# Math 15 Email hints:

The hardest thing about sending mathematics via email is that mathematics involves lots of notation that is not available on the computer keyboard. We need to establish some conventions to make this easier to do.

Here are some ideas that should help:

• Use "`^`" to represent superscripts, as in "`x^2`" for "x squared", and "`x^(1/2)`" for "the square root of x". Use parentheses to avoid confusion about what belongs in the power. E.g., "`x^(2x)+1`" rather than "```x^2x + 1```" since this could be read incorrectly as either "`(x^2)x + 1`" or "`x^(2x+1)`".

• Use "`_`" to represent subscripts, as in "`x_i`" for "x sub i". Use parentheses as above to make more complicated subscripts clear.

• Use spaces around low-precedence operators like addition, subtraction and equals, but not around multiplication and division, as in "`2x^2 + 3 = -1`" rather than "`2x^2+3=-1`"

• Use parentheses to make the numerator and denominator clear when you write fractions using "`/`", as in "`(x+1)/(2x-3)`", not "`x+1/2x-3`" since this could be read as "```x + (1/2)x - 3```" or any of a number of other ways.

• For long equations, set them off from the rest of the mail by blank lines and indentation. For example:
```   I can't figure out how to factor the equation

x^3 - 2x^2 + 1 = 0

Can you give me any advice?
```

• Use spaces, not tabs, of you are forming a multi-line equation (like a large fraction or a series of equalities). E.g.
```                1
f(x) =  -------
1 - x

-1
so f'(x) =  -------
(1-x)^2
```

• We need a notation for integrals. One suggestion is to use a dollar sign "`\$`" for the integral sign, and use superscript and subscript symbosl to give the limits. E.g., "```\$_0^1 x dx```" for "the integral from 0 to 1 of x (with respect to x)". This isn't great, but it works.

Another possibility would be to use "`I`" or "`Int`" instead. For example: ```Int_0^Infinity (1/x^2) dx``` for "the integral from 0 to infinity of 1 over x squared dx".

There is no standard for this, so we will try it out and see what we like best.

• We need a notation for limits. I suggest the following: `lim_(x -> infinity) e^x` for "the limit as x goes to infinity of e to the x".

• In general, use spaces and parentheses liberally to make your meaning as clear as possible.