LaTeX Syntax Reference in Markdown

---

1. Basic Structure

Function	Syntax	Example
Inline formula	$...$	$E=mc^2$
Display formula (block)	$$...$$ or \[...\]	$E=mc^2$

---

2. Greek Letters

Letter	Syntax	Example	Letter	Syntax	Example
α	\alpha	$\alpha$	β	\beta	$\beta$
γ	\gamma	$\gamma$	δ	\delta	$\delta$
ε	\epsilon	$\epsilon$	ζ	\zeta	$\zeta$
η	\eta	$\eta$	θ	\theta	$\theta$
ι	\iota	$\iota$	κ	\kappa	$\kappa$
λ	\lambda	$\lambda$	μ	\mu	$\mu$
ν	\nu	$\nu$	ξ	\xi	$\xi$
π	\pi	$\pi$	ρ	\rho	$\rho$
σ	\sigma	$\sigma$	τ	\tau	$\tau$
φ	\phi	$\phi$	χ	\chi	$\chi$
ψ	\psi	$\psi$	ω	\omega	$\omega$
Γ	\Gamma	$\Gamma$	Δ	\Delta	$\Delta$

---

3. Superscripts and Subscripts

Function	Syntax	Example
Superscript	^	$x^2$
Subscript	_	$x_i$
Combined	Use both	$x_i^2$
Multiple characters	Enclose in {}	$x^{10}$, $x_{ij}$

---

4. Fractions

Type	Syntax	Example
Standard fraction	\frac{numerator}{denominator}	$\frac{1}{2}$
Compact fraction	\tfrac	$\tfrac{1}{2}$
Display fraction	\dfrac	$\dfrac{1}{2}$

---

5. Radicals

Function	Syntax	Example
Square root	\sqrt{...}	$\sqrt{x}$
nth root	\sqrt[n]{...}	$\sqrt[3]{x}$

---

6. Brackets and Delimiters

Function	Syntax	Example
Parentheses	(...)	$(x+y)$
Square brackets	[...]	$[x+y]$
Braces	\{...\}	$\{x\}$
Auto-sizing	\left( ... \right)	$\left( \frac{1}{2} \right)$
Absolute value	\left\lvert ... \right\rvert	$\left\lvert x\right\rvert$
Norm	\left\lVert ... \right\rVert	$\left\lVert v\right\rVert$

---

7. Sums, Integrals, and Limits

Function	Syntax	Example
Summation	\sum_{lower}^{upper}	$\sum_{i=1}^{n} i$
Integral	\int_{lower}^{upper}	$\int_0^1 x\,dx$
Double integral	\iint	$\iint_D f(x,y)\,dA$
Triple integral	\iiint	$\iiint_V f(x,y,z)\,dV$
Contour integral	\oint	$\oint_C f(z)\,dz$
Limit	\lim_{x \to a}	$\lim_{x \to a} f(x)$
Product	\prod_{i=1}^{n}	$\prod_{i=1}^{n} a_i$

---

8. Common Operators

Function	Syntax	Example
Addition, subtraction, multiplication, division	+ - \times \div	$a+b-c\times d\div e$
Dot product	\cdot	$a\cdot b$
Cross product	\times	$a\times b$
Union	\cup	$A\cup B$
Intersection	\cap	$A\cap B$
Element of	\in	$x\in A$
Subset and superset	\subset, \supset	$A\subset B$, $B\supset A$
Not equal	\neq	$a\neq b$
Approximately equal	\approx	$\pi\approx 3.14$
Identically equal	\equiv	$a\equiv b$
Less than or equal	\le or \leq	$a\le b$
Greater than or equal	\ge or \geq	$a\ge b$
Plus or minus	\pm	$x=\pm 1$
Minus or plus	\mp	$a\mp b$
Infinity	\infty	$x\to\infty$
Partial derivative	\partial	$\frac{\partial f}{\partial x}$
Gradient	\nabla	$\nabla f$

---

9. Function Names (Upright)

Function	Syntax	Example
sin	\sin	$\sin x$
cos	\cos	$\cos x$
tan	\tan	$\tan x$
cot	\cot	$\cot x$
sec	\sec	$\sec x$
csc	\csc	$\csc x$
arcsin	\arcsin	$\arcsin x$
arccos	\arccos	$\arccos x$
log	\log	$\log x$
ln	\ln	$\ln x$
lg	\lg	$\lg x$
exp	\exp	$\exp x$
max	\max	$\max(a,b)$
min	\min	$\min(a,b)$
sup	\sup	$\sup A$
inf	\inf	$\inf A$
lim	\lim	$\lim_{x\to 0} x$
det	\det	$\det A$

