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 23: First Day! After attempting to learn names, we spent some time discussing what the course is all about and how the course will be structured. We also took a quick tour of the course webpage.
• Wednesday, August 25: After fielding some questions about course structure, I divided the class up into several small groups. Each group discussed the problems they chose to review and then generated a list of problems and/or topics they felt they needed more review on. After collecting the list of potential review topics, we jumped in and started discussing a few of them. We'll continue doing this on Friday.
• Friday, August 27: We didn't cover much ground today, but I think it was productive nonetheless. I presented partial proofs to Problems 2.23 and 2.47. This was intended to act as review. Next, we had RP present Problem 3.2. Lots of great discussion.

## Week 2

• Monday, August 30: Week 2! Next, we had LS, FB, LK, and PK present Problems 3.4, 3.8(c), 3.8(d), and 3.8(e), respectively. Along the way, I presented Problems 3.8(a) and 3.8(b).
• Wednesday, September 1: We finally got caught up! We had GM, LH, BH, MH, and MW present Problems 3.8(g), 3.13, 3.14, 3.15, and 3.16, respectively. Along the way, I presented Problems 3.8(h) and 3.9.
• Friday, September 3: Another awesome day! Super happy with how things are going. We had KF, BR, TB, TW, and AR present Problems 3.18(forward implication), 3.18(reverse implication), 3.19, and 3.21, respectively.

## Week 3

• Monday, September 6: Labor Day. No classes!
• Wednesday, September 8: We had KD/LH, MA, HJ, and JE present Problems 3.23, 3.25, 3.28, and 3.30, respectively. Along the way, we discussed Problems 3.26, 3.27, and 3.29.
• Friday, September 10: After answering a few questions, we had LH, FB, TB, and RP present Problems 3.31, 3.32, 3.33, and 3.35, respectively. Along the way, we discussed Problem 3.34.

## Week 4

• Monday, September 13: After discussing Definition 3.36, Problem 3.37, Definition 3.39, and Definition 3.40, we had KF, MW, GM, HJ, AR, and BH present Problems 3.38/3.42(ab), 3.38/3.42(cd), 3.38/3.42(ef), 3.38/3.42(gh), 3.38/3.42(ij), and 3.41, respectively. We had a very lively discussion about whether infinity was a point on the real line and what we should take for the supremum of the empty set.
• Wednesday, September 15: Today was an intense day. We covered a lot of ground and all of it was pretty serious. We had MA, LK, RP, BR, and LH present Problems 3.43(forward), 3.43(reverse), 3.44(forward), 3.44(reverse), and 3.47, respectively. We discussed Problem 3.45 along the way. We should revisit 3.47 on Friday.
• Friday, September 17: We began by revisiting Problem 3.47. We summarized a potential approach that JE proposed and reviewed LH's proof from last week (but with new notation). Next, I proved Problem 3.48(a) and outlined part (b), as well as the cases involving inf. We the time we had left, I proved Problem 3.49.

## Week 5

• Monday, September 20: We had JE, FB, PK, LS, and TW present Problems 3.50(a), 3.51, 3.52, 3.53, and 3.54, respectively.
• Wednesday, September 22: After a brief discussion of upcoming exam, we had MH and BH present Problems 3.55 and 3.56, respectively. Next, we discussed the big picture of Chapter 4 and provided some analogies for understanding the definition of "open set". We then discussed Problems 4.2 and 4.3 together.
• Friday, September 24: Busy day! We had TB, LH, KF, and KD present Problems 4.5(a), 4.5(b), 4.9(a), and 4.9(b), respectively. Along the way, we discussed Problems 4.4, 4.6-4.8.

## Week 6

• Monday, September 27: The students took the in-class portion of Exam 1.
• Wednesday, September 29: I spent the entire class session lecturing. I covered 4.11-4.27(a).
• Friday, October 1: More lecturing. We reviewed open, accumulation point, and closed and then I did a first pass throught the concepts of compact, disconnected, connected, and sequences. We will circle back and dig in more deeply on Monday.

## Week 7

• Monday, October 4: Last day of lecturing before the take-home portion of Exam 1 is due. I reviewed the concepts of open, accumulation point, closed, compact, disconnected, connected, and sequences and then worked through Problems 5.11, 5.13, and 5.14.
• Wednesday, Octocer 6: We had RP, LH, KD, and LK present Problems 5.9, 5.15, 5.16, and 5.17, respectively. I also presented Problem 5.8 and an alternate approach to Problem 5.15.
• Friday, October 8: We had TW, BR, and CI present Problems 5.19, 5.20, and 5.22, respectively.

