Complete LaTeX Tutorial
Learn mathematical typesetting from basic expressions to calculus, matrices, statistics, logic, and browser rendering with MathJax.
1. What LaTeX is
LaTeX is a typesetting language widely used for mathematics, engineering, science, technical documentation, and academic publishing.
\frac{x+1}{x-1}\[\frac{x+1}{x-1}\]
Commands usually begin with a backslash, and curly braces group content.
\sqrt{x}\[\sqrt{x}\]
x^{10}\[x^{10}\]
a_{n+1}\[a_{n+1}\]
\alpha+\beta\[\alpha+\beta\]
2. Inline and display mathematics
Inline
The function is \(f(x)=x^2\).The function is \(f(x)=x^2\).
Display
\[
f(x)=x^2
\]\[f(x)=x^2\]
In many Markdown systems, $...$ and $$...$$ are also supported.
3. Powers and subscripts
x^2\[x^2\]
x^{12}\[x^{12}\]
x_1\[x_1\]
a_{n+1}^{(k)}\[a_{n+1}^{(k)}\]
Use braces whenever an exponent or subscript contains more than one character.
4. Fractions, roots, and brackets
\frac{a}{b}\[\frac{a}{b}\]
\sqrt{x}\[\sqrt{x}\]
\sqrt[3]{x}\[\sqrt[3]{x}\]
\binom{n}{r}\[\binom{n}{r}\]
\left(\frac{x+1}{x-1}\right)\[\left(\frac{x+1}{x-1}\right)\]
x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]
5. Common symbols
| Purpose | LaTeX | Rendered |
|---|---|---|
| Not equal | \ne | \(\ne\) |
| Less/greater than or equal | \le \ge | \(\le,\ge\) |
| Approximately | \approx | \(\approx\) |
| Plus or minus | \pm | \(\pm\) |
| Multiplication | \times \cdot | \(\times,\cdot\) |
| Infinity | \infty | \(\infty\) |
| Arrow | \to \Rightarrow | \(\to,\Rightarrow\) |
| Therefore | \therefore | \(\therefore\) |
6. Greek letters
\alpha \beta \gamma \delta \theta \lambda \mu \pi \rho \sigma \phi \omega\[
\alpha,\beta,\gamma,\delta,\theta,\lambda,\mu,\pi,\rho,\sigma,\phi,\omega
\]
\Gamma \Delta \Theta \Lambda \Pi \Sigma \Phi \Omega\[
\Gamma,\Delta,\Theta,\Lambda,\Pi,\Sigma,\Phi,\Omega
\]
7. Sets and number systems
\[
\mathbb{N},\quad \mathbb{Z},\quad \mathbb{Q},\quad \mathbb{R},\quad \mathbb{C}
\]
\{x\in\mathbb{R}\mid x\ge 0\}\[\{x\in\mathbb{R}\mid x\ge 0\}\]
A\cup B\[A\cup B\]
A\cap B\[A\cap B\]
A\subseteq B\[A\subseteq B\]
\emptyset\[\emptyset\]
8. Functions, domain, range, and mappings
f:\mathbb{R}\to\mathbb{R},\qquad x\mapsto x^2\[
f:\mathbb{R}\to\mathbb{R},\qquad x\mapsto x^2
\]
\operatorname{Dom}(f)=[0,\infty)\[
\operatorname{Dom}(f)=[0,\infty),\qquad
\operatorname{Range}(f)=[0,\infty)
\]
(f\circ g)(x)=f(g(x))\[(f\circ g)(x)=f(g(x))\]
9. Aligned equations
\[
\begin{aligned}
2x+5 &= 17 \\
2x &= 12 \\
x &= 6
\end{aligned}
\]
\[
\begin{aligned}
2x+5 &= 17 \\
2x &= 12 \\
x &= 6
\end{aligned}
\]
The & marks the alignment point, and \\ starts a new line.
10. Piecewise functions
\[
f(x)=
\begin{cases}
x^2, & x\ge 0,\\
-x, & x<0.
\end{cases}
\]
\[
f(x)=
\begin{cases}
x^2, & x\ge 0,\\
-x, & x<0.
