Westfield State College Writer's Guide
Conventions for Writing in
Mathematics
"Easy reading is damned hard
writing."
Nathaniel Hawthorne. Want more quotes? See the Mathematical
and Educational Quotation Server at Westfield State College
- Naming Constants, Variables, Functions and Other Mathematical Objects
should be done only when necessary; that is when they will be used frequently throughout
the work, when they will appear in displayed formulas, or when they will be used as
composite functions. In general, constants are denoted by lowercase letters at the
beginning of the English alphabet: a,b,c; variables are denoted by lower case letters at
the end of the English alphabet: s,t,x,y,z; functions are generally denoted by lower case
letters in the middle of the English alphabet: f,g,h (although there are notable
exceptions, like using F to denote the antiderivative of f); matrices are generally
denoted by upper case letters in the English alphabet; the Greek delta and epsilon are
generally reserved for small variable quantities like those that appear in estimates in
limit proofs, analysis estimates, etc.
- Function Names should be used and used
consistently. If f(x)=2x+1 then the appropriate name for the function is f, not f(x).
The notation f(x) means, precisely, the value of the function f at the point x. Thus,
f(x) is only used as the name of the function when the nature of the independent variable
is important or when composite functions like f(g(x)) are utilized. Moreover, 2x+1 is not
a function, it is an expression. Functions show a relationship between an input or
independent variable and a output or dependent variable. If one wishes to use include
2x+1 without using the standard f(x)=2x+1 or y=2x+1 they can write x --> 2x+1 to show the
functional relationship.
- Mathematical Symbols are critical for clarity, but
often overused. Use symbols to clarify, not simply because you have discovered how to
write them or type them on your wordprocessor.
- References are universally
provided at the end of a paper; i.e. as endnotes rather than footnotes. Footnotes, while
sometimes utilized in mathematical writing, are almost never used to provide a reference.
The reference section is generally organized alphabetically by the author's last name and
then chronologically for a given author.
- Citation Style for References in
mathematical writing varies remarkably from journal to journal and publisher to publisher.
When you need to cite references follow guidelines from your teacher or the style of an
appropriate journal. Be consistent throughout a given paper.
- Citation Style for
Citations typically follows the following examples:
- [Fle] or [Fleron] for the
paper by Addie Fleron listed in the reference section
- [Fle 3] or [Fleron 3] for the
third paper by Jacob Fleron, listed chronologically, in the reference section
- [17] for
the seventeenth paper in the reference section, listed alphabetically and chronologically
for a given author
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