Choose a topic for your paper. Make sure your topic is broad enough for you to write the required number of pages, but narrow enough to be focused and concise.
Mathematical computer science papers are generally expected to make a contribution to the field. So rather than evaluating arguments other individuals have made, try to formulate your own argument based on published ideas or original research you've conducted.
Research your chosen topic and find credible sources backing up what you plan to say in your paper. You can find published research paper in journals like The Journal of Mathematics and Computer Science. Most journals have websites you can search, though some require a verification password to prove your school has a subscription. Others, like JMCS, offer free access to articles online.
Organize your ideas into an outline and write a rough draft. Order your arguments and supporting evidence in a clear and logical fashion. Introduce the purpose of your paper in the introduction section and reiterate important findings in the conclusions section. Don't let your paper get lost in mathematical symbols and notations; maintain a balance by writing out categories of mathematical representations (for example, clarifying "x" with "input x" or "A" with "algorithm A"). Cite sources for all ideas not your own.
Edit your paper. Check to make sure it meets length and content requirements, and add or subtract material as necessary. Read your paper again as if it had been written by someone else, and make sure the mathematical formulas and programming concepts are solid and understandable. Proofread for errors, clarity and thoroughness. Ask a friend, your class TA or a teacher to edit your paper, as well, particularly if writing papers is not your strong suit.
Incorporate the feedback you receive and perform any rewriting necessary. Put the final touches on your paper according to the specifications of the project, such as formatting, font and spacing as required. Read your paper one last time before printing.