Before taking a college-level math class, many students have never needed to write a mathematics essay. However, professional mathematicians, along with others working with higher-level math, must be able to communicate their ideas in ways that are comprehensible to others. Being able to write well about math is as important to mathematicians as being able to solve problems.
Choosing a Topic
The topic of your mathematics essay should be something that involves doing actual math -- not a history of Euclidean geometry or a biographical essay on Pierre de Fermat. In some cases, your instructor might provide you with a list of topics or problems. Otherwise, ask yourself what topics discussed in class have particularly interested you. Consider topics or ideas brought up in discussion that the instructor did not have time to explain in detail, or ways of applying ideas from class to new problems.
Structuring Your Essay
A well-structured mathematical essay will both show the connections between your work and the wider world of mathematics, and will carefully lead your reader through the logical structure of your work. A standard organizational form consists of four sections: background, introduction, body and implications. The background section gives the reader the history of the problem or ideas you're working with. The introduction introduces the reader to your work specifically and introduces any special definitions or symbols needed for your work. The body section contains most of your work, leading the reader through the specific problem or idea you're considering. The implications section gives your reader an idea of the consequences of your work, and what future work remains to be done.
Some instructors might allow students to write complex mathematical formulations by hand, though of course the main text of the paper should be typed. Formulas written by hand should be legible. To type formulas in Microsoft Word 2010, on the Insert tab, in the Symbols group, click the “Equation” arrow, then click “Insert New Equation.” If you're going to be writing many mathematics essays or other writing involving complex formulas, it might be worthwhile to learn a mathematical typesetting language such as TeX or LaTeX.
Punctuation and Grammar
Follow the rules of punctuation and grammar throughout your mathematics essay. Formulas are generally indented and given a separate line, but otherwise should be treated as elements of the composition, following the same rules of grammar that apply to words. Treat an equation, inequality or other “complete” mathematical statement as a sentence, followed by a period. Equations that do not constitute complete mathematical statements, such as “5x + 1,” should be treated as nouns.
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