2. Teaching
3. MAT511
4. Materials

Problem Sequence

We will not be using a traditional textbook this semester, but rather a problem sequence adopted for an inquiry-based learning (IBL) approach to abstract algebra. The problem sequence will be written by me on the fly. The problems will be released incrementally.

• Problem Sequence for MAT 511 (PDF)

I will not be covering every detail of the notes 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 of the notes 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?

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)

Exams

Below are links to take-home exams. If you are interested in using LaTeX to type up your solutions, simply replace .pdf with .tex in the URL.

• Exam 1 (PDF) (Due by 11:59PM on Tuesday, October 5)
• Exam 2 (Part 2) (PDF) (Due by start of class on Wednesday, November 17)
• Final Exam (Part 2) (PDF) (Due by 4pm Thursday, December 9)