A Beginner s Guide to LATEX. Last Revised: August 21, 2013

Transcription

1 A Beginner s Guide to LATEX Last Revised: August 21, 2013

2 Thanks In the (ongoing) creation of this document, I ask a lot of people for feedback and input. Some of them are classmates (past or present) or professors, and some of them are just people on the internet who were willing to help me out and look it over. I would like to thank these people here. Kia Braha Dylan Helliwell headbanger Ravin Kumar Chris B. Ang Li Dominic Maderazo If you happen to find an error in this document or simply feel I left something out feel free to me at a.m.klingensmith@gmail.com and I will update both this list and the document. 1

3 CONTENTS CONTENTS Contents 1 Preface: An Argument for L A TEX in Education 3 2 Introduction 5 3 Installation Compilers Editors Creating a Document The Language of L A TEX The Preamble Packages Making a Document 12 6 L A TEX Organizational Structure 13 7 Examples! Simple Text Math Mode More Complicated Math Adding Images Creating Lists Creating Tables Theorems, Lemmas, Proofs Miscellaneous Math L A TEX Special Characters If Things Go Wrong Appendix Package Information

4 1 PREFACE: AN ARGUMENT FOR L A TEX IN EDUCATION 1 Preface: An Argument for L A TEX in Education Whenever the idea of using L A TEX (pronounced: lah-tek) is brought up in education circles, the first response I usually hear is: What s the point? After all, we all know how to use programs like Mircosoft Word, and if we need to create even more complicated math, we can always just hand write equations. And sure, that s true, but here s my response (I m about to get a little preachy): First and foremost, L A TEX is pretty. It displays math how it ought to be seen. When I have to look at math that is clunky, uneven, or sloppy I am turned off by it. I mean, consider if you read a book where the letters were poorly spaced, and it simply looked like the editor was trying to make the text do something that it wasn t meant to do. Regardless of what the book was saying, I would probably have a bitter taste in my mouth when I remembered it just because of how unprofessional it looked. L A TEX is what professors use, it s what textbooks use, and it s what we should use. Because... L A TEX creates a stable environment for the students in terms of what to expect their tests (or assignments) to look like. If we, as teachers, rely on tools like Microsoft Word or our own hand-writing, we re adding an extra layer of work (albeit, arguably a small one) for our students: we re requiring them to be able to decipher our thoughts, and then learn someone else s thoughts each new year. If teacher A does z s with a bar and teacher B does z s without a bar, a student who goes from one class to the other is being asked to relearn how he or she interprets the letter z. This is a complication that doesn t have to exist. By using L A TEX, we create a uniform, clean guide for how math is displayed that will (likely) be what the student experiences in college (if that is where they end up). Lastly, L A TEX makes sharing math easier (bear with me as I unpack this). Or more accurately, it can make sharing math much easier. Right now, being a teacher and knowing L A TEX must bear an uncanny resemblance to Sisyphus: you constantly meet people who are invested in their practice, and you bring up L A TEX,...and you never hear from them again. Rinse, wash, repeat with 3

5 1 PREFACE: AN ARGUMENT FOR L A TEX IN EDUCATION each new person. I get that. Right now, arguably, L A TEX doesn t make math easier to share (at least amongst pre-college educators). But that doesn t have to be the case. If a department could all get together and use L A TEX, it could revolutionize how documents are created and shared amongst teachers. At the same time, it opens up an relatively new medium for teacher collaboration: the internet. With more teachers blogging/twittering/whatevering, many of these sites allow for the TEX typesetting, which means that any teacher who knows TEX immediately has a vast number of other doors open to them as well. This will lead to more communication and more innovation. And isn t that worth it? If you have any hesitations or doubts, or you honestly feel like you just don t have the technological capacity to take on this task, please please please seek me out. I will gladly do everything I can to make the learning process as painless (maybe even enjoyable?) as possible. I guarantee we will be better teachers as a result. 4

6 2 INTRODUCTION 2 Introduction Given that we all want to be math teachers, one issue that we re going to have to deal with is creating materials tests, handouts, worksheets, etc. While many teachers opt to do this by hand, and even more decide to use a program like Mircosoft Word, I would argue that both of these methods are less than desirable. That is where L A TEX comes in. L A TEX is a typesetting system that is very suitable for producing scientific and mathematical documents of high typographical quality. In essence, L A TEX makes math look uniform and professional, like it ought to. For example, t t 0 cos(x 2 )e x3 dx isn t something that is easy to create using a program like Word (let alone create quickly and looking so nicely; let s be real, that s a sexy integral right there). However, L A TEX can seem annoyingly cumbersome at first. The purpose of this guide is to minimize the difficulties by providing a place to turn for problems and examples information I wish I had when I was first learning as well as giving guidance on where to look when you find problems of your own. Of course, the best way to learn L A TEX is to just sit down and force yourself to do so. In no time at all you ll be creating beautiful documents. But first, we need to install some things... 5

