We’ll use this page to keep track of what has happened each day in class. It won’t contain any of the nitty-gritty details, but will instead serve to summarize what has transpired each day.

Week 1

  • Monday, August 27: First day! The first few minutes of class were devoted to me attempting to learn names. I think I got them all! Next, I summarized what to expect from the course, toured the the course webpage, and summarized a few items on the syllabus. With the time we had left, we discussed Problem 1 from the Problem Collection. ZK, NZ, and WS volunteered to discuss their approaches to Problem 1.
  • Wednesday, August 29: We had a great second day! After fielding a few questions about the syllabus and reminding students about the day-to-day structure, we divided the class up into 8 small groups, each tasked with discussing one of the homework problems. We had ST/JT, ER/JS, JJ/AP, RH presented their proposed solutions to Problems 2, 3, 5(b), and 5(c) respectively. We will wrap up Problems 4 and 5(a) on Friday.
  • Friday, August 31: We spent the first 10-15 minutes discussing growth vs fixed mindset, grit, and productive failure. Next, we had GM, HO, WC, and JM present Problems 5(a), 6, 7, and 4, respectively. I think we will revisit Problem 4 (Sunny Day Juice Stand) to make sure everyone is up to speed and to see alternate approaches.

Week 2

  • Monday, September 3: Labor Day! No classes.
  • Wednesday, September 5: We kicked off with some discussion of the upcoming quiz and then I revisited Problem 4 (Sunny Day Juice Stand). Next we had CB, CC, and BC present Problems 8, 9, and 11. We ran out of time for a thorough discussion of Problem 10, so we will come back to that one next week.
  • Friday, September 7: The students took Quiz 1.

Week 3

  • Monday, September 10: After a little chit chat, we split the class up into 8 small groups, where each group was tasked with coming to consensus on two of the assigned problems. After some time, we had AP, SW, RH, and JJ present Problems 10, 12, 13, and 14, respectively. We didn't quite have enough time to do Problem 14 justice, so we will revisit this one next time.
  • Wednesday, September 12: After handing back Quiz 1, I revisited Problems 4 and 14. Nex, we jumped into presentations. We had KW, KN, YF, JH, JJ, NZ, DH, SK, WC, and JM present Problems 15(a), 15(b), 15(c), 16, 17(a), 17(b), 17(c), 17(d), 17(e), and 18, respectively. Dang, we covered a lot.
  • Friday, September 14: We had JH, KW, DH, CC, AP, and RH volunteer to present Problems 19(a), 19(b), 19(c), 20, 21, and 22, respectively.

Week 4

  • Monday, September 17: I'm not sure everyone was as entertained as I was today. I really enjoyed the conversation. We had CC/WC/YF, KN, ER/ZK, and HO/ZK present Problems 23, 24, 25, and 26, respectively. As expected, Problems 23 and 26 generated some passionate discussion.
  • Wednesday, September 19: We devoted the first few minutes to making sure everyone was up to speed on the problems we were about to discuss. Then we briefly revisited Problem 26. Next, we split the class up into several small groups, each tasked with discussing two of the day's problems. After a few minutes, we had AS, YF, SK, and ST present Problems 29, 30(visual), 30(algebraic), and 27, respectively. With the few minutes we had left, I very quickly summarized Problem 28.
  • Friday, September 21: The students took Quiz 2.

Week 5

  • Monday, September 24: We spent a few minutes revisiting Problem 28 and then we divided into small groups. We had SK/JJ, WC/YF, and CB present their proposed solutions to Problems 31, 32, and 33, respectively.
  • Wednesday, September 26: Lots of cool stuff happened today. We had CB, HO, BC/ST, and NZ present Problems 34(algebraic), 34(visual), 35, and 36, respectivley. Typically, no one comes up with a solution for the visual proof for Problem 34, but HO pretty much had it. Also, rarely does anyone have a complete solution for Problem 36, but NZ nailed it.
  • Friday, September 28: After handing back Quiz 2, we spent some time discussing solutions to Problems B1 and B2 from the quiz. Next, we had JS/WC and GC/ER present Problems 37 and 38, respectively. We ran out of time for Problem 39, so we will kick off with that one next time.

Week 6

  • Monday, October 1: We had GC/ZK/RH, JH, and HO/WC present Problems 39, 40, and 41, respectively.
  • Wednesday, October 3: After revisiting Problem 39, NZ presented an alternative solution to Problem 41 and then we agreed that his solution could also be made to work for Problem 40. Next, we had JM and AS present Problems 42 and 43, respectively. With the few minutes we had left, we briefly discussed the next two problems.
  • Friday, October 5: The students took Quiz 3.

Week 7

  • Monday, October 8: After some stories about mountain lions, bears, and lightning, we had AP/SK and JM present Problems 44 and 45, respectively.
  • Wednesday, October 10: We had BC and KW/YF/CC present Problems 47 and 48. We didn't get to Problem 46, but we will come back to it on Friday.
  • Friday, October 12: Another productive day. We had WS, JJ, BC, and JT present Problems 46, 49, 50, and 51, respectively.

