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 course webpage, and summarized a few items on the syllabus. With the time we had left, we started discussing some of the content due on Wednesday.
• Wednesday, January 15: Unfortunately, I missed today due to being at a conference. Zach Parker covered for me while I was away. JJ, SS, FB, YF, AS, and ID presented Theorem 2.3, Theorem 2.4, Problem 2.5, Problem 2.7, Problem 2.8, and Problem 2.9, respectively. That's a lot of student presentations!
• Friday, January 17: Zach covered for me again while I was gone. IS, KB, NH, and JG presented Problem 2.12, Problem 2.13, Theorem 2.14, and Corollary 2.15, respectively. Next week, We will catch up on the ones that were not presented.

## 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 course expectations, we briefly discussed the use of LaTeX for the Weekly Homework assignments. Next, we had CH and AL present Problem 2.16 and Theorem 2.17, respectively. The proof of Theorem 2.17 generated lots of great discussion.
• Friday, January 24: Awesome day! We kicked off with presentations of Theorem 2.18 and Problem 2.19 by HG and JH. Next, we split the class up into several small groups, each tasked with discussing one of 2.20-2.23. After some time, we had LC/FB, PC, and RT present Theorem 2.20, Problem 2.21, and Theorem 2.22, respectively.

## Week 3

• Monday, January 27: I spent way too long discussing LaTeX, but hopefully it was helpful. Our only presentation of the day was of Theorem 2.23 by TF. With the time left, we discussed Exercise 2.25. We will play catch up on Wednesday.
• Wednesday, January 29: After a short discussion of growth mindset and grit, we had RB, RP, NC, JD, SR, and AL present Exercise 2.30, Exercise 2.33, Problem 2.34, Theorem 2.36, Theorem 2.37, and Problem 2.38, respectively.
• Friday, January 31: Fantastic day! Lots of ideas were synthesized. After a brief discussion of contrapositives and proof by contradiction, I split the class up into groups of size 2-3. Lots of great discussion! We had DW, GI, FB, and HG present Theorem 2.46, Problem 2.48, Theorem 2.49, and Theorem 2.50, respectively.

## Week 4

• Monday, February 3: Prior to the beginning of class, I wrote some stuff on the board for Theorem 2.52 and Exercise 2.54. Next, we had NC, KB, LC, and PC present Corollary 2.53, Exercise 2.55, Theorem 2.57, and Exercise 2.58, respectively. With the time we had left, I discussed the big picture of proof by contradiction.
• Wednesday, February 5: After some short discussion of the upcoming exam, we had IS and RP present Theorems 2.61 and 2.62. Both of these generated excellent discussion! With the time we had left, we discussed Exercises 2.63 and 2.64 as a class.
• Friday, February 7: Prior to the beginning of class, I wrote solutions for Exercises 2.67 and 2.72 on the board. Once class started, I split students up into several small groups. We had AP, GI, MW, HG, NH, and RB present Exercises 2.68(ab), 2.68(cd), 2.71(a), 2.71(b), 2.71(c), and 2.75, respectively.

## Week 5

• Monday, February 10: Lots of entertaining discussion today. We had FB, NC, SR, and JJ present Exercises 2.73(a), 2.73(b), 2.74, and 2.77, respectively. Along the way, we also discussed Exercise 2.69 and Theorem 2.78.
• Wednesday, February 12: We spent quite a bit of time discussing Exercise 2.79, Exercise 2.80, and Problem 2.85 as a whole class. With the time we had left, RT presented Theorem 2.86.
• Friday, February 14: After a brief discussion of the upcoming exam, we spent time discussing several of the new set-theoretic concepts. We also discussed Exercises 3.3, 3.4, 3.6, and 3.7 together as a class. We're a little off schedule, but we'll get caught up.

## Week 6

• Monday, February 17: We jumped right in and had JD, TF, JW, and ID present Exercise 3.8, Theorem 3.9, Exercise 3.14, and Exercise 3.15, respectively. With the time we had left, I presented proofs of Theorem 3.16 and 3.18.
• Wednesday, February 19: After discussing the upcoming exam, we fiddled around with confusing examples concerning power sets. Next, I presented a proof of Theorem 3.19(a) and then YF presented Theorem 3.20(a).
• Friday, February 21: The students took Exam 1.

## Week 7

• Monday, February 24: I lectured over 3.20-3.25.
• Wednesday, February 26: We had CH, ID, MW, and IS present Theorem 3.26, Problem 3.27, Problem 3.28, and Problems 3.29/3.30, respectively. This left us with a little time to discuss a couple more paradoxes and briefly introduce indexing sets.
• Friday, February 28: After handing back Exam 1, we divided the class up into several small groups. After a few minutes, we had PC, MW, SS, DW, HG, AS, RB, and TF present Exercises 3.33(a), 3.33(b), 3.35(a), 3.35(b), 3.36(a), 3.36(b), 3.37(a), and 3.37(b), respectively. Along the way we also discussed Exercise 3.34.

## Week 8

• Monday, March 2: The first few minutes were devoted to discussing the upcoming take-home exam. Next, we had NC and FB present the containments of Theorem 3.41(a). This brought up a variety of issues that students were struggling with and I did my best to alleviate any confusion.
• Wednesday, March 4: We had NH and SR present the two containments of the proof of Theorem 3.42(a), respectively. Next, I spent a few minutes discussing the big picture of induction and then proved Theorem 4.2. With the time we had left, DW presented Theorem 4.4.
• Friday, March 6: We had PC, JH, SS, and RP presented Theorem 4.5, Theorem 4.6, Theorem 4.7, and Problem 4.8, respectively.

## Week 9

• Monday, March 9: I lectured over content in Chapter 4.
• Wednesday, March 11: I continued lecturing over content in Chapter 4.
• Friday, March 13: Last day of face-to-face class. I started lecturing over Chapter 5 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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