7 3 INSTALLATION 3 Installation If you made it this far, you re doing great!...that being said, it s about to get more complicated, so don t give up! To get to a point where you are making your own documents, two items are needed: L A TEX itself and an editor program. Think of it like this: Microsoft Word is your editor, but all of the behind-the-scenes files that make up Word (the different font choices, the ability to change the font color, to adjust the size, etc etc), that s L A TEX. 3.1 Compilers Depending on whether or not you have a Mac or PC, you may or may not have to download a compiler. [Note: from here on out, everything in blue is a link.] For PCs, the most common is MikTeX. For Macs, the most common is MacTeX. I have a PC, so I can best speak about MikTeX. Basically, if you go to the website, you re going to want to download the installer (for MikTeX it s called the Basic MikTex 2.9 Installer, at the time of this writing). For Macs, depending on which editor you choose to use (which is addressed in the next section), you may not need to actually download the compiler separately. Specifically, if you decide to use TeXShop (which is arguably the most popular choice of an editor for Macs), you don t actually need to download MacTeX, as it s already included in the TeXShop program. However, if you do not choose to use TeXShop, you may have to download MacTeX, so pay attention to whatever program you decide to use! If you do need to download an installer for a compiler, once you ve done that you should... install it. Duh. And once you ve done that, it s time to get an editor! 6

8 3.2 Editors 3 INSTALLATION 3.2 Editors Unlike getting L A TEX, there are many editors to choose from. This website lists what a lot of them are (under the Editors section...). From my friends who had Macs, they seemed to all use TexShop. I myself use TeXnicCenter. But whatever. Look around. Explore. See if you find one that sticks out. [Note: If you chose to use TeXShop, you can ignore this paragraph.] Ok, this next step can get a little tricky. It might actually be (in my opinion) the hardest part of this entire process, largely because it s the least transparent (at least to me). The editor you ve installed needs to find a way to connect with L A TEX. This (for some reason that I have no idea why) seems to be a harder process than it needs to be (but then again, I ve only worked with TeXnicCenter...). Needless to say, the best piece of advice I can give is to google: (whatever L A TEX you installed) + (whatever editor you installed) + installation. There will usually be forum posts or guides on how to make everything work perfectly. I would follow these guides. If you re having any trouble with this step, don t give up! Give me a call or something and we ll find a way to make it work. Seriously, this program is too useful to not use. Anyways, moving on. Once that is all done... Congrats! You are now able to create beautiful math documents (I m getting excited just thinking about that past integral... whew...). 7

9 4 CREATING A DOCUMENT 4 Creating a Document 4.1 The Language of L A TEX L A TEX for the most part is very friendly...once you take the time to get to know it. It s like that friend that you were skeptical about at first, but now you can t imagine life without them. Prepare to meet your BTPFF (best typesetting program friend forever). While much of L A TEX is just normal typing, not unlike how you d type in Word or an , there are times when you have to make commands. These provide the beauty of L A TEX and let you do anything from create a list of objects, to display specific characters. L A TEX commands take one of two forms: They start with a backslash \ and then have a name consisting of letters only They consist of a backslash \ and then have exactly one non-letter. For example, the fancy L A TEX is created by typing \LaTeX (an example of the first item). Similarly, a mathematical symbol like is written from the command \neq. However, if I wanted to include a brace like { or }, I would merely type \{ or \} (examples of the second item). Some commands require more input (called parameters), and are thus written as \command{parameter}. Whereas the previous examples focus on displaying special characters, the commands that require additional information are usually to enable specific functions or environments to take place. Declaring a document style or including a package (both of which are covered in the next subsection) are good examples of these (although you will see throughout this document that there are many commands that have parameters). 4.2 The Preamble Before you can really begin typing your math, you have to set the stage. The process of setting up what sort of document you ll be creating, deciding what 8

10 4.2 The Preamble 4 CREATING A DOCUMENT sort of packages (more on these later), and how you want the document to look are all found in the preamble. The first step is declaring what sort of document you want to create. L A TEX can be used to create everything from articles (that s the document class of what you re reading right now!) to books, reports, letters, and even presentations (this class is called Beamer and is AMAZING. It s like Power- Point meets L A TEX so it s beautiful). To do so, at the beginning of every document (usually the first line) is the text: \documentclass[12pt]{article} In this, the {article} portion defines what type of document we re creating (so if you wanted to create a different sort of document, article is what you would change), and the [12pt] is considered an option. In the document class command, options can do things such as control the base font size, paper size, and even layout structures like double sided printing or landscape documents (so here, [12pt] means I ll be using fonts that have a base size of 12pt). When you feel up to it, explore different document classes and see if there is one that fits what you re trying to do best! While I ve tended to use the article class (mostly out of habit) there are many classes that may be even better suited for your goals. For example, if you decide to use the class amsart (which is the AMS American Mathematical Society article class), you might have to do less work later when it comes to what packages you need to declare (more on this in the very next section). [NOTE: If you are interested in learning more about AMS packages, I would suggest checking out their website. Two pieces of information worth checking out are the Short Math Guide for L A TEX and the amsmath user s guide, both of which can be found via the link to the AMS site.] From here, now that you ve defined a document class, you can begin creating your document. To do so, you would need to create the following code after your document class declaration: 9

11 4.3 Packages 4 CREATING A DOCUMENT \begin{document}... \end{document} The... is where you would put the text for your document. It should also be pointed out that \end{document} is essentially the end of the document (surprise!). So there you go! You can make a document!...but it s going to be a pretty boring document at this point, because all of the cool things we want to do (create math equations, tables, change the margins, insert pictures, etc.) require some additional items: packages. 4.3 Packages You can think of packages as the tools that allow you go from a normal text document to an intricate, beautiful, mathematical piece of art. (Remember those hyperlinks earlier in the document? I was able to add those thanks to a package.) Packages are usually found right after the document class declaration. There are a few different ways you can include packages. One such way is: \usepackage{package1, package2,... } Where package1 and package2 represent different packages. You can also add packages individually, like: \usepackage{package1} \usepackage{package2}... It really makes no difference which you prefer. The first way is nice since it requires you to only type \usepackage once, but the second is nice because sometimes certain packages require you to insert some optional information. (Remember the [12pt] option from before? The package optional information is formatted similarly to that hard brackets between the command and 10

