line - otherwise there is at least one error above that point. Delete the line and insert it further down or further up in order to narrow down your search. 2.2 System Errors Unfortunately, there have been occasional problems with the University Desktop System, where a student has been denied access to the TEXWorks for no apparent reason. Should this happen, try logging off and logging on again. If the problem persists, ITHelp. 3 Mathematics To type in mathematical expressions (including Greek letters) such as α + tβ = γ δ we enclose them within dollar signs. Note that each symbol is a L A TEX command. L A TEX 5

6 commands start with a backslash symbol, \. The dollar sign $ is used by L A TEX to toggle between ordinary text mode and math mode: $ \sqrt{3} $ is output as 3 Double dollars display the mathematics: $$ \sqrt{3} $$ is output as 3 Alternatively, we can use the equation environment to produce a display. Typing \begin{equation} \zeta(s)=\sum_{n=1}^\infty \frac{1}{n^s} \end{equation} produces the output ζ(s) = n=1 1 n s (1) Notice that the equation comes equipped with a number. This is often useful if we want to refer back to a particular equation see Section 5 below on citing and cross-referencing. 3.1 Some useful Mathematics commands Here is a selection of commonly used mathematical commands in L A TEX. Greek letters: \alpha, \beta, \gamma produces α, β, γ, etc. Arrows: \rightarrow, \leftarrow, \leftrightarrow, \Rightarrow produce,,, respectively. Fractions, square roots: $ \frac{a}{b} $ produces a b, $ \sqrt{a} $ produces a Subscripts and superscripts: $ aˆb$ produces a b, $ aˆ{long} $ produces a long ; $ a b$ produces a b, $ a {long}$ produces a long. (Note the use of braces for subscripts and superscripts more than one character long. The braces force L A TEX to treat the string as a single entity. If they are omitted, then only the first character will be typeset as a subscript or superscript, with strange looking outcomes: $ xˆ10$ produces x 1 0, for example. Blackboard bold letters $ \mathbb{r}$, $ \mathbb{c} $ for R, C etc. Set theory: \{... \} for {... } ; \cup, \cap for, ; \in, \notin for, /, \subset, \subseteq for, 6

7 \equiv, \sim, \cong for,, = \le, \ge, \ll, \gg, \pm, \mp for,,,, ±, A much longer list of useful symbols is available from the L A TEX website. Example The input: A quadratic equation of the form $ axˆ2+bx+c=0 $ can be solved by the quadratic formula $$ x=\frac{ -b \pm \sqrt{ bˆ2-4ac} }{2a} $$ Gives the output: A quadratic equation of the form ax 2 + bx + c = 0 can be solved by the quadratic formula x = b ± b 2 4ac 2a Recommendation: always include \usepackage{amssymb} in your preamble (between the \documentclass and \begin{document} commands). This loads a bigger range of mathematical symbols into the system, that are then available for your use.. 4 Theorems and Things Theorems (and their close relatives: lemmas, corollaries, and so on) are treated by L A TEX as special environments. L A TEX will typset the text of a theorem in italics, and will automatically assign it a number. The downside is that you have to explicitly declare all your theorem-like environments in the preamble to the document. Here is a typical setup: \documentclass{article} \newtheorem{thm}{theorem}[section] \newtheorem{lem}[thm]{lemma} \newtheorem{cor}[thm]{corollary} \begin{document}... 7

8 \begin{thm} Let $a,b$ be real numbers. Then $(a+b)ˆ2=aˆ2+2ab+bˆ2$. \end{thm} In the preamble, we have defined three different theorem-like environments using the \newtheorem command. The first of these is an environment thm, which we invoke in the text using \begin{thm}... \end{thm}. The second argument Theorem of the \newtheorem command tells L A TEX to head each thm with the word Theorem followed by its number. The optional argument section (optional arguments go in square brackets rather than braces) following {Theorem} tells L A TEX to number theorems within sections for example the second theorem in Section 4 will be Theorem 4.2. If you prefer your theorems to be numbered consecutively throughout the document, simply omit this optional argument. The second environment is lem, which L A TEX will head using the word Lemma. In this case there is an optional argument thm between the first and second main arguments (lem and Lemma). This time the optional argument tells L A TEX to number each lem as if they were a thm. The third environment cor is set up similarly. So in our document, we may have Lemma 3.1 immediately followed by Theorem 3.2 and then Corollary 3.3. This system makes it relatively easy for the reader to navigate the results in your document. But if you prefer to have Lemmas numbered independently from Theorems, then you can omit the optional argument. 5 Citing and Cross-referencing 5.1 Cross-referencing As mentioned earlier, L A TEX has an auotmatic numbering system that keeps track of the correct numbers for sections, theorems, equations, etc. and updates the information when you re-run L A TEX after editing the file. You can take advantage of this system for the purposes of cross-referencing. Rather than type in phrases such as see Theorem 4.2 in Section 4, which you may later need to edit, we can proceed as follows. Use the command \label{tag} immediately after your \section or \begin{environment} command. This associates the label tag with the section, theorem etc. in question, irrespective of what number is eventually assigned to it. To cross-refer to that section, theorem etc. in your text, use \ref{tag}. In practice, it makes sense to use an easily memorable tag. For example \section{introduction}\label{intro} In this paper we will prove the Binomial Theorem (Theorem \ref{binom} below).... 8

