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

• Wednesday, January 18: First day! After attempting to learn names, we took a tour of the course webpage and then discussed an overview of the course and the syllabus. Next, groups of 2-3 pondered Problem 1 from the problem collection for a short bit before we had a brief full-class discussion about it. We wrapped up with a quick discussion of Problem 2. Comically, I accidentally ended class 10 minutes early. I won't do that again.
• Friday, January 20: Great first day of student presentations. I'm extremely happy with how things went. After answering a few quick questions, we divided the class up into 6 small groups, each tasked with discussing one of the homework problems. Groups spent about 20 minutes kicking around ideas related to their respective problem and then we had representatives from each group share out. Both LL and LB each presented an approach to Problem 1 and then SS discussed Problem 3. KG chimed in on Problem 3 along the way. We wrapped up with BR presenting his take on Problem 4(a).

## Week 2

• Monday, January 23: Despite the weather we had great attendance and class went really well. After reviewing a few key ideas, we split the class up into four small groups to work on Problems 5, 4(b)/6, 7, and 8, respectively. I left the groups chat for about 5 minutes and then we started discussing proposed solutions. We had MH, JM, and RD present Problems 5, 4(b)/6, and 7, respectively. Along the way, several other people chimed in. We ran out of time to discuss Problem 8. I hope we can squeeze that one in next time.
• Wednesday, January 25: Today was a good day and we got a lot accomplished. After summarizing some key ideas and the status Problems 1-7, we moved onto Problems 8-11. SW shared her solution to Problem 8 and then MS summarized a slick solution that involved less analysis. For Problem 9, we had AT1 and AC present their solutions to Problem 9. Next, BG provided a nice take on Problem 10. I spent the last few minutes of class giving some hints on Problem 11.
• Friday, January 27: Despite being a tremendous amount of pain, I think things went well today. We were really productive. KG's explanation (with comments from LL) for Problem 7 finally put that one to rest. Next, we had RG discuss a conjecture for Problem 12, which connects with triangular numbers. Then BS, JK, and NP presented Problem 13, a visual approach to Problem 14, and an algebraic proof for Problem 14. We wrapped up with a general discussion of Problem 11, which included guidance from RD and MS.

## Week 3

• Monday, January 30: The week is off to a good start. We kicked off by having SS and MR present visual and algebraic proofs, respectively, for Problem 15. After allowed students to chat in small groups for a few minutes, JS2 presented a slick solution to Problem 16. Next, we had students chat in small groups about Problem 17. AS discussed a case analysis for Problem 17 and then we distilled the argument down to a single case. We wrapped up by discussing Erdos and the next few homework problems.
• Wednesday, February 1: The students took Quiz 1. We will get back to working on problems on Friday.
• Friday, February 3: While I was out of town, Monika Keindl covered for me. Monika handed out a half sheet of paper that contained 4 problems. Students spent the majority of the class meeting working on these problems in small groups. Along the way, BG and RD presented solutions to the first and second problems, respectively. The intention was for students to finish working on the remaining two problems over the weekend.

## Week 4

• Monday, February 6: After checking in to see how things went on Friday while I was out of town, we discussed solutions to the last 3 problems on Quiz 1. Next, we recapped the solutions to the first and second problems from Friday and then discussed the third and fourth problems. We had the class split up into two groups to act out the solution to the third problem involving the frogs. NP suggested there is a nice formula to count the number of steps in the general case. We wrapped up by discussing the fourth problem involving $x-y=85$ and $\sqrt{x}+\sqrt{y}=17$. MR presented a method for finding a solution, but we left it open as to whether there are any other solutions. We still need to discuss Problems 18-20, which we will do on Wednesday.
• Wednesday, February 8: We kicked off with a discussion of the problem involving $x-y=85$ and $\sqrt{x}+\sqrt{y}=17$. After discussing a few different approaches, we settled on there being a unique solution. However, after class, MR pointed out to me that what we said only guarantees that there are at most 2 solutions. Perhaps we will have time to address this one on Friday. Next, AC presented Problem 18, which generated good discussion about rigorous arguments compared to data having a pattern. This was followed by a nice argument for Problem 19 by KP. We finished up with AT1 giving a slick approach to Problem 21. We briefly discussed why we couldn't improve upon our answer in Problem 21.
• Friday, February 10: I really enjoyed today's class. We started with allowing students to chat in small groups about Problems 21 and 22. We had LB and SW present Problem 21 and then MH, JM, and RD discussed Problem 22. Next, AT2, AS, and JJ tackled Problem 23. We wrapped up with NP presenting Problem 24.

## Week 5

• Monday, February 13: We accomplished more today than I expected. We kicked off with small groups discussing potential solutions to Problem 25. We had JS1 share a solution he encountered when chatting with his group. Next, we had JS2 share his proposed solution to Problem 26, but we discovered it wasn't optimal because RB proposed a better solution. I suggested folks attempt to prove that RB's solution is the best we can do. After having AT2 share his proposed approach to Problem 27, we had BG present slick solutions to both Problems 27 and 28.
• Wednesday, February 15: The students took Quiz 2. I love watching the students collaborate for the few minutes I allow them to chat.
• Friday, February 17: I was energetic today, but I might have been the only one. We started with a brief follow-up discussion on Problems 27 and 28. NP told us how we could take the solutions from Problems 27 and 28 and combine them into a single strategy. Next, KG provided an argument about why 17 minutes is the best we can do on Problem 26. AT2 put Problem 33 to rest with easy; another example of triangular numbers. RD and AT1 tackled Problem 34 for us. I think everyone should be able to handle any problem like this one in the future. We spend the last 20 minutes of class discussing Problem 35. LL and RB presented their proposed solutions, but it turns out that we can do better. We'll revisit Problem 35 next week.

## Week 6

• Monday, February 20: Coming soon.
• Wednesday, February 22: Coming soon.
• Friday, February 24: Coming soon.

# Dana C. Ernst

Mathematics & Teaching

Northern Arizona University
Flagstaff, AZ
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