quicksort visualization

This is a great visualization of the quicksort algorithm:

https://www.youtube.com/watch?v=aXXWXz5rF64

Quicksort (sometimes called partition-exchange sort) is an efficient sorting algorithm, serving as a systematic method for placing the elements of an array in order. Developed by Tony Hoare in 1960, it is still a very commonly used algorithm for sorting. When implemented well, it can be about two or three times faster than its main competitors, merge sort and heapsort.[1]
Quicksort is a comparison sort, meaning that it can sort items of any type for which a "less-than" relation (formally, a total order) is defined. In efficient implementations it is not a stable sort, meaning that the relative order of equal sort items is not preserved. Quicksort can operate in-place on an array, requiring small additional amounts of memory to perform the sorting.
Mathematical analysis of quicksort shows that, on average, the algorithm takes O(n log n) comparisons to sort n items. In the worst case, it makes O(n2) comparisons, though this behavior is rare.

http://en.wikipedia.org/wiki/Quicksort

The Halting Problem

This is a great video that describes the halting problem.


https://www.youtube.com/watch?v=92WHN-pAFCs


What is the halting problem you ask?

In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running or continue to run forever.
Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist. A key part of the proof was a mathematical definition of a computer and program, which became known as a Turing machine; the halting problem is undecidable over Turing machines. It is one of the first examples of a decision problem.

http://en.wikipedia.org/wiki/Halting_problem

Easily distributing a parallel IPython Notebook on a cluster

I haven't tried this yet, but it is high on my todo list:

http://twiecki.github.io/blog/2014/02/24/ipython-nb-cluster/

Natural Language Processing with Python

This is a book about Natural Language Processing. By "natural language" we mean a language that is used for everyday communication by humans; languages like English, Hindi or Portuguese. In contrast to artificial languages such as programming languages and mathematical notations, natural languages have evolved as they pass from generation to generation, and are hard to pin down with explicit rules. We will take Natural Language Processing — or NLP for short — in a wide sense to cover any kind of computer manipulation of natural language. At one extreme, it could be as simple as counting word frequencies to compare different writing styles. At the other extreme, NLP involves "understanding" complete human utterances, at least to the extent of being able to give useful responses to them.
Online book:
http://www.nltk.org/book/ch00.html

NLTK 3.0 documentation:

http://www.nltk.org/

Python for Data Science

This short primer on Python is designed to provide a rapid "on-ramp" to enable computer programmers who are already familiar with concepts and constructs in other programming languages learn enough about Python to facilitate the effective use of open-source and proprietary Python-based machine learning and data science tools.
http://nbviewer.ipython.org/github/gumption/Python_for_Data_Science/blob/master/1_Introduction.ipynb

The Great, Big List of LATEX Symbols

LATEX symbols reference:

http://www.rpi.edu/dept/arc/training/latex/LaTeX_symbols.pdf

Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers

While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted.
Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics.
From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.

http://www.amazon.com/Enlightening-Symbols-History-Mathematical-Notation/dp/0691154635/

Article about the book:

http://www.theguardian.com/science/alexs-adventures-in-numberland/2014/may/21/notation-history-mathematical-symbols-joseph-mazur