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: Absolutely fantastic first day of student presentations. 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 JH, KG, YT, AL, and AH present Problems 2.1, 2.2, 2.3, 2.4, and 2.5, respectively. We'll get caught up on Problems 2.6-2.11 next time.
  • Friday, August 30: After briefly discussing LaTeX and the first Weekly Homework assignment, we jumped into presentations. We had AR, JC, YC, and MK present Problems 2.7, 2.9, 2.10, and 2.12, respectively. Along the way, I presented Problems 2.6, 2.8, and 2.11. We will attempt to get caught up on Problems 2.13 and 2.14 next time.

Week 2

  • Monday, September 2: Labor Day, no class.
  • Wednesday, September 4: Fun day of class today. We kicked off with a brief discussion of LaTeX and then jumped into student presentations. We had DT, BS, HA, HL, AR, and CM present Problems 2.13(a), 2.13(b), 2.13(c), 2.14, 2.20(a), and 2.20(b), respectively. Along the way, we also discussed Problems 2.17-2.19 and ended with a class discussion of Problem 2.21.
  • Friday, September 6: Busy day, but we managed to get through almost everything that was planned. We had TN, SB, and MG present Problems 2.22, 2.23, and 2.26, respectively. Along the way, we also discussed Problems 2.24 and 2.27.

Week 3

  • Monday, September 9: I haven't done a good job of keeping us on schedule or picking the correct number of problems for homework. Hopefully, we'll get on track soon. Nonetheless, I think things are going well. I kicked off today by discussing the axioms of a group. Next, we had SW, DC, and BS present Theorem 2.29, Problem 2.31(a), and Problem 2.38, respectively. Along the way, we discussed Problems 2.32-2.36. We will catch up on Theorems 2.37 and 2.39 next time.
  • Wednesday, September 11: After reviewing the axioms of a group, we discussed a few key ideas related to the recent proofs. We had RH, CM, and AA present proofs for Theorems 2.37, 2.39, and 2.45, respectively. We also discussed Problem 2.40. The goal is to tackle Theorems 2.41-2.44 next time.
  • Friday, September 13: We are making progress and I think the students are feeling much more comfortable with writing proofs, but we're still a bit behind where I'd like to be. After dividing the class up into small groups, we had HL, MG, and JT present Theorems 2.41, 2.42, and 2.44, respectively.

Week 4

  • Monday, September 16: Lots of awesome stuff happened today. Things are coming together! We had BS and SW present proofs for Theorem 2.48(a) and Theorem 2.51. Along the way, we discussed the proof of Theorem 2.48(b) and rehashed Theorem 2.51. In addition, we tackled Problem 2.49.
  • Wednesday, September 18: We had CW, DT, JS, HA, and KG present Problems 2.55(abc), 2.55(de), 2.56(a), 2.57(abcd), and 2.57(ef), respectively
  • Friday, September 20: We had SB, RH, AR, HL, and JH present Problems 2.58, 2.60(b), 2.60(c), 2.61, and 2.63, respectively. Along the way, we also discussed Problems 2.59, 2.60(a), and 2.65.

Week 5

  • Monday, September 23: I think a lot of connections were made today. We had RH, TN, JC, DC, AL, and HL present Theorem 2.64, Problem 2.70, Problem 2.71(a), Problem 2.71(b), Problem 2.71(c), and Problem 2.71(d), respectively. We also tackled Problems 2.66, 2.67, and 2.68.
  • Wednesday, September 25: The students took the in-class portion of Exam 1.
  • Friday, September 27: While the students are working on the take-home portion of Exam 1, I will lecture for the next few class meetings. I covered up to Theorem 2.75.

