2. Teaching
3. MAT226
4. Materials

Introduction to Discrete Mathematics

Our textbook for the semester is Introduction to Discrete Mathematics. Early versions of the book were originally written by NAU retired mathematics professor Dr. John Hagood (usuing the title MAT 226 Discrete Mathematics). Dr. Hagood was gracious enough to pass the source of the book along and has granted me permission to modify the content. Current iterations of the book are now my responsibility. The book is available as a freely-assessible PDF. Since I will be tweaking the book as we go, chapters will be released incrementally.

• Title Page and Front Matter
• Chapter 1: Sets and Counting Principles
• Chapter 2: Functions
• Chapter 3: Permutations
• Chapter 4: Combinations
• Chapter 5: The Binomial Theorem
• Chapter 6: Pigeonhole Principle
• Chapter 7: Principle of Inclusion and Exclusion
• Chapter 8: Mathematical Induction
• Chapter 9: Sequences and Recurrence Relations
• Chapter 10: Introduction to Graph Theory
• Chapter 11: Additional Graph Theory

I will not be covering every detail of the textbook and the only way to achieve a sufficient understanding of the material is to be digesting the reading in a meaningful way. You should be seeking clarification about the content whenever necessary by asking questions. Here’s one of my favorite quotes about reading mathematics.

Don’t just read it; fight it! Ask your own questions, 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?

If you’ve found an error or have suggestions for improvements, please let me know.

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 (1:46 min)
  • 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
• 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)