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# Introduction

$$\mathrm \TeX$$ is the state-of-the-art typesetting program used by many mathematicians and computer scientists, some scientists and social scientists, and most publishers of mathematics books and journals. $$\mathrm \TeX$$ was originally developed by the well known computer scientist Donald Knuth. There are a variety of implementations of $$\mathrm \TeX$$ available, for Macs, PC's and Linux. One of the advantages of $$\mathrm \TeX$$ is that is is entirely portable between implementations. For further information about $$\mathrm \TeX$$, please contact any of the faculty members in mathematics or computer science.

$$\mathrm \LaTeX$$ is the most widely used variety of $$\mathrm \TeX$$, and we recommend its use. Some introductory manuals for $$\mathrm \LaTeX$$, as well as style files for Bard senior projects and for homework, are available below.

For more about $$\mathrm \LaTeX$$, there is a lot of material available on the web (though a bit of care is needed, because some of it is out of date); a good place to start searching is the $$\mathrm \TeX$$ site of the American Mathematical Society.

# Free $$\mathrm \LaTeX$$ Implementations

To run $$\mathrm \LaTeX$$ on your computer, you need a complete $$\mathrm \LaTeX$$ package, which includes the $$\mathrm \TeX$$ engine itself, a front end that has an editor and viewer, and various packages that enhance $$\mathrm \LaTeX$$. A widely used such package, which is free and available for Mac, Windows and Linux, is $$\mathrm \TeX$$ Live.

The following links are sources for downloading $$\mathrm \TeX$$ Live. Be sure to follows the downloading and installation instructions carefully.

• Mac$$\mathrm \TeX$$ for Macs. This implementation of $$\mathrm \TeX$$ Live for Macs is easy to install, and includes the excellent front end $$\mathrm \TeX$$Shop, which is what I use.
• $$\mathrm \TeX$$ Live for Windows and Linux. This implementation of $$\mathrm \TeX$$ Live includes the front end $$\mathrm \TeX$$works, which is similar to, though not quite as good as, $$\mathrm \TeX$$Shop.

WARNING: Do not try to copy $$\mathrm \LaTeX$$ from someone else's computer; if you do that, you will likely miss some files that $$\mathrm \LaTeX$$ stores in places you might not think to look. Downloading $$\mathrm \LaTeX$$ from a reliable source is the only way to insure that your implementation will work properly.

# $$\mathrm \LaTeX$$ Manuals

There are many available manuals for $$\mathrm \LaTeX$$ that can be found on the web. Some useful manuals are available below.

• "Wikibooks -- $$\mathrm \LaTeX$$", a very thorough and reliable place to look up any questions you might have about $$\mathrm \LaTeX$$. If you do a web search for the word "LaTeX" together with any particlar topic, you often are directed to one of the pages on this website.
• "The Comprehensive $$\mathrm \LaTeX$$ Symbol List", an extensive list of mathematical symbols available in $$\mathrm \LaTeX$$; some of the symbols require the use of various $$\mathrm \LaTeX$$ packages. Start with the "Short Math Guide for $$\mathrm \LaTeX$$" before turning to this much lengthier list.
• "The Not So Short Introduction to LaTeX2e", a widely used introduction to $$\mathrm \LaTeX$$ by Tobias Oetiker, Hubert Partl, Irene Hyna and Elisabeth Schlegl, though it is not up-to-date with respect to some mathematical commands (for example, they use the obsolete eqnarray instead of the current align).

# Graphics in $$\mathrm \LaTeX$$

The standard way to insert graphics into $$\mathrm \LaTeX$$ documents is to use either the graphics.sty or the graphicx.sty package. The two packages are essentially the same, but use slightly different formats for a few commands; use whichever you prefer. These packages are often bundled with $$\mathrm \LaTeX$$ implementations. The manual for these two packages is:

For most $$\mathrm \LaTeX$$ implementations, graphics should be in EPS (encapsulated postscript) format. For TeXShop, and presumably any other implementation that uses PDF files instead of DVI files, the correct format for graphics is PDF, which is very convenient, given that PDF files are widely used.

There are two common ways to create mathematical graphics: via mathematical software such as Mathematica, or vector drawing programs such as Adobe Illustrator. Both these programs store graphics in their own proprietary formats, but when you are done making the graphics, they can be exported to EPS or PDF formats. Do not use bitmap graphics programs such as Adobe Photoshop; vector graphics programs are much better suited to mathematical drawing (and indeed are based upon mathematical ideas such as splines).

Mathematica and Maple are very powerful computer programs that can do a large variety of mathematics, including various types of graphing. At Bard we have a site lisence for Mathematica on campus; buying it for home use is rather expensive. A free alternative to Mathematics is the open source program

This program has can be accessed from any type of computer via the web. Sage can do both two and three dimensional graphing, and can export figures in JPG format (which can then be converted to PDF).

