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.
- Setting the Stage
- Elements of Style for Proofs
- Productive Failure and Productive Struggle BMX Video
- Problem Collection for Mathematical Reasoning
- Oliver's solution to Problem 64
- Quiz 1
- Quiz 2
- Quiz 3
- Quiz 4
- Quiz 5
- Quiz 6
- Quiz 7
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?
Dana C. Ernst
Mathematics & Teaching
Northern Arizona University
Flagstaff, AZ
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Current Courses
MAT 431: Intro to Analysis
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 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.