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, January 13: 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 started discussing the homework due Wednesday. We even had two presentations by HA and MB (Problem 2.6).
• Wednesday, January 15: Unfortunately, I missed today due to being at a conference. David Deville covered for me while I was away. AS, AA, SW, RT, NM, TH, CC, MK, LC, JS, and MB presented Exercises 2.4, 2.5(a), 2.5(b), 2.5(c), 2.9, 2.10, 2.11, 2.12, 2.14, 2.16, and 2.17, respectively. That's a lot of student presentations!
• Friday, January 17: David covered for me again. Prior to the start of class, he sketched solutions to 2.19, 2.20, 2.25, and 2.26 on the board. Once class stared, he split the students up into several small groups, each tasked with discussing one of the remaining problems. Apparently, there was a lengthy class discussion of Problem 2.20 and then NM and LC presented the two parts of Problem 2.21. We will revisit the ones that we not presented on Wednesday next week.

## Week 2

• Monday, January 20: MLK Day, no classes.
• Wednesday, January 22: Today was all about recalibrating after me being gone most of last week. After some discussion of the grading of homework, we revisited the order axioms and the big picture of where we are and where are headed. Next, I presented a proof of Problem 2.30. This was followed by presentations of Problem 2.23 and Exercise 2.27 (both left over from Friday) by AS/LC and JA, respectively.
• Friday, January 24: Today was awesome! I split the class up into four small groups, each tasked with working on one of 2.29-2.33. After a few minutes, we had WM, JI, JS, and JA present Problems 2.29, 2.31, 2.32, and 2.33, respectively. Along the way, we discussed alternate approaches to the proofs.

## Week 3

• Monday, January 27: Another productive day. We spent the first few minutes discussing the "big picture" of accumulation points. Then we had AC, CC, JQ, RT, and TH present Exercise 3.6, Problem 3.8, Problem 3.9, Problem 3.10, and Problem 3.11, respectively.
• Wednesday, January 29: I divided the class up into a few small groups. We had MK, TH, and JI present Problems 3.13, 3.13(a), and 3.13(b), respectively. We'll catch up on the ones we didn't get to next time.
• Friday, January 31: Today seemed like a good day for me to run the show. I spent some time reviewing the fundamentals of "accumulation point" and "limit of a sequence," which was followed by discussions of Problem 3.14, 3.18, 3.20, and 3.22.

## Week 4

• Monday, February 3: We started by tinkering with a bunch of examples involving accumulation points and convergence of sequences. Next, we sketched a solution to Problem 3.21 together. This was followed by presentations of Problems 3.23 and 3.26 by SW and JS, respectively.
• Wednesday, February 5: More hard stuff today! After discussing the upcoming exam, we had WM and LC present Problems 3.27 and 3.28. Both generated excellent discussions! With the time we had left, I sketched the general structure of the proof of Problem 3.35, which we will revisit next time.
• Friday, February 7: We jumped right into student presentations and had HA, MK, AS, and SW present Exercise 3.32, Problem 3.34, Problem 3.35, and Problem 3.38. Along the way, I sketched an alternate proof of Problem 3.35.

## Week 5

• Monday, February 10: We had AC present Problem 3.39 and then I divided students up into four small groups. After a bit, we had RT, JI/JS, and CC present Problem 3.40, Problem 3.41, and Exercise 3.42, respectively.
• Wednesday, February 12: We had AA, HA, and JA present Problems 3.46, 3.47, and 3.48, respectively.
• Friday, February 14: Lots of interesting discussion today, but most of it involved solidifying our understanding as opposed to making new progress. We discussed the upcoming exam, whether the Complete Axiom is an axiom, equivalent forms of the Completeness Axiom (including the Monotone Convergence Theorem), shortcomings of our attempted proof of Problem 3.48, and a proof of Problem 3.49. With the time we had left, MB presented a proof of Problem 3.50.

## Week 6

• Monday, February 17: We had JQ, MB, CC, and JS present Problems 3.52, 3.53, 3.54, and 3.55, respectively.
• Wednesday, February 19: After discussing the upcoming exam, we had JQ and AA present Problems 3.56 and 3.57, respectively.
• Friday, February 21: The students took Exam 1.

## Week 7

• Monday, February 24: I lectured over most of Chapter 4.
• Wednesday, February 26: I continued lecturing. We wrapped up Chapter 4 and started Chapter 5.
• Friday, February 28: Last day of lecturing for a bit. We continued discussing Chapter 5.

## Week 8

• Monday, March 2: We divided the class up into several small groups. Next, we had MK, JA, HA, AS, WM, and JS present Problems 5.8, 5.10, 5.14(a), 5.14(b), 5.14(c), and 5.14(d), respectively.
• Wednesday, March 4: We kicked off with a quick discussion of Exercise 5.15 and then we spent some time discussing a couple of sequences of partial sums that we will revisit later in the semester. Next, SW presented Problem 5.16. This was followed with some discussion about whether the image of a closed or bounded set under a continuous function was necessarily closed or bounded, respectively. Then we had MB and JA present parts of Problem 5.17.
• Friday, March 6: We had WM, JI, LC, AS, AA, TH, RT, JQ, and HA present Problem 5.18, Problem 5.19, Problem 5.20, Problem 5.21, Exercise 5.23(a), Exercise 5.23(b), Exercise 5.23(c), Exercise 5.23(d), and Exercise 5.23(e), respectively.

## Week 9

• Monday, March 9: After splitting the class up into small groups, we had MB and MK present Problems 5.25 and 5.26, respectively.
• Wednesday, March 11: Using pictures of board work from Monday, we had WM, TH, SW, JI, and CH present Problems 5.27, 5.28, 5.29, and 5.30, respectively.
• Friday, March 13: Last day of face-to-face class. I started lecturing over Chapter 6 material. In light of the COVID-19 Pandemic, all classes at NAU will be taught via remote instruction for the remainder of the Spring 2020 semester. I won't be updating the journal for the rest of the semester.

# Dana C. Ernst

Mathematics & Teaching

Northern Arizona University
Flagstaff, AZ
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