---

10. Matrices and Determinants

Environment	Syntax	Example
Matrix (no delimiters)	\begin{matrix} a & b \\ c & d \end{matrix}	$\begin{matrix} a & b \\ c & d \end{matrix}$
Parenthesized matrix	\begin{pmatrix} ... \end{pmatrix}	$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$
Square-bracketed matrix	\begin{bmatrix} ... \end{bmatrix}	$\begin{bmatrix} a & b \\ c & d \end{bmatrix}$
Braced matrix	\begin{Bmatrix} ... \end{Bmatrix}	$\begin{Bmatrix} a & b \\ c & d \end{Bmatrix}$
Determinant	\begin{vmatrix} ... \end{vmatrix}	$\begin{vmatrix} a & b \\ c & d \end{vmatrix}$
Norm matrix	\begin{Vmatrix} ... \end{Vmatrix}	$\begin{Vmatrix} a & b \\ c & d \end{Vmatrix}$

Separate columns with & and rows with \\.

---

11. Multiline Formulas

Function	Syntax	Example
Alignment	\begin{aligned} x &= 1 \\ y &= 2 \end{aligned}	$\begin{aligned} x &= 1 \\ y &= 2 \end{aligned}$
System of equations	\begin{cases} x+y=1 \\ x-y=2 \end{cases}	$\begin{cases} x+y=1 \\ x-y=2 \end{cases}$
Piecewise function	f(x)=\begin{cases} x^2 & x>0 \\ 0 & x=0 \\ -x & x<0 \end{cases}	$f(x)=\begin{cases} x^2 & x>0 \\ 0 & x=0 \\ -x & x<0 \end{cases}$

---

12. Superscript and Subscript Decorations

Function	Syntax	Example
Overbrace	\overbrace{...}^{text}	$\overbrace{a+b+c}^{text}$
Underbrace	\underbrace{...}_{text}	$\underbrace{a+b+c}_{text}$
Arrow with label	\xrightarrow{text}	$\xrightarrow{text}$
Overline	\overline{...}	$\overline{AB}$
Underline	\underline{...}	$\underline{AB}$
Vector arrow	\vec{...}	$\vec{v}$
Long arrow	\overrightarrow{AB}	$\overrightarrow{AB}$
Hat	\hat{a}	$\hat{a}$
Tilde	\tilde{a}	$\tilde{a}$
Dot	\dot{a}, \ddot{a}	$\dot{a}$, $\ddot{a}$

---

13. Arrow Symbols

Syntax	Example	Syntax	Example
\leftarrow	$\leftarrow$	\rightarrow	$\rightarrow$
\Leftarrow	$\Leftarrow$	\Rightarrow	$\Rightarrow$
\leftrightarrow	$\leftrightarrow$	\Leftrightarrow	$\Leftrightarrow$
\longleftarrow	$\longleftarrow$	\longrightarrow	$\longrightarrow$
\uparrow	$\uparrow$	\downarrow	$\downarrow$
\nearrow	$\nearrow$	\searrow	$\searrow$

---

14. Spacing and Line Breaks

Function	Syntax	Example
Small space	\,	$a\,b$
Medium space	\;	$a\;b$
Large space	\quad	$a\quad b$
Larger space	\qquad	$a\qquad b$
Forced line break	\\	$\begin{matrix} a \\ b \end{matrix}$

---

15. Colors

Syntax	Example
\color{red}{text}	$\color{red}{text}$
\color{blue}{text}	$\color{blue}{text}$
Supported: red, blue, green, yellow, purple, cyan, black, white, gray, etc.	$\color{green}{green}$, $\color{purple}{purple}$

---

16. Fonts

Function	Syntax	Example
Roman type	\mathrm{...}	$\mathrm{ABC}$
Bold	\mathbf{...}	$\mathbf{ABC}$
Calligraphic	\mathcal{...}	$\mathcal{ABC}$
Blackboard bold	\mathbb{...} (e.g. R, N, Z)	$\mathbb{R}$, $\mathbb{N}$, $\mathbb{Z}$
Monospace	\mathtt{...}	$\mathtt{ABC}$
Italic (default)	Enter directly	$ABC$

---

17. Special Symbols

Syntax	Example	Syntax	Example
\forall	$\forall$	\exists	$\exists$
\neg or \lnot	$\neg$	\emptyset	$\emptyset$
\infty	$\infty$	\nabla	$\nabla$
\bot	$\bot$	\top	$\top$
\angle	$\angle$	\degree	$90\degree$
\prime	$x^\prime$	\ldots	$\ldots$
\cdots	$\cdots$	\vdots	$\vdots$
\ddots	$\ddots$	\hbar	$\hbar$