Tutorial Brief

Video Tutorial: https://www.youtube.com/user/roshanRush

Jupyter has an implementation of markdown language that can be used in in markdown cells to create formatted text and media documentation in your notebook. LaTeX is also implemented to create high quality mathematical typeset.

Markdown

Headings

H1

H2

H3

H4

H5

H6

Code:

#H1
##H2
###H3
####H4
#####H5
######H6

Alternative Headings

Heading 1

Heading 2

Code:

Heading 1
=========

Heading 2
---------

Font Styles

Bold Font or Bold Font

Italic or Italic Font

~~Scratched Text~~

Markdown doesn't support underline. but you can do that using HTML Text

Code:

**Bold Font** or __Bold Font__

*Italic* or _Italic Font_

~~Scratched Text~~

Markdown doesn't support underline. but you can do that using HTML <u>Text</u>

Lists

item
item
- subitem
- subitem
item

item
item
1. sub item
2. sub item
item

Code:

- item
- item
 - subitem
 - subitem
- item


1. item
2. item
 1. sub item
 2. sub item
3. item

Links

http://www.github.com/

Github

Code:

http://www.github.com/

[Github](http://www.github.com/)

Images

Code:

![Turing's Device](http://www.google.com/logos/2012/turing-doodle-static.jpg "Alan Turing's 100th Birthday")

Quotes

Why, oh why, Javascript??? Wars, famine, planetary destruction... I guess as a species, we deserve this abomination...

Fernando Perez

Code:

> Why, oh why, Javascript??? Wars, famine, planetary destruction... I guess as a species, we deserve this abomination...
>
> [Fernando Perez](https://twitter.com/fperez_org)

Horizontal Line

Code:

---

Tables

Tables	Are	Cool
col 3 is	right-aligned	1600
col 2 is	centered	12
zebra stripes	are neat	1

Code:

| Tables        | Are           | Cool  |
| ------------- |:-------------:| -----:|
| col 3 is      | right-aligned |  1600 |
| col 2 is      | centered      |    12 |
| zebra stripes | are neat      |     1 |

HTML

You can render almost any HTML code you like.

Code:

<b>You</b> can <i>render</i> almost any <span style="color:red;">HTML</span> code you <u>like</u>.

Code

You can add in line code like this import numpy as np

Or block code:

Python Code:

x = 5
print "%.2f" % x

Java Script Code:

x = 5
alert(x);

Code:

Python Code:
```python
x = 5
print "%.2f" % x
```

Java Script Code:
```javascript
x = 5
alert(x);
```

LaTeX

References:

LaTeX is a large typeset system for scientific documentation which symbols for mathematics, statistics, physics, quantum mechanics, and computer science. It is beyond the scope of this tutorial to cover everything, but we will go over the basics of writing high quality mathematical equations using LaTeX.

You can use LaTeX in line by like this $y = x^2$ or in block like this $$y = x^2$$

Code:

You can use LaTeX in line by like this $y = x^2$ or in block like this $$y = x^2$$

Operators:

Add:
- $x + y$
Subtract:
- $x - y$
Multiply
- $x * y$
- $x \times y$
- $x . y$
Divide
- $x / y$
- $x \div y$
- $\frac{x}{y}$

Code:

- Add:
 - $x + y$
- Subtract:
 - $x - y$
- Multiply
 - $x * y$
 - $x \times y$ 
 - $x . y$ 
- Divide
 - $x / y$
 - $x \div y$
 - $\frac{x}{y}$

Relations

$\pi \approx 3.14159$
${1 \over 0} \neq \inf$
$0 < x > 1$
$0 \leq x \geq 1$

Code:

- $\pi \approx 3.14159$
- ${1 \over 0} \neq \inf$
- $0 < x > 1$
- $0 \leq x \geq 1$

Fractions

$^1/_2$
$\frac{1}{2x}$
${3 \over 4}$

Code:

- $^1/_2$
- $\frac{1}{2x}$
- ${3 \over 4}$

Greek Alphabet

Small Letter	Capical Letter	Alervative
$\alpha$ `\alpha`	$A$ `A`
$\beta$ `\beta`	$B$ `B`
$\gamma$ `\gamma`	$\Gamma$ `\Gamma`
$\delta$ `\delta`	$\Delta$ `\Delta`
$\epsilon$ `\epsilon`	$E$ `E`	$\varepsilon$ `\varepsilon`
$\zeta$ `\zeta`	$Z$ `Z`
$\eta$ `\eta`	$H$ `H`
$\theta$ `\theta`	$\Theta$ `\Theta`	$\vartheta$ `\vartheta`
$\iota$ `\zeta`	$I$ `I`
$\kappa$ `\kappa`	$K$ `K`	$\varkappa$ `\varkappa`
$\lambda$ `\lambda`	$\Lambda$ `\Lambda`
$\mu$ `\mu`	$M$ `M`
$\nu$ `\nu`	$N$ `N`
$\xi$ `\xi`	$Xi$ `\Xi`
$\omicron$ `\omicron`	$O$ `O`
$\pi$ `\pi`	$\Pi$ `\Pi`	$\varpi$ `\varpi`
$\rho$ `\rho`	$P$ `P`	$\varrho$ `\varrho`
$\sigma$ `\sigma`	$\Sigma$ `\Sigma`	$\varsigma$ `\varsigma`
$\tau$ `\tau`	$T$ `T`
$\upsilon$ `\upsilon`	$\Upsilon$ `\Upsilon`
$\phi$ `\phi`	$\Phi$ `\Phi`	$\varphi$ `\varphi`
$\chi$ `\chi`	$X$ `X`
$\psi$ `\psi`	$\Psi$ `\Psi`
$\omega$ `\omega`	$\Omega$ `\Omega`

