sourece:http://www.quora.com/Python-programming-language-1/What-are-some-interesting-things-to-do-with-Python
Python (programming language):

What are some interesting things to do with Python?

Siddharth Verma
Siddharth Verma
316 upvotes by Ashish Gahlot, Mahamadou Lawali, Prabhmanmeet Singh, (more)
First of all, congratulations for learning Python. Now you should take the next steps and learn how to write ‘pythonic’ code. These links will help you in this endeavour.

Code Like a Pythonista: Idiomatic Python
The Hitchhiker’s Guide to Python
Hidden features of Python

Install Jupyter and the future of IPython on your system. Its a great tool for python programmers. All you will be needing is a ‘?’ to access the docs, once you install ipython. And if you write your code in vim then here is a handy plugin davidhalter/jedi-vim.

Next up, as the description says you want to learn Big Data and Machine Learning. Now the getting the data part is as important as learning the algorithms involved. So, the logical step would be to learn how to scrape data.

You should start off with this video tutorial.
video lecture

Its pretty long but you will end up learning the standrd libraries involved in scraping data. You should also go through Scrapy and the Requests library. Both of them are pretty amazing.

A Fast and Powerful Scraping and Web Crawling Framework
Requests: HTTP for Humans

Here’s a great course that you should go through

CS109 Data Science

Finally we come to the algorithms involved in machine learning.
Here’s a great read to get you started

Programming Collective Intelligence: Building Smart Web 2.0 Applications: Toby Segaran: 9780596529321: Amazon.com: Books

This book will introduce you to all the major algorithms involved. There is no mathematics involved, but it serves as a great introductory book. It contains all the implemenatations in python. For advancing your knowledge you can take up these courses

CS1156x Course Info | edX
Page on coursera.org

Now you can use your gained prowess to create a web application that involves machine learning. The best way, according to me, will be to pick up Flask (A Python Microframework). Don’t get confused by the ‘Micro’, you can create anything with flask. It has some great documentation along with a lot of terrific addons that will help you in creating the web app.

And when you are done, you can show the world your baby by hosting it on pythonanywhere.comHost, run, and code Python in the cloud: PythonAnywhere.

Lastly, I would like to say, read as much docs as possible, as these are well managed and great source of information. And if you get stuck anywhere then just ask, python has a great community which will help you in every way possible.

Happy Coding.