Lectures

A complete set of fully illustrated course notes, in book format, is available here.

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These notes will consist of a more detailed discussion of what was done in the classroom. I intend the classroom to be a place to explore the ideas and interact with puzzles.

Lectures by Topic

# name
0 Intro to Course slides from class (pdf) recording
1 Permutation Puzzles Introduction   recording
2 A Bit of Set Theory notes template (pdf)
code from book: (view) (.ipynb) 		recording
B Basic Properties of Integers:
Extended Euclidean Algorithm
and Euler's $\phi$-function		 code from book: (view) (.ipynb) (SMC ) recording
3 Permutations notes for class (pdf)
code from book: (view) (.ipynb) 		recording
recording
4 Permutations: Cycle Form notes for class (pdf)
code from book: (view) (.ipynb) 		recording
5 From Puzzle to Permutations:
Representing Puzzles by Permutations		 notes for class (pdf)
code from book: (view) (.ipynb) 		recording
recording
6 Permutations: Products of 2-Cycles notes for class (pdf)
recording
7 Permutations: The Parity Theorem notes for class (pdf)
recording(1) recording(2)
8 Permutations: $A_n$ and $3$-Cycles notes for class (pdf)
recording
9 The $15$-Puzzle notes for class (pdf)
recording(1)
recording(2)
10 Groups notes for class (pdf)
code from book: (view) (.ipynb) 		recording(1)
recording(2)
Midterm 1 Review Session recording
11 Subgroups notes for class (pdf)
recording(1)
recording(2)
12 Puzzle Groups notes for class (pdf)
code from book: (view) (.ipynb)		 recording
13 Permutations: Commutators notes for class (pdf)


recording
14 Permutations: Conjugates notes for class (pdf)
recording
15 The Oval Track Puzzle notes for class (pdf)
recording(1)
recording(2)
16 The Hungarian Rings Puzzle    
17 Partitions and Equivalence Relations notes for class (pdf)
recording
18 Cosets and Lagrange's Theorem notes for class (pdf)
recording
19 Rubik's Cube:
Beginnings - A Solution Strategy		 notes for class (pdf)
5-step solution guide (pdf)
recording
Midterm 2 Review Session recording
20 Rubik's Cube:
Fundamental Theorem of Cubology		 notes for class (pdf)
CubeTwister
stickers:
orientation markings
orientation numbers
Identification Numbers: (view) (.ipynb) 		recording(1)
recording(2)
last example
additional examples
21 Rubik's Cube: Subgroups notes for class (pdf) recording
22 Symmetry and Counting I:
The Orbit-Stabilizer Theorem		    
23 Symmetry and Counting II:
Burnside's Theorem		    
24 Lights Out Puzzle matrix grid boards
code from book: (view) (.ipynb) (SMC )
 
A SageMath - An Introduction code from book: (view) (.ipynb) (SMC )  
X Futurama Episode:
The Prisoner of Benda		 Futurama Mind Swap Puzzle
notes (pdf)		 recording

References

Books: Rubik's cube and related math:

Books on Algebra: Group Theory (Permutations), Linear Algebra:

Web sites:

  • Jaaps Puzzle Page: Extensive information on twisty puzzles.

  • Cube 20: Twenty moves suffice to solve Rubik's cube.

  • Kociemba: Designer of the two-phase algorithm which most programs use to solve the cube.

SageMath:

Videos:

Articles for Further Reading about Group Theory:

Resources

Other files and images that you may find useful.