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 11: First day! We spent the majority of the time discussing logistics. In particular, we did took a brief tour of the course webpage, BbLearn, and Discord. We spent a few minutes discussing the first few homework problems.
  • Wednesday, January 13: After reviewing some nuts and bolts about the course, we quickly went over solutions to a few of the homework problems, and then we jumped into student presentations. We had ZM, AG/MH, and MW present 2.4, 2.5, and 2.13(a), respectively. Great first day of presentations!
  • Friday, January 15: Busy day. We didn't quite get through everything, but we had great discussions. After reviewing some brief solutions to some select problems, we had HG, DR, JH, and BT presented Problems 2.14, 2.18, 2.22(a), and 2.22(b), respectively.

Week 2

  • Monday, January 18: No classes. MLK Day!
  • Wednesday, January 20: Another busy day. We more or less got caught up. We had SA, KB, HG, MH, AR, MS, JL, ML, and EB present Problems 2.32(a), 2.32(b), 2.32(c), 2.32(d), 2.33, 2.34, 2.35, 2.42(a), and 2.42(c), respectively. Along the way, I presented Problems 2.24, 2.25, 2.30, 2.32(e), 2.37, 2.38, and 2.42(b).
  • Friday, January 22: We slowed way down today, but totally worth it. We had JC, ID, LG, and HH present Problems 2.43, 2.44, 2.46(a), and 2.46(b), respectively. I wrote a solution down to Problem 2.47 at the beginning of class and then I presented Problem 2.45 along the way.

Week 3

  • Monday, January 25: Snow day! Or not. We had ML/MS and AL present Problems 2.46(c) and 2.46(d), respectively. Next, I presented Problems 2.48 and 2.49. With the time we had left, I started discussing Section 2.3. I forgot class ended at 8:50am and ran my mouth until 9:00am. Doh! I guess I was excited.
  • Wednesday, January 27: First day teaching in classroom. Transition seemed to work out well. After I started us off with a presentation of Problem 2.53, we had BP, JO, and KD present Problems 2.55, 2.56, and 2.57, respectively.
  • Friday, January 29: We had TR, ID, HG, ZM, RM, and JL present Problems 2.58, 2.60, 2.61, 2.62, 2.63, and 2.64, respectively. Things seemed to go really smoothly today. Better than I would have expected.

Week 4

  • Monday, February 1: Today was a little chaotic. Not ideal while we are battling through some challenging problems. We probably need to recalibrate soon. We had CM and ND present Problems 2.65 and 2.67. Next, I summarized the statements of Problems 2.68-2.70 and started presenting Problem 2.69. Hopefully we can get caught up on Wednesday.
  • Wednesday, February 3: We got caught up! After I presented 2.69, we had JO, AR, JL, and EB present Problems 2.68, 2.70, 2.71, and 2.73, respectively. I put a sketch of Problem 2.72 on the screen at the beginning of class.
  • Friday, February 5: I displayed the proofs for Problems 2.74 and 2.76 and then MW and HG tackled the two directions of Problem 2.75. Next, I presented the proof of Problem 2.77 (Triangle Inequality) and briefly discussed the first definition in Chapter 3.

Week 5

  • Monday, February 8: After displaying a proof for Problem 2.78, we had BP, JH, and ML present Problems 3.2, 3.3, and 3.4, respectively.
  • Wednesday, February 10: We kicked off with communicating a typo I had on the solution for 2.78 and then had JC, MS, CM, and SA present Problems 3.5, 3.6, 3.8, and 3.7(b), respectively. We'll pick up where we left off next time.
  • Friday, February 12: After a quick discussion of upcoming exam, we had JO, JW, and LG present Problems 3.7(b), 3.12, and 3.14, respectively. I also did a quick summary of Problem 3.15.

Week 6

  • Monday, February 15: We had another quick chat about the upcoming exam and then I walked us through a solution to Problem 3.16. Next, we had RM, DR, AG/AR present Problems 3.17, 3.18, and 3.20, respectively.
  • Wednesday, February 17: Once again, we chatted about the upcoming exam and then jumped into student presentations. We had HH, ML, EB, KB, and AL present Problems 3.21, 3.22, 3.25/3.26, 3.27, and 3.28, respectively. We left one issue involving Problem 3.22 on the table to discuss later.
  • Friday, February 19: Students took Part 1 of Exam 1.