Week 6

  • Monday, September 30: More lecturing. We wrapped up Chapter 2 and got started on Chapter 3.
  • Wednesday, October 2: After handing back the in-class portion of Exam 1 and giving the class a short pep talk, I continued lecturing over Chapter 3. We got through Problem 3.18.
  • Friday, October 4: Busy day! I think we made substantial progress, but we will have to catch up on a few problems that we did not get to. After reviewing the key ideas of subgroups and center of a group, I split the class until into several small groups and then jumped into student presentations. We had AL, JS, HA, HL, and MK present Problems 3.15(a), 3.15(b), 3.15(c), 3.16(b), and 3.16(c), respectively. Along the way, I also discussed parts (d) and (e) of Problem 3.16.

Week 7

  • Monday, October 7: Somehow we got through everything, which I didn't expect to happen. We had SB, CM, HL, YC, YT, TN, MG, JC, SW, AR, RH, and DT present Problems 3.20, 3.22(abfg), 3.22(c), 3.22(d), 3.22(e), 3.22(h), 3.22(jk), 3.25, 3.27, 3.28, 3.29, and 3.30, respectively. Along the way, I presented Problem 3.22(i) and a proof of Theorem 3.26.
  • Wednesday, October 9: After handing back the take-home portion of Exam 1, I briefly discussed two of the problems from the exam. Next, we had BS, AR, HL, CW, and JS present Problems 3.32, 3.33, 3.35, 3.36, and 3.37, respectively. Along the way, I also discussed Theorem 3.34 and Problem 3.38.
  • Friday, October 11: We had DC, JC, JH, MG, and RH present Problems 3.39(c), 3.39(d), 3.40(b), 3.40(e), and 3.41, respectively. After the students presented, I summarized 3.42-3.45, and 3.47. We will catch up on Problems 3.48 and 3.49 next time.

Week 8

  • Monday, October 14: We had MG, AR, KG, SW, and MK present Problem 3.48, Problem 3.49, Problem 3.50, Theorem 3.51, and Theorem 3.53, respectively. Along the way, I presented a proof of Theorem 3.52.
  • Wednesday, October 16: Despite not getting through everything that was planned, we still covered a lot of ground. We had YC, HA, CM, JS, SW, and MK present Theorem 3.54, Problem 3.56, Problem 3.57, Problem 3.58,, Problem 3.59, and Theorem 3.60, respectively. Along the the way, I presented a proof of Theorem 3.55. MK will wrap up Theorem 3.60 next time and I will present Problem 3.61. I sent out written proofs for Theorems 3.62 and 3.63.
  • Friday, October 18: Massive progress today. Although, this was in large part because I wrote solutions to many of the problems on the board in advance. In particular, I sketched solutions to Problems 4.1, 4.3, 4.4, 4.12, and 4.13. We had MK wrap up the proof of Theorem 3.61 and then RH nailed the proof of Theorem 3.64. Next, BS presented a short and sweet solution to Problem 4.7.

Week 9

  • Monday, October 21: We had DT, SB, JH, YC, and YC present Theorems 4.24(forward), 4.24(reverse), 4.27, 4.28(forward), and 4.28(reverse), respectively. Along the way, we discussed Corollary 4.20, Problem 4.21, Problem 4.23, Corollary 4.25, and Theorem 4.26.
  • Wednesday, October 23: Productive day! We had HL, AR, JC, TN, DT, and MG present Theorem 4.29, Theorem 4.32(forward), Theorem 4.32(reverse), Problem 4.36, Problem 4.37, and Problem 4.38, respectively. I wrote sketches for Corollary 4.33 and Theorem 4.39 on the board.
  • Friday, October 18: We took some time to collect ourselves today. Instead of launching into the proofs for today, we attempted to wrap our heads around the current state of affairs. We had BS, AL, JS, and CW present Problem 4.43, Corollary 4.44, Problem 4.47(a), and Problem 4.47(b), respectively. We will tackle Theorems 4.42, 4.45, and 4.46 on Monday.