12 4.3 Packages 4 CREATING A DOCUMENT the parameter.) For more information about packages, I would definitely check out the appendix at the end of this document. For now, I wouldn t stress about them too much; packages can be an incredibly powerful tool, but they can also be unnecessarily overwhelming if they re introduced too early. In time, young padawan, you will master them. But not yet: we have more to learn! To include packages, you need to declare them in the preamble after your document class declaration, but before you begin your document. For this document, my preamble looks like this: \documentclass[12pt]{article} \usepackage{amsmath, graphicx, hyperref, amsthm} \usepackage{xcolor} \usepackage{longtable, cancel, amsfonts, amssymb, fancyhdr}... Here, amsmath allows me to make mathematical symbols, graphicx is what allowed me to use that Math for America image (and other images) in the document, hyperref is what gave me the ability to turn certain words into links, amsthm is what allows me to display theorems and definitions, and xcolor is what allows me to turn those links blue (or other words other colors like cyan or orange). Ok, but enough about that. Let s make a document. 11

13 5 MAKING A DOCUMENT 5 Making a Document Really, the best way to make a document is to just force yourself to do so. Think of it as tough mathematical love. That being said, I think there are some great references out there that can make the process a lot easier. These websites are (listed in how much I use them from most to least): L A TEX WikiBook Art of Problem Solving The Not So Short Introduction to L A TEX DeTEXify Along with these websites, you can literally just google any problem you re having (for example, in the process of making this document I googled latex adjusting font size ) and odds are it will direct you to a solution. Better yet, it will probably direct you to the WikiBook for your answer that book is legit. So yeah, toy around. Go crazy. Once you begin to explore L A TEX, my guess is you ll find that it follows a logical structure and over time you ll rely less on other sites and more on your knowledge. That being said, seeing a few examples is always great for getting the ball rolling, so... 12

14 6 L A TEX ORGANIZATIONAL STRUCTURE 6 L A TEX Organizational Structure Ok ok ok. I know. I made it seem like we were about to go into trying some examples. But then I remembered a few things that are SUPER important. First up: A little bit about the files we ll be interacting with. When you re typing in a program like Microsoft Word, the document you are modifying is the same as the document you output (which is, just a Word document). L A TEX behaves a bit differently. Here, the document that you physically modify (the document ending in.tex ) is different than the document you output (a pdf). Thus, when you re creating your tex (pronounced tek) file in your editor, you won t see your output until you compile your document. To do so, it really depends on your editor (TeXnicCenter has a button I just press on its toolbar; I m not sure what the other editors look like, but it s usually similar a button or keyboard shortcut). The act of compiling is also when L A TEX will let you know if there are any errors. If it finds any, it will usually not display the output and let you know an error exists. Because of this fact, you should compile your document often! That way, you can have a better idea where your error is if it shows up. (For example, imagine if you typed out an entire document and didn t compile it until the end. If an error shows up, you d have to search through the entire document to find it. But if you compile your document every now and then, if an error shows up, you only need to look at the last section you typed. Much nicer.) Next up: Organization. When using L A TEX, to create one output file (a pdf), many files have to be generated along the way (for starters, you have your L A TEX file, which ends in the.tex extension, then you have your output file what you actually see- which is often a.pdf, but you also might have specific files you want to include as well, like images)! Because of this, it is vital to keep your files organized (for the sake of your sanity). To help with this process, there are several facts and several organizational tips I can share. First is that every file your L A TEX file references (such as every image you include in your code) needs to be in the same folder as wherever your L A TEX file the one ending in.tex is! If it s not there, L A TEX can t find it. 13

15 6 L A TEX ORGANIZATIONAL STRUCTURE Thus, I suggest the following organizational system: Create a folder called Latex. In this folder, for every L A TEX file you make, create a new folder entitled whatever it is you re making, and save it there. For example, here is what it looks like when I open up my Latex folder: Each of those subfolders is ONE specific document I was making. This will save you loads of time and make everything nice and neat. If you want to include a picture, just put it in the subfolder for whatever you re working on. Boom. Done. Ok, let s move on to the fun now... 14

16 7 EXAMPLES! 7 Examples! In this section, I will present the code for creating several different items, and then display what the output would be (the output will be displayed after a page break of five red asterisks). In doing so, items worth point out will inevitably come up, and I ll explain those as necessary. I encourage you to look at these examples and try to recreate them in your own editor along the way; toying around with L A TEX is the best way to learn the program. 15

