Even when studying algebra, one sometimes needs notation from other areas, such as geometry. After algebra, one usually studies trigonometry and then calculus.

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The following table includes geometric, trigonometric, probability, and aditional mathematical notation.

Type-set formatting |
Text-only formatting |
Notes |

sin(x) |
sin(x) | Put parentheses around the argument of any function, including sine and cosine. |

sin^{2}(x)sin( x^{2}) |
sin^2(x) sin(x^2) |
If you're squaring the sine, put the power on the sine. If you're squaring the argument, put the power on the argument. Use parentheses to clearly delineate what goes where. |

sin(2x) |
sin(2x) | Use parentheses to make clear that you mean "the sine of 2x", not "the square of the sine of x". |

° | degrees ° * |
To indicate "degrees", either write the word out; use an asterisk and explain what it means; or else (on a PC), hold down the "ALT" key and type "0176" to insert the character directly. |

θ | theta @ t |
As long as you define yourself, it's okay to use "@" for "theta". Otherwise, spell it out, or pick a Latin letter, such as "t". |

β | beta ß b |
You can (on a PC) insert a character similar to "beta" by holding down the "ALT" key and typing "0223" on the numeric keypad. Otherwise, spell out the name, or replace "beta" in your exercise with a Latin letter. |

π | pi | Do not use "m" or "n" to stand for "π", since m and n are variables and π is a number. Instead, spell out the name. (And please spell it correctly. It's "pi", not "pye" or "pie".) You may find it helpful to use parentheses, as in "sin[(2/3)(pi)]". |

i |
i | When writing complex numbers, just use the "i" as usual. |

e |
e | The natural exponential e is a commonly-known value, just like pi. You don't have define what e is in your post. |

cis(x) |
cos(x) + isin(x) cis(x) |
Not everybody is familiar with the "cis" notation. If you use it, define it first, so they understand that you mean what is shown in the first line. |

∠A | angle A <A |
If you use the "less-than sign, angle name" format, define what you mean. Otherwise, you'll leave people wondering what, exactly, is less than A. |

m(∠A)m(A) |
measure of A m(A) |
If you use "m(A)", state that this means "the measure of angle A". (The "angle" part of the expression is often dropped. Dunno why.) |

a ⊥ b a ∥ b |
a perp. to b a parallel to b |
Spell out the "parallel" and "perpendicular" relations. |

mCnC( m, n) |
m-choose-n mCn C(m,n) |
Most tutors are familiar with the "mCn" abbreviation for the formula for combinations, but it wouldn't hurt to define it if you use it. |

mPnP( m, n) |
m-permute-n mPn |
Most tutors are familiar with the "mPn" abbreviation for the formula for permuations, but it wouldn't hurt to define it if you use it. |

<2, 3> | You can use the "less than" and "greater than" signs for vectors. | |

u-dot-v u * v |
As long as you define the asterisk to mean the dot product, you can use this for dotting two vectors. Use generous spacing. As long as you've specified that the context is vectors, you can ignore the arrows. | |

u-cross-v u × v |
Don't use the letter "X" between the vectors, as this will be confused as being a third vector. Instead, either spell out "cross" or else (on a PC) hold down the "ALT" key and type "0215" on the numeric keypad, using generous spacing so your meaning is clear. Don't worry about the arrows over the tops of the vectors. | |

A^{T}A ^{−1} |
A^T A^(-1) |
Write the transpose or inverse of a matrix using superscript notation. |

[[1 2 3] |
Matrices are just about impossible to format with text. The bracket design, using outer brackets for the matrix and inner brackets for the rows, has arisen from graphing-calculator notation. Be sure to say what you mean by this, and try to use "CODE" or "PRE" tags or a fixed-width font. | |

||1 2 3| |
Determinants are also hard to format with only text. Use bars (the "pipe" character, shown as a (possibly broken) line on your keyboard, somewhere above the "Enter" key) to delineate the rows. | |

|A| | det(A) |A| |
If you use the absolute-value-bar notation for the determinant, state what you mean. |

sum[i=1,n][a_i] sigma[1,n][a_i] |
Whatever notation you use for a summation, be sure to define what you mean by restating the first summation in words. | |

lim[i -> infty] a_i lim[x -> 3^+] f(x) |
The "lim" abbreviation for "limit" is standard. Follow this with brackets showing what is heading toward what, and then put the argument. | |

int[a,b] f(x) dx | The "int" abbreviation for "integral" is fairly standard. Follow this with the limits of integration (if any), the integrand, and the differential. | |

∂x |
partial-x | To indicate a partial derivative, just spell out "partial". |

(3x^2 + 2)[x=0,2] | To indicate the limits of evaluation, either bracket them after the expression you're evaluating, or else spell out "evaluated between (this) and (that)". |

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