Week 7

  • Monday, February 22: After a few announcements, I discussed an alternate viewpoint of accumulation points, convergence of sequences, and bounded sets that utilizes absolute value. Next, we introduced the notions of supremum and infimum of a set and did a few examples.
  • Wednesday, February 24: I continued lecturing today. We revisiting Problem 3.22 and then discussed Problem 3.33, Problem 3.34, the Completeness Axiom, and Problems 3.38/3.40.
  • Friday, February 26: We nearly wrapped up Chapter 3. Only Problems 3.53 and 3.54 remain. These are assigned as homework.

Week 8

  • Monday, March 1: Back to student presentations! We had ZM and ND present Problems 3.53 and 4.2, respectively. Along the way, I presented Problem 3.54 (Bolzano-Wiererstrass) and discussed the definition of open.
  • Wednesday, March 3: We had TR, BT, JO, AR, and AG present Problems 4.3, 4.5, 4.6, 4.7, and 4.8, respectively.
  • Friday, March 5: Super productive today! We had RM, EB, KD, SA, and ID present Problems 4.9, 4.10, 4.12, 4.13, and 4.14, respectively.

Week 9

  • Monday, March 8: Unfortunately, I was home sick today. Students were responsible for annotating their work based on solutions that I posted.
  • Wednesday, March 10: Mostly me running my mouth today in an attempt to solidify our understanding of continuity. I reviewed the definition and the equivalent form given in Problem 5.5 and then spent time playing with a couple of applets. Next, I sketched a solution to Problem 5.6. We will pick up where we left off next time.
  • Friday, March 12: After a bit of a "pep talk", we had AR, JH, and MW present Problems 5.7, 5.8, and 5.10, respectively. Along the way, I presented Problem 5.9.

Week 10

  • Monday, March 15: How is it week 10 already?! We didn't get through everything, but a productive day nonetheless. After a quick summary of the various approaches to proving continuity, we had JC, AG, HG, and CM present Problems 5.14(a), 5.14(b), 5.15, and 5.11(reverse implication), respectively.
  • Wednesday, March 17: We kicked off by revisiting Problems 5.11 and 5.13. Next, we had JL and SA present Problems 5.17 and 5.19, respectively. Along the way, I cranked out a few examples. We will go back to Problem 5.18 on Friday.
  • Friday, March 19: Awesome day, in my opinion. We had MW, MS, RM, and ID present Problems 5.18, 5.20, 5.23, and 5.26, respectively. Along the way, we discussed several examples, as well as Problem 5.25.

Week 11

  • Monday, March 22: Another busy day! After I presented the proof of the Intermediate Value Theorem (Problem 5.27), JW generalized it and proved Problem 5.28. Next, I discussed Problem 5.29, which was followed by a presentation of Problem 5.30 by EB. This completed Chapter 5 and then we launched into Chapter 6. After I discussed Definition 6.1 and Problems 6.2 and 6.3, KB presented Problem 6.6.
  • Wednesday, March 24: After a quick discussion of upcoming exam, we had BP and AL present Problems 6.9 and 6.13(forward implication), respectively. Along the way, I presented Problem 6.12.
  • Friday, March 26: We had DR and JH present Problems 6.14(a) and 7.7, respectively. Along the way, I presented Problems 7.5 and 7.6 and summarized Definition 7.1.

Week 12

  • Monday, March 29: We had ML, HH, and ND present Problems 7.8, 7.9 and 7.10(b), respectively. With the time we had left, I got started on Problem 7.12(a).
  • Wednesday, March 31: Another great day. After I presented Problems 7.12 and 7.14, we had TR and HG present Problems 7.15 and 7.16, respectively.
  • Friday, April 2: The students took part 1 of Exam 2.

Week 13

  • Monday, April 5: While students are working on take-home exam, I am lecturing. We wrapped up Chapter 7 and started Chapter 8.
  • Wednesday, April 7: More lecturing. I reviewed the definitions of Riemann sum, upper Riemann sum, and lower Riemann sum and then discussed Problems 8.8, 8.9, and 8.10.
  • Friday, April 9: We reviewed a bit and then discussed 8.11-8.16 (mixture of problems and definitions).

Week 14

  • Monday, April 12: Coming soon.
  • Wednesday, April 14: Coming soon.
  • Friday, April 16: Coming soon.

Week 15

  • Monday, April 19: Coming soon.
  • Wednesday, April 21: Coming soon.
  • Friday, April 23: Coming soon.

Dana C. Ernst

Mathematics & Teaching

  Northern Arizona University
  Flagstaff, AZ
  Google Scholar
  Impact Story

Current Courses

  MAT 431: Intro to Analysis
  MAT 526: Combinatorics

About This Site

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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.