17 7.1 Simple Text 7 EXAMPLES! 7.1 Simple Text Let s start with something small. Say you just want to create a document of text: \documentclass[12pt]{article} \begin{document} This is what that document could look like! \\ You can italicize text \emph{like this}. \\ Sometimes, you might want to \underline{underline} or \textbf{bold} text. \\ Of course, there are several other ways to italicize or bold text as well. For example, {\em this also italicizes text}, {\bfseries this also bolds text}. \end{document} Note that here, since we re only outputting text, we don t need to include any packages. I should also explain the use of \\. In L A TEX, that s code for skip to the next line. It s the equivalent of pressing enter on your keyboard in Word to move to the next line. But just like typing in Microsoft Word, this is primarily if you want to end a line early; otherwise L A TEXwill do just fine at creating line breaks at the margins (just like Word does). This is actually all going to be on one line would be very different than this: This is actually \\ going to be on two lines now! As far as how you want to italicize or bold words, it really doesn t make a difference. From some reason, I like to use \emph{...} for italicizing, and {\bf... } for making words bold. Makes no difference, really. 16

18 7.1 Simple Text 7 EXAMPLES! * * * * * This is what that document could look like! You can italicize text like this. Sometimes, you might want to underline or bold text. Of course, there are several other ways to italicize or bold text as well. For example, this also italicizes text, this also bolds text. 17

19 7.2 Math Mode 7 EXAMPLES! 7.2 Math Mode Say you want to create a document that shows some basic math opertations: \documentclass[12pt]{article} \begin{document} To get an exponent: $x^2$ \\ To get a subscript: $a_n$ \\ To do both an exponent and a subscript: $x_n^2$ \\ If you want to do an equation you can do: $x^2 + 3x = 0$ \\ Or you can be a little fancier and type: \begin{equation} x^2 + 3x = 0 \end{equation} \end{document} Lots to point out here. First, notice the use of $... $. These two dollar signs indicate math mode for L A TEX. As a result, everything that is printed in-between them will come out looking more mathematical. For example, this is done with math mode: x 2 [Note: L A TEX can actually tell when math mode is needed (at times) and will give you trouble if you exclude it. If I tried to compile the above code without the dollar signs, L A TEX would yell at me]. I should point out, though, that L A TEX also has some environments that are automatically in math mode. This can best be seen in the above code from the equation environment. By creating an equation environment, everything between \begin{equation} and \end{equation} is in math mode (and hence, no dollar signs are needed). L A TEX also centers equations and numbers them, so the output would look like: x 2 + 3x = 0 (1) For more on equations, just Google latex equations. 18

20 7.2 Math Mode 7 EXAMPLES! It s also worth pointing out how is used for superscripts (exponents) and is used for subscripts. If your exponent has more than one item in it, you can use { and } to raise everything, i.e.: x 99 is typeset as x {99}. (This is important because without braces L A TEX will only raise what is immediately to the right of the ). If you have multiple subscripts, it works the same way. * * * * * To get an exponent: x 2 To get a subscript: a n To do both an exponent and a subscript: x 2 n If you want to do an equation you can do: x 2 + 3x = 0 Or you can be a little fancier and type: x 2 + 3x = 0 (2) 19

21 7.3 More Complicated Math 7 EXAMPLES! 7.3 More Complicated Math For more complicated math things involving integrals, limits, summations, products, etc in which the typesetting is a bit more complex in terms of getting everything where it needs to be, I always suggest googling latex and whatever it is you re trying to do. In fact, to do the integral I displayed at the beginning of this document, that s exactly what I did. But anyways, let s say you want to create that integral, here s what the text would look like: \documentclass[12pt]{article} \usepackage{amsmath} \begin{document} \begin{equation*} \int_0^{t^t} cos(x^2)e^{-x^3}\, \mathrm{d}x \end{equation*} \end{document} First up should be the fact that most of the time I m doing math, I add the package amsmath. It s a package mostly for when more complicated symbols are needed, but it s so easy to add, I figure why not. You don t always have to add it, depending on the math you re doing (for example, you wouldn t need it to display something like x + 3 = 8, but as soon as you start moving to mathematical symbols beyond addition, subtraction, and equality, you re probably going to need it. I generally add it anytime there is the remote chance I ll be displaying math. So yeah, you don t always have to add it, but I mean, would it kill you if you did? Seriously, just add it. It s not worth the potential frustration later if you leave it out. One thing to note here is the use of equation* instead of just equation (as seen in the previous example). All the asterisk does is make it so the equation goes unnumbered). Also note how the subscript item 0 sets the lower bound of the integral while the exponent item {t t} sets the upper bound of the integral. Lastly, I should point out that the \, is used to create a space between what we re 20

22 7.3 More Complicated Math 7 EXAMPLES! integrating (cos(x 2 )e x3 ) and what we re integrating with respect to (dx). Lastly, note how instead of using the equation environment, I chose to use the equation* environment. While it looks like a small difference, it actually is rather significant. For starters, the equation* environment requires that I declare the amsmath package, otherwise it won t compile. In regards to output, the equation* environment only differs from equation in that it doesn t number the equations displayed (look at section 8.2 Math Mode to see what an example of how equations are labeled). Some more examples of more complicated things you can create are listed in the Miscellaneous Math section. t t 0 * * * * * cos(x 2 )e x3 dx 21

