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

• Wednesday, August 12: First Day! We spent the majority of the time discussing logistics. In particular, we did a brief overview of Zoom (chat, raise/lower hand, thumbs up, breakout rooms, polling) and toured the course webpage and BbLearn. We spent a few minutes discussing the framework for homework, but I'm leaving the rest of the syllabus for students to read on their own.
• Friday, August 14: Awesome first day of presentations! After reviewing a few logistics items, we jumped into student presentations (with me acting as scribe). We had RP/SS, FB/RL, JA, HG, and KB/BJ present Problems 2.1, 2.2, 2.3, 2.4, and 2.5, respectively.

## Week 2

• Monday, August 17: We got caught up on the leftovers from last time, but didn't have time to start the new ones. we will try to get caught up next time. After reviewing some key concepts, we jumped into student presentations with me usually acting as scribe. We had ZM, MJ, IS, SS, MC, and BJ present Problems 2.6, 2.7, 2.8, 2.9, 2.10, and 2.11, respectively.
• Wednesday, August 19: Productive day! We got caught up with some time to spare. After a quick review of some key concepts, we had AA, JW, JB, AC, AS, and CH present Problems 2.12, 2.13(a), 2.13(b), 2.13(c), 2.14, and 2.18, respectively. Along the way, I presented Problem 2.17.
• Friday, August 21: Friday! After some chit chat about the potential of classes staying remote vs NAUFlex, I quickly summarized Problem 2.19 and then we jumped into student presentations. We had JK, AL, SS, MK2, and KG present Problems 2.20, 2.21, 2.23, 2.26(a), and 2.26(b), respectively. Along the way, I discussed Problems 2.22 and 2.24.

## Week 3

• Monday, August 24: I'm happy with what we got through today. We had MK/AC, MW, RP/MC, JA, RL, and IS present Problem 2.27, Problem 2.29, Theorem 2.29, Problem 2.31(a), Problem 2.31(b), and Problem 2.32, respectively. In the last few minutes, I reviewed the definition of group.
• Wednesday, August 26: After briefly discussing the potential plan for next week, we had KB, FB, and BJ present Problem 2.34, Theorem 2.37, and Theorem 2.39, respectively. Along the way, I presented Problems 2.35, 2.36, and 2.38. We didn't quite finish Theorem 2.39, so we will start with that next time.
• Friday, August 28: Maybe our best day yet! After BJ wrapped up Theorem 2.39, we had NC, JF, IV, EB/SS/IS, and AC present Problem 2.40, Theorem 2.41, Theorem 2.42, Theorem 2.43, and Theorem 2.44, respectively.

## Week 4

• Monday, August 31: First day having a mix of face-to-face students and remote students. I'd say it wasn't awful. Wearing a mask for two hours straight is tough (but necessary!). After I sketched the proofs of the three parts of Theorem 2.47, we had MJ, MK, and JB present Problem 2.48, Problem 2.49, and Theorem 2.52. Hopefully, we will get caught up or close to it next time.
• Wednesday, September 2: I got thrown off my game with some technology issues before class started, but I think we managed just fine. We had ZM, MW, JK, AL, AB, AA, EB, and NC present Problems 2.55, 2.56(abc), 2.56(d), 2.56(e), 2.57, 2.58(ab), 2.58(cd), and 2.58(e), respectively.
• Friday, September 4: We had CH, HG, AS, MJ, NC, KG, MC, SS, and JW present Problems 2.58(f), 2.59, 2.60, 2.61(a), 2.61(b), 2.61(c), 2.62, 2.63, and 2.64, respectively.

## Week 5

• Monday, September 7: Labor Day. No classes!
• Wednesday, September 9: We briefly discussed the upcoming exam and then reviewed Problem 2.64. Next, we had RP, JA, HG, JF, and FB present Theorem 2.65, Problem 2.66, Problem 2.67, Problem 2.68, and Problem 2.71, respectively. Along the way, I presented Problem 2.69 and discussed some of the Cayley diagrams in Problem 2.72.
• Friday, September 11: After a quick discussion of next week's exam, we had AC, MJ, and ZM present Problems 2.73, 2.78, and 2.79, respectively. Along the way, I revisited Problem 2.72 and discussed Problem 2.74.

## Week 6

• Monday, September 14: We had AS and MW present Problems 2.80 and 2.81, respectively. I led discussions on Theorem 2.76, Theorem 2.77, Problem 2.82, Problem 3.1, Problem 3.2 and Problem 3.3. We will catch up on Problem 3.5 next time.
• Wednesday, September 16: Super productive day. We had BJ, MK, AL, AB, IV, and FB present Problem 3.5, Theorem 3.6, Theorem 3.7, Problem 3.8, Theorem 3.9, and Theorem 3.10, respectively.
• Friday, September 18: Students took Part 1 of Exam 1.

## Week 7

• Monday, September 21: While the students are working on the take-home portion of Exam 1, I will lecture this week. I discussed 3.11 through part of 3.16.
• Wednesday, September 23: After answering questions about Part 2 of Exam 1, I continued lecturing over Chapter 3 material. We got up to Problem 3.20.
• Friday, September 25: More lecturing. We got up to definition of subgroup lattice.