9 As mentioned in \S \ref{intro}, our main purpose is to prove the following result \begin{thm}[the Binomial Theorem]\label{binom} Let $ a,b $ be real numbers and $ n $ a positive integer. Then $$(a+b)ˆn = \sum {k=0}ˆn \frac{k!(n-k)!}{n!} aˆk bˆ{n-k}.$$ \end{thm} Note the use of \S for section ( ). Note also the optional square bracket after the \begin{thm} command. The phrase in square brackets will be typset in parentheses (round brackets) between the Theorem heading and the statement. The output will look something like: Theorem 5.1 (The Binomial Theorem) Let a, b be real numbers and n a positive integer. Then n (a + b) n k!(n k)! = a k b n k. n! k=0 Note also that \ref{tag} only knows the number associated to tag. It does not know what type of entity that is. So it is better to use a form of word like By Theorem \ref{tag}... rather than just By \ref{tag}.... In particular, equation numbers appear in parentheses beside the display, so you should insert parentheses when cross-referencing an equation: By Equation (\ref{tag}) Citing Citing is analogous to cross-referencing, the difference being that the reader is being refered to an external source rather than part of the same document. But the underlying principle is the same. We assign an easily remembered tag to each external source for example Ratho99 for Hamish Ratho s groundbreaking 1999 paper. To cite this paper (book, website,... ) we simply use the command \cite{ratho99}. If we wish to give a more detailed reference, with a page number for example, we can use an optional squarebracket argument such as \cite[page 32]{Ratho99} or \cite[theorem 2.7]{Ratho99}. We can also cite a list of references with a single command: \cite{howie07,ratho99,rynne09}. The references should be listed at the end of your document, in an environment called thebibliography. Each item in this list is preceded by the command \bibitem{tag}, and consists of bibliographic information as appropriate. For example:... The foundation work for this theory first appeared in the groundbreaking article \cite{ratho99} of Ratho. An account can also be found in \cite[chapter 4]{Howie07}.. 9

10 \begin{thebibliography} \bibitem{howie07} J. Howie, {\em An Exposition of the Groundbreaking Results of Ratho}, Disney-Kenn Publishing Corporation, Balerno (2007). \bibitem{ratho99} H. Ratho, Some observations on the mathematics of witchcraft, {\em J. Excellent Math.} {{\bf 47} (1999) \end{thebibliography} will yield the output:... The foundation work for this theory first appeared in the groundbreaking article [2] of Ratho. An account can also be found in [1,Chapter 4].. References [1] J. Howie, An Exposition of the Groundbreaking Results of Ratho, Disney-Kenn Publishing Corporation, Balerno (2007). [2] H. Ratho, Some observations on the mathematics of witchcraft, J. Excellent Math. 47 (1999) Lists and tables Lists can be created in L A TEX using one of several list environments. We have already seen one of these thebibliography. Here are two other commonly used examples. For a numbered list, use the enumerate environment. The input: \begin{enumerate} \item First item in list \item Next item in list \end{enumerate} will output 1. First item in list 2. Next item in list For a bullet-point list, we do exactly the same, but using the itemize environment: First item in list Next item in list 10

11 Tables can be produced using the tabular environment. \begin{center} (To put table in centre of page. Note US spelling of center.) \begin{tabular}{ l c r } (Alignment parameters left, centre, right; optional between columns). \hline (Optional horizontal line between rows) 1 & 2 & 3 \\ (Alignment characters: & = next column, \\ = next row) \hline 4 & 5 & 6 \hline \end{tabular} \end{center} will produce In the above example the table is itself put inside a center environment the effect of which is simply to place the output in the middle of the page. This is the natural place to put many tables. But it is not essential: in the absence of the center environment or other formatting commands, a table will be typeset left-justified. 6.1 Arrays and Matrices The array environment works like tabular, but in math mode. It can be used to produce matrices, for example. $$ \left( (big open bracket) \begin{array}{ll} (two columns, left-justified) a & b \\ c & d \\ \end{array} \right) $$ (big close bracket) will produce: ( a b ) c d 11

