A few semesters ago we launched a course for mathematics majors, called MAT 220: Introduction to Mathematical Reasoning. The focus of the course is on reasoning and communication through problem solving and written mathematical arguments in order to provide students with more experience and training early in their university studies. The goal is for the students to work on interesting yet challenging multi-step problems that require almost zero background knowledge. The hope is that students will develop (or at least move in the direction of) the habits of mind of a mathematician. The problem solving of the type in this course is a fundamental component of mathematics that receives little focused attention elsewhere in most mathematics programs. I love teaching this course!
This past semester I taught the course for the second time. You can find the syllabus, list of problems, etc. for the Spring 2017 semester by going here. On the students’ final exam, I asked them which problem was their favorite from the semester. Below is the list of problems that they mentioned including the number of votes that each received. The level of difficulty of the problems covers the spectrum. Some of these are not easy. Have fun playing!
A while back I wrote a similar post that highlighted 15 fun problems from the first time I taught the course. You’ll notice that there is some overlap between the two lists.
Mathematics & Teaching
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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.