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.

**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. We spent the last few minutes of class sketching proofs of Theorems 2.2 and 2.3.**Wednesday, August 25:**After fielding some questions about course structure, I spent some time reviewing some definitions and notation. Next, we revisited Theorem 2.2 and wrote down a detailed and careful proof. With the time we had left, SR wrote down a solution to Problem 2.4(a), but unfortunately, we didn't really have time to dig in. We'll revisit this one next time.**Friday, August 27:**What a great day! We kicked off by having a very fruitful discussion of SR's work from last time. Next, we had MB, JB, and MT present Problems 2.4(b), 2.4(c), and 2.4(d), respectively.

**Monday, August 30:**We kicked off class with a quick discussion of LaTeX and how to do Weekly Homework 1. Next, we had SC, PB, and NH present Problems 2.6, 2.7, and 2.8(a), respectivley. Before class I wrote the proofs for Problems 2.9 and 2.10 on the board, but we ended up not having time to discuss them.**Wednesday, September 1:**We almost got caught up. We had AR, JO, AC, RM, and KC present Problem 2.8(b), Problem 2.8(c), Theorem 2.11, Problem 2.12(a), and Problem 2.12(b), respectively. Along the way, I presented Corollary 2.9 and Theorem 2.10.**Friday, September 3:**After a quick discussion of an alternate approach to Problem 2.12(b), we had KB, SR, MT, and PB/JO present Problem 2.12(c), Theorem 2.13, Theorem 2.14, and Theorem 2.15, respectively.

**Monday, September 6:**Labor Day. No classes!**Wednesday, September 8:**We spent 15-20 minutes discussing LaTeX so that students would be able to attack Weekly Homework 1. Next, we discussed Problems 2.17 and 2.19 together. With the time we had left, we had KB and BT present Problems 2.22(ab) and 2.22(c), respectively.**Friday, September 10:**We kicked off by splitting the class up into several small groups. Each group was responsible for coming to consensus of a designated homework problem. After a few minutes, we had AC, JO, SC, AR, and MB present Problem 2.22(d), Problem 2.24, Theorem 2.25, Theorem 2.26, and Problem 2.27, respectively. With the time we had left, we discussed the majority of the upcoming homework.

**Monday, September 13:**We has SC, KC, and NH present Theorem 2.30, Problem 2.38, and Theorem 2.39, respectively. This went pretty quickly and then we discussed content up through Skeleton Proof 2.49.**Wednesday, September 15:**We split the class up into several small groups and then had SR, MT, PB, JO, and BT present Theorem 2.51, Theorem 2.52, Problem 2.55(a), Problem 2.55(b), and Theorem 2.56, respectively. We also discussed the structure of a proof by contradiction and had a quick discussion of Problem 2.50.**Friday, September 17:**After proving Theorem 2.57, we had JO, PB, and MT present Problems 2.58, 2.59, and 2.61, respectively.

**Monday, September 20:**We had JB and SR present parts of Problem 2.63 and then we tackled Problems 2.64 and 2.66-2.68 together.**Wednesday, September 22:**We covered quite a bit of ground today. After discussing Problems 2.70 and 2.71 together, we had RM and KB present Problems 2.72 and 2.73, respectively. Then we cranked through Problem 2.75, Theorem 2.76, and Problems 2.77 and 2.78.**Friday, September 24:**After MB and NH presented Problems 2.79 and 2.80, respectively, we divided the class up into several small groups. After a few minutes, we had SC, MT, RM, KC, PB, JB, NH, and JO present parts (a) through (h), respectively, of Problem 2.86. We will wrap up the stuff we didn't get to next time.

**Monday, September 27:**We kicked off with KB presenting Problem 2.86(i) and then we discussed Problem 2.87 and Theorem 2.88 together. Next, NH presented Theorem 2.91 and I buttoned it up. With the few minutes we had left, we briefly discussed the first couple definitions in Chapter 3.**Wednesday, September 29:**I discussed 3.2-3.8 and then KC presented Problem 3.9. We will tackle Theorem 3.10 next time.**Friday, October 1:**We first had SR present Theorem 3.10. Next, we marched through MB, KB, JB, PB, RM, KC, MT, and SC presenting Problems 3.16(abc), 3.16(def), 3.16(ghi), 3.16(j)/3.17(ab), 3.17(cde), 3.17(fgh), 3.17(i)/3.18(a), and 3.18(bc), respectively. Along the way, I presented Theorem 3.12.

