## Foundations of Math

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 14:**Our first day! Dana attempted to learn names and then spent some time discussing the syllabus and course expectations. As one short example, Dana crammed the proof of Theorem 1.3 into the last few minutes of class.**Wednesday, January 16:**Great first day of presentations. I was impressed. Class started by making some announcements and then Dana proved Theorem 1.4. For our first student presentation of the semester, RG did a great job of presenting a proof for Problem 1.5. Then MG showed us a counterexample for Problem 1.7. Lots of good discussion happened around this problem. We concluded with DH quickly writing down a proof of Problem 1.8. DH’s layout of the proof was spectacular, but only handled a special case. We’ll discuss this one a little more on Friday. We never got to Question 1.6 and Problem 1.9. We’ll probably skip discussing 1.6, but the plan is for YM to lead us off with a proof of 1.9 on Friday.**Friday, January 18:**Dana spent 15 minutes at the beginning of class giving a whirlwind introduction to $\LaTeX$ using writeLaTeX. After that YM did a fantastic job presenting 1.9. Next, MK made some wonderful mistakes with 1.11, which generated some great discussion. SA discussed a counterexample for 1.12, and then class finished with JP giving us a quick synapsis of the “meat and potatoes” of 1.13. Items 1.14 and 1.15 are still outstanding and we will resolve these first thing on Wednesday next week.

## Week 2

**Monday, January 21:**MLK Day. No class!**Wednesday, January 23:**Excellent class. I was impressed with how well things went. After a few brief announcements, MH lead us through a discussion of 1.14. After that JR presented a counterexample for 1.15. Despite the problem not being assigned, GK tackled a very specialized case of 1.16. Next, WW walked us through 1.17. WW had all the right ideas, but we had to tweak how they were written down. For our final presentation, CG showed us her proof of 1.18. Dana has some comments to make on this one, but they will have to wait until next class since we ran out of time.**Friday, January 25:**We did not have time to cover most of the problems, but the ones we did cover generated a lot of discussion. Here’s what transpired: MR presented 1.20, PT presented 1.21, and MK presented 1.32.

## Week 3

**Monday, January 28:**To start, we had DH, KF, MK, NF, SM, and MG simultaneously put 1.35, 1.36, 1.37, 1.40, 1.41, and 1.43, respectively, up on the board. Dana presented 1.42. Next, JC put a beautiful proof of 1.45 on the board. We finished by having BW tell us about 1.44.**Wednesday, January 30:**We had RG, GK, JP, JR, KF, MR, and SA present 1.46, 1.47, 1.48, 1.49, 1.50, 1.52, and 1.53, respectively. Afterwards, Dana spent some time introducing proof by contradiction.**Friday, February 1:**Despite the fact that we only discussed 3 problems, I think this was one of our best days so far this semester. DH started us off by discussing 1.56. Next, CO and MH showed up two different proofs (contradiction and contrapositive) for 1.57. The discussion around this problem too most of the class period, but the time was well spent. We finished off with SA presenting 1.58. Question 1.59 is still open.

## Week 4

**Monday, February 4:**We had MG, GK, CG, MK, SM, and MH presented 1.61, 1.62, 1.65, 1.67, 1.68, and 1.70, respectively.**Wednesday, February 6:**After a short presentation about the NASA Space Grant Program, we had JC, JP, DH, CG, WW, GK/MH, and YM simultaneously write down solutions to 1.76, 1.79, 1.80, 1.82, 1.83, 1.85, and 1.87, respectively. We never discussed the second half of 1.85 or 1.87.**Friday, February 8:**We were a bit all over the place today. GK, TF, MH, PT, and WW all made contributions to 1.89, 1.91, 1.92, 1.95, and 1.96.

## Week 5

**Monday, February 11:**Dana was absent and Dr. Falk covered the class. MR presented 1.101 while JP and BW tag-teamed 1.103. TF and GK got us started off with the notes for Section 2 by presenting 2.4 and 2.5, respectively.**Wednesday, February 13:**We spent some time at the beginning of class discussing the upcoming exam that takes place next week. After that we dove into the student presentations. DH started us off by discussing a method of attack for proving that one set is a subset of another (this is 2.8). Next, MK and SM each tackled a half of 2.9. After that GK tackled 2.10, BW presented 2.11, and SA wrote up 2.14.**Friday, February 15:**No one had questions on 2.20, so skipped it and had CO tell us all about 2.21. AFter that, MH attempted to prove 2.22, which generated lots of good discussion. We concluded with YM presenting 2.25 (which she had some help on prior to class). JR has volunteered to do 2.26, but we ran out of time.

## Week 6

**Monday, February 18:**Dana spent some time at the beginning of class discussing the upcoming exam. After that, he discussed proving 2.26 using a truth table. Immediately following Dana’s discussion, JR showed us his proof of 2.26, which required some minor adjustments. Next, MG and MK took different approaches on 2.27. We spent most of the class discussing this problem. We wrapped things up (a few minutes late) by having TF tell us her answer to 2.31. Problems 2.32, 2.33, and 2.34 are still outstanding.**Wednesday, February 20:**Snow day!**Friday, February 22:**I thought today was awesome! After Dana discussed notation related to sets and power sets, we had RG, JP, and MG write 2.32, 2.33, and 2.34 on the board, respectively. After that, SA and TF tag teamed 2.36. We finished with KF presenting a solid proof of 2.37.

