TEX INSTRUCTIONSK. IGUSAAbstract. These are instructions on how to write papers in LateX. It isapproximately the same thing that I explained in class.IntroductionThe final version of your final paper must be in TeX. You should write somethingvery short to practice. More on that later. These notes are to reiterate the things Iexplain to you in class. I explain the basic idea of TeX and the “begin-end” formatwhich is called “environments.”1. Basic concepts of TeXThe first concept that I explained was that of symbols. These are enclosed indollar signs $ and are the name of the symbol preceded by a backslash \. Forexample, if you type $\alpha$ you get: α The equation will be in the line of text.If you want an equation set off in the middle of its own line you surround thecommand with two dollars. So, $$\alpha$$ gives you:αNext, there are functions or operations. In math we write f(x) for a functionof x. In TeX function names have a backslash in front and (x) is replaced withbraces: {x}. The example I did in class was underline (or was it overline?) thisgoes like this: Type \underline{whatever} and you get: whatever. (If you type\overline{whatever} you get an error message because you don’t normally put linesover text, only over symbols.)Sometimes functions have two or more arguments: f(x, y). In Tex you write:\function{x}{y}. The example I did in class was the fraction whose command is\frac. Thus $$\alpha = \frac{1 + \beta}{\gamma}$$ givesα =1 + βγFinally, one very useful item is user defined shortcuts. For example, I don’t liketo type the words alpha or lambda over and over so I make the shortcuts:\def\a{\alpha}\def\ll{\lambda}\def is a function which takes two arguments. It defines the first item to be ashorthand for the second item. But, I forgot to say, your shorthand must be onlyletters, no symbols or spaces. Using this shorthand I write $$\a = \ll$$ to get:α = λDate: November 6, 2008.12 K. IGUSA2. LateX environmentsIn LateX you have parts of your document which are set off. These are “en-vironments.” For example, if you put two dollars $$ you start a set-off-equationenvironment which ends when you put two more dollars.Your paper should start with an abstract. You write the abstract between the“begin abstract” and “end abstract” commands:\begin{abstract}This is a paper about clusters and binary trees.\end{abstract}The abstract should be short with only a vague description of your paper. Afterthat there should be an introduction with more details and an outline of your paper:\section∗{Introduction}.The asterisk means no number on the section.\section{Basic definitions}.Most papers have as first section (after the introduction) a section which goesover the definitions of things that everybody knows. You start with a short para-graph stating what you will do in this section:“We will review the definitions of binary trees and noncrossing partitions.”The way you type a definition is:\begin{definition} A \emph{binary tree} is · · ·\end{definition}What you get is:Definition 1. A binary tree is · · ·3. referencesWe also talked about references. In the final output, e.g., in your midtermswhich you will probably write by hand, you put references in square brackets withnumbers or letters indicating the first initials of the authors. For example, youmight have [1] or [IT] and at the end you have references. References are one thingthat everyone cuts and pastes from some source.References[1] Kiyoshi Igusa and Gordana Todorov, A characterization of finite Auslander- Reiten quivers,J. Algebra 89 (1984), no. 1, 148–177.[2] Richard P. Stanley, Enumerative combinatorics. Vol. 1, Cambridge Studies in AdvancedMathematics, vol. 49, Cambridge University Press, Cambridge, 1997, With a foreword byGian-Carlo Rota, Corrected reprint of the 1986