TextCraft-Talk

     Join me for "TextCraft: Enhancing Documentation with LaTeX and Markdown in SageMaker," where we'll explore the powerful capabilities of LaTeX and Markdown to improve your documentation practices. This talk will provide insights into leveraging these tools within SageMaker to create clearer, more effective, and professionally styled documents. Whether you're documenting research, drafting reports, or preparing presentations, you’ll learn how to seamlessly integrate text and code in your workflows, enhancing readability and functionality. Ideal for data scientists, researchers, and anyone interested in advanced documentation techniques.

Table of Contents

1. Greek Letters
2. Arrows
3. Miscellaneous Symbols
4. Binary Operation/Relation Symbols
5. Math Constructs
6. Matrix
7. Aligning Equations

Greek Letters

Greek Letters	Jupyter Notebook Upper Case	Jupyter Notebook Lower Case
Α,$\alpha$	\Alpha	\alpha
Β,$\beta$	\Beta	\beta
Γ,$\gamma$	\Gamma	\gamma
Δ,$\delta$	\Delta	\delta
Ε,$\epsilon$	\Epsilon	\epsilon
Ζ,$\zeta$	\Zeta	\zeta
Η,$\eta$	\Eta	\eta
Θ,$\theta$	\Theta	\theta
Ι,$\iota$	\Iota	\iota
Κ,$\kappa$	\Kappa	\kappa
Λ,$\lambda$	\Lambda	\lambda
Μ,$\mu$	\Mu	\mu
Ν,$\nu$	\NU	\nu
Ξ,$\xi$	\Xi	\xi
Ο,$\omicron$	\Omicron	\omicron
Π,$\pi$	\Pi	\pi
Ρ,$\rho$	\Rho	\rho
Σ,$\sigma$	\Sigma	\sigma
Τ,$\tau$	\Tau	\tau
Υ,$\upsilon$	\Upsilon	\upsilon
Χ,$\chi$	\Chi	\chi
Ψ,$\psi$	\Psi	\Psi
Ω,$\omega$	\Omega	\omega

Arrows

Symbol	Latex Syntax	Symbols	Latex Syntax
$\leftarrow$	\leftarrow	$\Leftarrow$	\Leftarrow
$\rightarrow$	\rightarrow	$\Rightarrow$	\Rightarrow
$\leftrightarrow$	\leftrightarrow	$\rightleftharpoons$	\rightleftharpoons
$\uparrow$	\uparrow	$\downarrow$	\downarrow
$\Uparrow$	\Uparrow	$\Downarrow$	\Downarrow
$\Leftrightarrow$	\Leftrightarrow	$\Updownarrow$	\Updownarrow
$\mapsto$	\mapsto	$\longmapsto$	\longmapsto
$\nearrow$	\nearrow	$\searrow$	\searrow
$\leftharpoonup$	\leftharpoonup	$\rightharpoonup$	\rightharpoonup
$\leftharpoondown$	\leftharpoondown	$\rightharpoondown$	\rightharpoondown

Miscellaneous Symbols

Symbol	Latex Syntax	Symbol	Latex Syntax
$\infty$	\infty	$\forall$	\forall
$\Re $	\Re	$\Im$	\Im
$\nabla$	\nabla	$\exists$	\exists
$\partial$	\partial	$\nexists$	\nexists
$\emptyset $	\emptyset	$\varnothing$	\varnothing
$ \wp$	\wp	$\complement$	\complement
$\neg$	\neg	$\cdots$	\cdots
$\square$	\square	$ \surd$	\surd
$\blacksquare$	\blacksquare	$\triangle$	\triangle

Binary Operation/Relation Symbols

Symbol	Latex Syntax	Symbol	Latex Syntax
$\times$	\times	$\cdot$	\cdot
$\div$	\div	$\cap$	\cap
$\cup$	\cup	$\neq$	\neq
$\leq$	\leq	$\geq$	\geq
$\in$	\in	$\perp$	\perp
$\notin$	\notin	$\subset$	\subset
$\simeq$	\simeq	$\approx$	\approx

