Course Materials
Below you will find notes and resources that we will utilize. We will add to the problem collection as the semester progresses.
- Problem Collection for Mathematical Reasoning (PDF)
- 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)
- Quizzes:
- Solution for 7 spheres in the Martian Artifacts Problem (Problem 73) (PDF)
- Solution top player problem (Problem 96) (PDF)
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?
Dana C. Ernst
Mathematics & Teaching
Northern Arizona University
Flagstaff, AZ
Website
928.523.6852
Twitter
Instagram
Facebook
Strava
GitHub
arXiv
ResearchGate
LinkedIn
Mendeley
Google Scholar
Impact Story
ORCID
Current Courses
MAT 226: Discrete Math
MAT 526: Combinatorics
About This Site
This website was created using GitHub Pages and Jekyll together with Twitter Bootstrap.
Unless stated otherwise, content on this site is licensed under a Creative Commons Attribution-Share Alike 4.0 International License.
The views expressed on this site are my own and are not necessarily shared by my employer Northern Arizona University.
The source code is on GitHub.
Land Acknowledgement
Flagstaff and NAU sit at the base of the San Francisco Peaks, on homelands sacred to Native Americans throughout the region. The Peaks, which includes Humphreys Peak (12,633 feet), the highest point in Arizona, have religious significance to several Native American tribes. In particular, the Peaks form the Diné (Navajo) sacred mountain of the west, called Dook'o'oosłííd, which means "the summit that never melts". The Hopi name for the Peaks is Nuva'tukya'ovi, which translates to "place-of-snow-on-the-very-top". The land in the area surrounding Flagstaff is the ancestral homeland of the Hopi, Ndee/Nnēē (Western Apache), Yavapai, A:shiwi (Zuni Pueblo), and Diné (Navajo). We honor their past, present, and future generations, who have lived here for millennia and will forever call this place home.