\usepackage{amssymb, amsmath}
 
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The following commands are defined in the amsmath package; in other words,  to typeset with these commands, the document class should start with

\documentclass{article}      % article document class
\usepackage{amssymb, amsmath}

Note:

  Inline
math environment open and close with $
Examples:  $ a + b $,   $ a/b $
  Displayed
math environment open with \[   and closed with \]
Examples:
\[
  \frac{1 + 2x}{x + y + xz}
\]
Arithmatic
The arithmetic operations such as +, -, *, /, fraction (\frac)
Examples: $a + b$, $x - y$, $a \cdot b$, $x \times y$
Subscripts and superscripts
Subscripts are typed with _  (underscore)  and superscripts are typed with  ^ (caret).
Remember to enclose the subscripts and superscripts with { and }.
Examples:   $a^2$,  $a_i$,   $x_{ij}$
Accents (in math environment)
There are four most often used math accents:
Binomial coefficients
Use \binom{ }{ } for the binomial coefficients
Example:  $ \binom{n}{k} $
Congruences
The two most important (examples) forms are:
$a \equiv v \pmod{\theta}$
$a \equiv v \pod{\theta}$
Delimiters
These are parenthesis-like symbols that vertically expand to enclose a formular.
Examples:
\[
  \left( \frac{1 + x}{2 + y^{2}} \right) ^{2}
\]
\[
  \left| \frac{a + b}{2} \right|,
    \quad \left\| A^{2} \right\|
\]
Operators
Such as trig functions, limit; for instance, to typeset the sine function sin x
type: $\sin x$.
Examples:
\[
  \lim{x \to 0} f(x) = 0
\]
Ellipses
vertical dots: \vdots
low dots: \ldots
centered dots: \cdots
Note: \vdot, \ldot, \cdot produce a single dot.
Integrals
The command for an integral is \int; the lower limit is a subscript and the upper limit is a superscript.
Example: $\int_{0}^{2 \pi} \cos x \, dx$
Matrices
The amsmath package provide you with a matrix environment.  The matrix elements are separated by &; the rows are separted by \\. (View these matrices.)
Roots
\sqrt produces the square root.
For nth squart root, use \sqrt[n]{ }
Examples:  $\sqrt{a + 2b}$
Sums and products
The command for sum is \sum and for product is \prod .
Examples:  $\prod_{i = 1}^{n} x_{i}^2$
Text
Place text in a formula with an \mbox command
Example: 
  \[
    a = b \mbox{by assumption}
  \]
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