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 briefly tinkered with Spinpossible.
• Wednesday, August 29: Awesome first day of student presentations! We spent the first few minutes on announcements and making sure we were all on the same page. Next, we divided the class up into 9 small groups, where each group was tasked with writing their proposed solution to a designated problem. We had WR, AS1/JS, JH/WC, KP, AM, and YS present Problems 2.1, 2.2, 2.3, 2.4, 2.5, and 2.8 respectively. Along the way, I summarized Problems 2.6 and 2.7. We will wrap up 2.9-2.11 next time.
• Friday, August 31: We spent the first 15 minutes discussing LaTeX and the first Weekly Homework assignment. Next, we had TS, JO, AS, and RV present Problems 2.9, 2.10, 2.11, and 2.13(a), respectively. Along the way, I discussed Problems 2.12 and 2.14. We got caught up on the ones we ran out of time for last class, but then we didn't get to a few of the new ones. We will tackle those next week.

## Week 2

• Monday, September 3: Labor Day! No classes.
• Wednesday, September 5: Fun day and we accomplished quite a bit! We had WR, WC, KL, JH, MS, DD, RB, and SM present Problems 2.13(b), 2.13(c), 2.17, 2.18, 2.19, 2.20, 2.21, and 2.22, respectively. In last minute of class, I quickly summarized Problem 2.24. We will come back to Problem 2.23 on Friday.
• Friday, September 7: Busy day. After splitting up in small groups, we had AM, AS2, RB, JH, KP, RV, and KL present Problem 2.23, Problem 2.26, Problem 2.27, Theorem 2.29, Problem 2.31, Problem 2.32, and Problem 2.34, respectively. We opted to skip Problem 2.28 and I quickly summarized Problems 2.35 and 2.36 at the end of class. We will catch up on Theorem 2.37 and Problem 2.38 next time.

## Week 3

• Monday, September 10: We spent the first few minutes discussing LaTeX and then jumped into student presentations. We had SA, AS1, and JO present Theorem 2.37, Problem 2.38, and Theorem 2.39, respectively. We didn't cover much ground, but I think the conversations were fruitful. We'll try to get caught up on Wednesday.
• Wednesday, September 12: We didn't quite get caught up, but we made good progress. I think the discussions around the problems we discussed today were excellent. We had AS2, AM, WR, TS, and KL present Problem 2.40, Corollary 2.41, Theorem 2.42, Theorem 2.43, and Theorem 2.44, respectively.
• Friday, September 14: We kicked off with LH presenting a proof of Theorem 2.45. This was followed by leading a discussion about Theorem 2.47 and Problem 2.48. Next, we had WR and KP present Theorem 2.50 and Problem 2.54(abc).

## Week 4

• Monday, September 17: We finally got caught up! We had WC, SM, RV, YS, LH, and MS present Problems 2.55(a), 2.55(b), 2.57, 2.59(a), 2.59(b), and 2.59(c), respectively. Along the way, I discussed the remaining parts of Problem 2.54 and Problem 2.58.
• Wednesday, September 19: After a quick discussion of the upcoming exam, we jumped into student presentations. We had DD, TS, RB, and AS1 present Problem 2.60, Problem 2.61, Problem 2.62, and Theorem 2.63, respectively. With the time we had left, I summarized Problem 2.65. We will hit up Problems 2.67 and 2.69 on Monday next week.
• Friday, September 21: The students took the in-class portion of Exam 1.

## Week 5

• Monday, September 24: While the students are busy working on the take-home exam, I lectured over Chapter 2. In particular, we discussed Definition 2.68, Problem 2.69, and Problem 2.70(abc).
• Wednesday, September 26: I continued lecturing over Chapter 2 and made it through Problem 2.73.
• Friday, September 28: We wrapped up Chapter 2 and briefly discussed the Two-Step Subgroup Test from Chapter 3.

## Week 6

• Monday, October 1: I was impressed with the quality of the presentations today. AFter dividing the class up into small groups, we had AS2, AS1, JH/TS/RB, RV, and KL present Theorem 3.7/Problem 3.8, Theorem 3.9, Problem 3.12, Problem 3.14(abcdef), and Problem 3.14(ghi), respectively. Along the way, I presented Problem 3.5 and Problem 3.13.
• Wednesday, October 3: After handing back the take-home exam, we jumped into student presentations. We had AM/WR, KP, KP (again), and WC present Problem 3.15, Problem 3.17, Theorem 3.19, and Problem 3.20, respectively. Along the way, I led discussions on Problem 3.16, Problem 3.18, Problem 3.22, and Theorem 3.23. Hopefully, we can wrap up the ones we didn't have time for on Friday.
• Friday, October 5: Another action-packed day! We had AM, WR, JH, KL, SM, and RB present Theorem 3.21, Problem 3.27, Problem 3.28, Problem 3.29, Problem 3.30, and Problem 3.31, respectively. Along the way, I presented Theorem 3.26 and reviewed Theorem 3.10.

## Week 7

• Monday, October 8: We didn't quite through everything, but we still covered a lot of ground. We had JS, AS2, TS, AS1, WR, RV, and JO presented Problems 3.32, 3.33, 3.35, 3.36, 3.37, 3.38, 3.39, and 3.40, respectively.
• Wednesday, October 10: After revisiting Problem 3.40, we had TS, JS, YS, JO, and RV present Problems 3.41, 3.43, 3.47(mutliple parts), 3.49(a), and 3.49(b), respectively. Along the way, I presented Problem 3.42, Problem 3.44, and Theorem 3.45. We will come back to Problem 3.48 and Problem 3.49(c) next time.
• Friday, October 12: We covered a lot of ground today. We had AS2, SA, MS, JH, AS1, and WC present Problem 3.48, Problem 3.49(c), Problem 3.50, Theorem 3.51, Theorem 3.52, and Theorem 3.53, respectively. We will catch up on Theorems 3.54 and 3.55 on Monday.