**Monday, October 4:**The students took the in-class portion of Exam 1.**Wednesday, Octocer 6:**I lectured today. We discussed Theorem 3.21 through Problem 3.26.**Friday, October 8:**More lecturing. After discussing the ZFC axioms, we started discussing power sets. We played with examples and proved Theorem 3.30.

**Monday, October 11:**Today, we started discussing indexing sets. We covered lots of examples, including Problems 3.33-3.37, 3.39.**Wednesday, Octocer 13:**Back to student presentations! We had MT, JB, SC, and SR present Problems 3.48(a), 3.48(b), 3.50, and 3.51, respectively. We also discussed Problem 3.49 along the way and then got started on the problems on the next assignment. We ended up discussing Problems 3.52-3.55.**Friday, October 15:**We had KC, KB, RM, and MB present 3.56, 3.57, 3.58, and 3.59, respectively.

**Monday, October 18:**I divided the class up into five small groups, each tasked with discussing a subset of the problems due today. Eventually, we had MT, SC, RM, PB, and MB present various parts of Problem 3.61 and then SR walked us through most of Problem 3.62.**Wednesday, Octocer 20:**We spent quite a bit of time discussing the big picture of induction and then I proved the Principle of Mathematical Induction from the Axiom of Induction. Next, I wrote down a careful proof of Theorem 4.4. With the time we had left, SR got us started on Theorem 4.5.**Friday, October 22:**We wrapped up Theorem 4.5 and then discussed Problem 4.8 and Theorem 4.9.

**Monday, October 25:**We had AC and MT present Theorems 4.7 and 4.11, respectively. With the time we had left, we quickly discussed all the base cases on Theorems 4.13-4.23.**Wednesday, Octocer 27:**We divided the clas up into 4 small groups and then SR/SC, KC, and JO presented Theorems 4.22, 4.13, and 4.15, respectively. We also discussed most of a proof for Problem 4.24(a).**Friday, October 29:**We spent the majority of class time discussing parts (a) and (d) of Problem 4.24. We also discussed Theorem 4.25 and got started on Theorem 4.27.

**Monday, November 1:**We had MT, MB, and KB present Problems 4.31, 4.33, and 4.34, respectively.**Wednesday, November 3:**We had JO, SC, and KB present Theorems 4.36, 4.38, and 4.39, respectively. Along the way, we discussed Problem 4.37.**Friday, November 5:**After revisiting Theorem 4.39, we split the class up into several small groups and then had KC, SR, AC, JO, NH, and AR present Problems 7.10, 7.12, 7.13, 7.15(ab), 7.15(cd), and 7.16, respectively.

**Monday, November 8:**After splitting the class up into several small groups, we had SR, JB/AR, SC, MB, and JO present Problems 7.21, 7.22, 7.24, 7.27(a), and 7.27(b), respectively. We wrapped up by discussing Problems 7.28 and 7.29 and part of Problem 7.34.**Wednesday, November 10:**We got a lot done today. We discussed Problems 7.29, 7.30, , 7.34/7.39, and 7.38. We also had JB and AC present Problems 7.36 and 7.37, respectively.**Friday, November 12:**After dividing the class up in small groups, we had MB, BT, PB, and JB present Theorem 7.42(forward implication), Theorem 7.42(reverse implication), Theorem 7.43(a), and Theorem 7.43(b), respectively.

**Monday, November 15:**The students took the in-class portion of Exam 2.**Wednesday, November 17:**After handing back exams, I lectured over the rest of Section 7.3. We will start Chapter 8 next time.**Friday, November 19:**More lecturing. We started Chapter 8 and made good progress.

**Monday, November 22:**More lecturing. I covered up to and including Theorem 8.40.**Wednesday, November 24:**I continued lecturing. We more or less discussed 8.41-8.53.**Friday, November 26:**Thanksgiving break. No classes!

**Monday, November 29:**Coming soon.**Wednesday, December 1:**Coming soon.**Friday, December 3:**Coming soon.

Mathematics & Teaching

Northern Arizona University

Flagstaff, AZ

Website

928.523.6852

Twitter

Instagram

Facebook

Strava

GitHub

arXiv

ResearchGate

LinkedIn

Mendeley

Google Scholar

Impact Story

ORCID

MAT 320: Foundations of Math

MAT 431: Intro to Analysis

MAT 511: Abstract Algebra I

This website was created using GitHub Pages and Jekyll together with Twitter Bootstrap.

Unless stated otherwise, content on this site is licensed under a Creative Commons Attribution-Share Alike 4.0 International License.

The views expressed on this site are my own and are not necessarily shared by my employer Northern Arizona University.

The source code is on GitHub.

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.