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Before you move on to advanced commands and a library of symbols and keywords to memorize, look at a few LaTeX documents prepared by Art of Problem Solving Community members. Students wishing to submit examples should not feel obliged to make documents as intricate as those below - we would like to include some more introductory examples with these. The papers below are listed roughly in order of the complexity of LaTeX tools used.
The Basics: Twenty-Seven Problems
The Basics: Twenty-Seven Problems by Keone Hon. Click here for the source file. This file contains a collection of problems and solutions. Our beginning and newly intermediate-level problem solvers will find some good practice here.
A Diophantine Equation and Its Solution
A Diophantine Equation and Its Solution by Michael Viscardi. Click here for the source file. This paper contains a solution to the Diophantine Equation 1/x + 1/y = 1/z. (Note this was produced within a few days of the student learning about LaTeX from our site - look at the paper for evidence of how quickly you can learn to render math in LaTeX.)
The Area of a Circle
Solution for USAMTS Problem 4/4/15
Solution for USAMTS Problem 4/4/15 by Zachary Abel. Click here for the source file. This file gives an example of writing up a solution to a USAMTS solution. The LaTeX code includes an example of referencing. (Note: You will have to compile code with referencing in it twice - the first time you compile you will get warnings about undefined references.)
On the Existence and Uniqueness of Invariant Measures on Locally Compact Groups
On the Existence and Uniqueness of Invariant Measures on Locally Compact Groups by Simon Rubinstein-Salzedo. Click here for the source file. This will give you an example of a document that would be terrifying to typeset with basic word processors. It will also give students an idea of what to look forward to in very advanced mathematics. (In other words, middle and high school students shouldn't expect to understand much, if any of it, but it is a great example of how to clearly render advanced math with LaTeX.)
Calculus Review and Formulas
Calculus Review and Formulas by Keone Hon. Click here for the source file. This example contains review of trigonometric formulas and some items of calculus. The LaTeX code exhibits some referencing, and uses of the definition and formula environments. This also illustrates the package hyperref, which allows us to put links to jump to in the document (you'll see when you open the PDF document how useful these are).
Maxwell's Equations by Matt Hansen. Click here for main source file. Click here for bibliography file. This paper illustrates the use of BibTeX to compile a bibliography. To compile it completely, put both the main source file and the bibliography files in the same directory. Compile the source as usual. Then, in TeXnicCenter, click Build, then Current File, then BibTeX. Then compile the source as usual (you may need to compile the source twice after doing the BibTeX). This paper gives an overview of Maxwell's Equations.