## Week 8

• Monday, October 15: We kicked off with discussing Theorems 3.54 and 3.55 and then revisiting Theorem 3.53. Next, we split the class up into 6 small groups, where each group was tasked with writing up a solution to one of the problems due today. We had YS, KP, SM, JS, JH, and RB present Problem 3.56, Problem 3.57, Problem 3.58, Problem 3.59(case 1), Problem 3.59(case 2), and Theorem 3.61, respectively. We briefly discussed Theorem 3.60 and will come back to it on Wednesday.
• Wednesday, October 17: The first few minutes of class were devoted to me sketching proofs of Theorems 3.60 and 3.62. Next, we had KL and AM each prove parts of Theorem 3.63. This was followed by class discussions of Problems 3.64 and 3.65. With the few minutes we had left, WR quickly presented Problem 4.2. We will address the ones we didn't get to next time.
• Friday, October 19: Lots of presentations today! We had TS, AS2, KP, AS1, JH, MS, YS, SA, and SM present Problem 4.3, Problem 4.4, Problem 4.6, Problem 4.7, Theorem 4.8, Problem 4.11, Problem 4.12, Problem 4.14, and Theorem 4.15, respectively. Along the way, I presented Problem 4.13. We had time left at the end of class to review a couple of topics and I also did a very brief introduction to quotient groups.

## Week 9

• Monday, October 22: The students took the in-class portion of Exam 2.
• Wednesday, October 24: While the students are busy working on the take-home portion of Exam 2, I will spend the next few class meetings doing some lecturing. We covered Theorem 4.16-Problem 4.23.
• Friday, October 26: I continued lecturing over Chapter 4. We go through Theorem 4.27.

## Week 10

• Monday, October 29: Today was the last day of lecturing before jumping back into student presentations. I covered Theorem 4.28, Theorem 4.29, Definition 4.30, Example 4.31, Theorem 4.32, Corollary 4.33, Problem 4.36, and Problem 4.37.
• Wednesday, October 31: We had KP, TS, JH, and RV present Problem 4.38, Theorem 4.42, Problem 4.43, and the forward implication of Theorem 4.46, respectively. Along the way, I discussed Corollary 4.44 and Theorem 4.45.
• Friday, November 2: We kicked off with an awesome proof of the reverse implication of Theorem 4.46 by KL. Next, we cranked through presentations of Problem 4.47, Corollary 4.48, Problem 4.49, Corollary 4.51, and Problem 4.52, respectively. With the time we had left, I sketched arguments for Theorems 4.56 and 4.57. We will wrap up Theorem 4.58 next time.

## Week 11

• Monday, November 5: I spent the first several minutes sketching proofs for Theorems 4.58 and 4.59. Then we had AS2, AS1, KP, WR, SA, and TS present Problems 4.61, 4.66, 4.67, 4.68, 4.69, and 4.70, respectively. We wrapped up with me sketching a proof of Theorem 4.71.
• Wednesday, November 7: We covered a lot of ground today! We had JS, YS, KL, AM, JO, AS2, and MS present Problem 4.73, Problem 4.74, Problem 4.75, Theorem 4.76, Problem 4.78, Theorem 4.80, and Problem 4.82, respectively. Along the way, I presented Theorem 4.79.
• Friday, November 9: Lots of presentations today. We had WR, JS, TS, YS, WC, AS1, SM, and KL present Problems 4.83, 4.84, 4.85, 4.87(a), 4.87(b), 4.87(c), 4.88, and 4.89, respectively. In addition, I sketched the proofs of Theorem 4.90 and Corollary 4.91.

## Week 12

• Monday, November 12: No class due to Veteran's Day.
• Wednesday, November 14: The students took the in-class portion of Exam 3.
• Friday, November 16: I lectured over most of Section 5.1.

## Week 13

• Monday, November 19: I continued lecturing over Chapter 5.
• Wednesday, November 21: More lecturing. I covered the rest of Chapter 5 and part of Section 6.1.
• Friday, November 23: No class due to Thanksgiving break.

## Week 14

• Monday, November 26: We picked up where we left off and covered nearly all of Section 6.1.
• Wednesday, November 28: We finally got back to student presentations! It's really nice to get back to letting the students drive. We had SM, JS, RB, WC, WR, KL, JO, and MS present Theorem 4.99, Problem 4.102, Problem 4.104, 4.105, Theorem 4.107, Problem 4.109, Problem 4.111, and Problem 5.5, respectively. Along the way, we also discussed Problems 4.103, 4.108, 4.110, and 4.112.
• Friday, November 30: We kicked off with presentations of Problems 3.32(a) and 6.32(d) by WC and JO. Then I lectured over the rest of Section 6.1 and most of Section 7.2.

## Week 15

• Monday, December 3: We wrapped up Chapter 7, proved the First Isomorphism Theorem, and started Chapter 8.
• Wednesday, December 5: We tinkered with some problems involving the First Isomorphism Theorem for groups and then covered more of Chapter 8. Along the way, we had JH, WR, SM, TS, AS1, and JO present Problems 7.23, 7.24, 8.9(a), 8.9(b), 8.9(c), and 8.15, respectively.
• Friday, December 7: Last day! I've really enjoyed this group of students. We cranked through most of the rest of Chapter 8 and along the way, we had JS and JO present Problem 8.36 and Theorem 8.37(b), respectively.

# Dana C. Ernst

Mathematics & Teaching

Northern Arizona University
Flagstaff, AZ
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