23 7.4 Adding Images 7 EXAMPLES! 7.4 Adding Images Let s say you want to include a picture in your document: \documentclass[12pt]{article} \usepackage{graphicx} \begin{document} \includegraphics[scale=.3]{raccoon.jpg} \begin{center} \includegraphics[scale=.3]{raccoon.jpg} \\ This creates a sort of fake caption \end{center} \begin{figure} \centering \includegraphics[scale=.3]{raccoon.jpg} \caption{this is a more legit caption} \label{raccoon} \end{figure} Observe how you can \end{document} reference Figure \ref{raccoon} by using its label! First off, since we re including pictures, we have to include the graphicx package. Once we ve done that, all we have to do is use the \includegraphics{... } command, where... is the name of the file (including its extension). In this example, I also used an option ( [scale=.3] ) which just scales the original image to three-tenths it s original size. There are a ton of different ways to resize an image, but scale is generally my favorite. It should also be pointed out that I am displaying the image in three different ways. The first way will just include the picture; the second way will center the picture and give it a sort of unofficial caption; the last way (using the figure environment) will have a more official caption, number the figure, and allow me to reference it later in the document (using the 22

24 7.4 Adding Images 7 EXAMPLES! \ref command). As you ll see in the display of the actual text, though, images don t always behave like you would expect, and may get out of order of how you ve typed them. There are ways around this, but I ll be honest, it s not exactly as intuitive as I d like it to be. Incorporating images into L A TEX documents is probably the one area where a program like Word is better (since you can manipulate the images so easily). That being said, it s still very possible to make images work for you. I should also mention that not every file type is supported, but this actually depends on what editor you re using. With TeXnixCenter, I generally try to stick to pdfs, jpgs, and pngs. * * * * * This creates a sort of fake caption Observe how you can reference Figure 1 by using its label! 23

25 7.5 Creating Lists 7 EXAMPLES! 7.5 Creating Lists Figure 1: This is a more legit caption If you needed to create a list in your document, the enumerate or itemize environments are generally the best way to do this: \documentclass[12pt]{article} \usepackage{amsmath} \begin{document} \begin{itemize} \item This creates a list \item You can also use math mode in this! \item For example: $\frac{2x}{7+x^2}$ \end{itemize} \begin{enumerate} \item This gives you a more structured list \item Here is where my second point would go \item Etc, etc \end{enumerate} \end{document} Here, I think once you look at the output, it s pretty self-explanatory. Itemize is great for unordered lists, enumerate is great for ordered ones. Both use \item to distinguish a new item. I should mention, however, that creating lists (or really, anything that requires you to keep track of the numbering of 24

26 7.5 Creating Lists 7 EXAMPLES! an item) is a specialty of L A TEX. What I mean by that is, let s say in the above example, you wanted to add something after your This gives you a more structured list line, but before the Here is where my second point would go line. To do so, all you d have to do is type \item (whatever you want to insert), and L A TEX will automatically adjust the numbering for you (since the insertion of a line will influence how every line after should be numbered). Ok, so what. No big deal so far, right? I mean, even Microsoft Word does that. Wrong. Remember in the earlier section when we talked about how if you use the equation environment L A TEX will number your equations? Well, the same idea will hold here too: instead of manually having to go back and renumber all of your equations, L A TEX can do that for you. That way, if you re using L A TEX as it s meant to be used, you never have to manually type any sort of numbering for anything, and more importantly, you never have to worry that numbers will get out of order, regardless of where you add commands or environments to your document. Lastly, I should mention that this is how you make a fraction: \frac{<numerator>}{ <denominator>}. This creates a list * * * * * You can also use math mode in this! For example: 2x 7+x 2 1. This gives you a more structured list 2. Here is where my second point would go 3. Etc, etc 25

27 7.6 Creating Tables 7 EXAMPLES! 7.6 Creating Tables If you want to include a table in your document, you re going to want to use the tabular environment: \documentclass[12pt]{article} \usepackage{amsmath} \begin{document} Table 1: \\ \begin{tabular}{ l c r } 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ \end{tabular} \\ \\ Table 2: \\ \begin{tabular}{ l c r } 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ \end{tabular} \\[1in] Table 3: \\ \begin{tabular}{ l c r } \hline 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ \hline \end{tabular} \\ \\ Table 4: \\ \begin{center} \begin{tabular}{ l c r } \hline 1 & 2 & 3 \\ \hline 26

28 7.6 Creating Tables 7 EXAMPLES! 4 & 5 & 6 \\ \hline 7 & 8 & 9 \\ \hline \end{tabular} \\ \end{center} Table 5: \\ \\ \begin{tabular}{ c c c } Notice how you can & put text in the table & as well \\ 1 & 2 & 3 \\ 4 & 5 & 6 \\ \end{tabular} \\ \\ Table 6: \\ \begin{tabular}{ c c c } Notice how you can & put text in the table & as well \\ \hline but this can become really problematic if there is too much text & 2 & 3 \\ \hline 4 & 5 & 6 \\ \end{tabular} \\ \\ Table 7: \\ \begin{tabular}{ p{4cm} c c } Notice how you can & put text in the table & as well \\ \hline However, if you set up your column with p\{\emph{width}\}, then the table will create a column with the width you designated and automatically wrap text to match. & 2 & 3 \\ \hline 4 & 5 & 6 \\ \end{tabular} Lots to break down here. I suggest looking at the output as we discuss these tables, since seeing the actual outcome will allow things to make more sense. Anyways, here we go. So when creating a table, the first thing you need to do is bring up the tabular environment (\begin{tabular}... \end{tabular}). Notice, though, that right after this is done, there is another set of braces (in Table 1, it looks like: {l c r}). What these do are declare how your columns in the table are 27

