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 26: 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, I split the class up into small groups and them work on a few variations of the mind-swapping problem from the TV show Futurama. Great first day.
  • Wednesday, August 28: First day of student presentations went great! After discussing questions on the syllabus, we divided the class up into several small groups. Each groups was tasked with coming to consensus on a proposed solution to one of the assigned homework problems. We had BM/DE, DW, and MR present Problems 4, 3, 2, respectively. We'll get caught up on Problem 1 next time.
  • Friday, August 30: After discussing the upcoming homework, we jumped into student presentations. We had CS, HT, and MR present Problems 1, 5, and 6, respectively. I'm really happy with how things are going.

Week 2

  • Monday, September 2: Labor Day, no class.
  • Wednesday, September 4: Today was one of those days where I was reminded how awesome my job is. We kicked off by discussing the videos on grit and growth mindset I asked the students to watch. Perhaps I ran my mouth too much, but we had a nice discussion nonetheless. After discussing the videos, I asked the class to split up into groups of size 2-3. The intention was for people to work with people they hadn't interacted with much yet. Each group was tasked with discussing at least two parts of Problem 7 (soul swapping). We had DM/AS and TB present parts (a) and (b), respectively. It was nice to see a variety of approaches to notation. We'll catch up on parts (c) and (d) next time.
  • Friday, September 6: Another action-packed day. After discussing the upcoming quiz, we had BM and AL present parts (c) and (d) from Problem 7, which were left over from last time. I then spent a little bit of time discussing the big picture of the Futurama Theorem. This was followed by discussion about Problem 8 that was led by AC and MB. We wrapped with a quick presentation for Problem 10(a) by LF. We'll catch up on Problem 9 and the rest of Problem 10 next week.

Week 3

  • Monday, September 9: The students took Quiz 1.
  • Wednesday, September 11: I felt like we accomplished a lot today. We spent some time reviewing the solution to Problem 10(a) and then had CM, WE, TY, and SE present Problems 10(b), 10(c), 11, and 12, respectively. All of these problems had the same theme. With the few minutes we had left, VS did a quick run down of his approach to Problem 9. We'll revisit this one on Friday.
  • Friday, September 13: I think I ran my mouth too much today. After reviewing the big picture for Problems 13-15, we divided the class up into 5 small groups. After letting each group chat about their assigned problem for several minutes, we had CP, VS, DM, DB, and MB present Problems 13, 14(b), 14(c), 14(d), and 15, respectively. We still need to find time to revisit Problem 9.

Week 4

  • Monday, September 16: Today was mostly about catching up and reviewing previous problems. We spent some time discussing Problem 9 and then AC presented Problem 17. This was followed by revisiting Problems 14 and 15. We will catch up on Problem 16 next time.
  • Wednesday, September 18: We covered a lot of problems today! We had SS, VM, JL, TR, SC, DB, DE, LF, AL, AS, CS, HT/TB, DT present Problems 16(a), 16(b), 16(c), 16(d), 19(a), 19(b), 19(c), 20, 21(a), 21(b), 21(c), 21(d), and 21(e), respectively.
  • Friday, September 20: After revisiting Problem 21(d), we had DT/JL, CS, and CP present Problems 18, 22, and 23, respectively. We will likely revisit Problem 22 since we were a bit rushed at the end of class.

Week 5

  • Monday, September 23: The students took Quiz 2.
  • Wednesday, September 25: We started off by revisiting Problem 22 (ants on a stick) and then split the class up into a few small groups. We had SE, SS, WE, SC, and TR present Problems 24(a), 24(b), 24(c), 25, and 26, respectively.
  • Friday, September 27: We had DE, TY, and JL present Problems 27, 28, and 29, respectively. With the few minutes we had left at the end, we quickly discussed what "visual proof" means.

Week 6

  • Monday, September 30: I spent the first few minutes summarizing solutions to the problems on part B of Quiz 2. Next, we divided the class up into several small groups. We had MB and BM present Problems 30 and 31, respectively.
  • Wednesday, October 2: The first ten minutes or so were devoted to discussing the big picture of axiomatic systems and giving an introduction to Circle-Dot. Next, we had LF, DM, AL, CP, and DW present Problems 32(algebra), 32(visual), 33, 34, and 35, respectively.
  • Friday, October 4: We had CM, DT, AC, SC, SE, and WE present Problems 36(algebra), 37(Theorem D), 37(Theorem E), 37(Theorem F), 37(Theorem G), and 37(Theorem H), respectively. Along the way, I presented a visual proof of Problem 36. We will catch up on Theorems I, J, and K after next week's quiz.

Week 7

  • Monday, October 7: The students took Quiz 3.
  • Wednesday, October 9: We got caught up with Circle-Dot stuff, but didn't make much progress on the new stuff. We had DW, TB, and SS present Theorems I, J, and K, respectively, from Problem 37. Next, I spent a few minutes discussing how Problems 39 and 40 are related to sorting problems in computer science and how Problem 40 is connected to genetics. With the time we had left, we had MR and AS present two different approaches to Problem 39. We will come back to Problems 38 and 40 on Friday.
  • Friday, October 11: We cranked through stuff today! We had AR/DE, TR, DW, and MR present Problems 39, 40, 38, and 41, respectively. With the time we had left, I spent a few minutes summarizing the next few problems.