\end{cases}
\]
11. Calculus
\lim_{x\to 0}\frac{\sin x}{x}=1\[\lim_{x\to 0}\frac{\sin x}{x}=1\]
\frac{d}{dx}(x^2)=2x\[\frac{d}{dx}(x^2)=2x\]
\int_0^1x^2\,dx\[\int_0^1x^2\,dx\]
\sum_{i=1}^{n}i\[\sum_{i=1}^{n}i\]
\frac{\partial f}{\partial x}
\qquad
\frac{d^2y}{dx^2}
\qquad
\iint_D f(x,y)\,dA\[
\frac{\partial f}{\partial x}
\qquad
\frac{d^2y}{dx^2}
\qquad
\iint_D f(x,y)\,dA
\]
12. Trigonometry and logarithms
\[
\sin x,\quad \cos x,\quad \tan x,\quad
\log x,\quad \ln x,\quad e^x
\]
\sin^2\theta+\cos^2\theta=1\[\sin^2\theta+\cos^2\theta=1\]
13. Vectors and matrices
\begin{pmatrix}
a & b\\
c & d
\end{pmatrix}\[
\begin{pmatrix}
a & b\\
c & d
\end{pmatrix}
\]
\[
\vec{v},\qquad \mathbf{v},\qquad
\begin{vmatrix}
a & b\\
c & d
\end{vmatrix}=ad-bc
\]
14. Probability and statistics
\[
P(A\mid B)=\frac{P(A\cap B)}{P(B)}
\]
\[
\mathbb{E}[X],\qquad \operatorname{Var}(X),\qquad
X\sim\mathcal{N}(\mu,\sigma^2)
\]
s^2=\frac{1}{n-1}\sum_{i=1}^{n}(x_i-\bar{x})^2\[
s^2=\frac{1}{n-1}\sum_{i=1}^{n}(x_i-\bar{x})^2
\]
15. Geometry
a^2+b^2=c^2\[a^2+b^2=c^2\]
A=\pi r^2\[A=\pi r^2\]
90^\circ\[90^\circ\]
AB\perp CD\[AB\perp CD\]
d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\[
d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
\]
16. Logic and relations
\[
\forall,\quad \exists,\quad \neg,\quad \land,\quad \lor,\quad
\implies,\quad \iff
\]
\forall x\in\mathbb{R},\quad x^2\ge 0\[\forall x\in\mathbb{R},\quad x^2\ge 0\]
17. Text, spacing, and decoration
x=3\text{ or }x=-3\[x=3\text{ or }x=-3\]
f(x)=\sqrt{x},\qquad x\ge 0\[f(x)=\sqrt{x},\qquad x\ge 0\]
\[
\hat{x},\quad \bar{x},\quad \vec{x},\quad \dot{x},\quad
\ddot{x},\quad \tilde{x}
\]
18. LaTeX in HTML with MathJax
HTML needs a renderer. This page uses MathJax.
<script>
window.MathJax = {
tex: {
inlineMath: [['\\(', '\\)'], ['$', '$']],
displayMath: [['\\[', '\\]'], ['$$', '$$']]
}
};
</script>
<script
async
src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js">
</script>Dynamic content
const area = document.getElementById('math-area');
area.textContent = String.raw`\[
\frac{-b\pm\sqrt{b^2-4ac}}{2a}
\]`;
MathJax.typesetPromise([area]);Use String.raw in JavaScript to avoid repeatedly escaping backslashes.
19. Common mistakes
| Problem | Incorrect | Correct |
|---|---|---|
| Multi-digit power | x^12 | x^{12} |
| Visible set braces | {x} | \{x\} |
| Trigonometric name | sin x | \sin x |
| Words in math | x=3 or x=-3 | x=3\text{ or }x=-3 |
| Tall brackets | (\frac ab) | \left(\frac ab\right) |
20. Practice exercises
- Write \(x^2+y^2=r^2\).
- Write \(\sqrt{\frac{x+1}{x-1}}\).
- Write \(\sum_{i=1}^{n}i^2\).
- Write \(\frac{d}{dx}(x^3)=3x^2\).
- Write the quadratic formula.
- Write a \(2\times2\) matrix.
- Write a piecewise absolute-value function.
Show answers
x^2+y^2=r^2
\sqrt{\frac{x+1}{x-1}}
\sum_{i=1}^{n}i^2
\frac{d}{dx}(x^3)=3x^2
x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
\begin{pmatrix}
a & b\\
c & d
\end{pmatrix}
|x|=
\begin{cases}
x, & x\ge 0,\\
-x, & x<0.
\end{cases}21. Quick reference
Powers: x^2, x^{10}
Subscripts: x_1, a_{n+1}
Fractions: \frac{a}{b}
Roots: \sqrt{x}, \sqrt[n]{x}
Sets: \in, \subseteq, \cup, \cap, \mathbb{R}
Calculus: \sum, \lim, \frac{d}{dx}, \int
Logic: \forall, \exists, \neg, \land, \lor, \implies
Spacing: \,, \quad, \qquad
Text: \text{...}, \operatorname{...}
Layouts: aligned, cases, pmatrix, bmatrix, arrayThe fastest way to learn is to copy a working expression, change one part at a time, and render it immediately.
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