29 7.6 Creating Tables 7 EXAMPLES! going to be justified. The l stands for left-justified, c is for center, and r is for right. I m actually not great with the minute differences between these (I generally just use c for everything), so I encourage you to toy around with these. Ok, once we ve done those steps, the next task is to actually fill in the table! To do so, you merely type in whatever you want, and use & to differentiate between the columns. So to add more columns, just insert more & s. If you want to add another row, you just use \\ at the end of your line. Now looking at Table 2, we can see how vertical bars can be added to separate the columns. These show up from the and found in the column justification braces. Table 3 shows how we can add horizontal bars using the \hline command. And Table 4 shows how we can also use \hline to separate our rows as well (also note how Table 4 is centered). Table 5 shows that we can put text in tables as well, but Table 6 demonstrates why sometimes this creates bad output if we re not careful. Luckily, Table 7 demonstrates how this problem can be fixed using p{width}. Lastly, I should point out something about how I formatted line-breaks in this section. Observe how between the title of a table (such as Table 1: ) and the actually table itself (the tabular environment), there is an actual line break (a blank line in the code). L A TEX reads a blank line like that as the end of a paragraph, so it will indent whatever text comes after it (which is why in the output, the tables aren t directly under their titles. Further, notice how after I end a tabular environment, I used \\\\ instead of just the normal one set. That s because I wanted to create even more spacing between a table and the title of the table that follows it. There is another way to have control of how much spacing is determined, and that s seen at the end of table two s tabular environment in which I type an option ( [.5cm] ) after the backslashes (with no spacing in-between). This option allows me to dictate just how much space I want there to be between the two lines (Observe how there is much more space between table two and table 3). * * * * * 28

30 7.6 Creating Tables 7 EXAMPLES! Table 1: Table 2: Table 3: Table 4: Table 5: Table 6: Notice how you can put text in the table as well Notice how you can put text in the table as w but this can become really problematic if there is too much text

31 7.6 Creating Tables 7 EXAMPLES! Table 7: Notice how you can put text in the table as well However, if you set 2 3 up your column with p{width}, then the table will create a column with the width you designated and automatically wrap text to match

32 7.7 Theorems, Lemmas, Proofs 7 EXAMPLES! 7.7 Theorems, Lemmas, Proofs If you wanted to give a handout of notes, or maybe put your class notes online so your students could access them, being able to point out definitions, theorems, lemmas, and (if the class calls for it) proofs will be essential: \documentclass[12pt]{article} \usepackage{amsmath, amsthm} \newtheorem*{mydef}{definition} \newtheorem{mythm}{theorem} \begin{document} \begin{mydef} A triangle is a three-sided polygon. \end{mydef} \begin{mydef}[triangle] A triangle is a three-sided polygon. \end{mydef} \begin{mythm} Let $f(x)$ be differentiable on the open interval $(a,b)$ and continuous on the closed interval $[a,b]$. Then there is at least one point $c \in (a,b)$ such that \begin{equation*} f (c)= \frac{f(b)-f(a)}{b-a} \end{equation*} \end{mythm} \begin{mythm}[mean Value Theorem] Let $f(x)$ be differentiable on the open interval $(a,b)$ and continuous on the closed interval $[a,b]$. Then there is at least one point $c \in (a,b)$ such that \begin{equation*} 31

33 7.7 Theorems, Lemmas, Proofs 7 EXAMPLES! f (c)= \frac{f(b)-f(a)}{b-a} \end{equation*} \end{mythm} \begin{proof} This is a proof. \end{proof} \begin{proof}[there are infinitely many primes.] ~Supposed that there are not infinitely many primes. \\ That is, let $\{p_1, p_2, p_3, \dots, p_r\}$ be all of the primes that exist. \\ Define a new number $P$ such that \begin{equation} P = p_1p_2p_3\ldots p_r+1 \end{equation} Observe if $P$ is prime, then it was a prime not in our list. Since our list was that of all primes, it must be the case that $P$ is not prime. \\ Thus there exists some prime number $p$ such that $p$ divides $P$. \\ Notice that $p \notin \{p_1, p_2, p_3, \dots, p_r\}$, since if it was, it would imply that $p$ divides 1, which is impossible. Thus, $p$ is a prime number that was not in our original list, which creates a contradiction that there is a finite number of primes. \\ Thus we have shown there are infinitely many primes. \end{proof} \end{document} Let s break this one down. Observe that the package amsthm is required. Further, the use of this package requires us to declare a few more items in the preamble. These can be seen as the \newtheorem declarations that occur before the document begins. (Note how definitions are declared with an asterisk, which results in them not being numbered in the output, unlike the theorems.) 32

34 7.7 Theorems, Lemmas, Proofs 7 EXAMPLES! In these declarations, mydef and mythm act as the code words that signal I m calling forth the definition or theorem environments. Definition and Theorem are what will be displayed in bold in the output. Once we ve declared these new commands, we can then utilize them in the document. Note when we re in the definition, theorem, or proof environment, we also have an option to name what it is that we re defining, presenting, or proving. These take the form of [Triangle], [Mean Value Theorem], and [There are infinitely many primes.]. * * * * * Definition. A triangle is a three-sided polygon. Definition (Triangle). A triangle is a three-sided polygon. Theorem 1. Let f(x) be differentiable on the open interval (a, b) and continuous on the closed interval [a, b]. Then there is at least one point c (a, b) such that f (c) = f(b) f(a) b a Theorem 2 (Mean Value Theorem). Let f(x) be differentiable on the open interval (a, b) and continuous on the closed interval [a, b]. Then there is at least one point c (a, b) such that Proof. This is a proof. f (c) = f(b) f(a) b a There are infinitely many primes. Supposed that there are not infinitely many primes. That is, let {p 1, p 2, p 3,..., p r } be all of the primes that exist. Define a new number P such that P = p 1 p 2 p 3 p r + 1 Observe if P is prime, then it was a prime not in our list. Since our list was that of all primes, it must be the case that P is not prime. 33