Adobe Illustrator is the professional standard vector graphics program. It is fairly expensive, though it can be found at reduced prices at the various educational discount software sites found on the web. A free alternative to Illustrator is the open source program

This program has implementations for Mac, Windows and Linux. Inkspace is not as good as Illustrator, but is quite satisfactory for many types of illustrations.

One tricky matter when creating graphics is to have the right amount of white space surrounding the graphic, which means a little bit of white space, but not too much. EPS files have a "bounding box" that determines how much white space is inserted; the bounding box is usually created automatically with as little white space as possible, though that can be modified in vector graphics programs by inserting an invisible rectangle of the right size around the graphic. For PDF files, which are often created with the graphic on an entire blank page, the white space can be cropped using an appropriate program (such as Preview on the Mac).

# Fonts in $$\mathrm \LaTeX$$

The default font used in $$\mathrm \TeX$$ is Computer Modern, which was designed by Donald Knuth, the creator of $$\mathrm \TeX$$. The advantage of Computer Modern is that it has an extensive set of mathematical symbols, and that, by being built into every implementation of $$\mathrm \TeX$$, and by being the default font, it is very easy to use. The disadvantage of Computer Modern is that, for some people, it isn't the most aesthetically pleasing font. In particular, it is rather thin and spindly.

Switching fonts in $$\mathrm \TeX$$ is not as simple as it is in standard word processors. In part the difficulty is due to the way $$\mathrm \TeX$$ works internally, and in part it is due to the fact that the various fonts available for regular word processors do not have the needed mathematical symbols. However, while it is not simple to use a variety of different fonts throughout a single document, there are a number of free packages that change the overall fonts (text and mathematics) for a document. (It is also possible to purchase fonts for $$\mathrm \TeX$$; while some of the commercial fonts are very nice looking, for most uses it is not worth the expense.)

There are a number of font packages that are included with standard implementations of $$\mathrm \TeX$$, and can be used simply via the \usepackage{} command, located in the preamble. The following is a list of font packages that appear to be available. The first of these packages uses Times New Roman for the text font, and is a good, basic alternative to Computer Modern.

• mathptmx
• fourier
• cmbright
• pxfonts
• mathpazo
• mathpple
• arev
• fouriernc
• [charter]{mathdesign}
• [utopia]{mathdesign}

In addition to the above types of font packages, there is another method to make use of additional fonts in $$\mathrm \TeX$$, which is to use not regular $$\mathrm \LaTeX$$, but rather a variant called Xe$$\mathrm \LaTeX$$. To use Xe$$\mathrm \LaTeX$$, it has to be available in the implementation that you use; it is available in TeXShop and TeXworks. The advantage of Xe$$\mathrm \LaTeX$$ is that it allows you to use any font that is installed on your computer. The disadvantage is that the regular fonts on your computer do not have mathematical symbols, and so when you use Xe$$\mathrm \LaTeX$$ it uses the font from your computer for text together with the mathematical symbols in Computer Modern, and that does not necessarily look good. Additionally, Xe$$\mathrm \LaTeX$$ sometimes runs slower than $$\mathrm \LaTeX$$. For most cases, it is best to use regular $$\mathrm \LaTeX$$ with font packages such as those listed above.

# $$\mathrm \LaTeX$$ in Web Pages

Although $$\mathrm \LaTeX$$ commands cannot be used directly in HTML, there are a few methods that have been developed to include formulae in $$\mathrm \LaTeX$$ in web pages. A particularly convenient method for doing so is the open source program

An example of MathJax is the formula $\lim_{T \to \{p\}} \ \frac{\text{Area}_o(\hat n(T))}{\text{Area}(T)} = \lim_{T \to \{p\}} \ \frac{\int\!\!\!\int_{x^{-1}(T)} \langle n_1 \times n_2, n\rangle \,ds\,dt}{\int\!\!\!\int_{x^{-1}(T)} \sqrt {\det \left(g_{ij}\right)} \,ds\,dt},$ which was typed using $$\mathrm \LaTeX$$ commands, and is displayed properly in this web page because this page is linked to the MathJAX server.

# Bard Project Style

This style file, called bardproj.sty, is designed for both Bard senior projects and Bard M.A.T. mathematics research projects. This style file takes care of a number of formatting issues for such projects, such as the title page, dedication, acknowledgements and correct margins; it also includes formatting for theorems, definitions and the like, as well as a few miscellaneous items. There is a template, a brief manual for this style file and writing guidelines for senior projects. Click below to download these files.

