Course Materials
Course Materials
Below is the task sequence for the course. I will incrementally add to this as we go.
- Enumerative Combinatorics (PDF). Note: This PDF should be an accessible document. Please let me know if there are any issues.
- Cards sets for combinatorial structures. Each PDF contains 27 cards. Note: My memory is that there is at least one error that someone mentioned to me that I forgot to fix. Maybe there is a duplicate card or an incorrect rank. If you find the error, please let me know!
- Ballot Paths
- Binary Strings
- Binary Trees
- Cayley Permutations
- Compositions
- Dodger Rooks
- Domino Stacking
- Domino Tilings
- Fraenkel Trees
- Fubini Arrangements
- Increasing Trees
- Integer Partitions
- Knuth Rooks
- Lattice Paths
- Nonattacking Rooks
- Noncrossing Partitions
- Odd Compositions
- Parking Functions
- Pebble Piles
- Penrose Doodles
- Permutations
- Pixel Strips
- Set Partitions
- Sparce Strips
- Starfolks Paths
- Triangulated Polygons
- Unlabeled Trees
Don’t just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?
Miscellaneous Materials
- Setting the Stage (PDF)
- Living Proof
- The Secret to Raising Smart Kids | Carol Dweck (article on Scientific American)
- 7 Things Growth Mindset is Not (article on Turn Around for Children)
- Videos on Growth Mindset and Productive Failure
- Grit: the power of passion and perseverance | Angela Lee Duckworth (6:12 min)
- How to Become a Better Learner | Learner Lab (13:30 min)
- Learning Like a Jungle Tiger | Trevor Ragan (5:23 min, similar to previous video)
- Productive Failure/Struggle Skateboard Video 1 (1:25min)
- Productive Failure/Struggle Skateboard Video 2 (0:40 min)
- Productive Failure/Struggle BMX Video (1:39 min)
- Michael Jordan Failure Commercial (0:32 min)
- Mindsets: Fixed Versus Growth (2:19 min)
- Growth Mindset Animation (3:50 min)
- KhanAcademy interview with Carol Dweck about growth mindset (3:06 min)
- Make Mistakes | Michael Starbird (2:11 min)
- Ira Glass on the Creative Process (1:54 min)
- Productive Failure | Manu Kapur | TEDxLugano (17:28 min)
- The State of Being Stuck | Ben Orlin (blog post on Math with Bad Drawings)
- The Chinese Farmer | Alan Watts (2:26 min)
- Do Schools Kill Creativity? | Ken Robinson (19:22 min)
- The Learner Lab Podcast
- Do Hard Things | The Learner Lab (2:41 min)
- The Subtle Art of the Mathematical Conjecture (article on Quanta Magazine)
- Lessons from My Math Degree That Have Nothing to Do with Math (6 min read on Medium)
- Is Mathematics Invented or Discovered? | Roger Penrose (4:14 min)
- What is Mathematics? The Most Misunderstood Subject (short article by Dr. Robert H. Lewis, Professor of Mathematics, Fordham University)