Week 8

  • Monday, October 15: We divided the class up into six small groups and each group was tasked with writing up at least two of the problems that were due today. After about 15 minutes, we had YF/HO, CC, and AP present Problems 52, 53, and 54, respectively. Along the way, I presented an alternate solution to Problem 52 and discussed the two competing definitions of trapezoid.
  • Wednesday, October 17: We had KN, ER, and CB present Problems 55, 56, and 57, respectively. The first two went fairly quickly and then we discussed Problem 57 for quite a while. I accidentally let the class go 10 minutes early. Oops.
  • Friday, October 19: The students took Quiz 4.

Week 9

  • Monday, October 22: We had JS, JH, and DH present Problems 58, 59, and 60, respectively. All three problems were a team effort, but we got them done.
  • Wednesday, October 24: After time for some groups to discuss problems, we had RH/AP, JS/NZ, and ZK present Problems 61, 62, and 63, respectively
  • Friday, October 26: The students divided themselves into small groups and then spent several minutes discussing their proposed solutions to Problems 64-66. Next, we had CC and RH present Problems 64 and 65, respectively. After this GC presented an alternate solutions to both Problems 64 and 65. The rest of the class period was devoted to losing our minds about Problem 66. We heard from KW, AP, and SK concerning Problem 66. We will spend a few minutes at the beginning of Monday's class revisiting Problem 66.

Week 10

  • Monday, October 29: After revisiting Problem 66, we had BC, CB, KW, and KN/YF present Problems 67(a), 67(b), 68, and 69, respectively.
  • Wednesday, October 31: We had ST, JT, JM, BC, NZ, JJ, CB, WC, and DH present Problem 70(a), Problem 70(b), Problem 71($1\times 3$), Problem 71($1\times 4$), Problem 71($1\times 5$), Problem 71($2\times 2$), Problem 71($2\times 3$), Problem 71($3\times 3$), and Problem 72, respectively.
  • Friday, November 2: The students took Quiz 5.

Week 11

  • Monday, November 5: After dividing the class up into several small groups, we had ER, AS, and YF present Problems 73, 74, and 75, respectively. I was impressed with the quality of all three arguments.
  • Wednesday, November 7: We split the class up into several groups and each group tried to come to consensus on as many of the homework problems as possible. We had KW/AP/JJ, KN/RH/JS, and BC/ST present Problems 76, 77, and 78, respectively.
  • Friday, November 9: We started with JJ showing us an alternative approach to Problem 78. After that, we had JS, CC, CB, GC, and JH present Problems 79(a), 79(b), 79(c), 80, and 81, respectively.

Week 12

  • Monday, November 12: No class due to Veteran's Day.
  • Wednesday, November 14: As we've been doing a lot lately, we split the class up into several small groups, where each group was tasked with coming to consensus about solutions for Problems 82-84. We had CB and RH present Problems 82 and 84, respectively. It appeared no one made much progress on Problem 83, so I sketched the argument at the end of class.
  • Friday, November 16: The students took Quiz 6.

Week 13

  • Monday, November 19: After splitting up into groups, we had DH and JM present Problems 86 and 87, respectively. This was followed by a short discussion of the connection of these problems to the Monty Hall Problem. We wrapped up with a presentation by SK of Problem 85.
  • Wednesday, November 21: Attendance wasn't too bad considering it was the day before Thanksgiving. We had JJ and YF/JJ/AP present Problems 88 and 89, respectively. We also got a start on Problem 90, but didn't quite wrap it up.
  • Friday, November 23: No class due to Thanksgiving break.

Week 14

  • Monday, November 26: After revisiting Problem 90, we had BC present his proposed solution to Problem 91. We also had JS and RH each present their proposed solutions to a modified version of Problem 91.
  • Wednesday, November 28: We had lots of good discussion today, but didn't cover much ground. We had ER and HO/WS/WC present their proposed solutions to Problems 92 and 93. We made good progress on a system for finding a solution for 92, but we sort of fizzled out towards the end. We ended up finding a function that satisfied the constraints, but we came up with it by guessing. There was lots of good discussion about Problem 93 (12 coins), but things got a little chaotic towards the end. We will revisit both of these next week if we have some spare time.
  • Friday, November 30: The students took Quiz 7.

Week 15

  • Monday, December 3: After discussing the basics of induction, we revisited Problem 93 (which has nothing to do with induction). Next, we had ER present Problem 97, which was followed by some short presentations of the $n=2, 3, 4$ cases for Problem 96 by JH, AP, and SK, respectively.
  • Wednesday, December 5: We started off with Problem 95. HO showed how we could circumnavigate my outline and get to the desired conclusion via a much easier approach! I had been hoping to find an easier way to do that problem for a few years now. Yay! Next, AS and ZK did a really nice job showcasing induction by presenting Problems 98 and 99, respectively.
  • Friday, December 7: Last day! I'm miss this group of students. After some discussion of all the things we've accomplished this semester, we divided up into groups of size 2-4 and spread around the room to discuss Problem 100, 101, and 102. We had KN and JT/WS present Problems 100 and 102, respectively. I spent the final few minutes wrapping up Problem 102. Unfortunately, we ran out of time to discuss Problem 101.

Dana C. Ernst

Mathematics & Teaching

  Northern Arizona University
  Flagstaff, AZ
  Google Scholar
  Impact Story

Current Courses

  MAT 411: Abstract Algebra
  MAT 690: Genome Combinatorics

About This Site

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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.