Course Materials
Below you will find notes and handouts that we have used in class, as well as some other useful stuff. We will add to the problem collection as the semester progresses.
- Problem Collection for Mathematical Reasoning (PDF)
- Setting the Stage (PDF)
- Elements of Style for Proofs (PDF)
- Videos on Growth Mindset and Productive Failure
- Productive Failure/Struggle Skateboard Video (1:46 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)
- Grit: the power of passion and perseverance | Angela Lee Duckworth (6:12 min)
- KhanAcademy interview with Carol Dweck about growth mindset (3:06 min)
- Make Mistakes | Michael Starbird (2:11 min)
- Learning Like a Jungle Tiger | Trevor Ragan (5:23 min)
- Ira Glass on the Creative Process (1:54 min)
- The Chinese Farmer | Alan Watts (2:26 min)
- The Secret to Raising Smart Kids | Carol Dweck (article on Scientific American)
- Do Schools Kill Creativity? | Ken Robinson (19:22 min)
- Lessons from My Math Degree That Have Nothing to Do with Math (6 min read on Medium)
- Pictures of board work that we ran out of time to discuss. Note: You should not assume that the solutions/proofs posted below are valid or sufficient.
- Problem 5(a) (version 1), Problem 5(a) (version 2)
- Quiz 1 (PDF)
- Quiz 2 (PDF)
- Quiz 3 (PDF)
- Quiz 4 (PDF)
- Quiz 5 (PDF)
- Quiz 6 (PDF)
- Quiz 7 (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
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Current Courses
MAT 226: Discrete Math
MAT 526: Combinatorics
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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.