Math Constructs

Math Construct	Latex Code	Output
Sumation	Sum \sum_{n=1}^{\infty} 2^{-n}=1	Sum $$\sum_{n=1}^{\infty} 2^{-n}=1$$
Product	[\prod_{i=a}^{b} f(i) ]	$$[\prod_{i=a}^{b} f(i) ] $$
Coproduct	\coprod{abc}^{xyz}	$$\coprod{abc}^{xyz}$$
Integral	\int_{abc}^{xyz}	\int_{abc}^{xyz}
Integral Over a Closed Contour	\oint{abc}{xyz}	$$\oint{abc}{xyz}$$
Double integral	\iint_{abc}^{xyz}	$$\iint_{abc}^{xyz}$$
Fracton	\frac{abc}{xyz}	$$\frac{abc}{xyz}$$
Prime	f`	$$f`$$
Square Root	\sqrt{abc}	$$\sqrt{abc}$$
Nth-Root	\sqrt[n]{abc}	$$\sqrt[n]{abc}$$
Overline	\overline{abc}	$$\overline{abc}$$
Underline	\underline{abc}	$$\underline{abc}$$
wide hat	\widehat{abc}	$$\widehat{abc}$$

Matrix

3x3 Matrix

\begin{bmatrix}
\frac{5}{6} & \frac{1}{6} & 0 \\
\frac{5}{6} & 0 & \frac{1}{6} \\
0 & \frac{5}{6} & \frac{1}{6}
\end{bmatrix}

$$\begin{bmatrix} \frac{5}{6} & \frac{1}{6} & 0 \\ \frac{5}{6} & 0 & \frac{1}{6} \\ 0 & \frac{5}{6} & \frac{1}{6} \end{bmatrix}$$

MxN Matrix

$$
A_{m,n} = 
\begin{bmatrix}
a_{1,1} &  a_{1,2} & \cdots & a_{1,n} \\ 
a_{2,1} &  a_{2,2} & \cdots & a_{2,n} \\
\vdots & \vdots & \ddots & vdots \\
a_{m,1} &  a_{m,2} & \cdots & a_{m,n}
\end{bmatrix}
$$

$$ A_{m,n} = \begin{bmatrix} a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\ a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\ \vdots & \vdots & \ddots & vdots \\ a_{m,1} & a_{m,2} & \cdots & a_{m,n} \end{bmatrix} $$

\begin{align}
\sigma &= \sqrt{E\left[ \left(X -\mu\right)^2 \right] } \\
&= \sqrt{E\left[ X^2 \right]+ E\left[\left(-2\mu X\right)\right] +E\left[ \mu^2\right]} \\
&= \sqrt{E\left[ X^2 \right] -2\mu E\left[X\right] + \mu^2}\\
&= \sqrt{E\left[X^2 \right]- 2\mu^2 + \mu^2 }\\
&= \sqrt{E\left[ X^2 \right]-\mu^2}\\
&= \sqrt{E\left[ X^2 \right] - \left(E\left[X\right]\right)^2}
\end{align}

$$ \begin{align} \sigma &= \sqrt{E\left[ \left(X -\mu\right)^2 \right] } \\ &= \sqrt{E\left[ X^2 \right]+ E\left[\left(-2\mu X\right)\right] +E\left[ \mu^2\right]} \\ &= \sqrt{E\left[ X^2 \right] -2\mu E\left[X\right] + \mu^2}\\ &= \sqrt{E\left[X^2 \right]- 2\mu^2 + \mu^2 }\\ &= \sqrt{E\left[ X^2 \right]-\mu^2}\\ &= \sqrt{E\left[ X^2 \right] - \left(E\left[X\right]\right)^2} \end{align} $$