Language

"An unitary" or "an union" or "an university" were used in the 18th century, but now "a" rather than "an" is standard when the initial sound is "yoo".

Naming convention

${\displaystyle N(x):=\sum _{j=0}^{k}a_{j}\prod _{i=0}^{j}(x-x_{i-1})}$

HTML math

Minus sign

Use [−1,1] instead of [-1,1]. The little hyphen is too short to be a minus sign.

TeX

Colon

${\displaystyle f\colon (0,1)\rightarrow \mathbb {R} }$

instead of

${\displaystyle f:(0,1)\rightarrow \mathbb {R} }$

Mapping arrows

When you want to define the domain and codomain of the mapping use

${\displaystyle \mathrm {sq} :\mathbb {R} \to \mathbb {R} }$

but when you define the actual mapping function use

${\displaystyle x\mapsto x^{2}.}$

Standard function names

Use

${\displaystyle e^{\mathrm {i} x}=\cos x+\mathrm {i} \sin x}$

instead of

${\displaystyle e^{\mathrm {i} x}=cosx+\mathrm {i} sinx}$

to prevent the function names from looking like a variable.

Imaginary unit

The imaginary unit i should not be confused with the common variable i. So to make the imaginary unit look different it is better to write

${\displaystyle e^{\mathrm {i} x}=\cos x+\mathrm {i} \sin x}$

than

${\displaystyle e^{ix}=\cos x+i\sin x}$

Embedded fractions

When a fraction is in a superscript or otherwise deeply embedded within some other notation, it is often more legible like this

${\displaystyle e^{-x^{2}/2}}$

than like this

${\displaystyle e^{-x^{2} \over 2}}$

Spacing

Integrals

Use

${\displaystyle \int f(x)\,dx}$

rather than

${\displaystyle \int f(x)dx}$

Sets defined by using braces

This is another place where small spacing adjustments make notation look better. This

${\displaystyle \{\,f(x):0<x<2\,\}}$

is better than this

${\displaystyle \{f(x):0<x<2\}}$

Rate of change: The relationship between two numbers that are changing. To find it, you must divide. Formula: change in dependent variable/change in independent variable. Information by Daron Brown.

Probability: tells how likely something will happan. ex. The probability of a die landing on 4. Information by Daron Brown.

Equation: a math sentence that has an equal sign. ex. x + 3 = 10