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some text some text some text some text some text some text some text some text some textsome text some text some text some text some text some text some text some text some text sometext some text some text some text ab   f (x)  dx   \(...\)   LATEX shorthand for inline text   ab

f (x)  dx   \[...\]   LATEX shorthand for displayed equations ab  f (x)  dx   $...$   TEX shorthand for inline text   ab

f (x)  dx   $$...$$   TEX shorthand for displayed equations

some text some text some text some text some text some text some text some text some text sometext some text some text some text some text some text some text some text some text some text

some text some text some text ab  f (x)  dx   \begin{math}...\end{math}   inline math environment   ab

f (x)  dx   \begin{displaymath}...\end{displaymath}   displayed math environment

some text some text some text some text some text some text some text some text some text sometext some text some text some text some text

∀x ∈ X,∃y ≤ some text some text some text some text some text some text some text some text some text some

text some text some text some text some text

α,   \alpha

γ,   \gamma

Γ,   \Gammaπ,   \pi

Π,   \Piϕ,   \varphi

µ,   \mu

Φ,   \Phi

some text some text some text some text some text some text some text some text some text sometext some text some text some text some text some text

cos(2θ) = cos2 θ − sin2 θsome text some text some text some text some text some text some text some text some text sometext

limx→∞

exp(−x) = 0some text some text some text some text some text some text some text some text some text sometext some text some text some text some text

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a \bmod b . . . . . . . . . . . . . . . . . . . . . . . . . .a mod bx \equiv a \pmod b . . . . . . . . . . . . . . . . . . . .x ≡ a   (mod  b)

some text some text some text some text some text some text some text some text some text some

text some text some text some text some text some text

kn+1 =  n2 + k2n − kn−1

some text some text some text some text some text some text some text some text some text sometext

f (n)|n=17 =  n5 + 4n2 + 2|n=17 = 1421015some text some text some text some text some text some text some text some text some text sometext some text some text some text some text

n!

k!(n − k)!  = nksome text some text some text some text some text some text some text some text some text sometext some text

1

x +   1

y

y − z some text some text some text some text some text some text some text some text some text sometext some text some text some text some text

{n! \over k!(n-k)!}={n \choose k}  n!

k!(n −

 k)! =

n

ksome text some text some text some text some text some text some text some text some text sometext some text some text some text some text some text some text some text some text some textsome text

x =  a0 +1

a1 +1

a2 +1

a3 +1

a4

some text some text some text some text some text

\sqrt{\frac{a}{b}}

 a

b

some text some text some text some text some text some text some text some text

\sqrt[n]{1+x+x^2x^3+\ldots}  n

√ 1 + x + x2 + x3 + . . .

The \sum and  \int commands insert the sum and integral symbols respectively, with limits spec-ified using the caret (^) and underscore (_).

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\sum_{i=1}^{10} t_i10

i=1 ti

\displaystyle \sum_{i=1}^{10} t_1

10

i=1t1

The limits of integrals follow the same notation. It’s also important to represent the integrationvariables with upright d, which in math mode is obtained through the   \mathrm{}  command, andwith small space separating it from the integrand, which is attained with the  \, command.

\int_0^\infty \mathrm{e}^{-x} \, \mathrm{d}x

   ∞

0

e−x dx

The   \substack  command allows the use of  \\  to write the limits over multiple lines.

0