## Lectures

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

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
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

#### 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.

## Resources

• ### Puzzle Boards

Make your own Swap and 15-puzzle
• ### Puzzle Templates

Use these templates in your homework assignments.
• ### SageMath Demos

Either view using Jupyter viewer , download the Jupyter notebook file (.ipynb) , or run on CoCalc
• SageMath Intro:
• Lights Out:
• Integers:
• ### Final Checklist

End of course learning outcomes.

final-checklist.pdf