# Writing Mathematics in Plain Text Email

This is a description, intended for people who don't know TeX, including students in calculus courses, precalculus courses, or upper division undergraduate courses, of how to write common mathematical expressions in plain text email. A number of standard symbols are not available, and one can't write subscripts and superscripts in the normal way. This is needed, for example, when emailing me questions about homework problems. Sudents in calculus classes will need this, for example, when using the "email instructor" button on WeBWorK.

1. Do not send binary characters. Use only standard letters and symbols on an English language keyboard. Arrows should be "-->" or similar. No traditional multiplication symbols, no "≤", no Greek letters (write out their names, for example "theta"), etc. These symbols may show up as garbage on other computer systems.
2. Remember the order of operations, and use enough parentheses. (See many individual cases below.) But don't overuse parentheses. Even when mathematically correct, several extra sets of parentheses can make your mathematics hard to read.
3. Use space in math expressions. "x^2 + 3 x - 17" is much more readable than "x^2+3x+17". (The readability difference in email is greater than it appears in my web browser.) See the extra space in the examples below.
4. Use "^" for superscripts: 2^6, e^3, etc. ("**" instead of "^" is also OK.) Use parentheses if either the base or the exponent contains more than one mathematical symbol. Thus:  (3 x)^2,  (x - 17)^2,  e^(3 / x),  e^(x + 7).
5. Use "_" (underscore) for subscripts. If the subscript has more than one character, enclose it in braces: "lim_{x --> 0} sin (x) / x". (This is what mathematicians are used to.)
6. Use "/" for division, but remember the parentheses! The expression "x - 6 / x + 9" is x - (6 / x) + 9. If you mean (x - 6) / (x + 9), both sets of parentheses are necessary. If you mean 1 divided by 3 x, you also need parentheses: 1 / (3 x).
7. Use "*" for multiplication when ambiguity is possible. Thus, "4 * 3". Here, "(4) (3)" is also possible, but usually this form is less readable.
8. Use parentheses for all function evaluations: "sin (x)", not "sin x". This reduces possible confusion.
9. The square root of x is "x^(1 / 2)" (parentheses needed). Similarly for cube roots etc. Specifically for square roots, there is a standard abbreviation, namely "sqrt (x)" for the square root of x.
10. "e^x" can also be written "exp (x)". This is usually better if the exponent is complicated, for example: "exp (x^3 + 17)".

Calculus expressions:

1. Infinity is "infinity" or "\infty". (The second is TeX code.) In lower division classes, "inf" is probably OK, but you run the risk of confusing it with "infimum", for which "inf" is the standard abbreviation.
2. Example for limits: "lim_{x --> 3^+} 1 / (x - 3)".
3. For derivatives, use an apostrophe: "f' (x)". Make sure to use the kind that appears on the keyboard (which is straight), not the curved kind found in printed text (which is a binary character and may be unintelligible, ruining your meaning). If you want to use physicists' notation, use parentheses: "(d / d t) (a t^2 + b t)". You don't need parentheses around the "d t" part; this is considered a single symbol.
4. For integrals, use "\int" with usual notation for subscripts and superscripts. You can also write "integral", or the whole thing in words. Examples:
• "\int_a^b f (x) d x"
• "\int f (x) d x"
• "integral_a^b f (x) d x"
• "the integral of f (x) d x from a to b"
• "the indefinite integral of f (x)"

This page maintained by N. Christopher Phillips, email. Please email plain text (7 bit ASCII) only (no web page coded files, Microsoft Word documents, binary characters, etc.; see the email page for more).

Last significant change 11 December 2015.