# Bard Junior Seminar Style

This style file, called bardjuniorsem.sty, is designed for the Bard Mathematics Junior Seminar. This style file takes care of a number of formatting issues for the expository writing project of the seminar, such as the title page, abstract and correct margins; it also includes formatting for theorems, definitions and the like, as well as a few miscellaneous items. There is a template and a brief manual for this style file. Click below to download these files.

# Bard Poster Style

This style file, called bardposter.sty, is designed for posters to be used at events such as the Bard Senior Projects Poster Session. There is a template, a brief manual, and a sample poster (available in both $$\mathrm \LaTeX$$ and PDF formats) for this style file. Click below to download these files.

This video shows how to use the Bard poster style file.

# Bard Macros Style

This style file, called bardmacros.sty, is designed for homework assignments in upper level mathematics classes, such as Proofs and Fundamentals, Abstract Algebra, Real Analysis and Topology. It takes care of a number of formatting issues such as exercises, definitions and the like, and has specific macros for various upper level classes. There is a template, a brief manual for this style file and writing guidelines for proofs-based homework. Click below to download these files.

This video shows how to use the Bard macros style file.

# Bard Presentation Style

There are two options for making computer presentations that include mathematical content: either use general purpose presentation software (such as Powerpoint), and import mathematical formulae as graphics, or use $$\mathrm \LaTeX$$ to produce a PDF file that can be viewed in a PDF viewer. Using presentation software allows for fancier formatting, but using $$\mathrm \LaTeX$$ directly allows for easier insertion of mathematical symbols and formulae, and allows for text to be cut-and-pasted from other $$\mathrm \LaTeX$$ documents. A commonly used $$\mathrm \LaTeX$$ package for creating presentations is Beamer.

The bardpresentation.sty style file, which is an add-on to the seminar.cls, is a very easy to use, though also very limited package for making presentations in $$\mathrm \LaTeX$$. For fancy presentations, learn Beamer. Click below to download these files.

# Various Useful $$\mathrm \LaTeX$$ Packages

There exist a large number of $$\mathrm \LaTeX$$ packages for various purposes that can be downloaded. Available below are a few of the packages that I have found particularly useful. A good place to look for more packages is at the TeX site of the American Mathematical Society listed above. All packages are invoked with the \usepackage{} command, located in the preamble.

• amsrefs.sty, an excellent package for making bibliographies in $$\mathrm \LaTeX$$. The manual is amsrdoc.pdf.
• color.sty, a package that allows for the use of colored text and background. The manual is grfguide.pdf.
• verbatim.sty, a very useful package, which allows for lengthy verbatim text, and for commenting out large sections of text.

# Spell Checking $$\mathrm \LaTeX$$ Documents

Using a regular spell checker for $$\mathrm \LaTeX$$ documents is very frustrating, because a regular spell checker will identify as a spelling error most $$\mathrm \LaTeX$$ commands, and also many collections of symbols inside mathematical formulae. To avoid this problem, a $$\mathrm \LaTeX$$-aware spell checker must be used. There are a number of free $$\mathrm \LaTeX$$-aware spell checkers that can be downloaded from the web. We list one for Windows and one for Macs. Both spell checkers can be set to ignore all $$\mathrm \LaTeX$$ commands, and everything inside environments such as $$\ ... \$$, and $$\\ ... \\$$, and \text{\begin{align}} ... \text{\end{align}}.

# $$\mathrm \LaTeX$$ Videos Preliminary Version

The following videos show the basic ideas for using $$\mathrm \LaTeX$$, as well as various Bard style files.

These videos are preliminary versions. If you have any comments or suggestions, please email me.

• Using $$\mathrm \LaTeX$$ Part 1 - What is $$\mathrm \LaTeX$$

This video discusses what $$\mathrm \LaTeX$$ is, the benefits and drawbacks of $$\mathrm \LaTeX$$, implementations of $$\mathrm \LaTeX$$, and resources for learning $$\mathrm \LaTeX$$.

• Using $$\mathrm \LaTeX$$ Part 2 - Basic Typesetting

This video discusses the basics of how to write text in $$\mathrm \LaTeX$$, how to structure a $$\mathrm \LaTeX$$ document, some standard commands, errors and $$\mathrm \LaTeX$$ environments.

• Using $$\mathrm \LaTeX$$ Part 3 - Typesetting Mathematics

This video discusses the basics of how to write mathematics in $$\mathrm \LaTeX$$, including defining macros and theorems.

• Using $$\mathrm \LaTeX$$ Part 4 - Useful Packages

This video discusses the some useful $$\mathrm \LaTeX$$ packages, fonts in $$\mathrm \LaTeX$$, bibliographies and $$\mathrm \LaTeX$$ in web pages.

• Using $$\mathrm \LaTeX$$ - Graphics

This video discusses the format for figures used in $$\mathrm \LaTeX$$ documents, some methods for creating figures and how to insert figures into $$\mathrm \LaTeX$$ documents.

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