Lecture notes on the mathematics of the Rubik's cube

I've written some lecture notes for the Math 485 course Mathematics of the Rubik's cube. The latest "latex" version is nicer (better looking stylistically and has more material) and is now available on the web. For that, go to my books page. The book these notes eventually became has been published by Johns Hopkins University Press: Adventures in group theory. (All royalties go directly to charity - EII.)

The older ascii version (below) can also be downloaded. They assume a high school mathematics background, some mathematical ability, and that you have a Rubik's cube. For more (online) background on group theory, see for example Prof Gaglione's Introduction to group theory or the book Applied abstract algebra.

• Introduction
• chapter 0 : Logic
• chapter 1 : Functions on sets
• chapter 2 : Permutations
• chapter 3 : Permutation puzzles
  • part 1
  • part 2
  • part 3,
• chapter 4 : Some solution strategies
• chapter 5 : Groups, I
• chapter 6 : Orbits, actions and cosets
• chapter 7 : Cayley graphs and God's algorithm
• chapter 8 : Symmetry groups of the Platonic solids
• chapter 9 : Groups, II
• chapter 10 : Structure of the Rubik's cube group
• chapter 11 : Rubika esoterica
• chapter 12 : Realizing PGL(2,F5) inside the Rubik's cube group
• References
  

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  Last modified 5-19-2003

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