Power & Index

You can add power using the carrot ^ symbol. If you have more than one character you have to enclose them in a curly brackets.

$$f(x) = x^2 - x^{1 \over \pi}$$

For index you can use the underscore symbol:

$$f(X,n) = X_n + X_{n-1}$$

Code:

$$f(x) = x^2 - x^{1 \over \pi}$$
$$f(X,n) = X_n + X_{n-1}$$

Roots & Log

You can express a square root in LaTeX using the \sqrt and to change the level of the root you can use \sqrt[n] where n is the level of the root.

$$f(x) = \sqrt[3]{2x} + \sqrt{x-2}$$

To represent a log use \log[base] where base is the base of the logarithmic term.

$$\log[x] x = 1$$

Code:

$$f(x) = \sqrt[3]{2x} + \sqrt{x-2}$$

Sums & Products

You can represent a sum with a sigma using \sum\limits_{a}^{b} where a and b are the lower and higher limits of the sum.

$$\sum\limits_{x=1}^{\infty} {1 \over x} = 2$$

Also you can represent a product with \prod\limits_{a}^{a} where a and b are the lower and higher limits.

$$\prod\limits_{i=1}^{n} x_i - 1$$

Code:

$$\sum\limits_{x=1}^{\infty} {1 \over x} = 2$$
$$\prod\limits_{i=1}^{n} x_i - 1$$

Statistics

To represent basic concepts in statistics about sample space S, you can represent a maximum:

$$max(S) = \max\limits_{i: S_i \in S} S_i$$

In the same way you can get the minimum:

$$min(S) = \min\limits_{i: S_i \in S} S_i$$

To represent a binomial coefficient with n choose k, use the following:

$$\frac{n!}{k!(n-k)!} = {n \choose k}$$

for :

Code:

$$max(S) = \max\limits_{i: x_i \in \{S\}} x_i$$
$$min (S) = \min\limits_{i: x_i \in \{S\}} x_i$$
$$\frac{n!}{k!(n-k)!} = {n \choose k}$$

Calculus

Limits are represented using \lim\limits_{x \to a} as x approaches a.

$$\lim\limits_{x \to 0^+} {1 \over 0} = \infty$$

For integral equations use \int\limits_{a}^{b} where a and b are the lower and higher limits.

$$\int\limits_a^b 2x \, dx$$

Code:

$$\lim\limits_{x \to 0^+} {1 \over 0} = \inf$$
$$\int\limits_a^b 2x \, dx$$

Function definition over periods

Defining a function that is calculated differently over a number of period can done using LaTeX. There are a few tricks that we will use to do that:

The large curly bracket \left\{ ... \right. Notice it you want to use ( or [ you don't have to add a back slash(\). You can also place a right side matching bracket by replacing the . after \right like this .right}
Array to hold the definitions in place. it has two columns with left alignment. \begin{array}{ll} ... \end{array}
Line Breaker \\
Text alignment box \mbox{Text}

$f(x) =\left\{\begin{array}{ll}0 & \mbox{if } x = 0 \\{1 \over x} & \mbox{if } x \neq 0\end{array}\right.$

Code:

$f(x) =
\left\{
    \begin{array}{ll}
        0  & \mbox{if } x = 0 \\
        {1 \over x} & \mbox{if } x \neq 0
    \end{array}
\right.$

Note: If you are planning to show your notebook in NBViewer write your latex code in one line. For example you can write the code above like this:

$f(x) =\left\{\begin{array}{ll}0  & \mbox{if } x = 0 \\{1 \over x} & \mbox{if } x \neq 0\end{array}\right.$

Quick Quiz (Normal Distribution)

Try to replicate the Normal Distribution formula using LaTeX. If you solve it, leave the LaTeX code in the comments below. $Don't\ cheat$.

$$P(x,\sigma,\mu) = \frac{1}{{\sigma \sqrt {2\pi } }}e^{{-(x - \mu)^2 } / {2\sigma ^2}}$$

Tips to help with the quiz:

$\mu$ is \mu
$\sigma$ is \sigma
$e$ is e