In order to receive my Master's degree I needed to give a presentation to display my ability to read and understand mathematics. The topic I chose was an interesting dilemma known as the Banach - Tarski Paradox. The idea behind this paradox can be easily explained by the following. Any pea sized ball can be cut up into a finite number of pieces, the pieces can then be reassembled, after rotation, into a ball the size of the earth. In order to prepare for the presentation I took extensive notes which I have since polished up and saved in PDF format for your viewing pleasure.
If you find any typos or other errors please let me know.
Enjoy