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LaTeX is renowned for its superior mathematical typesetting. This guide will take you from basic equations to advanced mathematical expressions.
Fun fact: LaTeX’s math rendering is so good that even Microsoft Word now uses a LaTeX-like syntax for its equation editor!

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Why LaTeX for Math?

Compare these approaches to writing the quadratic formula: Plain text: x = (-b +/- sqrt(b^2 - 4ac)) / 2a LaTeX result: x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} The difference is clear – LaTeX produces publication-quality mathematics.

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Math Modes

LaTeX has two math modes:

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1. Inline Math Mode

For math within text, use $...$ or \(...\):

Expected output

The famous equation E=mc2E = mc^2 was discovered by Einstein. We can also write a2+b2=c2a^2 + b^2 = c^2 for the Pythagorean theorem.

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2. Display Math Mode

For centered equations on their own line, use \[...\] or equation environment:

Expected output

The quadratic formula is:x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}For numbered equations:\int_0^\infty e^{-x^2} dx = \frac{\sqrt{\pi}}{2} \tag{1}
Use \[...\] for important formulas you want to highlight. Use $...$ for variables and simple expressions within sentences.

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Basic Math Elements

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Superscripts and Subscripts

Expected output

Superscripts: x2x^2, x10x^{10}, xn+1x^{n+1}Subscripts: x1x_1, x10x_{10}, xi,jx_{i,j}Combined: x12x_1^2, ank+1a_n^{k+1}Chemical formulas: H2O\text{H}_2\text{O}, CO2\text{CO}_2

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Fractions

Expected output

Simple fractions: 12\frac{1}{2}, ab\frac{a}{b}Nested fractions: 11+12\frac{1}{1 + \frac{1}{2}}Display style: a+bc+d\displaystyle\frac{a+b}{c+d}Alternative notation: a/ba/b or a/b^a/_b

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Roots

Expected output

Square root: 2\sqrt{2}, x2+y2\sqrt{x^2 + y^2}nth root: 83\sqrt[3]{8}, xn\sqrt[n]{x}Nested roots: 2+3\sqrt{2 + \sqrt{3}}

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Common Math Symbols

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Greek Letters

Expected output

Lowercase: α,β,γ,δ,ϵ\alpha, \beta, \gamma, \delta, \epsilon and θ,λ,μ,π,σ,ϕ\theta, \lambda, \mu, \pi, \sigma, \phiUppercase: Γ,Δ,Θ,Λ,Σ,Φ\Gamma, \Delta, \Theta, \Lambda, \Sigma, \PhiVariants: ϵ\epsilon vs ε\varepsilon and ϕ\phi vs φ\varphi

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Operators and Relations

Expected output

Basic operators: a+b−c×d÷ea + b - c \times d \div eComparison: a<b≤c=d≥e>fa < b \leq c = d \geq e > f and a≠b≈c≡da \neq b \approx c \equiv dSet operations: A∪B∩C⊂DA \cup B \cap C \subset D and x∈A,y∉Bx \in A, y \notin BLogic: p∧q∨r  ⟹  sp \land q \lor r \implies s and ∀x∃y\forall x \exists y

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Arrows

Expected output

Basic arrows: →,←,↔\rightarrow, \leftarrow, \leftrightarrow and ⇒,⇐,⇔\Rightarrow, \Leftarrow, \LeftrightarrowLong arrows: ⟶,⟵\longrightarrow, \longleftarrowSpecial arrows: ↑,↓,↕\uparrow, \downarrow, \updownarrow and ↗,↘,↙,↖\nearrow, \searrow, \swarrow, \nwarrow

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Functions and Operators

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Standard Functions

Expected output

Trigonometric: sin⁡θ,cos⁡θ,tan⁡θ\sin\theta, \cos\theta, \tan\thetaLogarithms: log⁡x,ln⁡x,log⁡2x\log x, \ln x, \log_2 xLimits: lim⁡x→0sin⁡xx=1\displaystyle\lim_{x \to 0} \frac{\sin x}{x} = 1Min/Max: min⁡(a,b),max⁡(a,b)\min(a,b), \max(a,b)

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Sums and Products

Expected output

Summation: ∑i=1ni=n(n+1)2\displaystyle\sum_{i=1}^{n} i = \frac{n(n+1)}{2}Product: ∏i=1ni=n!\displaystyle\prod_{i=1}^{n} i = n!Multiple lines: ∑i=1i≠jnai\displaystyle\sum_{\substack{i=1 \\ i \neq j}}^{n} a_i

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Integrals and Derivatives

Expected output

Derivatives: f′(x),f′′(x),f(n)(x)f'(x), f''(x), f^{(n)}(x) and dfdx,d2fdx2\frac{df}{dx}, \frac{d^2f}{dx^2} and ∂f∂x\frac{\partial f}{\partial x}Integrals: ∫f(x) dx\displaystyle\int f(x)\,dx and ∫abf(x) dx\displaystyle\int_a^b f(x)\,dx and ∬Df(x,y) dx dy\displaystyle\iint_D f(x,y)\,dx\,dySpecial notation: ∮CF⋅dr\displaystyle\oint_C F \cdot dr

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Matrices and Arrays

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Basic Matrices

Expected output

pmatrix (parentheses): (abcd)\begin{pmatrix} a & b \\ c & d \end{pmatrix}bmatrix (brackets): [123456789]\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}vmatrix (determinant): ∣abcd∣=ad−bc\begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc

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Advanced Arrays

Expected output

Custom arrays: [123456]\left[ \begin{array}{cc|c} 1 & 2 & 3 \\ 4 & 5 & 6 \end{array} \right]Cases (piecewise functions): f(x)={x2if x≥0−xif x<0f(x) = \begin{cases} x^2 & \text{if } x \geq 0 \\ -x & \text{if } x < 0 \end{cases}

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Spacing in Math Mode

Expected output

Default: aba b vs ababThin space: a ba\,b | Medium space: a ba\:b | Thick space: a  ba\;bQuad space: aba\quad b | Double quad: aba\qquad bNegative space: a ⁣ba\!b
Use \, before differentials in integrals: \int f(x)\,dx looks better than \int f(x)dx.

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Advanced Features

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Theorem Environments

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Aligning Equations

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Common Mistakes to Avoid

1. Forgetting braces for multi-character super/subscripts
  • Wrong: $x^10$ → x¹0
  • Right: $x^{10}$ → x¹⁰
2. Using text in math mode
  • Wrong: $x = speed * time$
  • Right: $x = \text{speed} \times \text{time}$
3. Incorrect fraction syntax
  • Wrong: $\frac{1/2}$
  • Right: $\frac{1}{2}$

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Math Packages

Essential packages for advanced mathematics:

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Practice Exercises

Try typesetting these formulas:
  1. Euler’s Identity: eiπ+1=0e^{i\pi} + 1 = 0
  2. Gaussian Integral: ∫−∞∞e−x2dx=π\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}
  3. Binomial Theorem: (x+y)n=∑k=0n(nk)xn−kyk(x+y)^n = \sum_{k=0}^{n} \binom{n}{k} x^{n-k} y^k
  4. Maxwell’s Equation: ∇×E=−∂B∂t\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}

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Quick Reference

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Next Steps

Math Symbols Reference

Complete list of mathematical symbols

Advanced Equations

Multi-line equations and advanced layouts

Matrices & Arrays

Complex matrix operations and layouts

Scientific Notation

Physics, chemistry, and scientific formatting
Ready to create beautiful mathematical documents? You now have the foundation to typeset any mathematical expression in LaTeX!