Happy 200th Birthday George Boole!

Today (November 2, 2015) is the 200th Birthday of the mathematician George Boole.  To celebrate, here is a fantastic song and video created specially for this occasion.

“The Mathematician – The Bould Georgie Boole”
Performed by The Arthur Céilí Band, featuring Jim Flanagan & Mike Simpson

You can also download the song so you can listen to it all the time here:

Besides being a lot of fun, this song and video is a great little biography.  Of course, if you want more info, you can check out George Boole’s Wikipedia page:
https://en.wikipedia.org/wiki/George_Boole

That being said, there is one story I would like to point out here.  George Boole worked in many areas, but perhaps the most important area today is what we now call Boolean algebra  (https://en.wikipedia.org/wiki/Boolean_algebra).

Introduced by Boole in the around 1850, it was not until the 1930’s that an undergraduate at the University of Michigan named Claude Shannon realized this hitherto abstract theory could be applied to electromechanical relays.   Shannon went on to write a master’s thesis on this topic at MIT.  Since then Boolean algebra has become the basis of digital circuit design.

Here is my challenge to all you undergraduates out there: can you make a connection like Shannon and use a seemingly totally abstract mathematical theory to model some real world phenomena?  Maybe you too can make some revolutionary discovery!

From the Department of “I have too much time and I want to waste some”, here is a fabulous game that you can check out. The beauty of it is that you figure out the rules as you go (the silly comments when you clear each level are just a bonus), and some mathematician (Jens Massberg) just wrote a paper on the game showing it is NP-hard.

and here is the link to the article on NP-completeness:

http://arxiv.org/abs/1408.3645

What is NP-hard? Well… here you go:

http://en.wikipedia.org/wiki/NP-hard

Some cheap textbook alternatives.

The high price of textbooks is very much on the minds of most students. While these books have not quite been adopted in the standard curricula at most schools, these are still good options for self study, or to suggest to your instructors! The following link gives a sample of many cheap or free textbooks approved by a board of mathematicians at AIM (American Institute of Mathematics). Most of these books are free to download as PDFs.

http://aimath.org/textbooks/approved-textbooks/

TED Math talks.

TED is a nonprofit devoted to spreading ideas, usually in the form of short, powerful talks (18 minutes or less). TED began in 1984 as a conference where Technology, Entertainment and Design converged, and today covers almost all topics — from science to business to global issues — in more than 100 languages.

Here is a collection of some entertaining and excellent TED talks in mathematics.

http://blog.ted.com/2012/11/21/8-math-talks-to-blow-your-mind/

Enjoy!!

The Perfect Cipher: the one time pad.

Is there such a thing as a perfect cipher? Yes, but using it is rather impractical. But it is nice to know such a thing exists. Here is a nice explanation of the one time pad.