35 7.7 Theorems, Lemmas, Proofs 7 EXAMPLES! Thus there exists some prime number p such that p divides P. Notice that p / {p 1, p 2, p 3,..., p r }, since if it was, it would imply that p divides 1, which is impossible. Thus, p is a prime number that was not in our original list, which creates a contradiction that there is a finite number of primes. Thus we have shown there are infinitely many primes. 34

36 7.8 Miscellaneous Math 7 EXAMPLES! 7.8 Miscellaneous Math Here are just some examples of (just a few) things L A TEX can typeset: \documentclass[12pt]{article} \usepackage{amsmath} \begin{document} Want to create a function? \begin{equation*} f(x) = (x+a)(x+b) \end{equation*} \\ What about a square root? \begin{equation*} g(x) = \sqrt{\frac{b^2-4ac}{2a}} \end{equation*} \\ A more general root? \begin{equation*} g(x) = \sqrt[n]{1 + x^2 + x^3 + \ldots + x^n} \end{equation*} \\ And limits? \begin{equation*} \lim_{h\to 0}{\frac{f(x+h)-f(x)}{h}} \end{equation*} \\ What about an equation with multiple lines? \begin{align*} f(x) &= (x+a)(x+b) \\ &= x^2 + ax + bx + ab \\ &= x^2 + (a+b)x + ab \end{align*} \\ If you want to reference specific lines, you can remove the asterisk from the align command: \\ \begin{align} f(x) &= (x+a)(x+b) \\ 35

37 7.8 Miscellaneous Math 7 EXAMPLES! &= x^2 + ax + bx + ab \\ &= x^2 + (a+b)x + ab \end{align} \\ Piecewise functions? \begin{equation*} f(x) = \begin{cases} e^x + 4 & \text{if } x > 0 \\ 5\sin(x^3) & \text{if } x \leq 0 \end{cases} \end{equation*} \\ Combinatorics anyone? \begin{equation*} {n \choose k} = \frac{n!}{k!(n-k)!} \end{equation*} \\ Summations? \begin{equation*} \sum_{n=1}^\infty (\frac{1}{2})^n \end{equation*} \\ Notice how we can change how the parenthesis look in the fraction: \begin{equation*} \sum_{n=1}^\infty \left(\frac{1}{2}\right)^n \end{equation*} \\ This is a useful tool, if you ever want to show how an integral would be evaluated: \begin{equation*} \left.\frac{x^3}{3}\right _{-1}^{1} \end{equation*} \\ Matrices? \begin{equation*} \begin{matrix} 1 & 0 & 0 \\ 36

38 7.8 Miscellaneous Math 7 EXAMPLES! 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix} \\ \end{equation*} But usually we prefer to have our matrices boxed in by something (or at least I do): \begin{equation*} \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \\ \end{equation*} Maybe brackets are more your thing with matrices: \begin{equation*} \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \\ \end{equation*} \end{document} While most of these examples are relatively self-explanatory (I think if you look at what I typed and what was displayed, it ll be decently clear how things are working for the most part), there are some areas in which I should expand on a little. One thing to note is that in my equation with multiple lines, I didn t use the equation environment, but instead used the align environment. In actuality, these two environments (align and equation) are very similar, but align has a unique feature: the ability to line up items based on &. By using an &, you indicate to L A TEX the point at which the lines should be aligned. 37

39 7.8 Miscellaneous Math 7 EXAMPLES! Further, in the summations, you hopefully noticed that they look different. In one, the parenthesis seem to not quite fit the fraction, while in the other it looks much more appropriately sized. That was done using the commands \left and \right along with the standard parenthesis ( and ). However you can use these commands to make other characters (such as braces or a vertical bar as seen in the example after) automatically be resized to match what s around them as well. Want to create a function? * * * * * f(x) = (x + a)(x + b) What about a square root? b2 4ac g(x) = 2a A more general root? h(x) = n 1 + x 2 + x x n And limits? f(x + h) f(x) lim h 0 h What about an equation with multiple lines? f(x) = (x + a)(x + b) = x 2 + ax + bx + ab = x 2 + (a + b)x + ab 38

40 7.8 Miscellaneous Math 7 EXAMPLES! If you want to reference specific lines, you can remove the asterisk from the align command: f(x) = (x + a)(x + b) (3) = x 2 + ax + bx + ab (4) = x 2 + (a + b)x + ab (5) Piecewise functions? f(x) = { e x + 4 if x > 0 5 sin(x 3 ) if x 0 Combinatorics anyone? ( ) n = k n! k!(n k)! Summations? ( 1 2 )n n=1 Notice how we can change how the parenthesis look in the fraction: ( ) n 1 2 n=1 This is a useful tool, if you ever want to show how an integral would be evaluated: x

