Inline math
Best for a symbol or short expression inside a sentence.
$x^2 + y^2 = z^2$$x^2 + y^2 = z^2$
StudyPilot LaTeX Guide
Wrap your math in dollar signs
This is the one rule to remember. Use one dollar sign on each side for math inside a sentence, or two on each side for a centered equation.
Display math
Best for an important equation on its own line.
$$\frac{a}{b} = c$$$$\frac{a}{b} = c$$
Beginner
Build everyday expressions
Copy an example and replace the letters or numbers with your own.
Fraction
$\frac{a}{b}$$\frac{a}{b}$
Powers and subscripts
$x^2 + a_{10}$$x^2 + a_{10}$
Roots
$\sqrt{x+1} + \sqrt[3]{8}$$\sqrt{x+1} + \sqrt[3]{8}$
Symbols and relations
$a \times b,\ x \le y,\ p \neq q$$a \times b,\ x \le y,\ p \neq q$
Intermediate
Greek letters, sums, and calculus
Use a backslash before a command name. Uppercase Greek letters usually start with a capital letter, such as \Delta.
Greek letters
$\alpha, \beta, \theta, \pi, \Delta$$\alpha, \beta, \theta, \pi, \Delta$
Summation
$$\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$$$$\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$$
Definite integral
$$\int_a^b f(x)\,dx$$$$\int_a^b f(x)\,dx$$
Limit and derivative
$$f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$$$$f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$$
Advanced
Lay out complex math clearly
These examples combine commands. Keep the full expression inside double dollar signs.
Aligned equations
$$\begin{aligned} 2x+3&=11 \\ 2x&=8 \\ x&=4 \end{aligned}$$$$\begin{aligned} 2x+3&=11 \\ 2x&=8 \\ x&=4 \end{aligned}$$
Matrix
$$A=\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$$$$A=\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$$
Piecewise function
$$f(x)=\begin{cases} x^2 & x\ge0 \\ -x & x<0 \end{cases}$$$$f(x)=\begin{cases} x^2 & x\ge0 \\ -x & x<0 \end{cases}$$
Sets and logic
$$A\cap B=\{x\in A\mid x\in B\},\quad \forall x\in\mathbb{R}$$$$A\cap B=\{x\in A\mid x\in B\},\quad \forall x\in\mathbb{R}$$
Vectors and notation
$$\vec{v}=\langle v_1,v_2\rangle,\quad \hat{x},\ \bar{x},\ \overline{AB}$$$$\vec{v}=\langle v_1,v_2\rangle,\quad \hat{x},\ \bar{x},\ \overline{AB}$$
Cheat sheet
Useful commands at a glance
A quick reference for the symbols you are most likely to need.
| Use | Type | Result |
|---|---|---|
| Arrows | \to, \Rightarrow, \leftrightarrow | $\to, \Rightarrow, \leftrightarrow$ |
| Comparisons | \le, \ge, \neq, \approx | $\le, \ge, \neq, \approx$ |
| Operations | \cdot, \times, \div, \pm | $\cdot, \times, \div, \pm$ |
| Sets | \in, \notin, \subset, \cup, \cap | $\in, \notin, \subset, \cup, \cap$ |
| Spacing | a\,b \quad a\qquad b | $a\,b \quad a\qquad b$ |
| Text in math | x=2\text{ when }y=4 | $x=2\text{ when }y=4$ |
| Automatic brackets | \left(\frac{x}{y}\right) | $\left(\frac{x}{y}\right)$ |