12 7 Graphics in L A TEX Documents Graphic files in PDF, JPEG, PNG and some other formats can be included in a L A TEX document using the graphicx package. More details can be found on the weblinks from the L A TEX website. Prepare your graphics file using whatever software is appropriate and save it in one of the usable formats in the same directory as your L A TEX file. Insert the line \usepackage{graphicx} in your preamble. The sensible place is together with any other \usepackage commands such as \usepackage{amssymb}, immediately after the \documentclass command. Where you want graphics in your document, insert: \includegraphics{filename.pdf} or \includegraphics{filename.jpg} etc., depending on the type of your graphics file. It is usually best to do this within a center environment, to ensure that the image is centred on the page (unless, of course, you specifically want the image not to be centred). You may find that your image does not fit the page, or appears upside down. Rotation and/or scaling parameters can be included in square brackets in the \includegraphics command: \includegraphics[width=80mm]{filename.pdf} \includegraphics[angle=90,height=50mm]{filename.jpg} etcetera. The rules are fairly self-explanatory. But the best approach is to experiment until you find the most appropriate size and orientation for your image. 8 Presentations in L A TEX The beamer document class produces PDF output suitable for use in a presentation using a data projection system. (From the German: Beamer = Overhead Projector.) \documentclass{beamer} There is a template Beamer file on the L A TEX website. This contains some commands in the preamble that help keep the output as simple and uncluttered as possible. It also contains some example slides to indicate some of the features that you can use. After reading this section, I recommend that you look at the Template file and experiment with it to create a presentation of your own. 12

13 Each slide of your output file corresponds to the contents of a frame environment in the Beamer L A TEX file. It is your responsibility to make sure that the slides do not contain too much material. If you try to put too much into a slide, then the excess material simply will not show up on the screen. So in preparing a L A TEX presentation it is good practice to keep viewing the output to make sure that the material fits. If in doubt, split a big slide into two smaller ones. It is also good practice to use a more succinct prose style than you would in a typeset document (bullet points rather than paragraphs, short phrases rather than long sentences). Most of the standard features of L A TEX are present in the beamer document class: mathematical symbols, displayed equations, lists, tables, graphics and so on. These are used in the same way as when writing a document for typesetting. The main difference is that the output is to be viewed on a screen, rather than a page, so you need to make every effort to ensure that the effort is visible. Be prepared to use additional \medskip or \bigskip commands to spread your text out, for example. Graphics in a presentation can be particularly effective, but take good care that they do not get in the way of the text. 8.1 Colours Two additional features of Beamer are worthy of note. One is the use of colours, which are not catered for in standard L A TEX. Colour can be very effective in a presentation, for example to highlight text it is better to colour it red than to typeset it in bold or italic font. But care should be taken with choice of colour(s) for various reasons. Strong colours such as red are effective: pale colours such as yellow or pink do not show up well on a screen, so should be avoided. Red-green colour-blindness is relatively common, so you should avoid using red and green for different purposes on the same slide. Finally, too many colours on a single slide (other than in a photograph or similar graphic) can be distracting. In practice, I tend to use only red and blue but that is partly a matter of taste; you should experiment and decide what works best for you. To typeset a piece of text or mathematics in red, simply enclose it in braces with the command \color{red}. (Note the US spelling of colour.) Similarly for other colours. For example {\color{blue} Definition} An integer $ n $ is {\color{red} even} if it is divisible by $ 2$. will highlight the heading Definition in one colour and the word being defined even in another. In a typescript document, these would naturally appear in bold and italics respectively, but the colours work better on a slide. 13

14 8.2 Overlays Overlays are pieces of content that can be added and/or removed from a slide to create a particular effect. For example, you may wish to have a slide showing the statement of a theorem with the final conclusion missing, then click to reveal the full statement. This can be achieved using overlays. In practice the output document will contain two or more pages that look identical except for the material that is being overlaid. (This can make the PDF file be large, but can sometimes be effective.) To produce an overlay within a frame, use the command \uncover number(s) {content}, where content is the material that you wish to be included in the overlay, and number(s) is the number, or list of numbers of the versions of the slide in which you wish this material to be displayed. This could be a single number such as 2, a range of numbers: 2-3, or a list of numbers and/or ranges: -2,4,6-8. If the beginning of a range is missing, it is given the default value 1. If the end is missing, the default value is the maximum. You can have several overlays on any single frame. The number of slides produced is equal to to largest number in any of the numbers lists. An overlay will be displayed on slide n if and only if n is one of the numbers (or within one of the ranges) in its numbers list. The simple example mentioned above, of a theorem statement with overlaid conclusion, could be typeset something like: \begin{frame} \begin{theorem} Let $ a,b $ be real numbers. Then \overlay 2 {$$ (a+b)ˆ2 = aˆ2 + 2ab + bˆ2. $$} \end{theorem} \end{frame} See the Beamer template for more examples. Recommendation: Be careful not to over-use overlays. Used well, they can be effective in helping get your message across. But if used too much they become a distraction. 14