WRITING MATHEMATICS

"Why do I have to write mathematics?"

• In order to share your ideas with people who are not physically present, you have to write them down. Mathematical ideas have to be written using mathematics. Just as English prose is needed for writing in subjects other than English, mathematical writing is needed for writing in any subject where mathematical ideas or models are used. Scientists, engineers, and some social scientists have to write mathematics.
  
  

Every year, we buy ten cases of paper at $35 each; and every year we sell them for about $1 million each. Writing well is very important to us.

- Bill Browning, President of Applied Mathematics, Inc.

Some General Guidelines

• Your mathematical work should be embedded in a narrative. Good mathematical writing must be self-contained. A knowledgeable reader must be able to read your paper without referring to the textbook or question sheet.
  
• Know your audience. Most of your mathematical writing has been for an audience of people more knowledgeable than you. Outside of academics, most of your mathematical writing will be for an audience of people less knowledgeable than you. A good general rule is to omit details that should be obvious to the reader. For example, you needn't demonstrate the solution of a quadratic equation to readers who are calculus students. Generally it is best to focus on the problem statement, description of methods, and explanation of results rather than on the details of the calculations.
  
• Organize your writing carefully. Any paper longer than one page should be divided into sections with descriptive headings. Sections will often correspond to steps in an investigation or parts of a problem. For example, you might need separate sections to describe the problem, state the assumptions in the mathematical model or theorem, briefly state the major result, describe the plan of the study, present relevant details, summarize the results, and/or discuss the results.
  
• Use active language and the present tense. You are writing about the problem and its analysis, not the history of your work on it. Instead of "The computer showed me that the solution is...," try "The solution is..." or "We find the solution to be..." Note that in academic writing, the pronoun "we" is used rather than "I" even in papers written by a single author.
  
  

A Brief Checklist for Self-Evaluation

• Is the problem clearly stated?
• Are the assumptions clearly stated and the variables defined?
• Is the answer clearly stated?
• Are the solution techniques clearly documented?
• Are visual aids, if used, helpful and clearly labeled?
• Are formulas either derived in the paper or a reference given?
• Are outside sources of information and ideas clearly identified?
• Are the spelling, grammar, and punctuation correct?
  • Equations are part of English sentences and should have appropriate punctuation.
  • Use mathematical symbols such as "=" only in formulas and not as English words.
  • Math phrases need subjects and verbs.

  Ex: "The area of a triangle is given by A=bh/2, where b and h are the base and height of the triangle."