## Week 7

**Monday, February 25:**The students took the in-class portion of Exam 1.**Wednesday, February 27:**The class spent the entire class meeting working on the take-home portion of Exam 1.**Friday, March 1:**In a sleep-deprived state, Dana discussed 2.38, 2.39, 2.40, 2.41, 2.42, and 2.43. The last few problems deal with paradoxes.

## Week 8

**Monday, March 4:**After briefly discussing the in-class portion of Exam 1, Dana spent a few minutes lecturing over indexing sets. After that we had BW, GK, and SA crank out solutions to 2.50, 2.51, and 2.52, respectively. Next, MH worked through both 2.53 and 2.54. We finished by having SM present 3.5.**Wednesday, March 6:**Class started with RG making short work of 2.57. Next up, MG presented 2.58. MR and NF tag-teamed 2.59, and then class finished with GK and MG each presenting half of 2.60.**Friday, March 8:**First off, MR and CG each presented their version of 2.63. After that, CO, JP, MH, GK, and MK presented 2.69, 2.71, 2.72, 2.73, and 2.74, respectively.

## Week 9

**Monday, March 11:**Dana was out today and Dr. Jim Swift covered for him. CG started 2.75 and then MG finished it with some help from the class.

Next, BW did 2.76, which involved changing a few symbols from MG’s proof of 2.75. After that SA sketched an informal proof of 2.77. Class finished with MG completing 2.78 (which apparently involved a nice use of WLOG). The class never got to the last two problems (2.79 and 2.80). We’ll pick up with those on Wednesday.**Wednesday, March 13:**Dana spent nearly the entire class session reviewing the concepts of open and limit point.**Friday, March 15:**Today was a highly productive day. We had WW, MH, MG, SA, JP, and DH present 2.78, 2.80, 2.81, 2.83, 2.85, and 2.86, respectively.

## Week 10

**Monday, March 25:**Another lecture day. Dana discussed several problems from the end of Section 2.4.**Wednesday, March 27:**Dana was away at a conference and Dr. Jim Swift covered for us again. Apparently, most of the class period was spent on 2.100, which DH presented. After that JP and MG tackled 2.101 and 2.102, respectively.**Friday, March 29:**We spent the entire class session discussing induction. In particular, CG, KF, RG, and PT had a go at 3.3, 3.6, 3.7, and 3.8, respectively.

## Week 11

**Monday, April 1:**We finally wrapped up Section 3.1 on induction. We had SA and JP present 3.9 and 3.10, respectively. After that we started Section 4.1. As a class, we quickly discussed 4.2 and then spent the remainder of class focusing on 4.4, which PT presented for us.**Wednesday, April 3:**We started class by watching Hitler Learns Topology on YouTube. After that, we had MK present 4.5 and MH present 4.6. Both of these involve “proofs from the book”.**Friday, April 5:**We spent the entire class session on just two problems. Nonetheless, it was highly productive. We had both NF and JP present 4.8 and then MG showed us 4.9.

## Week 12

**Monday, April 8:**Another productive day! After a slow start, we cranked through a few problems. First, we had both JR and BW show us what they had for 4.11 ($\sqrt{2}$ is irrational). Following a lengthy discussion of 4.11, MG, SA, and MH presented 4.12, 4.13, and 4.14, respectively.**Wednesday, April 10:**Lots of students at the board today! We had JC, JR, JP, MK, MH, SA, WW, and NF present 4.15, 4.16, 5.5, 5.6, 5.7, 5.8, 5.9, and 5.10, respectively.**Friday, April 12:**Good stuff! All excellent presentations. MK, NF, KF, SM, PT, and YM showed us 5.13, 5.20, 5.21, 5.23, 5.26, and 5.27, respectively.

## Week 13

**Monday, April 15:**Yet another busy day. We had JC present both 5.32 and 5.37. In addition, MH, KF, SA, MK, SM, and WW presented 5.31, 5.33, 5.34, 5.36, 5.38, and 5.40, respectively.**Wednesday, April 17:**Dana spent quite a bit of time going over examples. With the time we had left, NF presented 5.42.**Friday, April 19:**The students took the in-class portion of Exam 2.

## Week 14

**Monday, April 22:**I have no idea what happened this day…**Wednesday, April 24:**I don’t know what happened here either.**Friday, April 26:**CG presented 5.55 and BW showed us 5.60.

## Week 15

**Monday, April 29:**Our last Monday! We had SM, JP, SA, MG, WW, KF, and MH present 5.74, 5.76, 5.77, 5.80, 5.85, 5.86, and 5.88, respectively.**Wednesday, May 1:**We only got through a couple of tough problems. KF flawlessly presented 5.91 while SM finished strong with 5.97.**Friday, May 3:**Last day of the semester. Dang, I’ll miss this class. First, we had JC and BW jointly present 5.102. This was followed by GK discussing 5.103. Next up, YM and PT presented 5.104. This same duo finished with 5.109. We also had DH and MK present 5.105 and 5.106, respectively.