MathLab/skills/math-textbook-compiler/references/latex-rules.md

LaTeX Formula Rules

Strict Formatting Requirements

Inline Formulas

• Format: $formula$
• Rule: NO spaces inside delimiters
• Examples:
  • ✅ $x + y$
  • ✅ $\sum_{i=1}^{n} x_i$
  • ❌ $ x + y $
  • ❌ $x+y$ (missing spaces around operators is ok, but be consistent)

Display Formulas

• Format: $$formula$$
• Rule: NO spaces inside delimiters
• Examples:
  • ✅ $$\nabla f(x)$$
  • ✅ $$\mathbb{E}_{x \sim p}[f(x)]$$
  • ❌ $$ \nabla f(x) $$

Common Symbols

Symbol	LaTeX	Meaning
Σ	\sum	Summation (for loop)
∏	\prod	Product
∫	\int	Integral
∇	\nabla	Gradient (.grad)
∂	\partial	Partial derivative
∈	\in	Element of
⊂	\subset	Subset
∀	\forall	For all
∃	\exists	Exists
ℝ	\mathbb{R}	Real numbers
𝔼	\mathbb{E}	Expectation
θ	\theta	Parameters
∇_θ	\nabla_\theta	Gradient w.r.t. θ

Greek Letters (Common in ML)

α \alpha    β \beta    γ \gamma    δ \delta
ε \epsilon  ζ \zeta    η \eta      θ \theta
λ \lambda   μ \mu      ν \nu       ξ \xi
π \pi       ρ \rho     σ \sigma    τ \tau
φ \phi      χ \chi     ψ \psi      ω \omega

Best Practices

1. Always escape special characters: #, $, %, &, _, {, }
2. Use \left( and \right) for auto-sizing parentheses
3. Use \cdot for multiplication dots: $x \cdot y$
4. Use \frac{num}{den} for fractions: $\frac{1}{n}$
5. Use \sqrt{} for square roots: $\sqrt{x^2 + y^2}$