Week 10

  • Monday, October 28: I proved Theorem 4.42, Theorem 4.46, and Corollary 4.48. With the time we had left, HL attempted Problem 4.49.
  • Wednesday, October 30: I revisitd Problem 4.49 and then sketched proofs for Corollary 4.51 and Problem 4.52. Next, we had AR, SW, CM, SW, HA, and RH present Problems 4.53, 4.71, 4.72, 4.73, 4.75, and 4.77, respectively. Along the way, I proved Theorem 4.76.
  • Friday, November 1: We had MK, CW, SB, and AL present Problems 4.79, 4.80, 4.82, and 4.83, respectively.

Week 11

  • Monday, November 4: We cranked through a surprising amount of material. I kicked off my sketching the proof of Theorem 4.85 and then we split the class up into several small groups. We had J, HL, AA, JC, MG, YT, JH, and SB present Problems 4.86/4.87, 4.88, 4.89, 4.90, 4.91(a), 4.91(b), 4.93, and 4.94, respectively. Along the way, I presented Problem 4.92, Theorem 4.95, and Corollary 4.96.
  • Wednesday, November 6: The students took the in-class portion of Exam 2.
  • Friday, November 8: Due to my wife having surgery, I missed class and Zach Parker filled in for me. The students worked on the take-home portion of Exam 2.

Week 12

  • Monday, November 11: Veteran's Day. No classes.
  • Wednesday, November 13: After answering questions about the take-home exam, I lectured over most of what remained in Chapter 4.
  • Friday, November 15: I continued lecturing. We wrapped up Chapter 4 and started discussing Chapter 5.

Week 13

  • Monday, November 18: More lecturing. I finished covering Chapter 5.
  • Wednesday, November 20: After splitting up into several small groups, we had DC, BS, AL, AA, AR, KG, and TR presented Problem 6.2, Problem 6.9, Problem 6.10, Problem 6.11, Theorem 6.12, Problem 6.13, and Problem 6.14, respectively.
  • Friday, November 22: At first it seemed we were going to have poor attendance, but within a few minutes of the start of class most of the students were there. We divided the class up into several small groups and then had AR, BS, KG, RH, MG, SW, DT and JC present Theorem 6.15(forward), Theorem 6.15(reverse), Problem 6.18, Theorem 6.21, Problem 6.23, Problem 6.25/Problem 6.26(a), Problem 6.26(b)(c), and Problem 6.26(d)(e), respectively.

Week 14

  • Monday, November 25: After splitting the class up into a few small groups, we had SW, YT, JC, AL, and HA present Problem 6.34(a), 6.34(b), 6.34(c), 6.34(d), and 6.34(e), respectively. Along the way, I presented Problems 6.27, 6.28, 6.33, 6.35, and 6.36.
  • Wednesday, November 27: Attendance was pretty darn good for the day before the holiday! It was an action-packed day and we covered a lot of ground. Prior to class, I wrote solutions for Problems 7.2, 7.9, 7.10, and 7.19 on the board. We had MG and JH present Problem 6.29 and Theorem 7.13. Next, I presented Problems 7.14 and 7.16. This was followed by a proof of the First Isomorphism Theorem.
  • Friday, November 29: Thanksgiving Break. No classes.

Week 15

  • Monday, December 2: After cranking out some examples that utilized the First Isomorphism Theorem, I started lecturing over Chapter 8.
  • Wednesday, December 4: After a quick review, we jumped back into Chapter 8. We more or less discussed content up to and including Problem 8.27. Along the way, we had JH and HA present Problems 8.11 and 8.15, respectively.
  • Friday, December 6: Last day! After discussing the Final Exam, I flew through a summary of the remaining content in Chapter 8. I thoroughly enjoyed this class this semester.

Dana C. Ernst

Mathematics & Teaching

  Northern Arizona University
  Flagstaff, AZ
  Google Scholar
  Impact Story

Current Courses

  MAT 411: Abstract Algebra
  MAT 690: Genome Combinatorics

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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.