- Basic Guidelines
- Raising Something to a Power
- Products
- Square Roots
- Using Parentheses
- Absolute Values
- Derivatives
- Limits, Summations, and Integrals
- Quotients and Division
- Subscripting
- Inequalities and Relational Symbols
- Greek Letters
- Vector Operators
- Special Functions
- Also see these examples from The Math Forum at Swarthmore

If web page options leave something to be desired with regard to rendering math expressions, email can be a nightmare. But on various math discussion usenet groups, some standard notations seem to have evolved.

**Basic Guidelines:**
First, before you compose any math expressions for sending over
the email, *you should set the font of your email composition
window to an equal-space font like Courier*. This will assure
that columns will line up the same way for both sender and
receiver. Also it is **very important** to remember to
press the enter key before you reach the 80th column of each
line. Do *not* count on the auto-wrap to insert the
end-of-lines -- **please** explicitly press the enter key at the end of
each line.
Many mail readers render email very poorly if it contains
no hard end-of-lines, and your colums will not line up
for me the same way as they did for you if you fail to
follow this guidline.
And please, **do NOT ever use tabs anywhere**. If you do you will very
nearly assure that columns will not line up for the recipient as they did for
you. So always use spaces instead of tabs.

The notation `x^n` is almost universally taken to mean
`x ^{n}`. It is much easier to do exponentiation
using the

Most of the time you can indicate the product of two things simply by
listing them, one after the other, with no operator symbol in between.
For example, `2a` is taken to mean two times `a`. There
may be cases, though, where this can be hard to read or ambiguous.
For example, `asin(x)` could be taken to mean `a` times
sine of `x`, or it could be taken to mean arcsine of `x`.
It would be better to write the former as
` a sin(x)`` a*sin(x)`` a * sin(x)``*` symbol is always taken to mean multiplication unless
specified otherwise. If you put the `*` in to indicate
multiplication even where it isn't necessary, there is no harm done.

To render the square root of an expression, you can use
`sqrt(expression)``(expression)^(1/2)``(expression)^(1/3)`

Use parentheses wherever there is any opportunity for amiguity.

ambiguous unambiguous unambiguousGenerally, if no parentheses are shown, exponentiation is assumed to be done first, followed by multiplication, division, subtraction, and addition, in that order. Even if you follow that convention, when leaving out the parentheses, it often behooves you to put an additional blank to offset the later-applied operators:~~1/2a 1/(2a) (1/2)a 2^n-1 2^(n-1) (2^n) - 1 e^x^2 e^(x^2) (e^x)^2~~

y = x^2 + a x + bThis makes it much easier to read. And if you put in parentheses even where they are redundant, you haven't hurt anything. So when in doubt, put them in.

**Do use parentheses when you are using functions:**

y = sin(2x)

y = sin^2(2x)

Use `|x|` to means *absolute value of* `x`.
You can find the key that produces the `|` symbol in
the upper right of your keyboard, near the backspace key on
most standard keyboards. The symbol silk-screened onto the key
usually looks like a funny-looking colon.
Typing this symbol requires you to
use the shift key on the majority of keyboards.
You can put any expression you like inside the `|`
symbols.

The `f'(x)` notation is a lot easier than the

df -- dxnotation. Use the

d^n y ----- dx^nI will also recognize

For partial derivatives, go ahead and use the `dy/dx`
notation, but annotate on the line just before or just after
which `d`-expressions are partials. Or you can do what
one of my correspondents has done, and that is to indicate
partial derivatives using a `<>` notation:

<dx/dt>means

Each of these has its own peculiar notation in math books. There is an easy way to write them in email, though, that is self-evident to the reader.

lim{x->0} x ln(x)is "the limit as

integral{0 to r} f(x) dxis the definite integral taken from

double integral{r=0 to 1; theta=0 to 2pi} f(r, theta) r dr dthetaFor summations, use, for example

sum{k=0 to infinity} x^k/k!You can see that the behavior of the counting variable is described here inside the curly-brackets.

No easy way to do these. For small expressions you can use something
like `1 / (x^2 + 1)`

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

There are two commonly used ways of doing this. If you are going to be putting expressions into the subscript, use something like

b[n] = n(b[n-1] + b[n-2])If you are simply going to be using the subscript as a label, for example taking a difference between

delta v = v_f - v_i

Use `<=` for "less than or equal" and `>=` for "greater
than or equal". You can use either `<>` or `!=` as
a symbol for "not equal". The squiggle, `~`, is a good symbol
for "approximately equal". Also, `<<` means "much less
than", and `>>` means "much greater than".
For the equivalence symbol, `º`,
simply use `equiv`.

You can either spell them out, like `delta`, `epsilon` and
`omega`, or you can use the Roman equivalent, which in these cases
would be, `d`, `e`, and `w` respectively. Usually
the context will make it clear what you mean.

If you are sending stuff that involves vectors, you can represent
the dot product of two vectors, `v` and `w` as

v dot wLikewise, their cross product would be

v cross wThe norm or length of a vector,

If you are dealing with vector fields, use the following equivalents for the "del" operator:

expression email version~~Ñf grad f Ñ·f div f Ñ´f curl f Ñ~~^{2}f del^2 f

The expression, `[x]`, is usually used to mean the *floor*
function of `x`. Another phrase for this function is the
*greatest integer* function. It means, take the greatest integer that is
less than or equal to `x`. So, for example:

[1.5] = 1 [0.99] = 0 [-1.1] = -2You can use the

The function, `sgn(x)`, is `1` for
positive values of `x`,
`-1` for negative values of `x`,
and zero for ` x = 0`

The function, `step(x)`, is `1` for
positive values of `x`,
zero for negative values of `x`,
and is undefined for ` x = 0`

`sinh(x)`,
`cosh(x)`,
`tanh(x)`,
`coth(x)`,
`sech(x)`, and
`csch(x)`
are the hyperbolic sine, hyperbolic cosine,
hyperbolic tangent, hyperbolic cotangent,
hyperbolic secant, and hyperbolic cosecant
respectively. For the inverse of any of these,
just precede its name with `arc` (e.g.,
`arctanh(x)`).

email me at *hahn@netsrq.com*