## Week 8

• Monday, September 28: After a quick discussion of Theorem 3.24 and Problem 3.25, we had MJ, AS, KG, SS, KB, and CH present Theorem 3.26, Problem 3.27, Problem 3.28, Problem 3.29, Problem 3.30, and Problem 3.32, respectively. With the time we had left at the end, I presented Problem 3.31.
• Wednesday, September 30: We didn't get through everything, but it was still a productive day. A few people passed on presentations today. Doing this a couple times is no big deal, but it'll have a negative impact if done repeatedly (see syllabus). We had RP, JB, ZM, MJ, and AS present Problems 3.33, 3.34, 3.35, 3.36 and 3.37, respectively.
• Friday, October 2: First, we had MW, IV, MK, and AB present Problems 3.38, 3.39, 3.40, and 3.41, respectively. Next, I outlined the proofs of Problems 3.42-3.44 and Theorem 3.45. We try to get caught up next class.

## Week 9

• Monday, October 5: We made a lot of progress, but we are still a bit behind. We had SS, JA, and EB present Problems 3.47, 3.48, and 3.49, respectively. We also discussed isomorphisms and the homomorphic property.
• Wednesday, October 7: We had MC, RP, AL, and KG present Problem 3.50, Theorem 3.53, Theorem 3.54, and Theorem 3.55, respectively. Along the way, we revisited Theorems 3.51 and 3.52 and summarized some key points about Theorems 3.51-3.55.
• Friday, October 9: We had JF, MJ, NC, KB, IS/MJ, and RL present Problem 3.56, Problem 3.57, Problem 3.58, Problem 3.59, Theorem 3.60, and Problem 3.61, respectively.

## Week 10

• Monday, October 12: We had FB, IS, MC, MJ, and NC present Theorem 3.62, Theorem 3.63, Theorem 3.64, Problem 3.65, and Problem 3.66, respectively.
• Wednesday, October 14: Dang, we covered a lot of ground today. After a quick summary of Problems 4.1 and 4.2, we had AA, JW, HG, JK, MK, JF, CH, and JB/MC present Problem 4.3, Problem 4.4, Theorem 4.5, Problem 4.6, Problem 4.7, Theorem 4.8, Theorem 4.9, and Theorem 4.10, respectively. With the time we had left, I discussed Problems 4.11 and 4.12.
• Friday, October 16: After discussing upcoming exam, we had MW, NC, MJ, RP, AS, and BJ present Problem 4.13, Theorem 4.15, Theorem 4.17(forward implication), Theorem 4.17(reverse implication), Corollary 4.18, and Corollary 4.20, respectively.

## Week 11

• Monday, October 19: Another productive day. We had KB, SS, EB, MK, and KG present Problem 4.21, Problem 4.22, Problem 4.23, Corollary 4.25, and Theorem 4.28, respectively. Along the way, we discussed Theorems 4.24, 4.26, and 4.27.
• Wednesday, October 21: After a quick discussion of the upcoming exam, we had FB, IV, BJ, and RL present Theorem 4.32, Problem 4.36, Problem 4.37, and Problem 4.38, respectively. Along the way, I presented Theorem 4.29, Corollary 4.33, Theorem 4.39, and Theorem 4.40.
• Friday, October 23: After discussing the upcoming exam, we had HG, MJ, IS, EB, AB, and RP present Theorem 4.41, Problem 4.42, Corollary 4.43, Problem 4.46, Corollary 4.47(forward implication), and Corollary 4.47(reverse implication), respectively. With the few minutes we had left at the end of class, we discussed Problems 4.48 and 4.49.

## Week 12

• Monday, October 26: The students took Part 1 of Exam 2.
• Wednesday, October 28: I lectured today while students are working on Part 2 of Exam 2. We discussed up to Problem 4.75.
• Friday, October 30: More lecturing. I discussed material in Chapter 4 up to Theorem 4.84.

## Week 13

• Monday, November 2: I continued lecturing. We more or less covered content up to and including Cayley's Theorem and the example that follows.
• Wednesday, November 4: After a short discussion about Exam 3, we had SS, ZM, JB, JA, and JF present Problems 4.86, 4.90, 4.92, 4.93, and 4.94, respectively. Along the way, I presented Problem 4.87 and sketched a solution to Problem 4.101.
• Friday, November 6: We had KG/IS, RL, MJ, and RP present Problem 4.100, Problem 4.102, Theorem 4.104, and Problem 4.106, respectively. Along the way, I presented Problem 4.107.

## Week 14

• Monday, November 9: We had IS, AB, AL, RP, and NC present Problems 4.108, 4.109, 4.113, 4.114, and 4.115, respectively. Along the way, I presented Problem 4.110 and Theorem 4.112.
• Wednesday, November 11: Veteran's Day. No classes.
• Friday, November 13: We kicked off with CH presenting Problem 4.117 and then I presented Problems 5.5-5.7 and Theorem 5.8. Next, we had RL, JB, and MJ present Problems 5.17, 5.27, and 5.31, respectively. Along the way, I squeezed in Problem 5.18.

## Week 15

• Monday, November 16: We had JK, ZM, and KB present Problems 6.18, 6.27, and 6.28. Next, I blitzed through 6.29-6.32, 6.34.
• Wednesday, November 18: Last day! After a very quick summary of Section 7.1, which included proofs of Theorems 7.11 and 7.13, we had JB, RP, and AL present the 3 parts of Problem 7.16. Next, we discussed the First Isomorphism Theorem and did some examples. That more or less wrapped things up nicely.

# Dana C. Ernst

Mathematics & Teaching

Northern Arizona University
Flagstaff, AZ
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