Week 8

  • Monday, October 14: After handing back Quiz 3, I briefly discussed "good" versus "bad" approaches to Problem B1 on Quiz 3. Next, we split the class up into several small groups, each tasked with discussing one of Problems 42-44. We had CS, SE, and AS present Problems 42, 43, and 44, respectively.
  • Wednesday, October 16: We started with me doing a quick presentation of a visual proof of Problem 36. I had meant to do this ages ago, but had forgotten. Next, we had TB show us some cool images that he produced using code and illustrated which points we could get to in Problem 45. This was followed by a rather lengthy discussion of a sketch of a proof that we can get to the point $(a,b)$ if and only if $\gcd(a,b)=1$. With the time we had left, AC presented an elegant solution to Problem 46.
  • Friday, October 18: JL presented an alternative approach to Problem 46 and then I split the class up into several small groups, each tasked with discussing one of Problems 47, 48, and 49. We had MB and SC present two different approaches to Problem 47. I quickly summarized Problem 48 in the last few minutes of class, but we did not have time to discuss Problem 49. We will come back to that problem next week after the quiz.

Week 9

  • Monday, October 21: The students took Quiz 4.
  • Wednesday, October 23: Productive day! After reviewing Problem 48, we had DT/MR, DM, JL, and CP present Problems 49, 50, 51, and 52, respectively.
  • Friday, October 18: I enjoy every day of class, but today was particularly enjoyable. We kicked off with a quick solution to Problem 54 presented by TY. This was followed by an elegant solution to Problem 55, which HT presented. Next, SS did a really nice job at presenting a solution to Problem 53. With the time we had left, we started discussing Problem 56 (chameleons). MB thought he had a solution, but realized while he was presenting that it didn't quite work.

Week 10

  • Monday, October 28: We had BM, TY, DB/TL present Problems 56, 57, and 58, respectively.
  • Wednesday, October 30: After handing back Quiz 4, we split up into several small groups. After some time, we had VM, AL, TR, CS, and TY/DT/DE present Problems 59(a), 59(b), 59(c), 60, and 61, respectively.
  • Friday, November 1: We divided up the class into several small groups of size 2-3. Each group was tasked with discussing at least two of Problems 61-64. After 15 or so minutes, we had SS, HT, WE/TY, and LF/TR present Problems 61, 62, 63, and 64, respectively.

Week 11

  • Monday, November 4: The students took Quiz 5.
  • Wednesday, November 6: After twisting some arms, we had VM/SC/DE/CS, DB, and CM present Problems 65, 66, and 67, respectively.
  • Friday, November 8: Due to my wife having surgery, I missed class and Adam Leighton filled in for me. Adam divided the class up into small groups to discuss the problems due today. Near the end of class, MR presented Problem 69, which they argued pretty straightforwardly that it was a Pigeonhole Principle problem, but without using that phrasing. DM presented Problem 70 about the prime numbers argued that 2 of the numbers had to multiply to unity and they couldn't share polarity. The remaining number had to be the negative of a prime whose average with $-1$ was $1$ or whose average with $1$ was $-1$. So, $(p+1)/2=-1$ which implies that $p=-3$, or $(p-1)/2=1$, which implies that $p=3$, but this one is positive.

Week 12

  • Monday, November 11: Veteran's Day. No classes.
  • Wednesday, November 13: We had VS/VM, DB, and HT/DW presented Problems 68, 71, and 72, respectively. After the initial discussion of Problem 68, we spent quite a bit of time chatting about the general approach.
  • Friday, November 15: After CM presented Problem 73, we discussed Problem 74 and 75 as a class.

Week 13

  • Monday, November 18: First, we revisited Problem 75 and discussed "necessary" vs "sufficient" conditions, as well as what it means for a bound to be sharp. Next, we had DW and MR made attempts at Problem 76. With the time we had left, we started discussing Problem 77.
  • Wednesday, November 20: The students took Quiz 6.
  • Friday, November 22: We had LF, WE, JL, and AL present Problems 77, 78, 79, and 80, respectively. Discussing Problem 77 was quite entertaining.

Week 14

  • Monday, November 25: We had CP, SE, and TB present Problems 81, 82, and 83, respectively. With the time we had remaining, I briefly discussed Ramsey Theory and got us started on Problem 84.
  • Wednesday, November 27: Attendance was pretty darn good! I presented Problems 84 and 86 while DT presented an example for Problem 86 and BM presented a solution to Problem 87. We didn't get to Problems 88 and 89.
  • Friday, November 29: Thanksgiving Break. No classes.

Week 15

  • Monday, December 2: The students took the final quiz of the semester.
  • Wednesday, December 4: After discussing the Final Exam, I presented solutions to B1 and B3 on Quiz 6. Next, DW, CS, and SC presented their proposed solutions to Problems 88, 89, and 90. I'm hoping we have time to discuss Problems 91, 92, and 93 next time.
  • Friday, December 6: Last day! We had BM, AC, VS, and AS present Problems 91, 92, 93, and 94, respectively. We never go to Problem 95, but that's okay.

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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  The views expressed on this site are my own and are not necessarily shared by my employer Northern Arizona University.

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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.