LaTeX math tutorial

LaTeX is a powerful language used for writing academic papers. In this article, we'll focus not on the full language, but only the portions relevant to math typesetting.

In this article, there will be one code block for the LaTeX code, as well as one equation block right after with the rendered results.

Basic equations

Variables in LaTeX can be written much as you'd expect:

x + y

$$ x + y $$

You can add multiplication with \times or \cdot:

3 \times 3 = 9

$$ 3 \times 3 = 9 $$

4 \cdot 1 = 4

$$ 4 \cdot 1 = 4 $$

Fractions are written with \frac{}{}, with the first argument being the numerator, and second argument being the denominator:

\frac{3x + 1}{x^2}

$$ \frac{3x + 1}{x^2} $$

Superscripts are written with ^ and subscripts are written with _:

E = mc^2

$$ E = mc^2 $$

x_i = 3

$$ x_i = 3 $$

If we have some content inside of a superscript or subscript, we wrap it in curly braces {}:

x_{i + 1} = x_i + 1

$$ x_{i + 1} = x_i + 1 $$

Sums are written with \sum followed by the starting index on the subscript and the ending index on the superscript:

\sum_{i = 0}^n i

$$ \sum_{i = 0}^n i $$

Derivatives and integrals can be written like this:

\frac{dy}{dx}

$$ \frac{dy}{dx} $$

\int \limits_0^5 x^2 dx

$$ \int \limits_0^5 x^2 dx $$

Text can be rendered with \text{} or \mathrm{}:

x = 3 \text{ or } x = -5

$$ x = 3 \text{ or } x = -5 $$

Sine, cosine, and tangent each have their respective functions:

2 \sin(x) + 5 \cos(x) - \tan(x)

$$ 2 \sin(x) + 5 \cos(x) - \tan(x) $$

Square roots can be written with \sqrt{}:

\sqrt{x + 5}

$$ \sqrt{x + 5} $$

And nth roots can be written with \sqrt[n]{}:

$$ \sqrt[3]{81} $$

\sqrt[3]{81}

Natural log is denoted by \ln and log by \log:

\ln (x) = \log_e (x)

$$ \ln (x) = \log_e (x) $$

That should be enough for a working knowledge of LaTeX math!