Week 1 · Fri, Aug 28 Meeting 1 Great first day! I learned everyone's name today (and even got some of them on the first try). We spent the first few minutes discussing how learning works and the structure of the course. After a group discussion on "How does a person learn something new?" we quickly went through the most important aspects of the syllabus. Our word cloud is at the top of the page. Then we jumped into some number theory. After discussing the definition of divisibility and an Example Theorem, we split into groups and proved our first theorems. We had student presentations on Theorems 1.1, 1.2, and 1.3.

Week 2 · Mon, Aug 31 Meeting 2 Excellent day! Students presented 1.4 through 1.8, all volunteers. In 1.4 we noticed that Friday's proof of 1.3 never used the hypothesis $a \mid c$, which gave us 1.6 for free, and we also proved the stronger conclusion $a^2 \mid bc$. Two conjectures came up for 1.5, both proved. The second prompted a great discussion of the cancellation property in $\mathbb{Z}$, which we have not proved and which the book never proves. We agreed to accept it as a background fact about arithmetic, so I will start a running list of allowed results and post it on the Materials page. We got tripped up on the characterization part of 1.8. We ran out of time for 1.9 and saved it Wednesday.

Week 2 · Wed, Sep 2 Meeting 3 We had presentations for 1.9, 1.10, and 1.11. We discussed an alternative proof of 1.11 using Theorem 1.1 as well. After that I lectured on relations and equivalence relations, and we discussed examples and non-examples. Finally, we established that by 1.9, 1.10, and 1.11, congruence modulo $n$ is an equivalence relation on the set of integers.

Week 2 · Fri, Sep 4 Meeting 4 Today we had student presentations on 1.12 through 1.14. The presenter of 1.13 caught a flaw in their initial argument, but fixed it on the fly using previously proved theorems. We spent some time discussing how Theorems 1.1–1.3 and 1.6 could be used to simplify various arguments used in the proofs of 1.12 through 1.14. Then we had a presentation on Question 1.20, which prompted the best discussion so far! Several students came to the board and shared different types of counterexamples. This prompted the question: which integers can be "cancelled"? Finally, we had a presentation on R.13.