## Week 8

• Monday, October 11: We had FB, AR, TB, and RP present Problems 5.24, 5.25, 5.26, and 5.29, respectively. Just for fun, we also quickly discussed Problem 5.27. We will come back to Problem 5.28 on Wednesday.
• Wednesday, Octocer 13: We kicked off by me presenting a proof of Problem 5.28, which was left over from last time. Next, we had LS and TW present Problems 5.30 and 5.31, respectively. I then spent quite a bit of time discussing our definition of continuity and tinkering with a few examples.
• Friday, October 15: Productive day. We had GM, KF, and PK present Problems 6.4, 6.5, and 6.6, respectively. Afterwards, I presented Problems 6.7 and 6.8.

## Week 9

• Monday, October 18: In attempt to carefully synthesize ideas, I ended up presenting everything today. In particular, I presented Problems 6.9-6.12 with two approaches to Problem 6.12. We will catch up on Problems 6.13 and 6.14 next time.
• Wednesday, Octocer 20: After a quick review of all of the recent concepts, we had LK present Problem 6.13. Next, I presented a detailed argument for Problem 6.14. This was followed by a presentation of Problem 6.16 by CI. We'll come back to Problem 6.15 next time.
• Friday, October 22: We had TB, MW, KD, and FB present Problems 6.15(forward implication), 6.15(reverse implication), 6.19(a), and 6.19(b), respectively. Along the way, I presented Problem 6.18.

## Week 10

• Monday, October 25: After some quick discussion of Problems 6.20, 6.21, and 6.24, we had RP present an excellent proof of Problem 6.22. With the time we had left, LH presented Problem 6.23.
• Wednesday, Octocer 27: I wrote solutions to Problems 6.30 and 6.31 on the board at the beginning of class and then we discussed 6.31. Next, we had TW, FB, and BR present Problems 6.25, 6.27, and 6.28, respectively. With the couple minutes we had left, we discussed on to modify the proof for 6.28 to proof 6.29.
• Friday, October 29: We had BH, PK, and JE present Problems 6.33, 6.34, and 6.35, respectively.

## Week 11

• Monday, November 1: We had GM, MW/LH, and AR present Problems 6.36, 6.37, and 6.38, respectively. We need to wrap up Problem 6.38 next time.
• Wednesday, November 3: We wrapped up Problem 6.38 and then discussed the big picture of limits for the remainder of the class. This discussion included Problems 7.2 and 7.3.
• Friday, November 5: After discussing the upcoming exam, we had MA, TB, and KF present Problems 7.6, 7.7, 7.8, respectively.

## Week 12

• Monday, November 8: The students took the in-class portion of Exam 2.
• Wednesday, November 10: We cranked through lots of stuff today. We discussed Problems 7.9, 7.10, 7.11, 7.13, and Definition 8.1.
• Friday, November 12: More lecturing over stuff in Chapter 7 and dipped into Chapter 8.

## Week 13

• Monday, November 15: We continued discussing Chapter 8 and got close to wrapping it up.
• Wednesday, November 17: We wrapped up Chapter 8 and get a good start on Chapter 9.
• Friday, November 19: Awesome day. We had GM, BH, HJ, LS, CI, and AM present Problems 9.9(ab), 9.9(c), 9.10(ab), 9.10(cd), 9.11, and 9.12, respectively.

## Week 14

• Monday, November 22: Very productive day. We had LK, MA, MW, and FB present Problems 9.14, 9.17, 9.18, and 9.19, respectively.
• Wednesday, November 24: We had AR, LS, RP, and PK present Problems 9.15/9.21, 9.24(forward), 9.24(reverse), and 9.25, respectively.
• Friday, November 26: Thanksgiving break. No classes!

## Week 15

• Monday, November 29:Last week of classes! We more or less discussed Problems 9.27-9.30.
• Wednesday, December 1: We had TW, JE, and AR present Problems 9.31, 9.34, and 9.35, respectively.
• Friday, December 3: Last day of class! I'm thankful for a great semester. We had TB, HJ, and JE present Problems 9.37, 9.39, and 9.40, respectively.

# Dana C. Ernst

Mathematics & Teaching

Northern Arizona University
Flagstaff, AZ
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