## Mathematical research and writing: getting started

Let us suppose that you have a topic or question in mind for your research project, be it for a course, for a work term, or for a thesis. Finding your own way through the ins and outs of your research questions is part of the process and part of the fun. This page is just about some of the common ground we all walk on as we work on research in mathematics.

## Some excellent internet research tools for mathematics

- Google, of course.
- The indispensable MathSciNet -- a database of all mathematical articles published for the past 100 years, with reviews, amazing searchability, and links both forward and backward in time. (Accessible on campus.)
- IEEE Xplore, for Engineering topics. (Accessible on campus.)
- Math StackExchange, and for deeper research questions, Math Overflow.
- Encyclopedias: Wikipedia is great for getting started, but beware that it is not reliable enough to ever cite as a source. Instead, try Wolfram Mathworld.
- The Mathematix ArXiv, where many preprints are stored.

Please note that only refereed items (articles published in journals, textbooks, or Wolfram Mathworld, for example) are acceptable for citation-in-lieu-of-proof in any mathematical writing. Citations to (stable!) websites as acknowledgements or general interest can be OK and should be identified by URL and date accessed.

## How to write mathematics

Once you've done your research, and have worked out some examples by hand (that is, done the math!), you'll want to start writing. For theses, it's often helpful to map out chapters and organize the bits of things you work on but putting them under the right headings.

Writing in proper mathematical style means being clear and unambiguous, as well as adhering to the rules of grammar and punctuation (which apply to sentences which contain equations, for example). Some advice on mathematical writing style by by Ashley Reiter at MIT.

## Using LaTeX

The perfect tool for writing mathematics is called LaTeX (or TeX or other variants thereof); it takes ASCII text files (interspersed with markup commands) as input and generates perfectly formatted, textbook-quality documents. Some resources for, and implementations of, this free software include:

- Overleaf, an online LaTeX editor and a good place to start
- The LaTeX project
- MikTeX, an implementation for Windows
- TeXworks, another popular choice
- TeXMaker, another popular choice
- Getting Started with LaTeX By David R. Wilkins.
- Basic Tips for new authors
- Latex Command Help
- Detexify: LaTeX handwritten symbol recognition, very handy

## Samples

- Here is a sample math research report, a text file that you can read directly. When you compile it with pdfLaTeX, you get something which looks like this pdf file.
- Here is another LaTeX primer that was compiled from this text. Voici aussi des versions francaises avec fichier LaTeX.
- You can find style files for your uOttawa thesis on the intranet of the department.
- An example of how to include a postscript figure into your LaTeX document.
- French version of the report class and style files (necessary if you want "Table of Contents" to become "Table des Matières").