Monday, January 24, 2011

Draft of Second half of Chapter 16 is available

The second half of Chapter 16, on field extensions and formal power series, is available. These two sections will be expanded in the near future to include more examples and theory.

http://applied-discrete-structures.wiki.uml.edu/Chapter+16

Wednesday, January 12, 2011

Bulgarian Solitaire follow-up


I played Bulgarian Solitaire with math teachers at Lawrence High on January 11, 2011. What's Bulgarian Solitaire? See http://en.wikipedia.org/wiki/Bulgarian_solitaire , although we used coins instead of cards.

Three follow-up items:



  • We didn't get a chance to discuss "Garden of Eden" configurations, but I wanted to point out how this is such a great name. A Garden of Eden position is one that can't be reached from any other configuration in the game. The name does such a good job of capturing the idea behind it!
  • Unlike positions that create one-cycles, which we discussed and seem to be rare, there seem to be lots of Gardens of Eden as you increase the number of coins/cards in the game. For example (2,2,2,2,.....) where there are at least four 2's is Garden of Eden. Do you see why?
  • Technology. You get some interesting macroscopic information about what happens when you change the number of coins by generating state graphs like the one you see above for 10 coins.

    I've prepared a Mathematica Notebook that has more images. They can be viewed using Mathematica or the free Mathematica Player application.

Draft of Chapter 14: Modoids and Automata

A draft of Chapter 14 is now available at http://applied-discrete-structures.wiki.uml.edu/Monoids+and+Automata.

Thursday, January 6, 2011

Draft of Chapter 15

Chapter 15: Group Theory and Applications, is now available. It needs proofreading. Let me know if there are any typos or if you suggest any changes. Plans for the future include an additional section to this chapter that discusses CAS implementations of groups.

http://applied-discrete-structures.wiki.uml.edu/Chapter+15

Ken