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: Coming soon.
  • Friday, October 29: Coming soon.


Dana C. Ernst

Mathematics & Teaching

  Northern Arizona University
  Flagstaff, AZ
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  MAT 320: Foundations of Math
  MAT 431: Intro to Analysis
  MAT 511: Abstract Algebra I

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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.