LaTeX Math Reference
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# ConstructsConstructs

LaTeX provides a number of commands to generate mathematical constructs.

# Basics

1
1,2,3,\ldots
sequence
2
1+2+3+\cdots
sequence
3
\frac{a}{b}
fraction
4
\cfrac{a}{1+\cfrac{b}{c}}
continued fraction
5
^3/_7
simple fraction
6
\sqrt{x}
square root
7
\sqrt[n]{x}
nth root
8
a^b
exponentiation
9
a_b
subscript
10
|x|
absolute value
11
\ln(x)
natural log
12
\log_{a} b
logarithm
13
\binom{n}{k}
binomial
14
|x| = \begin{cases} x & x\ge 0\\ -x & x<0 \end{cases}
piecewise function
15
$$\begin{split} \label{x5} x &= a + b \\ &= c + d + e. \end{split}$$
multi-line equation
There are no rows in this table

# Geometry and trigonometry

1
\angle 45^\circ
angle and degree
2
\triangle ABC
triangle
3
\overline{AB}
segment
4
\sin
sine
5
\cos
cosine
6
\tan
tangent
7
\cot
cotangent
8
\sec
secant
9
\csc
cosecant
10
\arcsin
arcsine
11
\arccos
arccosine
12
\arctan
arctangent
There are no rows in this table

# Matrices and arrays

Matrices can be created using a number of environments, depending on the desired delimiter and spacing.
1
\begin{matrix} a & b & c \\ d & e & f \\ g & h & i \end{matrix}
matrix
2
\begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix}
matrix (parentheses)
3
\begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix}
matrix (brackets)
4
\begin{Bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{Bmatrix}
matrix (braces)
5
\begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix}
matrix (verts)
6
\begin{Vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{Vmatrix}
matrix (double verts)
7
A_{m,n} = \begin{pmatrix} a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\ a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m,1} & a_{m,2} & \cdots & a_{m,n} \end{pmatrix}
A_{m,n} = \begin{pmatrix} a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\ a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m,1} & a_{m,2} & \cdots & a_{m,n} \end{pmatrix}
arbitrarily sized matrix with dots
8
n \cdot ( \begin{smallmatrix} a & b\\ c & d \end{smallmatrix} )
small matrix
9
\begin{array}{l|r} 20 & -30\\ 30 & -40 \end{array}
array
10
\left| \begin{array}{ccc} 1 & 2 & 3\\ 4 & 5 & 6\\ 7 & 8 & 9 \end{array} \right|
determinant
There are no rows in this table

# Set theory

1
\angle 45^\circ
angle and degree
2
\triangle ABC
triangle
3
\overline{AB}
segment
4
\sin
sine
5
\cos
cosine
6
\tan
tangent
7
\cot
cotangent
8
\sec
secant
9
\csc
cosecant
10
\arcsin
arcsine
11
\arccos
arccosine
12
\arctan
arctangent
There are no rows in this table

# Calculus

1
\frac{df}{dx}
derivative
2
f'
derivative
3
\frac{\partial f}{\partial x}
partial derivative
4
\int, \int_{-N}^{N} e^x dx
integral
5
\iint
double integral
6
\iiint
triple integral
7
\oint
contour integral
8
\lim_{x \to \infty}
limit
9
\sum_{n=1}^{\infty}a_n
summation
10
\prod_{n=1}^{\infty}a_n
product
There are no rows in this table