41 7.8 Miscellaneous Math 7 EXAMPLES! Matrices? But usually we prefer to have our matrices boxed in by something (or at least I do): Maybe brackets are more your thing with matrices:

42 7.9 L A TEX Special Characters 7 EXAMPLES! 7.9 L A TEX Special Characters In this subsection, I m going to break from what I had been doing previously. Instead of showing you my input, discussing it a little, and then showing you the output, I m instead going to just direct you to some excellent websites for figuring out what the L A TEX commands are for special characters. For example if you wanted to learn how to create the standard arithmetic signs for multiple or divide ( or ), incorporate some Greek letters (β, σ, θ, etc), have those cool ellipsis show up in a list or matrix (...,,.,...), or even just insert some unique symbols (,, or whatever), you re going to want a place to turn to to do so. While I generally just Google latex + (whatever symbol I need), I ve also used this website specifically. It s a great resource that lists a ton of commands for L A TEX. 41

43 8 IF THINGS GO WRONG... 8 If Things Go Wrong... [Note: Special thanks to Dylan Helliwell for the inclusion of this section!] There will be times when you go to compile a document, and your compiler is not happy with you: somewhere lurks an error in your text. Maybe it s a misplaced bracket, or maybe you re missing a necessary package. Either way, it s inevitable. We all get errors, and often, we get more than one. When that happens, these steps are a great way to make the process of finding and fixing your code as painless as possible: 1. At times, your compiler may direct you specifically to the line of code where the problem is. If this is the case, try to go back to your document and find the error or typo there. (A good indication that a small typo may be the root of the problem is if you get the error undefined control sequence.) 2. Sometimes, people just forget to end whatever environment they needed at a given moment (it s easy to remember to type \begin{equation}, but not always easy to remember to end it!). Try looking at what you recently typed (because you should be compiling often!) and make sure all your environments and brackets are proper. 3. If for some reason you can t seem to find a typo in your code, there is a way to make it so the compiler will ignore portions of your text, better allowing you to find the error. When you make L A TEX ignore your text, you are commenting it out, and can be done by using a % sign. For example, if you were to type This is text in your document, the compiler would be sure to compile that text. But if you typed %This is text then it would not be compiled because it s been commented out. Keep in mind, however, you need to place a % at the start of each line you want to comment out. By doing so, however, you can have the 42

44 8 IF THINGS GO WRONG... compiler skip certain portions of text in an attempt to narrow down where exactly the error is occuring a tool that can save you loads of time! 4. If through all of this, you still cannot seem to find an error, there is a way to force a compiler to compile the document anyways, using its own attempt to fix the error, by pressing the return or enter key. This will likely result in new errors, but after you force the document to compile a few times (by hitting return or enter), it should eventually compile. This is useful as it now allows you see the output, and possible piece together where the code is running into trouble. 5. This last step is very rare, but every now and then, one of the files that the compiler automatically creates (in your specific folder you created for your document, remember...) may be a little messed up. The nice thing is, you can delete any document that is created when you compile your.tex file, because they will be created again the next time you compile your document. (Note, DO NOT delete your.tex file! Only the files that are created via the compiling process!) A large portion of errors can likely be resolved by following these guidelines, but the most important thing to remember is to compile your document often! 43

45 9 APPENDIX 9 Appendix 9.1 Package Information Packages are my favorite part of L A TEX. Almost every problem (we re talking about 98% of them) I ve ever had has been resolved by adding including a package. Want a table spread over multiple pages? Boom, there s a package for that. Want more control over the styling of the page? Double boom, there s a package for that too. BUT FIRST! When you install L A TEX (either MikTex or MacTek), with it comes a few packages that are considered standard, but not every package comes along! What this means is that some packages require you to install them. Installing packages is not a hard process. For MikTex, all you do is open up the Package Manager, type in the package you re looking for, and then select it and click install (you might have to right click it and hit install or something, either way it s very easy). I believe MacTex is the same (but the last time I was doing this with a friend, I do recall having to make sure we were looking at packages instead of themes or something. I don t know, call me if you have any trouble). Now, some editors are really cool and will alert you when you need to install a package when you try to compile your document, and will then do it for you. But I don t know anything about those and personally they sound like they re for the weak. So whatever. Installing packages is important, but not difficult! Don t be discouraged! I should also point out that just because you have packages installed, doesn t mean you have to use them in every document. As you saw when I first introduced packages, I m using ten packages to make this document, but I probably have somewhere between 50 and 100 installed. 44

46 9.1 Package Information 9 APPENDIX Package Name amsmath amsthm cancel color fancyhdr geometry subfig Description This is the package you need to add advanced math! This package introduces the proof environment, along with the theoremstyle command Remember all those times when you would be doing math and have to cancel something from each side? What would you do? Strike a line through it? Well this package does just that. Using the \cancel{} or \cancelto{}{} command, you can get output that looks like 4 or 4. This is how you add color in your documents! This package is a little more hands on, and I would suggest looking it up if you choose to use it. What it can do for you is amazing, though: give you way more control on the header and footer of your document. Want a footer on every page, but a header only on the first? Done. Want the header and footer to be in different places depending on the page number? No sweat. It s a great package. This is a great package to manage the margins of the document, as well as the page size. Because I think the standard margins L A TEXuses are pretty big, I pretty much always use this package. Want to have multiple images or tables in one figure? You need this package. It allows you to have a subfigure environment which you can nest within a figure environment. Super useful. 3 45